Cyclotron lines in highly magnetized neutron stars

AampA 622 A61 (2019)httpsdoiorg1010510004-6361201834479ccopy ESO 2019

AstronomyampAstrophysics

Cyclotron lines in highly magnetized neutron starsR Staubert1 J Truumlmper2 E Kendziorra1 D Klochkov1 K Postnov3 P Kretschmar4 K Pottschmidt56

F Haberl2 R E Rothschild7 A Santangelo1 J Wilms8 I Kreykenbohm8 and F Fuumlrst4

1 Institut fuumlr Astronomie und Astrophysik Universitaumlt Tuumlbingen Sand 1 72076 Tuumlbingen Germanye-mail staubertastrouni-tuebingende

2 Max-Planck-Institut fuumlr extraterrestrische Physik Giessenbachstr 1 85748 Garching Germany3 Sternberg Astronomical Institute Lomonossov University 119992 Moscow Russia4 European Space Agency ndash European Space Astronomy Center (ESAndashESAC) Camino Bajo del Castillo sn Urb Villafranca del

Castillo 28692 Villanueva de la Canada Madrid Spain5 NASA Goddard Spaceflight Center 8800 Greenbelt Rd Greenbelt MD 20771 USA6 CRESST Department of Physics and Center for Space Science and Technology UMBC Baltimore MD 21250 USA7 Center for Astrophysics and Space Sciences University of California at San Diego La Jolla CA 92093-0424 USA8 Dr Remeis Sternwarte Astronomisches Institut der Universitaumlt Erlangen-Nuumlrnberg Sternwartstr 7 96049 Bamberg Germany

Received 21 October 2018 Accepted 17 November 2018

ABSTRACT

Cyclotron lines also called cyclotron resonant scattering features are spectral features generally appearing in absorption in the X-rayspectra of objects containing highly magnetized neutron stars allowing the direct measurement of the magnetic field strength in theseobjects Cyclotron features are thought to be due to resonant scattering of photons by electrons in the strong magnetic fields The maincontent of this contribution focusses on electron cyclotron lines as found in accreting X-ray binary pulsars (XRBP) with magneticfields on the order of several 1012 Gauss Also possible proton cyclotron lines from single neutron stars with even stronger magneticfields are briefly discussed With regard to electron cyclotron lines we present an updated list of XRBPs that show evidence of suchabsorption lines The first such line was discovered in a 1976 balloon observation of the accreting binary pulsar Hercules X-1 itis considered to be the first direct measurement of the magnetic field of a neutron star As of today (end 2018) we list 35 XRBPsshowing evidence of one ore more electron cyclotron absorption line(s) A few have been measured only once and must be confirmed(several more objects are listed as candidates) In addition to the Tables of objects we summarize the evidence of variability of thecyclotron line as a function of various parameters (especially pulse phase luminosity and time) and add a discussion of the differentobserved phenomena and associated attempts of theoretical modeling We also discuss our understanding of the underlying physicsof accretion onto highly magnetized neutron stars For proton cyclotron lines we present tables with seven neutron stars and discusstheir nature and the physics in these objects

Key words accretion accretion disks ndash magnetic fields ndash radiation mechanisms non-thermal ndash binaries general ndash X-rays binaries ndashstars neutron

1 Introduction

In this contribution we review the status of cyclotron lineresearch in the X-ray range preferentially from an observationalpoint of view together with the related theoretical backgroundand some recent progress in modeling the relevant physicsHighly magnetized accreting neutron stars (NSs) in binary sys-tems generally reveal themselves as X-ray pulsars A substan-tial fraction of those objects show line-like features in theirhigh energy X-ray spectra mostly in absorption at energies fromsim10 keV to sim100 keV called cyclotron lines or cyclotron res-onant scattering features (CRSFs) The following introductorystatements are for objects with electron cyclotron lines (we willcome to proton cyclotron line objects below) Such lines are gen-erated close to the magnetic poles of accreting neutron stars inthe hot highly magnetized plasma where the kinetic energy ofthe in-falling material is converted to heat and radiation Elec-trons assume discrete energies with respect to their movementperpendicular to the magnetic field so called Landau levelsResonant scattering of photons on these electrons then leads to

In memoriam

scattering of photons at the resonance energy and to the genera-tion of resonance features (in absorption) in the X-ray spectrumThe fundamental energy quantum corresponds to the energy dif-ference between adjacent Landau levels given by ~ω whereω = eBmec is the gyro frequency e is the electron charge Bis the magnetic field in the scattering region me is the mass ofthe electron and c is the speed of light The Landau levels (tofirst order equidistant) are linearly related to the strength of themagnetic field The observation of such features then allows forthe measurement of the magnetic field strength The followingcentroid line energies Ecyc are expected

Ecyc =n

(1 + z)~eBmec

asympn

(1 + z)116 [keV] times B12 (1)

where B12 is the magnetic field strength in units of 1012 Gaussz is the gravitational redshift due to the NS mass and n is thenumber of Landau levels involved eg n = 1 is the case of ascattering from the ground level to the first excited Landau leveland the resulting line is called the fundamental line In the caseof n = 2 (or higher) the lines are called harmonics

The same physics is valid for other charged particles forexample protons for which the difference between Landau

Article published by EDP Sciences A61 page 1 of 30

AampA 622 A61 (2019)

levels is smaller by a factor of 1836 (the ratio of the proton toelectron mass) Such lines are thought to be observed from iso-lated thermally radiating neutron stars in the range 01 keV to afew keV For the proton cyclotron lines to appear in the X-rayrange the magnetic field must typically be two orders of magni-tude stronger than for electron cyclotron lines

Cyclotron line research with accreting X-ray binaries (or iso-lated neutron stars) has become a field of its own within X-rayastronomy It is a vibrant field in both theoretical and in observa-tional work dealing not only with the detection of new lines butalso with various recently discovered properties of these linessuch as the dependence of the line energy width and depth onX-ray luminosity and its long-term evolution with timeCyclotron lines are an important diagnostic tool to investigatethe physics of accretion onto the magnetic poles of highly mag-netized neutron stars

Here we give a brief history of the beginning of cyclotronline research and its evolution up to the present The dis-covery of cyclotron lines in 1976 in the X-ray spectrum ofHer X-1 (Truumlmper et al 1977 1978 see Fig 1) was not the resultof a targeted search but came as a surprise A joint group ofthe Astronomical Institute Tuumlbingen (AIT) and the Max PlanckInstitute for Extraterrestrial Physics (MPE) had flown a hardX-ray balloon payload (ldquoBalloon HEXErdquo) on 2ndash3 May 1976observing Her X-1 and Cygnus X-1 at energies from 20 keVto 200 keV While the AIT group concentrated on the analy-sis of the energy dependent pulse profiles (Kendziorra et al1977) their colleagues at MPE dealt with the energy spec-trum They found an unexpected shoulder-like deviation fromthe steep total energy spectrum around 50 keV which lookedlike a resonance feature Detailed investigations showed that thefeature was present in the pulsed spectrum and absent in theCygnus X-1 spectrum taken on the same balloon flight exclud-ing the possibility of a spurious origin Because of its highenergy and intensity it could be attributed only to the electroncyclotron resonance

This discovery was first reported in a very late talk ndash pro-posed and accepted during the meeting ndash at the Eighth TexasSymposium on Relativistic Astrophysics on 16 December 1976(Truumlmper et al 1977) and became a highlight of that meet-ing An extended version that appeared later (Truumlmper et al1978) has become the standard reference for the discovery whichrevealed a new phenomenon in X-ray astronomy and providedthe first direct measurement of a neutron star magnetic fieldopening a new avenue of research in the field The limited spec-tral resolution of the Balloon-HEXE did not allow us to distin-guish between an emission or absorption line (Truumlmper et al1978) For the answer to this question we had to await radia-tive transfer calculations in strong magnetic fields For that thepioneering work on the magnetic photon-electron cross sectionswas important (Lodenquai et al 1974 Gnedin amp Sunyaev 1974)The latter work ndash based on the assumption of a (Thomson) opti-cally thin radiation source ndash also predicted that at the cyclotronenergy a resonance emission line would occur (see also Basko ampSunyaev 1975)

The discovery of the Her X-1 cyclotron lines spurred a burstof early theoretical papers on the radiative transfer in stronglymagnetized plasmas Some of them provided support for anemission line interpretation of the feature (eg Daugherty ampVentura 1977 Meszaros 1978 Yahel 1979ab Wasserman ampSalpeter 1980 Melrose amp Zhelezniyakov 1981) The first sup-port for an absorption line interpretation came from a talk byAndy Fabian at the first international workshop on cyclotronlines organized by the Max-Planck-Institut fuumlr extraterrestrische

Physik (MPE) in fall 1978 His argument was the radiating hightemperature plasma would be optically thick In the cyclotronresonance region the reflectivity would be high and accordingto the Kirchhoff law the emissivity would be low (Fabian 1978unpublished) Other important early theoretical papers followed(eg Bonazzola et al 1979 Ventura et al 1979 Bussard 1980Kirk amp Meszaros 1980 Langer et al 1980 Nagel 1980 1981abYahel 1980ab Pravdo amp Bussard 1981 Meszaros et al 1983)All these and many following works led to the current viewthat these lines are seen ldquoin absorptionrdquo This was also obser-vationally verified for Her X-1 in 1996 through data from Mir-HEXE (Staubert 2003) The first significant confirmation of thecyclotron line in Her X-1 came in 1980 on the basis of HEAO-1A4 observations (Gruber et al 1980) The same experimentdiscovered a cyclotron line at 20 keV in the source 4U 0115+63(Wheaton et al 1979) A re-examination of the data uncoveredthe existence of two lines at 115 and 23 keV which were inter-preted as the fundamental and harmonic electron cyclotron res-onances seen in absorption (White et al 1983) Later observa-tions of the source found it to show three (Heindl et al 1999)four (Santangelo et al 1999) and finally up to five lines in total(Heindl et al 2004)

In many accreting X-ray binary pulsars (XRBPs) the cen-troid energy Ecyc of cyclotron lines is seen to vary The firstvariations seen were variations of Ecyc with pulse phase (egVoges et al 1982 Soong et al 1990 Vasco et al 2013)and are attributed to a varying viewing angle to the scatter-ing region A negative correlation between Ecyc and the X-rayluminosity was reported during high luminosity outbursts of twoX-ray transients V 0332+53 and 4U 0115+63 (Makishima et al1990a Mihara 1995) Today we consider this to be real only inV 0332+53 (see Sect 42) It was again in Her X-1 that two morevariability phenomena were first detected firstly a positive cor-relation of Ecyc with the X-ray luminosity (Staubert et al 2007)and secondly a long-term decay of Ecyc with time (Staubert et al2014 revealing a sim5 keV reduction over the last 20 years) Todaywe know a total of seven objects showing the same positive cor-relation (see Sect 42) and one more example for a long-termdecay (Vela X-1 La Parola et al 2016 Sect 44)

In the last 40 years the number of known electron cyclotronsources has increased to sim35 (see Table A1) due to investi-gations with many X-ray observatories like Ginga Mir-HEXERXTE BeppoSAX INTEGRAL Suzaku and NuSTAR For pre-vious reviews about cyclotron line sources see for exampleCoburn et al (2002) Staubert (2003) Heindl et al (2004)Terada et al (2007) Wilms (2012) Caballero amp Wilms (2012)Revnivtsev amp Mereghetti (2016) Maitra (2017) Lists of CRSFsources can also be found at the webpages of Dr Remeis-Sternwarte Bamberg1 and the Istituto Astrrofisica SpazialeBologna2 Recent theoretical work has followed two linesanalytical calculations (Nishimura 2008 2011 2013 2014)or making use of Monte Carlo techniques (Araya amp Hard-ing 1999 Araya-Goacutechez amp Harding 2000 Schoumlnherr et al2007 Schwarm et al 2017ab) In addition evidence for thedetection of proton cyclotron lines in the thermal spectra ofisolated neutron stars was provided by Chandra and XMM-Newton (Haberl 2007 see Tables 2 and 3) In this paperwe review the status of cyclotron line research by summa-rizing the current knowledge about cyclotron line sources(both electron- and proton-cyclotron line sources) and the

1 httpwwwsternwarteuni-erlangendewikidokuphpid=xrpstart2 httpwwwiasfboinafit~mauropulsar_listhtml

A61 page 2 of 30

R Staubert et al Cyclotron line sources

Fig 1 X-ray spectrum of Her X-1 as obtained in a balloon observa-tion in 1976 constituting the first detection of a cyclotron line (fromTruumlmper et al 1978)

state of our understanding of the details of the underlyingphysics

This paper is structured as follows in Sect 2 we presenta series of tables which contain detailed information aboutall objects known to us which show conclusive evidence forthe existence of electron cyclotron lines (together with appro-priate references) plus several uncertain candidate objects InSect 3 we discuss issues of spectral fitting including a list ofpopular functions for the modeling of the continuum and thecyclotron lines as well as systematic differences that must betaken into consideration when different results from the liter-ature are to be compared Section 4 discusses observed vari-ations of measured cyclotron line energies (as summarized inTable A4) we find that the line energy can vary with pulsephase with luminosity (both positive and negative) with timeand (in Her X-1) with phase of the super-orbital period Thewidth and depth of the cyclotron line(s) can also vary sys-tematically with luminosity It is also found that the spectralhardness of the continuum can vary with X-ray luminosity inclose correlation with variations of the cyclotron line energy InSect 44 we review the evidence for variations of the cyclotronline energy on medium to long timescales In Sect 45 the cur-rent knowledge about correlations between the various spec-tral parameters is discussed and in Sect 46 we discuss a fewindividual sources mostly those that show systematic varia-tions with X-ray luminosity In Sect 5 we discuss the relevantphysics at work in accreting binary X-ray pulsars the forma-tion of spectral continua and cyclotron lines and the physicsbehind their systematic variations In Sect 52 we briefly referto theoretical modeling of cyclotron features by both analyti-cal and Monte Carlo methods In Sect 6 three methods of howto estimate the magnetic field strength of neutron stars are dis-cussed and compared In Sect 7 we present a statistical analysis

describing the overall mean properties of the discussed objectsFinally in Sect 8 we discuss objects thought to show protoncyclotron lines and conclude in Sect 9 with a short generalsummary

2 Collection of cyclotron line sources

This review attempts to summarize the current knowledge ofcyclotron line sources ndash both electron- and proton-cyclotronline sources For both types of cyclotron line sources we pro-vide a series of tables with information about a total of morethan sim40 objects that we consider to show one (or more)cyclotron lines in their X-ray spectra Tables 2 and 3 list sevenobjects with proton-cyclotron lines For electron-cyclotron lineobjects we present a total of five tables with the followingcontent

ndash Table A1 35 objects with confirmed or reasonably secureCRSFs (14 of them still need further confirmation) Thecolumns are source name type of object pulse periodorbital period eclipse (yesno) cyclotron line energy (orenergies) instrument of first detection confirmations yesnoreferences

ndash Table A2 Objects which we call ldquocandidatesrdquo for whichCRSFs have been claimed but where sufficient doubts aboutthe reality of the cyclotron line(s) exist or where additionalobservations are needed for confirmation (or not)

ndash Table A3 HEASARC type position optical counterpart itsspectral type masses distance references

ndash Table A4 Variation of Ecyc with pulse phase and with Lxvariation of spectral hardness with Lx references

ndash Table A5 Ecyc width ldquostrengthrdquo and optical depth ofcyclotron lines at certain Lx references notes

3 Spectral fitting

X-ray spectra of XRBPs are of thermal nature They are formedin a hot plasma (T sim 108 K) over the NS magnetic poles whereinfalling matter arrives with half the speed of light at the stel-lar surface The emission process is believed to be governedby Comptonization of thermal photons which gain energy byscattering off hot plasma electrons (thermal Comptonization) Inaddition bulk motion Comptonization in the fast moving plasmaabove the deceleration region and cyclotron emission plays animportant role (eg Becker amp Wolff 2007 Ferrigno et al 2013)The shape of the spectral continuum formed by Comptonizedphotons emitted in the breaking plasma at the polar caps of anaccreting magnetized NS was first computed in the seminal workof Lyubarskii amp Sunyaev (1982) It has been shown that non-saturated Comptonization leads to a power law-like continuumwhich cuts off at energies ampkTe where Te denotes the electrontemperature in the plasma

The calculations of Lyubarskii amp Sunyaev (1982) and thenumerical computations performed later provided a physicalmotivation for the usage of analytic power law functions withexponential cutoff to model the spectral continua of XRBPsHistorically the following realizations of such functions becamemost popular and are included in some of the standard spectralfitting packages such as XSPEC3 Sherpa4 and ISIS5 The mostsimple one with just three free fit parameters is the so-calledcutoffpl model (these names are the same in all mentioned

3 httpheasarcnasagovxanaduxspec4 httpcxcharvardedusherpa5 httpspacemiteduascisis

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AampA 622 A61 (2019)

fitting packages)

IE = K middot EminusΓ exp (minusEEfold) (2)

where E is the photon energy and the free fit parameters K Γ andEfold determine the normalization coefficient the photon indexand the exponential folding energy6 respectively We note thatthis represents a continuously steepening continuum

The next function has an additional free parameter the cutoffenergy Ecutoff

K middot EminusΓ ifE le Ecutoff

K middot EminusΓ exp(minus

EminusEcutoff

) ifE gt Ecutoff

In the spectral fitting packages mentioned here this functionis realized as a product of a power law and a multiplica-tive exponential factor power law times highecut Although thisfunction is generally more flexible due to one more free param-eters it contains a discontinuity of its first derivative (a ldquobreakrdquo)at E = Ecutoff Since the observed X-ray spectra are generallysmooth an absorption-line like feature appears in the fit residu-als when using this model with high quality data To eliminatethis feature one either includes an artificial narrow absorptionline in the model (eg Coburn et al 2002) or substitutes the partof the function around the ldquobreakrdquo with a third order polyno-mial such that no discontinuity in the derivative appears (egKlochkov et al 2008a) Here the power law is unaffected untilthe cutoff energy is reached

Another form of the power law-cutoff function is a powerlaw with a FermindashDirac form of the cutoff (Tanaka 1986)

IE = K middot EminusΓ

[1 + exp

(E minus Ecutoff

)]minus1

which has the same number of free parameters as the previousfunction This function is not included any more in the currentversions of the fitting packages

Finally a sum of two power laws with a positive and a nega-tive photon index multiplied by an exponential cutoff is used inthe literature (the NPEX model Mihara 1995)

IE = K1(EminusΓ1 + K2E+Γ2 ) exp (minusEEfold) (5)

In many applications using this model Γ2 is set to a value of twoin order to represent the Wien portion of the thermal distribution

In some spectra of XRBPs with high photon statistics devi-ations from these simple phenomenological models are seen Inmany cases a wave-like feature in the fit residuals is presentbetween a few and sim10ndash20 keV It is often referred to as theldquo10 keV-featurerdquo (eg Coburn et al 2002) The residuals can beflattened by including a broad emission or absorption line com-ponent Although sometimes interpreted as a separate physicalcomponent the 10 keV-feature most probably reflects the limita-tions of the simple phenomenological models described above

To model the cyclotron line one modifies the continuumfunctions described above by the inclusion of a correspond-ing multiplicative component The following three functions areused in most cases to model CRSFs The most popular one is amultiplicative factor of the form eminusτ(E) where the optical depthτ(E) has a Gaussian profile

τ(E) = τ0 expminus (E minus Ecyc)2

2σ2cyc

6 In XSPEC the folding energy for this function is called Ecut

10minus4

10minus2

cminus

Vminus

10minus8

10minus6

10minus4

10minus2

photons cm minus2 sec minus

1 keVminus

1photons cm minus

2 sec minus1 keV

minus1

1 keVminus

1photons cm minus

2 sec minus1 keV

minus1

1 keVminus

V0332+53

20 25 3006

Energy [keV]

minus60minus40minus20

0204060

minus10minus5

minus6minus4minus2

minus4minus2

10 100Channel Energy [keV]

minus4minus2

Fig 2 Example of a spectral modeling for continuum plus cyclotronlines Reproduction of Fig 2 of Pottschmidt et al (2005) showingthe phase averaged spectrum of V 0332+53 as observed with RXTEfor a FermindashDirac continuum and up to three cyclotron lines (mod-eled using the Gaussian optical depth profile gabs) Panel a com-bined PCAHEXTE spectrum (crosses) best-fit model (histogram) andunfolded spectrum (dotted and solid lines right y-axis label) illustrat-ing the cumulative effect of the CRSFs on the continuum Panels bndashfresiduals for models taking increasing numbers of CRSFs into accountpanel b no line panel c one line at 255 keV panel d two lines at256 keV and at 50 keV panel e two lines the fundamental line mod-eled by two Gaussian components at 252 keV and 266 keV and its har-monic at 499 keV panel f three lines the fundamental modeled by twocomponents at sim25 keV and sim27 keV and two harmonics at sim51 keVand at sim74 keV For further explanation see Pottschmidt et al (2005)

with τ0 Ecyc and σcyc being the central optical depth the cen-troid energy and the width of the line We note that in the popu-lar XSPEC realization of this function gabs τ0 is not explicitelyused as a fit parameter Instead a product τ0 σcyc

radic2π is defined

that is often called the ldquostrengthrdquo of the line The physical moti-vation for the described line models stems from the formal solu-tion of the transfer equation in the case of true absorption linesfor example due to transitions between the atomic levels in stel-lar atmospheres The Gaussian profile forms as a result of thethermal motion of atoms and reflects their Maxwellian distribu-tion Such a physical picture cannot be applied to the cyclotronfeatures whose nature is completely different The gabs functionshould thus be considered as a pure phenomenological model inthe case of CRSFs

The second widely used phenomenological model has beenspecifically created to model cyclotron features It is imple-mented in the XSPEC cyclabs function which similarly togabs provides a multiplicative factor of the form eminusτ(E) for the

A61 page 4 of 30

continuum (Mihara et al 1990 Makishima et al 1990b) In thismodel the line profile is determined by a Lorentzian functionmultiplied by a factor (EEcyc)2 (not a pure Lorentzian as it isoften claimed in the literature) Equation (7) shows the formulaused for τ(E) for the case of two lines the fundamental at Ecycand the first harmonic at 2Ecyc

τ(E) = τ1(W1EEcyc)2

(E minus Ecyc)2 + W21

+ τ2(W2E[2Ecyc])2

(E minus 2Ecyc)2 + W22

where τ12 are the central optical depths of the two lines whileW12 characterize their width One can fix τ1 or τ2 to zero if nec-essary When using cyclabs however one needs to be carefulsince the ratio of the true energy centroids may not always beexactly equal to two Figure 2 gives an example for a spectral fit-ting of the spectrum of V 0332+53 as observed with RXTE PCAand HEXTE (Pottschmidt et al 2005) for a FermindashDirac contin-uum model and up to three cyclotron lines modeled by Gaussianoptical depth profiles gabs

For a substantial fraction of confirmed CRSF sources listedin Table A1 multiple cyclotron lines are reported The harmoniclines correspond to resonant scattering between the ground Lan-dau level and higher excited levels (see Eq (1)) The energies ofthe harmonic lines are thus expected to be multiples of the fun-damental line energy However the broad and complex profilesof CRSFs the influence of the spectral continuum shape on themeasured line parameters and various physical effects lead todeviations of the line centroid energies from the harmonic spac-ing (see eg Nishimura 2008 Schoumlnherr et al 2007) To modelmultiple cyclotron lines it is best to introduce several indepen-dent absorption line models (as described above) into the spec-tral function leaving the line centroid energies uncoupled

Soon after the discovery of the cyclotron line in Her X-1 a third possibility was occasionally used The X-ray contin-uum was multiplied by a factor [1 minus G(E)] where G(E) is aGaussian function with an amplitude between zero and one (egVoges et al 1982)

The usage of different spectral functions both for the contin-uum and for the cyclotron lines poses a natural problem whenobservational results are to be compared to those that wereobtained using different fit functions It is obvious that the widthand the strengthdepth of the line are defined in different ways inthe models above such that they cannot be directly comparedwith each other Even more challenging is the determinationof the centroid energy of the line In case of a symmetric andsufficiently narrow absorption line for which variations of thecontinuum over the energy range affected by the line can beneglected one naturally expects that the models above wouldreturn very similar centroid energies But the cyclotron lines are(i) mostly quite broad and (ii) are overlaid on a highly inclinedcontinuum which changes exponentially with energy Further-more real lines can be noticeably asymmetric (eg Fuumlrst et al2015) The line centroids measured with different spectral func-tions are therefore systematically different Specifically our sys-tematic analysis7 had shown that a fit with the cyclabsmodel orusing the aforementioned multiplicative [1 minusG(E)] factor resultin a systematically lower (typically by a few keV) centroid ener-gies Ecyc compared to the gabs model (see also Lutovinov et al2017a) For the cyclotron feature in Her X-1 Staubert et al(2014) had therefore added 28 keV to the Suzaku values pub-lished by Enoto et al (2008)

7 Staubert et al 2007 Poster at San Diego Conf Dec 2007 ldquoTheSuzaku X-ray universerdquo

00 05 10 15 20φ

Fig 3 Example of a two-dimensional plot showing color-coded fluxfor photon energy versus pulse phase (for GS 0834-430 Fig 3 ofMiyasaka et al 2013) Horizontal cuts are pulse profiles for the selectedenergy range vertical cuts are spectra for the selected phase interval

Starting with the work by Wang amp Frank (1981) andLyubarskii amp Sunyaev (1982) attempts have been made to fitthe observed spectra with physical models of the polar emit-ting region in accreting pulsars by computing numerically theproperties of the emerging radiation (eg also Becker amp Wolff2007 Farinelli et al 2012 2016 Postnov et al 2015) Eventhough the use of heuristic mathematical functions has beenquite successful in describing the observed spectral shapes theresulting fit parameters generally do not have a unique physicalmeaning Achieving exactly this is the goal of physical mod-els A few such physical spectral models are publicly avail-able for fitting observational data through implementations inXSPEC for example by Becker amp Wolff (2007 BW8) Wolff et al(2016 BWsim) or by Farinelli et al (2016 compmag9) The num-ber of free parameters in these models is however relativelylarge such that some of them need to be fixed or constraineda priori to obtain a meaningful fit (see eg Ferrigno et al2009 Wolff et al 2016 for details) A number of Comptoniza-tion spectral models are available in XSPEC which are usedin the literature to fit spectra of accreting pulsars and of otherastrophysical objects whose spectrum is shaped by Comptoniza-tion compbbcomplscomppscompstcomptbcomptt andincluding CRSFs cyclo (see the XSPEC manual webpagefor details10) These models are calculated for a set of rela-tively simple geometries and do not (except cyclo) take intoaccount magnetic field and other features characteristic foraccreting pulsars The best-fit parameters obtained from spec-tral fitting should therefore be interpreted with caution Oth-erwise with their relatively low number of input parametersand (mostly) short computing time these models provide aviable alternative to the phenomenological models describedearlier

In Sect 45 we discuss physical correlations between vari-ous spectral parameters Since mathematical inter-dependenciesbetween fit parameters are unavoidable in multiparameter fitsit is worth noting that fitted values of the centroid cyclotronline energy Ecyc the focus of this contribution appear to belargely insensitive to the choice of different continuum functions

8 httpwwwisdcunigech~ferrignoimagesDocumentsBW_distributionBW_cookbookhtml9 httpsheasarcgsfcnasagovxanaduxspecmanualXSmodelCompmaghtml10 httpsheasarcgsfcnasagovxanaduxspecmanualAdditivehtml

A61 page 5 of 30

AampA 622 A61 (2019)

Fig 4 Dependence of cyclotron line energy on pulse phase for Her X-1together with pulse profiles for different phases of the 35 d modulation(see Fig 2 of Staubert et al 2014) The right-hand scale is normalizedflux (0ndash100) for the pulse profiles

as was shown in the two systematic studies of ten (respectivenine) X-ray binary pulsars showing CRSFs using observationaldata of RXTE (Coburn et al 2002) and BeppoSAX (Doroshenko2017)

4 Observed variations in cyclotron line energy

The cyclotron line energy has been found to vary with pulsephase (in almost all objects) with luminosity (both positiveand negative in nine objects so far) with time (so far in twoobjects) and with phase of the super-orbital period (so far only inHer X-1) In addition the width and depth of the cyclotronline(s) can also systematically vary with luminosity The spec-tral hardness of the continuum can vary with X-ray luminosityin close correlation with variations of the cyclotron line energy

41 Cyclotron line parameters as function of pulse phase

Throughout a full rotation of the neutron star we see the accre-tion mound or column under different angles We thereforeexpect to observe significant changes in flux in the shape ofthe continuum and in the CRSF parameters as function of pulsephase The variation of flux as function of pulse phase is calledthe pulse profile Each accreting pulsar has its own characteris-tic pulse profile which is often highly energy dependent Withincreasing energy the pulse profiles tend to become smoother(less structured) and the pulsed fraction (the fraction of photonscontributing to the modulated part of the flux) increases (Nagase1989 Bildsten et al 1997) Furthermore those profiles can varyfrom observation to observation due to changes in the physicalconditions of the accretion process for example varying accre-tion rates One way of presenting energy dependent pulse pro-files is a two-dimensional plot energy bins versus phase binswith the flux coded by colors (see Fig 3) In this plot hori-zontal lines represent pulse profiles (for selected energies) andcolumns represent spectra (for selected pulse phases) The cen-troid energy of cyclotron lines are generally also pulse phasedependent The range of variability is from a few percent to 40(see Table A4) As an example Fig 4 shows the variation ofEcyc for Her X-1 which is on the order of 25 (see Fig 2 ofStaubert et al 2014)

In a simple picture the changes of the CRSF energy are aresult of sampling different heights of the line forming region asa function of pulse phase Modeling these variations can helpto constrain the geometry (under the assumption of a dipole

Fig 5 Her X-1 the photon index Γ as function of pulse phase for thefour different 35 d phase intervals interval 1 in black (0007ndash0056)interval 2 in green (009ndash0112) interval 3 in red (0137ndash0161) andinterval 4 in blue (0186ndash0217) (see Fig 7 and Table 1 of Vasco et al2013)

magnetic field) of the accretion column with respect to the rota-tional axis as well as the inclination under which the system isviewed (see eg Suchy et al 2012) However for a more phys-ical constraint on those variations the general relativistic effectssuch as light-bending around the neutron star have to be takeninto account These effects result in a large number of degreesof freedom making it difficult to find a unique solution of theaccretion geometry

In most sources the strength of the CRSF depends stronglyon pulse phase In particular the fundamental line is some-times only seen at certain pulse phases for example Vela X-1(Kreykenbohm et al 2002) or KS 1947+300 (Fuumlrst et al 2014a)This behavior could indicate that the contributions of the twoaccretion columns vary andor that the emission pattern duringlarge parts of the pulse is such that the CRSF is very shallowor filled by spawned photons (Schwarm et al 2017b) The lattermodel agrees with the fact that the harmonic line typically showsless depth variability with phase

Continuum parameters are also known to change as func-tion of pulse phase but not necessarily in step with the observedCRSF variation (see Fig 5) These changes can occur on alltimescales often varying smoothly as function of pulse phase(eg Suchy et al 2008 Maitra amp Paul 2013a Jaisawal amp Naik2016 for a summary see Table A4) However also sharp fea-tures are sometimes observed where the spectrum is changingdramatically over only a few percent of the rotational period ofthe NS The most extreme example is probably EXO 2030+375where the photon-index changes by ∆Γ gt 12 and the absorp-tion column also varies by over an order of magnitude (Ferrignoet al 2016a Fuumlrst et al 2017) This effect is interpreted as anaccretion curtain moving through our line of sight indicating aunique accretion geometry in EXO 2030+375

Another peculiar effect has been observed in the pulse pro-files of some X-ray pulsars the pulse profile shifts in phase atthe energy of the CRSFs (eg in 4U 0115+63 Ferrigno et al2011) This can be explained by the different cross sections atthe CRSF energies leading to changes in emission pattern ascalculated by Schoumlnherr et al (2014)

42 Cyclotron line parameters as function of luminosity

The spectral properties of several cyclotron line sources show adependence on X-ray luminosity (Lx) In particular the cyclotronline energy Ecyc was found to vary with Lx in a systematic

A61 page 6 of 30

Fig 6 Negative EcycLx correlation as observed in V 0332+57 byINTEGRAL and RXTE during an outburst in 20042005 (Fig 4 ofTsygankov et al 2006)

way in correlation with the spectral hardness of the underly-ing continuum Also the line width and depth of the cyclotronline(s) can vary The first detection of a negative dependenceof Ecyc on Lx was claimed by Makishima et al (1990a) andMihara (1995) in high luminosity outbursts of three transientsources 4U 0115+63 V 0332+53 and Cep X-4 observed byGinga ldquoNegativerdquo dependence means that Ecyc decreases withincreasing Lx Figure 6 shows the clear and strong negativecorrelation in V 0332+53 from observations by INTEGRALand RXTE (Fig 4 of Tsygankov et al 2006) However ofthe three sourcesrsquo dependencies originally quoted only oneV 0332+53 can today be considered a secure result (Staubertet al 2016) in Cep X-4 the effect was not confirmed (thesource is instead now considered to belong to the group ofobjects with a ldquopositiverdquo dependence Vybornov et al 2017)In 4U 0115+63 the reported negative (or anticorrelated) depen-dencies (Tsygankov et al 2006 2007 Nakajima et al 2006Klochkov et al 2011) have been shown to be most likely an arti-fact introduced by the way the continuum was modeled (Muumllleret al 2013a see also Iyer et al 2015) More recently a secondsource with a negative EcycLx correlation was found SMC X-2(see Fig 9)

A simple idea about the physical reason for a negative corre-lation was advanced by Burnard et al (1991) Based on Basko ampSunyaev (1976) who had shown that the height of the radiativeshock above the neutron star surface (and with it the line formingregion) should grow linearly with increasing accretion rate Theynoted that this means a reduction in field strength and thereforea reduction of Ecyc Thus with changing mass accretion rate thestrength of the (assumed dipole) magnetic field and Ecyc shouldvary according to the law

Ecyc(M) = E0

Hl(M) + RNS

where E0 corresponds to the line emitted from the neutron starsurface magnetic field BBs RNS is the radius of the NS and Hl isthe actual height of the line forming region above the NS surfaceRegarding the physics of the scaling of the height of the lineforming region see Sect 51

The first positive correlation (Ecyc increases with increasingLx) was finally discovered in 2007 by Staubert et al (2007) inHer X-1 a persistent medium luminosity source (Fig 7) Since

4 5 6 7 8 9max ASM ctss

Fig 7 The originally discovered EcycLx correlation in Her X-1 (repro-duced from Staubert et al 2007)

Fig 8 EcycLx correlation observed in GX 304minus1 (reproduced fromRothschild et al 2017)

then six (possibly seven) more sources (all at moderate to lowluminosities) have been found with Ecyc increasing with increa-sing luminosity (see Table A4) Vela X-1 (Fuumlrst et al 2014bLa Parola et al 2016) A 0535+26 (Klochkov et al 2011Sartore et al 2015) GX 304-1 (Yamamoto et al 2011 Malacariaet al 2015 Rothschild et al 2017) Cep X-4 (Vybornov et al2017) 4U 16266-5156 (DeCesar et al 2013) and V 0332+53(the only source with a strong negative EcycLx correlation athigh luminosities see above) has been confirmed to switch to apositive correlation at very low flux levels at the end of an out-burst (Doroshenko et al 2017 Vybornov et al 2018) A possiblepositive correlation in 4U 1907+09 (Hemphill et al 2013) needsto be confirmed

An interesting deviation from a purely linear correlation(only detectable when the dynamical range in Lx is sufficientlylarge) has recently been noticed in GX 304-1 and Cep X-4namely a flattening toward higher luminosity (Rothschild et al2017 Vybornov et al 2017 see eg Fig 8) This behavior istheoretically well explained by the model of a collisionless shock(see Sect 5)

There are indications that in some objects the line width(and possibly the depth) also correlate with the luminosity (seeTable A5) positively (at least up to a few times 1037 erg sminus1)This is not surprising since the line energy itself correlates withluminosity and the line width and depth generally correlate withthe line energy (see Sect 45) Measured values for the width andthe depth of cyclotron lines are compiled in Table A5 Howeverthe information on line width and depth are overall incompleteand rather scattered

A61 page 7 of 30

AampA 622 A61 (2019)

SMC X-2V0332+53

Her X-1

Cep X-4

Vela X-1

Luminosity [1037 erg sminus1]

01 1 10

GX304minus1

A0535+26

4U1538minus522

Fig 9 Compilation of correlations between Ecyc and Lx Data are taken from the following sources (the numbers in parentheses are the numbersof the references as given in Table A1 SMC X-2 (91) 4U 1538minus522 (81) GX 304minus1 (20 24 54) Cep X-4 (48 130) Vela X-1 (32) A 0535+26(73 74) V 0332+53 (99 123) Her X-1 (25) The luminosities are calculated using the distances measured by Gaia as given in parentheses inTable A3

In the discovery paper of the positive EcycLx correlation inHer X-1 Staubert et al (2007) had proposed that for low tomedium luminosity sources the physics of deceleration of theaccreted matter close to the surface of the NS is very differentfrom the case of the (transient) high luminosity sources thereis no radiation dominated shock that breaks the in-falling mate-rial (moving to larger heights when the accretion rate increases)Rather the deceleration of the material is achieved throughCoulomb interactions that produce the opposite behavior forincreasing accretion rate the line forming region is pushed fur-ther down toward the NS surface (that is to regions with astronger B-field) leading to an increase in Ecyc This picture issupported by the theoretical work by Becker et al (2012) thatdemonstrated that there are two regimes of high and lowmediumaccretion rates (luminosities) separated by a ldquocritical luminos-ityrdquo Lcrit on the order of sim1037 erg sminus1 Figure 9 is an updatedversion of Fig 2 in Becker et al (2012) showing our cur-rent knowledge of those sources that appear to show EcycLxcorrelations For further details of the physics which is clearlymore complicated than the simple picture above see Sect 5 andthe remarks about individual sources in Sect 46

For completeness we mention alternative ideas regardingthe luminosity dependence of Ecyc for example Poutanen et al(2013) who ndash for high luminosity sources ndash follow the idea of anincreasing height of the radiation dominated shock but producethe CRSFs in the radiation reflected from larger and variableareas of the NS surface We note however that it still needs to beshown that cyclotron absorption features can indeed be producedby reflection and the model does not work for the positive cor-relation which is ndash by far ndash the more frequently observed corre-lation Mushtukov et al (2015a) on the other hand suggest thatthe varying cyclotron line energy is produced by Doppler-shiftdue to the radiating plasma the movement of which dependson the accretion rate A further extensive effort to model theluminosity dependence of Ecyc on luminosity by analyticalcalculations is from Nishimura (2008 2011 2013 2014) By

combining changes of the height and the area of the accre-tion mound with changes in the emission profile he claims tobe able to explain both ndash negative and the positive ndash EcycLxcorrelations

43 EcycLx correlations on different timescales andline-continuum correlation

The original discoveries of the EcycLx correlations were basedon observations with variation of Lx on long timescales days tomonths for the negative correlation (eg outburst of V 0332+53Tsygankov et al 2006) and months to years for the first positivecorrelation in Her X-1 (Staubert et al 2007) It was first shown byKlochkov et al (2011) that the same correlations are also observedon short timescales that is on timescales of individual pulses anew technique of analysis was introduced the so-called pulse-to-pulse or pulse-amplitude-resolved analysis Most accreting pul-sars exhibit strong variations in pulse flux (or amplitude) due tovariations in the accretion rate (or luminosity) on timescales at orbelow the duration of single pulses Any variations of the rate ofcapture of material at the magnetospheric boundary to the accre-tion disk are instantaneously mirrored in the release of gravita-tional energy close to the surface of the neutron star (the free falltimescale is on the order of milliseconds) So in selecting pulsesof similar amplitude and generating spectra of all photons in thosedifferent groups one can study the luminosity dependence ofspectral parameters Klochkov et al (2011) analyse observationaldata from INTEGRAL and RXTE of the two high-luminositytransient sources V 0332+53 and 4U 0115+63 as well as themedium to low luminosity sources Her X-1 and A 0535+26 Thesignificance of this work is twofold First the luminosity depen-dence of the cyclotron line energy as known from the earlier work(dealing with long-term variations) is reproduced the correlationis negative for the high luminosity sources and positive for themedium to low luminosity sources Second the spectral index ofthe power law continuum varies with luminosity in the same way

A61 page 8 of 30

as the cyclotron line energy ndashΓ correlates negatively (the spectrabecome softer) for the high luminosity sources and positively (thespectra become harder ndashΓ gets less negative) for the medium tolow luminosity sources11 A supporting result with respect to thecontinuum was found by Postnov et al (2015) who used hard-ness ratios F(5ndash12 keV)F(13ndash3 keV) in all sources analyzedthe continuum becomes harder for increasing luminosity up toLx of sim(5ndash6) 1037 erg sminus1 For three objects where data beyondthis luminosity were available (EXO 2030+375 4U 0115+63and V 0332+53) the correlation changed sign (here we may seethe transition from subcritical to supercritical accretion ndash seeSect 51)

In Table A4 we collate information about variations of Ecycwith pulse phase and with luminosity Lx and about changes ofΓ (or spectral hardness) with Lx Those sources that show a sys-tematic EcycLx correlation are discussed individually below Itis interesting to note that the sources with a positive correlationgreatly outnumber those with the (first detected) negative cor-relation We suggest that the positive correlation is a commonproperty of low to medium luminosity accreting binary pulsarsIt is also worth noting that the luminosity dependence of Ecycis found on different timescales ranging from years over daysto seconds (the typical time frame of one pulse) Further detailsabout the width and the depth of the cyclotron lines are com-piled in Table A5 These parameters are also variable but theinformation on this is unfortunately still rather scattered

44 Long-term variations of the cyclotron line energy

So far only two sources show a clear variability of the CRSFcentroid energy over long timescales (tens of years) Her X-1and Vela X-1 We discuss both sources below For completenesswe mention 4U 1538-522 as a possible candidate for a long-term increase (Hemphill et al 2016) Only further monitoringof this source over several years will tell whether the suspicionis justified A peculiar variation on medium timescales (100 d)was observed in V 0332+53 during an outburst (Cusumano et al2016 Doroshenko et al 2017 Vybornov et al 2018) and fromone outburst to the next (sim400 d) (Vybornov et al 2018) Duringthe outburst of JunendashSeptember 2015 the source showed the wellknown anticorrelation of Ecyc with luminosity during the riseand the decay of the burst but at the end of the burst the CRSFenergy did not come back to its initial value (as was observedseveral times before) The data are consistent with a linear decayof Ecyc over the 100 d outburst by sim5 (Cusumano et al 2016)But at the next outburst 400 d later Ecyc had in fact resumed itsoriginal value of sim30 keV The physics of this phenomenon isunclear

The first and best documented case for a long-term varia-tion of the CRSF energy is Her X-1 (Staubert et al 2007 20142016) At the time of discovery in 1976 the cyclotron line energywas around 37 keV (interpreted as absorption line) During thefollowing sim14 years several instruments (including the enlargedBalloon-HEXE HEAO-A4 Mir-HEXE and Ginga) measuredvalues between 33 and 37 keV (with uncertainties which allowedthis energy to be considered well established and constant)(Gruber et al 2001 Staubert et al 2014) After a few years ofno coverage a surprisingly high value (sim44 keV) from obser-vations with the GROBATSE instrument in 1993ndash1995 wasannounced (Freeman amp Freeman 1996) Greeted with strongdoubts at the time values around 41 keV were subsequently

11 In contrast to earlier wording (eg Klochkov et al 2011) we preferto say Ecyc and ndashΓ vary in the ldquosame wayrdquo

50000 51000 52000 53000 54000 55000 56000 57000 58000

E_cyc (keV)

Time (MJD)

RXTE 09

Integral 05

NuSTAR 12

Suzaku 05 cor

Suzaku 06 cor

Suzaku 10

Suzaku 12

Integral 11 Integral

NuSTAR 15

NuSTAR 16

Integral 16b

Integral 16a

Fig 10 Cyclotron line energy Ecyc in Her X-1 The long-term decaystopped in 2016 (see Fig 1 in Staubert et al 2017)

measured by RXTE (Gruber et al 1999) and BeppoSAX (DalFiume et al 1998) confirming that the cyclotron line energy hadindeed increased substantially between 1990 and 1993 Furtherobservations then yielded hints for a possible slow decay Whiletrying to consolidate the evidence for such a decay using a uni-form set of RXTE observations Staubert et al (2007) insteadfound a new effect a positive correlation between the pulsephase averaged Ecyc and the X-ray flux (or luminosity) of thesource (Sect 42) letting the apparent decrease largely appearas an artifact However with the inclusion of further data anda refined method of analysis namely fitting Ecyc values withtwo variables (flux and time) simultaneously it was possibleto establish statistically significant evidence of a true long-termdecay of the phase averaged cyclotron line energy by sim5 keVover 20 years (Staubert et al 2014 2016 Staubert 2014) Bothdependencies ndash on flux and on time ndash seem to be always presentThe decay of Ecyc was independently confirmed by the anal-ysis of SwiftBAT data (Klochkov et al 2015) Further mea-surements however yield evidence that the decay of Ecyc mayhave stopped with a hint to an inversion (Staubert et al 2017see Fig 10) Since then an intensified effort has been under-way to monitor the cyclotron line energy with all instrumentscurrently available The analysis of the very latest observationsbetween August 2017 and September 2018 seems to confirm thistrend

The physics of the long-term variation of Ecyc is not under-stood We do however believe that this is not a sign of a changein the global (dipole) field of the NS but rather a phenomenonassociated with the field configuration localized to the regionwhere the CRSF is produced Apparently the magnetic fieldstrength at the place of the resonant scattering of photons tryingto escape from the accretion mound surface must have changedwith time A few thoughts about how such changes could occurare advanced by Staubert et al (2014 2016) and Staubert (2014)Putting internal NS physics aside changes could be connected toeither a geometric displacement of the cyclotron resonant scat-tering region in the dipole field or to a true physical change in themagnetic field configuration at the polar cap The latter couldbe introduced by continued accretion with a slight imbalancebetween the rate of accretion and the rate of ldquolosingrdquo materialat the bottom of the accretion mound (either by incorporationinto the neutron star crust or leaking of material to larger areasof the NS surface) leading to a change of the mass loading andconsequently of the structure of the accretion mound height orB-field configuration (eg ldquoballooningrdquo Mukherjee et al 20132014) It is also interesting to note that the measured Ecyc cor-responds to a magnetic field strength (sim38 times 1012 Gauss) which

A61 page 9 of 30

AampA 622 A61 (2019)

is a factor of two larger than the polar surface field strength esti-mated from applying accretion torque models (see Sect 6) Thisdiscrepancy could mean that the B-field measured by Ecyc isfor a local quadrupole field that is stronger and might be vul-nerable to changes on short timescales (but see Sect 6) Around2015 the cyclotron line energy in Her X-1 seems to have reacheda bottom value comparable to the value of its original discov-ery (sim37 keV) with a possible slight increase (Staubert et al2017) leading to the question of whether we could ndash at sometime ndash expect another jump upwards (as seen between 1990 and1993)

Besides Her X-1 we know one more source with a long-term(over 11 year) decay of the CRSF energy Vela X-1 (La Parolaet al 2016) Vela X-1 is also one of seven sources showing a pos-itive EcycLx dependence originally discovered by Fuumlrst et al(2014b) and confirmed by La Parola et al (2016) The samephysics is probably at work in both sources Most likely moresources with this phenomenon will be found as monitoring forexample with SwiftBAT continues

45 Correlations between Ecyc and other spectral parameters

Before entering discussion about the physics associated withthe generation of X-ray spectra in general and cyclotron linesin particular we briefly mention an interesting observationalphenomenon there are several correlations between spectralparameters of the continuum and those of the CRSFs Histori-cally the first such correlation is that between the cutoff energyEcutoff (see Eqs (3) and (4)) and the CRSF centroid energyEcyc first noted by Makishima amp Mihara (1992 also Makishimaet al 1999) who realized that the relationship is probably notlinear but closer to Ecutoff prop E07

cyc Then a clear (linear) rela-tionship was found between the width of the CRSF σcyc andthe centroid energy Ecyc (Heindl et al 2000 dal Fiume et al2000) It followed a systematic study in 2002 of all accretingpulsars showing CRSFs that were observed by RXTE (Coburnet al 2002) Here the above mentioned correlations were con-firmed and one additional identified the relative line widthσcycEcyc versus the optical depth τ of the line As a conse-quence almost every spectral parameter is ndash to some degreendash correlated with all the others (see the correlation matricesTables 8 and 9 in Coburn et al 2002) Through Monte Carlosimulations Coburn et al (2002) have shown that the correla-tions between the parameters are not an artifact (eg due to amathematical coupling in the fitting process) but are actuallyof physical nature Even though some ideas about the phys-ical meaning of the observed correlations had been put for-ward a rigorous check of the viability of those ideas is stillneeded

Recently a similar systematic study using observationaldata from BeppoSAX (on nearly the same set of objectsobserved around the same time as by RXTE) was completedby Doroshenko (2017)12 This study largely confirms the earlierresults Combining the results of both studies two interest-ing features appear First the dependence of Ecutoff on Ecyc

is even weaker more like Ecutoff prop E04cyc (see Fig 11) And

second the linear correlation σcyc prop Ecyc is well demon-strated (the data points from BeppoSAX and RXTE are ingood agreement) However there is considerable scatter whenall eleven objects are to be fit by one relationship The scat-ter can be drastically reduced by assuming that there are two

12 httpastrouni-tuebingendepublicationsdissshtml

0 10 20 30 40 50

E_cut (keV)

E_cyc (keV)

Cen X-3

1538-52

1907+09

1946+274

Her X-1

0115+63

fit E^041

Vela X-1

red RXTE

$amp()+-

Fig 11 Cutoff energy Ecut versus cyclotron line energy Ecyc for objectsstudied by RXTE (Coburn et al 2002) and BeppoSAX (Doroshenko2017) The cutoff energy is roughly proportional to the square root ofEcyc The two objects 4U 1744-28 and 4U 1626-67 are extreme outliersto this relationship and not included in the fit

0 10 20 30 40 50

sigma (keV)

E_cyc (keV)

Her X-1

1626-67

0115+63

1538-52

1744-28

1907+09

1946+274

Cen X-3

GX 301-2

0352+309

Vela X-1

slopes 0236

red RXTE $amp()+-

Fig 12 Width σ of the CRSFs versus cyclotron line energy Ecycfor objects studied by RXTE (Coburn et al 2002) and BeppoSAX(Doroshenko 2017) There seem to be two groups of objects each witha linear relationship and similar slopes but separated by an offset insigma by sim2 keV

groups both following the same slope but with a constantoffset of sim2 keV in σ to one another (Fig 12) The objects inthe group with the smaller σ values appear to be the more ldquoreg-ularrdquo objects that tend to obey most other correlations fairlywell The objects in the other group are more often ldquooutliersrdquo inother correlations and have other or extreme properties such asvery high luminosity (Cen X-3 4U 0115+63) a different contin-uum (4U 0352+309) or are otherwise peculiar as is the burst-ing pulsar (4U 1744-28) Generally we find that as the widthσ and depth τ of the CRSF increase with increasing centroidenergy Ecyc two continuum parameters also increase the cut-off energy Ecutoff and the power law index minusΓ (the continuumhardens)

46 Individual sources

Here we summarize the main characteristics of all sources show-ing a correlation between Ecyc and Lx We start with sources oflow to medium luminosity showing a positive correlation (sevensources) followed by the two sources at very high luminositiesshowing a negative correlation

Her X-1 This source is in many ways unique it belongs tothe class of low mass accreting binary pulsars with the highlymagnetized neutron star accreting through an accretion diskThe optical companion HZ Hercules is a low mass mainsequence star with spectral type A to F It was known well

A61 page 10 of 30

before the discovery of the X-ray source as an interesting vari-able star The optical light is modulated at the binary periodof 170 d due to heating by the X-rays from the neutron starA long-term optical history showing periods of extended lowsis documented on several photographic plates from differentobservatories dating back to 1890 (Jones et al 1973) Thebinary system shows a large number of observational fea-tures (also due to the low inclination of its binary orbit) thatare characteristic for the whole class of objects Apart frombeing one (together with Cen X-3) of the two first detectedbinary X-ray pulsars (Tananbaum et al 1972) Her X-1 is asso-ciated with several other ldquofirst detectionsrdquo (see eg Staubert2014) in particular with respect to cyclotron line research(1) the detection of the first cyclotron line ever (Fig 1Truumlmper et al 1977 1978) constituting the first ldquodirectrdquo mea-surement of the magnetic field strength in a neutron star (2)the detection of the first positive correlation of the cyclotronline energy Ecyc with X-ray luminosity (Staubert et al 2007see Sects 43 and 3) the first detection of a long-term decay ofEcyc (by sim5 keV over 20 years Staubert et al 2014 2016 seeSect 44)

The positive correlation is also found on a timescale of sec-onds using the ldquopulse-to-pulserdquo (or ldquoamplitude-resolvedrdquo anal-ysis Klochkov et al 2011 see Sect 43) In this analysis it isdemonstrated that together with the cyclotron line energy thecontinuum also varies for Her X-1 the continuum gets harder(the power law index Γ decreases minusΓ increases) with increasingLx This appears to hold for all objects with a positive EcycLxcorrelation and the opposite is true for that with a negativeEcycLx correlation In addition Her X-1 is one of the few binaryX-ray pulsars exhibiting a super-orbital period of sim35 daysstrongly modulating the overall X-ray flux as well as the shapeof the pulse profile (see eg Staubert 2014) This modulation isthought to be due to an obscuration of the areas on the neutronstar surface where X-rays are produced by the accretion diskThe super-orbital modulation is not a good clock and has itsown quite intriguing timing properties (Staubert et al 2010a2013 2014) It is an open question whether the suggestion offree precession of the neutron star (Truumlmper et al 1986 Staubertet al 2009 2010bc Postnov et al 2013) is indeed viable It isinteresting to note that Ecyc appears to change slightly with 35d-phase (Staubert et al 2014)

GX 304minus1 Originally discovered at hard X-ray energies (above20 keV) during a set of MIT balloon scans of the Galactic planein the late 1960s and early 1970s (McClintock et al 1971) andseen as an UHURU source at 2minus10 keV (Giacconi et al 1972)the source went into quiescence for nearly 30 years (Pietsch et al1986) until its re-emergence in 2008 (Manousakis et al 2008)The binary orbit is 1322 d (from the separation between out-bursts Sugizaki et al 2015 Yamamoto et al 2011 Malacariaet al 2015) and the pulse period is 275 s (McClintock et al1977) The star V850 Cen was identified as the optical compan-ion (Mason et al 1978) The first detection of a cyclotron lineat sim54 keV and its possible luminosity dependence is based onRXTE observations of an outburst in August 2010 (Yamamotoet al 2011) The positive luminosity correlation was confirmedthrough INTEGRAL results (Klochkov et al 2012 Malacariaet al 2015) Recent analysis of all of the RXTE observations ofGX 304minus1 by Rothschild et al (2016 2017) covered four out-bursts in 2010 and 2011 This analysis not only confirmed thepositive correlation of the CRSF energy with luminosity but alsoshowed a positive correlation of the line width and depth withluminosity In addition a positive correlation was seen for the

power law index (the spectrum getting harder with increasingluminosity) and for the iron line flux For the first time all theCRSF correlations were seen to flatten with increasing luminos-ity (see Fig 8) As will be discussed in Sect 5 this behavior canbe successfully modeled assuming a slow down of the accretionflow by a collisionless shock in which the radiation pressure isof minor importance

Vela X-1 An eclipsing high-mass X-ray binary discovered inthe early years of X-ray astronomy by Chodil et al (1967) thissource is considered as an archetypal wind accretor It is a per-sistent source with essentially random flux variations explainedby accretion from a dense structured wind surrounding the opti-cal companion HD 77581 (eg Fuumlrst et al 2014b) HD 77581is a 24 M main sequence giant in a binary orbit of 896 d andmoderate eccentricity (e = 009)

The first evidence for cyclotron lines in this source ndash a fun-damental around sim25 keV and a first harmonic near 50 keV ndashwas found by Kendziorra et al (1992) using Mir-HEXE andfurther detailed by Kretschmar et al (1996) Early observa-tions with RXTE confirmed these detections (Kretschmar et al1997) Based on NuSTAR observations Fuumlrst et al (2014b)reported a clear increase of the energy of the harmonic line fea-ture with luminosity the first clear example for such behaviorin a persistent HMXB In contrast the central energy of thefundamental line shows a complex evolution with luminositywhich might be caused by limitations of the phenomenologi-cal models used From a study of long-term data of SwiftBATLa Parola et al (2016) confirmed the positive correlation of theharmonic line energy with luminosity and noted that the funda-mental line is not always present In addition they found a sec-ular variation of the line energy decreasing by sim036 keV yrminus1

between 2004 and 2010 This establishes Vela X-1 as the sec-ond source (after Her X-1) for which a long-term decay isobserved

A 0535+26 The transient X-ray binary A 0535+26 wasdiscovered in outburst during observations of the Crab with theRotation Modulation Collimator on Ariel V showing X-ray pul-sations of sim104 s (Rosenberg et al 1975) The system was foundto consist of an O97IIIe donor star and a magnetized neutronstar (Liller 1975 Steele et al 1998) It has an eccentricity ofe = 047 plusmn 002 and an orbital period of Porb = 1103 plusmn 03 d(Finger et al 1996) The distance to A 0535+26 is sim2 kpc(Giangrande et al 1980 Steele et al 1998) which has beenrecently confirmed by Gaia (Bailer-Jones et al 2018)

Absorption line-like features at sim50 and sim100 keV wherethe former was of low significance were first detected with MirTTMHEXE during a 1989 outburst of the source (Kendziorraet al 1994) They were interpreted as the fundamental andfirst harmonic cyclotron resonances An sim110 keV feature wasconfirmed with CGRO OSSE during a 1994 outburst (Groveet al 1995 with no definite statement on the presence ofthe low energy line due to OSSErsquos 45 keV threshold) In thefollowing years the fundamental line was independently con-firmed near sim46 keV with different missions during a 2005AugustSeptember outburst (Kretschmar et al 2005 Wilsonet al 2005 Inoue et al 2005) and it has been studied for sev-eral outbursts since then (eg Ballhausen et al 2017)

The outbursts of A 0535+26 show varying peak brightnessesreaching 15ndash50 keV fluxes from a few 100 mCrab to sim55 Crab(Camero-Arranz et al 2012a Caballero et al 2013a) Bright so-called giant outbursts are known to have occured in 1975 19801983 1989 1994 2005 2009 and 2011 (Caballero et al 20072013ab and references therein) The source has been observed

A61 page 11 of 30

AampA 622 A61 (2019)

over a large range of luminosities High quality data couldbe obtained down to comparatively low outburst luminosities(Terada et al 2006 Ballhausen et al 2017) and even in quies-cence (Rothschild et al 2013) The fundamental cyclotron lineenergy generally does not change significantly with luminosity(over a wide range) (see Fig 9 and eg Caballero et al 2007)There are however tantalizing indications for a more complexbehavior (i) clear increase of the line energy up to 52+16

minus14 keVwas observed for a flare during the rising phase of the 2005 giantoutburst (Caballero et al 2008) (ii) similar to Her X-1 a positiveEcycLx correlation was found using the ldquopulse-to-pulserdquo analy-sis (Klochkov et al 2011 Muumlller et al 2013b) and (iii) the pos-itive correlation might also be visible at the highest luminosities(see Fig 9 and eg Sartore et al 2015) The continuum emis-sion of A 0535+26 has been observed to harden with increasingluminosity (Klochkov et al 2011 Caballero et al 2013b) withpossible saturation at the highest luminosities (Postnov et al2015) and a more strongly peaked rollover at the lowest outburstluminosities (Ballhausen et al 2017)

Cep X-4 This source was discovered by OSO-7 in 1972(Ulmer et al 1973) During an outburst in 1988 observed byGinga regular pulsations with a pulse period around 66 s werediscovered and evidence for a CRSF around 30 keV was found(Mihara et al 1991) The optical counterpart was identified byBonnet-Bidaud amp Mouchet (1998) who measured a distance of38plusmn06 kpc Mihara (1995) on the basis of Ginga observationshad claimed that Cep X-4 (together with the high luminositysources 4U 0115+63 and V 0332+53) showed a negative EcycLxcorrelation This has never been confirmed Instead a positivecorrelation was discovered in NuSTAR data (Fuumlrst et al 2015) ndashalthough with two data points only Jaisawal amp Naik (2015a)detected the first harmonic in observations by Suzaku Vybornovet al (2017) analyzing an outburst observed in 2014 byNuSTAR using the pulse-amplitude-resolving technique(Klochkov et al 2011) confirmed the existence of the twocyclotron lines at sim30 keV and sim55 keV and found a strongpositive EcycLx correlation that is well modeled by assuming acollisionless shock

Swift 16266ndash5156 The source was discovered by SwiftBATduring an outburst in 2005 as a transient pulsar with sim15 s pulseperiod (Palmer et al 2005) The optical companion was iden-tified as a Be-star (Negueruela amp Marco 2006) After differentsuggestions a convincing orbital solution was finally found byBaykal et al (2010) with a period of 1329 d and a very smalleccentricity (008) Several observations over three years (2006ndash2008) by RXTEPCA led to the discovery of a CRSF at about10 keV (DeCesar et al 2013) Even though the discovery ofthis CRSF needs confirmation by further observations (and otherinstruments) we list this source not under the category ldquocandi-datesrdquo because the evidence from the different observations isquite strong and there are clear signatures of the usual behaviorof CRSFs including a strong correlation of the phase resolvedCRSF energy with pulse phase an indication for a positive cor-relation with luminosity and a hint to a first harmonic at sim18 keV

V 0332+53 The transient X-ray binary V 0332+53 was discov-ered in outburst in 1983 by Tenma (Tanaka 1983 Makishimaet al 1990b) and in parallel an earlier outburst was revealed inVela 5B data from 1973 (Terrell amp Priedhorsky 1983 1984) Infollow-up observations by EXOSAT during the 1983 activity44 s pulsations were discovered an accurate position was mea-sured and the orbital period and eccentricity were determined tobe 34 days and 037 respectively (Stella et al 1985 see alsoZhang et al 2005) The O8ndash9Ve star BQ Cam was identified

as the optical counterpart (Argyle et al 1983 Negueruela et al1999) The distance to the system was estimated to be 6ndash9 kpc(Negueruela et al 1999 but see also Corbet et al 1986)

V 0332+53 displays normal as well as giant outburstsOccurrences of the latter have been observed in 197320042005 and 2015 (Ferrigno et al 2016b) During giant out-bursts the source can become one of the most luminous X-raysources in the Galaxy reaching a few times 1038 erg sminus1 Quasi-periodic oscillations with frequencies of sim005 Hz and sim022 Hzhave been observed (Takeshima et al 1994 Qu et al 2005Caballero-Garciacutea et al 2016)

The Tenma observation of V 0332+53 also provided evi-dence for a fundamental cyclotron line feature at sim28 keV(Makishima et al 1990b) Its presence was confirmed with highsignificance by Ginga observations of the source during a 1989outburst which also showed indications for a harmonic fea-ture at sim53 keV (Makishima et al 1990a) The giant outburstin 20042005 allowed for the confirmation of this harmonic aswell as the detection of a rare second harmonic at sim74 keV withINTEGRAL and RXTE (Kreykenbohm et al 2005 Pottschmidtet al 2005)

These observations of the giant outburst in 20042005 fur-ther revealed that the energy of the fundamental cyclotron linedecreased with increasing luminosity (Tsygankov et al 20062010 Mowlavi et al 2006) Additional studies showed that thecorrelation was also present for the first harmonic line (althoughcharacterized by a weaker fractional change in energy Nakajimaet al 2010) as well as for the pulse-to-pulse analysis of the fun-damental line (Klochkov et al 2011) A qualitative discussion ofresults from pulse phase-resolved spectroscopy of this outburstin terms of the reflection model for cyclotron line formation hasbeen presented (Poutanen et al 2013 Lutovinov et al 2015)Swift INTEGRAL and NuSTAR observations of the most recentgiant outburst in 2015 also showed the negative correlation andprovided evidence that the overall line energy and thus theassociated B-field was lower just after the outburst indicatingsome decay over the time of the outburst (Cusumano et al 2016Ferrigno et al 2016b Doroshenko et al 2017 Vybornov et al2018 see also the discussion in Sect 44)

V 0332+53 is singled out by the fact that it is the only sourceto date in which we find both EcycLx correlations the neg-ative at high luminosities and the positive at low luminosity(Doroshenko et al 2017 Vybornov et al 2018) It is also theonly one with a very strong negative correlation accompaniedby a second source ndash SMC X-2 ndash which shows a much weakerdependence (see Fig 9) This two-fold behavior is in line withthe correlation between the spectral index (or spectral hardening)as found in several other accreting pulsars a hardening at lowluminosities and a softening at very high luminosities (Klochkovet al 2011 Postnov et al 2015)

SMC X-2 This transient source in the Small Magellanic Cloudwas detected by SAS-3 during an outburst in 1977 (Clark et al1978 1979) Later outbursts were observed by several satellitesIn 2000 the source was identified as an X-ray pulsar by RXTEand ASCA with a period of 237 s (Torii et al 2000 Corbet et al2001 Yokogawa et al 2001) The optical companion suggestedby Crampton et al (1978) was later resolved into two objectsand the northern one identified as the true companion basedon an optical periodicity of sim186 d (Schurch et al 2011) thatappeared to coincide with an X-ray period of sim184 d found inRXTE data (Townsend et al 2011) The optical classification ofthe companion was determined to be O95 III-V (McBride et al2008) During an outburst in 2015 Jaisawal amp Naik (2016) found

A61 page 12 of 30

a cyclotron line at sim27 keV in NuSTAR data that showed a weaknegative correlation with luminosity (see Fig 9) If this is con-firmed SMC X-2 is the second high luminosity source showingthis negative correlation with luminosity As with Swift 16266-5156 the detection of the cyclotron line needs confirmationLutovinov et al (2017b) using observations by SwiftXRT ofthe same outburst in 2015 detected a sudden drop in luminosityto below a few times 1034 erg sminus1 which interpreted as the sig-nature of the propeller effect allows us to estimate the strengthof the magnetic field to be around 3 times 1012 Gauss This is quiteclose to the B-field value found from the cyclotron line energy(see also Sect 6)

4U 0115+63 This source is included here since historically itwas thought to be a high luminosity source showing a nega-tive EcycLx correlation As we discuss below we now believehowever that this is probably not correct 4U 0115+63 is a highmass X-ray binary system first discovered in the sky survey byUHURU (Giacconi et al 1972) with repeated outbursts reach-ing high luminosities (Boldin et al 2013) The system con-sists of a pulsating neutron star with a spin period of 361 s(Cominsky et al 1978) and a B02Ve main sequence star (Johnset al 1978) orbiting each other in 243 d (Rappaport et al1978) The distance to this system has been estimated at sim7 kpc(Negueruela amp Okazaki 2001) As early as 1980 a cyclotron lineat 20 keV was discovered in 4U 0115+63 in observational dataof HEAO-1A4 (Wheaton et al 1979) A re-examination of thedata uncovered the existence of two lines at 115 and 23 keVwhich were immediately interpreted as the fundamental and har-monic electron cyclotron resonances (White et al 1983) Laterobservations of the source found three (Heindl et al 1999) thenfour (Santangelo et al 1999) and finally up to five lines in total(Heindl et al 2004) 4U 0115+63 is still the record holder in thenumbers of harmonics

A negative correlation between the pulse phase averagedcyclotron line energy and the X-ray luminosity (a decrease inEcyc with increasing Lx) was claimed for the first time in thissource by Mihara (1995) on the basis of observations with Ginga(together with two other high luminosity transient sourcesCep X-4 and V 0332+53) This negative correlation was associ-ated with the high accretion rate during the X-ray outbursts andas due to a change in height of the shock (and emission) regionabove the surface of the neutron star with changing mass accre-tion rate M In the model of Burnard et al (1991) the heightof the polar accretion structure is tied to M (see above) A sim-ilar behavior was observed in further outbursts of 4U 0115+63in MarchndashApril 1999 and SepndashOct 2004 both Nakajima et al(2006) and Tsygankov et al (2007) had found a general anticor-relation between Ecyc and luminosity The negative correlationwas also confirmed by Klochkov et al (2011) using the pulse-amplitude-resolved analysis technique together with the soften-ing of the continuum when reaching very high luminosities (seealso Postnov et al 2015)

However Muumlller et al (2013a) analyzing data of a dif-ferent outburst of this source in MarchndashApril 2008 observedby RXTE and INTEGRAL have found that the negative cor-relation for the fundamental cyclotron line is likely an arti-fact due to correlations between continuum and line parame-ters when using the NPEX continuum model Further no anti-correlation is seen in any of the harmonics Iyer et al (2015)have suggested an alternative explanation there may be twosystems of cyclotron lines with fundamentals at sim11 keV andsim15 keV produced in two different emission regions (possi-bly at different poles) In this model the second harmonic of

the first system coincides roughly with the 1st harmonic inthe second system In summary we conclude that 4U 0115+63does not show an established dependence of a CRSF energy onluminosity

5 Physics of the accretion column

In this Section we discuss the basic physics with relevance tothe accretion onto highly magnetized neutron stars The genera-tion of the X-ray continuum and the cyclotron lines as well astheir short- and long-term variability depends on the structureof the accretion column the physical state of the hot magne-tized plasma the magnetic field configuration and many detailswith regard to fundamental interaction processes between parti-cles and photons that govern the energy and radiation transportwithin the accretion column

Our basic understanding is that material transferred froma binary companion couples to the magnetosphere of the neu-tron star (assuming a simple dipole field initially) The accretedplasma falls along the magnetic field lines down to the surfaceof the NS onto a small area at the polar caps where it is stoppedand its kinetic energy is converted to heat and radiation Fromthe resulting ldquoaccretion moundrdquo the radiation escapes in direc-tions that depend on the structure of the mound the B-fieldand the gravitational bending by the NS mass If the magneticand spin axes of the neutron star are not aligned a terrestrialobserver sees a flux modulated at the rotation frequency of thestar

We refer to the following fundamental contributions tothe vast literature on this topic Gnedin amp Sunyaev (1974)Lodenquai et al (1974) Basko amp Sunyaev (1975) Shapiro ampSalpeter (1975) Wang amp Frank (1981) Langer amp Rappaport(1982) Braun amp Yahel (1984) Arons et al (1987) Miller et al(1987) Meszaros (1992) Nelson et al (1993) Becker et al(2012) Further references are given in the detailed discussionbelow

51 Accretion regimes

In the simplest case of a dipole magnetic field the plasmafilled polar cap area is A = πr2

p with polar cap radius rp

RNSradic

RNSRm where Rm is the magnetospheric radius The lat-ter is determined by the balance of the magnetic field and matterpressure and is a function of the mass accretion rate M and theNS magnetic field which can be characterized by the surfaceNS value Bs or equivalently by the dipole magnetic momentmicro = (BsR3

NS)213 The accreting matter moves toward the NSwith free-fall velocity which is about ν0 = 1010 cm sminus1 close tothe NS The matter stops at (or near) the NS surface with itskinetic energy being ultimately released in the form of radia-tion with a total luminosity of La = Mν0

22 The continuum isbelieved to be due to thermal bremsstrahlung radiation from thesim108 K hot plasma blackbody radiation from the NS surface andcyclotron continuum radiation ndash all modified by Comptonisation(Basko amp Sunyaev 1975 Becker amp Wolff 2007 Becker et al2012) and the cyclotron line by resonant scattering of photons onelectrons with discrete energies of Landau levels (Ventura et al1979 Bonazzola et al 1979 Langer et al 1980 Nagel 1980Meszaros et al 1983)

13 We note that the factor of a half required by electrodynamicsdescribing the B-field at the magnetic poles (see eg Landau-LifschitsTheory of fields) is often missing in the literature (see also the com-ments in Table 1)

A61 page 13 of 30

AampA 622 A61 (2019)

Since the discovery of negative and positive EcycLx cor-relations first found for V 0332+53 (Makishima et al 1990aMihara 1995) and Her X-1 (Staubert et al 2007) respectively ithas become very clear that there are different accretion regimesdepending on the mass accretion rate (X-ray luminosity) Animportant value separating low and high accretion rates is theldquocritical luminosityrdquo Llowast sim 1037 erg sminus1 (see below) The differ-ent accretion regimes correspond to different breaking regimesthat is different physics by which the in-falling material is decel-erated So the study of the EcycLx dependence provides a newtool for probing physical processes involved in stopping theaccretion flow above the surface of strongly magnetized neutronstars in accreting X-ray pulsars

The different breaking regimes are as follows If the accre-tion rate is very small the plasma blobs frozen in the NSmagnetosphere arrive almost at the NS surface without break-ing and the final breaking occurs in the NS atmosphere viaCoulomb interactions various collective plasma processes andnuclear interactions This regime was first considered in thecase of spherical accretion onto NS without magnetic fields byZelrsquodovich amp Shakura (1969) and later in the case of magnetizedneutron stars (eg Miller et al 1987 Nelson et al 1993) Theself-consistent calculations of the layer in which energy of theaccreting flow was released carried out in these papers showedthat the stopping length of a proton due to Coulomb interactionsamounts to y =

intρdz sim 50 g cmminus2 where ρ is the plasma density

and the height of this layer is comparable to the NS atmospheresize Clearly in this case the CRSF feature (if measured) shouldreflect the magnetic field strength close to the NS surface andshould not appreciably vary with changing accretion luminosity

With increasing mass accretion rate M the accreting flow(treated gas-dynamically) starts decelerating with the formationof a collisionless shock (CS) The possibility of deceleration viaa CS was first considered in the case of accretion of plasmaonto a neutron star with a magnetic field by Bisnovatyi-Kogan ampFridman (1970) Later several authors (eg Shapiro amp Salpeter1975 Langer amp Rappaport 1982 Braun amp Yahel 1984) postu-lated the existence of a stationary CS above the neutron star sur-face if the accretion luminosity is much less than the Edding-ton luminosity The formation and structure of the CS in thiscase accounting for detailed microphysics (cyclotron electronand proton cooling bremsstrahlung losses resonant interactionof photons in diffusion approximation etc) is calculated numer-ically by Bykov amp Krasilrsquoshchikov (2004) in 1D-approximationThese calculations confirmed the basic feature of CS (1) theformation above the neutron star surface at the height Hl sim

(ν04)tei where ν0 asymp c3 is the upstream velocity and tei is theequilibration time between protons and electrons via Coulombinteractions which follows from the requirement to transfermost of the kinetic energy carried by ions to radiating electrons(2) the release of a substantial fraction (about half) of the in-falling kinetic energy of the accretion flow downstream of theCS in a thin interaction region of the flow

The CS breaking regime persists until the role of the emittedphotons becomes decisive which can be quantified (to an orderof magnitude) by equating the photon diffusion time across theaccretion column td sim r2

P(clγ) where lγ is the photon meanfree path in the strong magnetic field and the free-fall time ofplasma from the shock height tff sim Hl(ν04) sim rpν0 This rela-tion yields the so-called ldquocritical luminosityrdquo Llowast sim 1037 erg sminus1above which the in-falling accretion flow is decelerated by aradiative shock (RS Basko amp Sunyaev 1975 1976 Arons et al1987) In the literature there are several attempts to calculate thiscritical luminosity (which should depend on the magnetic field

the geometry of the flow etc) more precisely (see eg Wangamp Frank 1981 Becker et al 2012 Mushtukov et al 2015b) Itshould be kept in mind however that the transition to a radiationdominated (RD)-dominated regime occurs rather smoothly andthis critical luminosity should be perceived as a guidance value(and not a strict boundary) for the separation between the pureCS or RS regimes in a particular source

511 Scaling CRSF relations in collisionless shock regime

In the CS regime that can be realized in accreting X-ray pul-sars with low or moderate X-ray luminosity (eg Her X-1GX 304-1 Cep X-4 etc) there are simple and physically clearrelations between the CRSF properties (energy width depth)and X-ray luminosity which have been checked by X-ray obser-vations Indeed the typical CS height is a few hundred metersabove the neutron star surface and scales with the plasma num-ber density as Hl sim 1ne and through the mass conservationM sim r2

pneν0 as Hl sim 1M (Shapiro amp Salpeter 1975 Baskoamp Sunyaev 1976) confirmed through detailed numerical simu-lations by Bykov amp Krasilrsquoshchikov 2004 (see their Fig 5) Atthese heights the dipole structure of the neutron star magneticfield is already important The theory of CRSF formation in aninhomogeneous magnetic field can be found in Zheleznyakov(1996) In the inhomogeneous magnetic field the cyclotron lineis formed in a resonant layer The width of the resonant layerfor the assumed dipole magnetic field is ∆rres sim βTe rres3where βTe = νT ec sim 110 is the thermal velocity of post-shock electrons and rres is the radial height of the resonantlayer for typical temperatures Te sim 10 keV and cyclotron pho-ton energies ~ωcyc sim 30minus50 keV the size of the resonant layer∆rres sim 6 times 104 cm can be comparable with the shock heightHs and thus can substantially affect the CRSF formation Wenote that the post-shock electron temperature Te does not varysubstantially

The characteristic optical depth of the resonant layer in theinhomogeneous dipole magnetic field B is (Zheleznyakov 1996)

τres =163π2e2

mecne∆rres

ωcycsim 104

1020 cmminus3

)times

50 keVtimes

106 cmtimes

1012 Gmiddot (9)

This means that diffusion of resonant photons occurs As the CSdownstream sidewall area 2πrpHl is typically smaller than thepolar cap area A = πr2

p (at least if Hl rp) most of the diffusingphotons escape from the uppermost parts of the structure

Clearly the line dependence on the observed X-ray flux isentirely determined by how the collisionless shock height Hsresponds to variable mass accretion rate This scaling indeedwas first observed in Her X-1 and explained in terms of theline formation in the varying magnetic field with height inStaubert et al (2007) As discussed above we now knowfour additional X-ray pulsars presumably in the CS break-ing regime showing a positive EcycLx correlation Vela X-1 A 0535+26 GX 304-1 Cep X-4 (see Sect 42) A factorfive to six in the dynamic range in Lx has allowed for thelast two objects to detect the theoretically expected deviationsfrom a purely linear correlation We note that not only theenergy Ecyc but also its width W and depth τcyc show varia-tions with the observed X-ray flux consistent with this non-linear scaling (see Rothschild et al 2017 for more detail)thus lending credence to the simple physical picture outlinedabove

A61 page 14 of 30

512 Scaling CRSF relations in radiative shock regime

In the case of RS deceleration of the accretion flow at highX-ray luminosities the situation with CRSF formation is not sostraightforward as in the CS-regime considered above Indeedin this case an optically thick extended intrinsically 2D struc-ture is formed (Davidson 1973 Basko amp Sunyaev 1976 Wangamp Frank 1981 Postnov et al 2015) and the line formationshould be calculated by solving the 2D radiation transfer prob-lem Still the assumption that the shock height (and the lineemitting region) should increase with increasing mass accre-tion rate (Basko amp Sunyaev 1976) should hold and Ecyc shouldvary according to Eq (8) as first suggested by Burnard et al(1991) In addition reflection of radiation from the neutron starsurface could play a role While physically feasible the reflec-tion model for CRSF formation and change with X-ray flux inhigh-luminosity accreting X-ray pulsars advanced by Poutanenet al (2013) may not be universally applied in all cases sincethe negative CRSF correlation with luminosity is now reliablyconfirmed by X-ray observations of only one bright transient X-ray pulsar V0332+53 (Tsygankov et al 2006) and tentativelydiagnosed for SMC X-2 (Jaisawal amp Naik 2016) Clearly futureobservations (possibly with X-ray polarization measurements)are needed here to study the intriguing CRSF behavior in theRS-case

52 Cyclotron line modeling

This paper concentrates on the observational aspects of objectsfrom which spectra with cyclotron lines are observed A descrip-tion of the state of theoretical modeling of the CRSF is beyondthe scope of this contribution ndash a comprehensive review as acounterpart would however be highly useful

In the Introduction and in Sect 5 above we mention the his-tory of the early theoretical work that attempted to calculateexpected spectra analytically and that has been ground break-ing for our understanding of the basic physics in highly mag-netized hot plasma ndash the source of high energy X-ray spectrawith cyclotron lines Wang et al (1988) give a good summaryof the early work which is mostly from the 70s and 80s ofthe last century More recent analytical calculations are fromNishimura (2008 2011 2013 2014 2015) Nishimura invokesseveral specific conditions for example changes of the heightand the area of the accretion mound changes in the emissionprofile non-uniform illumination of the emission region super-position of lines from different regions changing relative contri-butions from the two accreting poles and other to explain obser-vational details The success of this may however be due to alarge number of free parameters andor assumptions that enterthe calculations from the start

A completely different technique to understand and modelthe physical conditions that lead to the observed cyclotronline spectra are Monte Carlo calculations (Isenberg et al1998 Araya amp Harding 1999 Araya-Goacutechez amp Harding 2000Schoumlnherr et al 2007 Nobili et al 2008 Schwarm et al2017ab) Here individual particles (electrons photons protons)are followed through some extended volume of highly magne-tized hot plasma calculating their interactions with each otherand with the magnetic field At the boundaries of the volumephotons escape some of them finding their way into the tele-scopes of observers where the energy distribution (spectra) andthe timing distribution (pulse profiles and other time variations)are measured Usually some input continuum spectrum is cho-sen that illuminates a certain volume under specific geometriesThe method is rather flexible allowing for the testing of different

input continua and geometries (eg illumination from the bot-tom from the top from a centrally extended source or oth-ers) and angle- and energy dependent interaction cross-sectionscan easily be adjusted The most recent and complete calcula-tions are by Fritz Schwarm14 (Schwarm et al 2017ba) Thiswork represents the current state of the art and provides for thefirst time a framework (usable by the general scientific commu-nity)15 for a direct comparison and fitting of observed spectrawith Monte-Carlo-simulated spectra such that physical condi-tions and parameters can be estimated

6 Empirical knowledge of the magnetic fieldstrength of a neutron star

Even though we assume that the observation of the cyclotronline energy gives a direct measure of the strength of the mag-netic field at the site where the resonant scattering occurs itdoes not provide an accurate value for the global magnetic field(thought to be a dipole) This is because the cyclotron scatteringregion may be at some distance above the neutron star surfaceandor there may be local field structures which could have adifferent (even stronger) field strength A classical method toestimate the magnetic moment of a neutron star is to infer itthrough timing observations of pulsars This has been done fornon-accreting pulsars by applying the theory of dipole radia-tion to observational data of the change of the pulse period withtime (Gold 1968 Goldreich amp Julian 1969 Ostriker amp Gunn1969) B = 32 times 1019(PP)12 with B in Gauss P in s andP in s sminus1 (leading eg to an estimate of the field strength ofthe Crab pulsar of sim38 times 1012 Gauss) In the case of accret-ing pulsars ndash relevant for cyclotron line objects discussed here ndashaccretion torque models are applied to describe the spin-upspin-down behavior observed in these objects The most widely usedmodel applicable to the accretion through an accretion disk isthe one developed by Ghosh amp Lamb (1979a Paper III withthe preceding Paper I Ghosh et al 1977 and Paper II Ghoshamp Lamb 1979b) The model provides a set of equations forthe relationship between the magnetic moment of the neutronstar and the three observables pulse period P its time deriva-tive dPdt and the X-ray luminosity Lx (estimated through theX-ray flux and the distance to the source) and two unknownquantities the magnetic moment micro and a dimensionless torqueparameter n(ωs) which itself is a complicated function of a ldquofast-ness parameterrdquo ωs (the ratio of the magnetospheric radius to theco-rotation radius to the power three-half) In addition there aretwo dimensionless factors S 1 and S 1 (of order one) that dependon the neutron star mass and radius Similar models (some alsofor the case of wind accretion) have been presented by Wang(1987) Lovelace et al (1995) Kluzniak amp Rappaport (2007)Postnov et al (2011) Shakura et al (2012) Shi et al (2015)Parfrey et al (2016)

For a given magnetic moment micro of an accreting pulsar thehistory of the accretion torque over time (largely determined bythe adopted values of the mass accretion rate and the ratio of themagnetospheric radius to the co-rotation radius) determines thefinal value of the pulse period that is when the system reachesa state at or near an equilibrium the spin-up and spin-downtorques are nearly equal leading to a net torque and a period

14 Schwarm PhD Thesis University of Erlangen-Nuumlrnberg httpswwwsternwarteuni-erlangendedocstheses2017-05_Schwarmpdf15 httpswwwsternwarteuni-erlangende~schwarmpubliccyclo

A61 page 15 of 30

AampA 622 A61 (2019)

Table 1 Magnetic field strength for a few selected sources comparing measurements based on the observed cyclotron line energy with estimatesbased on applying accretion torque models

System Refer micro30(GL)b B12 =d Cyclotron B12 B(Wang) Btorqueldquorotatorrdquoa or 2 times micro30 line from B(GL) Bcyc

micro30(Wang) =c = Btorque Energy Ecyc or5 times ε30(Wang) Ecyc (= Bcyc) B(Klus)[1030 G cm3] [1012 G] [keV] [1012 G] B(GL)

Her X-1 GLldquofastrdquo 047e 094 37 383 22 025 Wang 105 210 37 383 055GX 301-2 GL ldquoslowrdquo 03 06 37 383 0164U 0115+63 GL ldquofastrdquo 14 28 12 124 21 23 Wang 295 59 12 124 484U 1626-67 Wang 435 87 37 383 23A 0535+26 GL ldquoslowrdquo 33 66 50 517 21 13 Klus 14 50 517 27Cen X-3 GL ldquofastrdquo 45 9 28 290 21 31 Wang 955 191 28 290 66X Per GL ldquoslowrdquo 48 96 29 219 44 GL ldquoslowrdquo 48 96 29 219 44 Klus 42 29 219 192Vela X-1 f GL ldquofastrdquo 86 172 25 260 66A 0535+26 GL ldquofastrdquo 148 296 50 517 57GX 301-2 GL ldquofastrdquo 394 788 37 383 206

Notes (a)ldquoSlowrdquo or ldquofastrdquo solution according to Ghosh amp Lamb (1979a) (b)original values from the literature (c)the original values of Wang (1987)are ε30 micro30 = 5 times ε30 (d)we use the definition B = 2microRminus3 (unlike Ghosh amp Lamb 1979b see text) and consider this to be the field strength B0 atthe surface of the neutron star at the magnetic poles (e)we note that micro30 = 047 is a valid solution for Her X-1 within the GL-model but it requiresL37 = 27 (not 10 as in Table 1 of Ghosh amp Lamb 1979a) ( f )for Vela X-1 the GL ldquoslowrdquo solution yields micro30 = 27 10minus5 G cm3 obviously not validReferences ldquoGLrdquo Ghosh amp Lamb (1979a) ldquoWangrdquo Wang (1987) ldquoKlusrdquo Klus et al (2014)

derivative dPdt near zero Many of the cyclotron line sourcesdiscussed here are actually close to equilibrium

The question of how B-field estimates gained through accre-tion torque models compare with direct measurements throughcyclotron line energies has been addressed in the literature InTable 1 we present an updated summary of values from Ghoshamp Lamb (1979a) Wang (1987) and Klus et al (2014) for a fewobjects and perform a comparison with the information fromcyclotron lines The polar magnetic field strength at the surfaceof the neutron star is calculated16 as B12 = 2 micro30 Rminus3 while thecyclotron line measurements (values are taken from Table A1)lead to B12 = 12 Ecyc116 It is important to note that the Ghoshamp Lamb-model generally provides two solutions for the mag-netic moment micro a ldquoslow rotatorrdquo solution and a ldquofast rotatorrdquosolution (see Ghosh amp Lamb 1979a Table 2 and Figs 12 13)In the upper part of Table 1 we have reproduced the solutionswhich best match the results from the cyclotron line measure-ments and we find a discrepancy by factors of a few for Her X-1and GX 301-2 the ratio BtorqueBcyc (Col 9) is sim12 and sim13while for the other objects listed this ratio is above a factor ofthree and more Toward the end of Table 1 we list the ldquofastrotatorrdquo solutions for the four long period objects A 0535+26(P = 104 s) Vela X-1 (P = 283 s) GX 301-2 (P = 681 s) andX Per (P = 837 s) for which the ratio BtorqueBcyc reaches valuesabove 10017

16 We note that we need the field strength at the poles which is twotimes that at the equator apparently used by Ghosh amp Lamb (1979b)17 We note that the ldquoslow rotatorrdquo solution for Vela X-1 yields micro30 =27 times 10minus5 G cm3 obviously not valid and for X Per the two solutionsare equal

It has been correctly argued that the magnetic field strengthdetermined from the CRSF must not be identical to the polardipole field Ecyc measures the local field strength at the placewhere the resonant scattering occurs which produces the linefeature but this place could be at a significant height above theneutron star surface where the field is weaker A possible expla-nation for ratios smaller than one in the final column of Table 1 isa possible enhancement of the polar magnetic field by a changein the field structure due to the accumulated material as sug-gested by Mukherjee amp Bhattacharya (2012) Mukherjee et al(2013 2014) field lines are pushed out radially from the centerof the accretion mound resulting in bunching of field lines andincreasing the local field strength in the outer parts of the accre-tion column which is the likely place where the cyclotron line isgenerated See also calculations of field ldquoballooningrdquo by Payneamp Melatos (2007) Litwin et al (2001) and the discussion of thelong-term change of Ecyc (Sect 44) Ghosh amp Lamb (1979a)had noted that the Ecyc measured in Her X-1 indicates a strongerfield than obtained from applying the accretion torque model andsuggested that the field structure could contain ldquohigher multipolemomentsrdquo with stronger magnetic fields than the global dipolefield18 Mukherjee amp Bhattacharya (2012) showed that for spe-cific geometries the field strength could be increased by up toa factor 46 In Fig 13 we reproduce Fig 3 from Mukherjee ampBhattacharya (2012) showing calculated field distortions for twoaccretion mounds with different height and mass loading

However we point out that differences by a factor of a feware not necessarily due to physical effects Torque model cal-culations make assumptions about the mass and radius of the

18 A deviation from a pure dipole structure is in the literature oftenreferred to as contribution from ldquomultipole componentsrdquo

A61 page 16 of 30

00 02 04 06 08 10Radius in Km

Field line plot for Zc = 55m

00 02 04 06 08 10Radius in Km

Fig 13 Calculation of field distortion at the polar cap of an accret-ing neutron star reproduction of Fig 3 of Mukherjee amp Bhattacharya(2012) visulizing model calculations for two accretion mounds of dif-ferent heights (55 m and 70 m) and mass loading (09 and 231 times10minus12 M) respectively

neutron star (which also determine the moment of inertia andthe gravitational redshift) changes of which individually or incombination can change the determined magnetic field strengthby several tens of percent19 In addition some of the observedvalues may have rather large uncertainties especially the lumi-nosity which scales with the square of the assumed distanceto the source With these observational uncertainties an accre-tion torque model will not yield a unique solution for the mag-netic moment micro or magnetic field strength B (note for this con-version the radius RNS enters again with the third power) butrather an allowed range that may cover almost an order ofmagnitude

We also note quite fundamentally that accretion torquemodels generally assume an aligned rotator while the spinningneutron stars in accreting binary pulsars are surely not alignedrotators Unfortunately 3D-calculations of magnetospheres asdone for T Tauri stars or CVs (see eg Romanova et al 2008Kulkarni amp Romanova 2013) have so far not been done for thegeometrically much larger systems of neutron stars with terra-Gauss fields

The above considerations make apparent that one should nottake the observed cyclotron line energy and the derived fieldstrength as a measure of the global dipole field and to calcu-

19 For example assume M = 13 M a change of RNS from 10 km to12 km results in a reduction of the B estimate in Her X-1 by sim40 orincreasing M to 15 M combined with reducing R to 9 km will producean increase in B by a similar amount

late other system parameters like the distance ndash or even basicneutron star parameters like mass and radius ndash by applying anaccretion torque model (as has been done in the literature forexample Takagi et al 2016)

For completeness we mention a third method to estimatethe magnetic moment micro based on flux and timing observationswhen the mass accretion rate becomes very low the magneto-spheric radius increases reaching and exceeding the co-rotationradius Then the so called propeller effect (Illarionov amp Sunyaev1975 Stella et al 1986 Christodoulou et al 2017) sets in bywhich material at the inner edge of the accretion disk is thrownout by the rotating magnetic field (often referred to as ldquocentrifu-gal barrierrdquo) efficiently inhibiting accretion and leading to a dra-matic drop (approximately two orders of magnitude) in X-rayluminosity The onset of the ldquopropeller effectrdquo starts at a limit-ing accretion rate which can be calculated by equating the co-rotation radius Rc = (GMP24π2)13 (where the angular velocityof the magnetosphere equals that of the material in the Keplerorbit at the inner edge of the accretion disk) with the magne-tospheric radius Rm = kMminus27micro47(2GM)minus17 G is the gravita-tional constant P the spin period M the mass of the NS M theaccretion rate micro the magnetic moment of the NS and k a numeri-cal factor (usually 05) The limiting accretion rate Mlim deter-mines a limiting luminosity Llim (Campana et al 2002 Fuumlrstet al 2017)

Llim =GMMlim

R 39 times 1037 ξ72 B2

12 P73 Mminus23 R56 [erg sminus1]

with quantities as defined above plus R6 being the NS radiusin units of 106 cm B12 being the polar magnetic field strengthin units of 1012 Gauss (related to the magnetic moment micro =05 BR3) ξ being a numerical factor on the order of oneTsygankov et al (2016ab) give an impressive example of fiveobjects showing the ldquopropeller effectrdquo which demonstrates thatthe relation Llim times P73 prop B holds for sim7 orders of magnitude inB (see Fig 14) This method however does not have the powerto resolve the above discussed differences between B-estimatesthrough torque models and CRSF energies since the systematicuncertainties are of similar magnitude

7 Statistical analysis

Here we summarize some statistics regarding electron CRSFsources numbers of sources showing specific characteristics

ndash sim350 known X-ray binary pulsars (XRBP eg Bildstenet al 1997 or see footnotes20 and21)

ndash 35 cyclotron line sources (sim10 of all XRBP) (seeTable A1) 13 persistent High Mass X-ray Binaries(HMXB) 19 Be transients 4 Low Mass X-ray Binaries(LMXB) plus sim16 candidates see Table A2)

ndash 11 sources with multiple cyclotron lines (see Table A1)7 sources with 2 lines 3 sources with 3 lines (V 0332+53MAXI J1409-619 GRO J1744-28) 1 source with more than3 lines (4U 0115+63)

ndash 7 sources with positive correlation of Ecyc with Lx(see Table A4) Her X-1 GX 304-1 Vela X-1 Cep X-4V 0332+53 A 0535+26 4U 16266-5156 (plus 4U 1907+09to be confirmed)

20 httpwwwiasfboinafit~mauropulsar_listhtmlCRSF21 httpwwwsternwarteuni-erlangendewikidokuphpid=xrpstart

A61 page 17 of 30

AampA 622 A61 (2019)

Fig 14 ldquoPropeller effectrdquo (reproduced Fig 4 of Tsygankov et al2016c) observations of five sources confirm the expected relationshipLlim P73 prop B with Llim being the limiting luminosity at which thiseffect sets in The dashed lines are for two slightly different values of ξin Eq (10)

ndash 2 sources with negative correlation of Ecyc with Lx (seeTable A4) V 0332+53 (at very high Lx) and SMC X-2

ndash 2 sources with long-term variation of Ecyc (see Sect 44)Her X-1 (Staubert et al 2017) Vela X-1 (La Parola et al2016) plus one source with intermediate-term variationV 0332+53 (Cusumano et al 2016) plus possibly 4U 1538-522 (Hemphill et al 2014)

ndash 18 sources with correlation of photon index with Lx (seeTable A4)

8 Proton cyclotron lines

The resonances produced by protons gyrating in a strongmagnetic field are lower in energy compared with those of elec-trons by a factor given by their mass ratio memp Absorptionlines seen by Chandra XMM-Newton in the 02minus10 keV bandrequire very strong magnetic fields 1014 G In contrast to elec-tron cyclotron lines those produced by protons (or nuclei) appearonly at the fundamental frequency (Potekhin 2010) The prob-lem with proton line observations is that the absorption lines maybe explained as well by other effects (Potekhin et al 2015) forexample by photo-ionisation in a dense cloud in the vicinity ofthe neutron star (Hambaryan et al 2009) or as the result of acomplex inhomogeneous temperature distribution on the surfaceof the neutron star (Viganograve et al 2014) The discovery of pos-sible proton cyclotron lines has been reported for a number ofobjects (including ULXs and magnetars which we do not discussin detail here because of the problems of the just described con-fusion) We only mention the magnetar SGR 1806minus20 (Ibrahimet al 2002 2003) for which the magnetic field strength estimatedfrom P and P is consistent with that inferred from an absorp-tion line seen at sim5 keV assuming that it is a proton cyclotronline The criterion also holds for a class of seven isolated neu-tron stars which were discovered in ROSAT data They are brightX-ray sources but given their relatively small distances of typi-cally a few hundred parsec they are intrinsically X-ray dim Hencethey are often called X-ray dim isolated neutron stars (XDINS)or simply the Magnificent Seven (M7) At least five of the sevenobjects exhibit absorption line features in the ChandraXMM-Newton energy band (02ndash10 keV) When interpreted as protoncyclotron lines their corresponding magnetic field strengths agreewith those derived from the measured P P data within a factor of

Fig 15 Pulse phase resolved EPIC-pn spectra of RX J07204-3125observed by XMM-Newton a reproduction of Fig 5 of Haberl (2007)showing an absorption feature around 300 eV which is interpreted asa proton cyclotron line produced in a magnetic field of about 56 times1013 Gauss The different colors give the spectra for different pulsephase intervals 00ndash02 black 02ndash04 red 04ndash06 green 06ndash08blue and 08ndash10 light blue

a few (Haberl 2007) In the following an update concerning thesesources is given In Sect 81 we introduce the M 7 stars and sum-marize their timing properties which help to constrain the largescale structure of their magnetic fields The observed absorptionfeatures in their X-ray spectra are described in Sects 82 and 83the evidence for them being proton cyclotron lines is discussedfollowed by a short summary Figure 15 shows an example ofpulse phase resolved spectra of RX J07204-3125 with an absorp-tion feature around 300 eV as observed by XMM-Newton (Haberl2007)

81 The Magnificent Seven

RX J18565ndash3754 was the first isolated neutron star (INS) dis-covered in ROSAT data (Walter et al 1996) Despite extensivesearches only six further objects with similar properties as sum-marized in Table 2 were found in the ROSAT data (Rutledgeet al 2003 Chieregato et al 2005 Posselt et al 2008 Aguumleroset al 2011) The X-ray emission of these seven objects is char-acterized by soft blackbody-like emission attenuated by lowphoto-electric absorption by the interstellar medium but in atleast five cases with broad absorption features The X-ray spectrashow no indication of hard non-thermal X-ray emission com-ponents which could originate from magneto-spheric activityNo flux variations on timescales of years are observed (but seeRX J07204minus3125 below) which suggests that we see thermalemission directly from the surface of cooling isolated neutronstars Their distances range from sim120 pc for RX J18565minus3754determined from parallax measurements (Walter et al 2010) andseveral hundred pc constrained from absorption column densi-ties (Posselt et al 2007)

At least six of the M 7 stars are X-ray pulsars withspin periods between 345 s (RX J04200minus5022) and 1678 s(RX J07204minus3125) The modulation in the X-ray flux variesstrongly from star to star with semi-amplitudes between 1(RX J18565minus3754) and 18 (RX J13086+2127) The lattershows a clear double-peaked pulse profile (Haberl et al 2003)indicating a spin period of the NS twice as long as origi-nally thought The others are characterized by more gradualsinusoidal variations Hambaryan et al (2017) recently reported

A61 page 18 of 30

Table 2 The Magnificent Seven

Object kTinfin P pfa P Bdip τ tkin mBb dc Ref

(eV) (s) () (s sminus1) (1013 G) (Myr) (Myr) (mag) (pc)

RX J04200minus5022 48 345 17 minus28 times 10minus14 10 195 266 sim345 (1)RX J07204minus3125 84minus94 1678 8minus15 minus140 times 10minus13 50 191 085 266 286+27

minus23 (2)RX J08064minus4123 95 1137 6 minus550 times 10minus14 25 324 gt24 sim250 (3)RX J13086+2127 100 1031 18 minus112 times 10minus13 35 145 055090138 284 (4)RX J16053+3249 100 lt2 045 272 sim390 (5)RX J18565minus3754 61 706 1 minus297 times 10minus14 15 380 042minus046 252 120+11

minus15 (6)RX J21430+0654 104 943 4 minus400 times 10minus14 19 372 gt26 sim430 (7)

Notes Values in the table were taken from Haberl (2007) and Pires et al (2014) and updated when more recent results were available (a)Pulsedfraction (b)Optical magnitudes are taken from Kaplan (2008) (c)Distance estimates indicated by sim are from Posselt et al (2007)References (1) Haberl et al (1999 2004a) Kaplan amp van Kerkwijk (2011) (2) Haberl et al (1997) Cropper et al (2001) Zane et al (2002)de Vries et al (2004) Haberl et al (2004b) Kaplan amp van Kerkwijk (2005a) Tetzlaff et al (2011) Hohle et al (2012a) Borghese et al (2015)Hambaryan et al (2017) (3) Haberl et al (1998 2004a) Kaplan amp van Kerkwijk (2009a) (4) Schwope et al (1999) Haberl et al (2003) Kaplanamp van Kerkwijk (2005b) Schwope et al (2007) Tetzlaff et al (2010) Hambaryan et al (2011) Borghese et al (2017) (5) Motch et al (1999)van Kerkwijk et al (2004) Motch et al (2009) Tetzlaff et al (2012) Pires et al (2014 2017) (6) Walter et al (1996) Walter (2001) Burwitzet al (2001 2003) Tiengo amp Mereghetti (2007) Walter et al (2010) Tetzlaff et al (2011) Mignani et al (2013) (7) Zampieri et al (2001) Zaneet al (2005) Kaplan amp van Kerkwijk (2009b)

a double-hump pulse profile also for RX J07204minus3125 (simi-lar to RX J13086+2127) suggesting a spin period of 1678 sSpin down is observed from the M 7 stars with known spinperiods using a series of Chandra and XMM-Newton observa-tions with accurate spin-down rates obtained from coherent tim-ing solutions Assuming the model of magnetic dipole breaking(see also Sect 6) the knowledge of the spin period P and itsderivative P allows one to estimate the magnetic field strength(B = 32 times 1019(PP)12 with B in Gauss P in s and P in s sminus1)which yields values between 1 times 1013 Gauss (RX J04200minus5022)and 50 times 1013 Gauss (RX J07204minus3125) The characteristicages estimated from the dipole model (τ = P(2P)) of typicallya few million years are a factor of a few longer than kinetic agesderived from back tracing the proper motion of the stars to likelybirth places (Motch et al 2009 Tetzlaff et al 2010 2011 2012)

RX J04200ndash5022 was discovered serendipitously inROSAT data (Haberl et al 1999) as X-ray source with asoft blackbody-like spectrum and no optical counterpart(mB gt 2525 mag) XMM-Newton observations with the EPIC-pn instrument revealed pulsations with a period of 345 s theshortest confirmed spin period among the M 7 stars (Haberl et al2004a) Using 14 observations with XMM-Newton Kaplan ampvan Kerkwijk (2011) obtained a phase-coherent timing solutionand measured a spin-down rate of P = (28 plusmn 03) times 10minus14 s sminus1which yields the lowest dipolar magnetic field strength of10 times 1013 G

RX J07204ndash3125 is the second brightest M 7 star discov-ered in ROSAT all-sky survey data and pulsations with a periodof 839 s were indicated in the data of follow-up ROSAT PSPCand HRI pointed observations (Haberl et al 1997) Howeverfrom a re-analysis of all available XMM-Newton high statisticalquality data Hambaryan et al (2017) concluded that the truespin period is 1674 s The pulse profile folded at this periodshows two humps with similar but still clearly distinguishableshape The object is unique as the only M 7 star showing long-term variations in the X-ray spectrum on timescales of years(de Vries et al 2004) A final analysis of monitoring obser-vations with the EPIC-pn instrument of XMM-Newton span-ning more than 11 years revealed a temperature increase fromkT = 85 eV to 94 eV within about 15 yr After reaching the

maximum temperature the spectra indicate a very slow coolingby sim2 eV over 7 yr (Hohle et al 2012a)

RX J08064ndash4123 was discovered in a dedicated search forINS in the ROSAT all-sky survey (Haberl et al 1998) The spinperiod of 1137 s was detected in XMM-Newton data (Haberl ampZavlin 2002) and the period derivative could be constrained froma series of follow-up observations although with large uncertain-ties (Kaplan amp van Kerkwijk 2009a)

RX J13086+2127 = RBS 1223 was identified as sourcewith empty error circle in the ROSAT Bright Survey (RBS) cat-alog (Schwope et al 1999 2000) Follow-up Chandra observa-tions first suggested a period of 516 s (Hambaryan et al 2002)before XMM-Newton observations provided data of high statisti-cal quality which revealed a double-peak pulse profile with trueperiod of 1031 s (Haberl et al 2003) A coherent timing solu-tion was obtained from Chandra and XMM-Newton observationsspanning a period of five years yielding accurate values for spinperiod and derivative (Kaplan amp van Kerkwijk 2005b)

RX J16053+3249 = RBS 1556 was selected as INS fromthe ROSAT all-sky survey on the basis of its spectral softnessand lack of bright optical counterpart (Motch et al 1999) Anindication for a spin period (339 s) was reported at a 4σ con-fidence level together with uncertain constraints for the pulsarspin-down rate (Pires et al 2014) However using recent deepXMM-Newton observations Pires et al (2017) could not confirmthe period with upper limits for the pulsed fraction of sim26

RX J18565ndash3754 is the X-ray brightest M 7 star and wasfirst found in a ROSAT pointed PSPC observation as brightestsource in the field of view (Walter et al 1996) Together withthe ROSAT all-sky survey detection and a ROSAT HRI obser-vation no evidence for variability was found and the limit forFxFopt of gt7000 strongly suggested an INS nature of the objectThis first discovery triggered the search for other sources inthe ROSAT all-sky survey with similar properties The ROSATPSPC spectrum could be modeled by pure blackbody emis-sion and also the high-resolution Chandra LETG spectra didnot reveal any significant deviations from a Planckian energydistribution (Burwitz et al 2001 2003) Although being thebrightest M 7 star no absorption feature similar to those found

A61 page 19 of 30

AampA 622 A61 (2019)

in other M 7 stars was significantly detected so far A very shal-low modulation (sim1) with a period of 706 s was discoveredin XMM-Newton EPIC-pn data (Tiengo amp Mereghetti 2007)and constraints on the period derivative indicate a magneticfield strength comparable to what was found for the other M7(van Kerkwijk amp Kaplan 2008)

RX J21430+0654 = 1RXS J2143037+065419 =RBS 1774 was the last of the M7 discovered in ROSATdata (Zampieri et al 2001) Again XMM-Newton observa-tions led to the discovery of X-ray pulsations (period 9437 s)and an absorption feature at 700ndash750 eV (Zane et al 2005Cropper et al 2007) From an additional series of XMM-Newtonobservations Kaplan amp van Kerkwijk (2009b) measured the spin-down rate which indicates a magnetic dipole field strength ofsim2 times 1013 G

82 Proton absorption features

The ROSAT PSPC spectra of the M7 were modeled with black-body emission attenuated by small amounts of absorption whichis interpreted to be induced by the interstellar medium Theenergy resolution of the PSPC was not sufficient to discern addi-tional absorption features Moreover the entrance window ofthe detector caused a deep carbon absorption edge with strongdepression of the effective area between 300 eV and 500 eV theenergy band in which features were later found in the XMM-Newton and Chandra spectra The line properties are describedin the following and summarized in Table 3

The first absorption feature was discovered by Haberl et al(2003) in data collected from RX J13086+2127 by the EPIC-pn instrument of XMM-Newton The X-ray spectra show strongdeviations from a Planckian energy distribution at energiesbelow 500 eV which can be modeled by a Gaussian-shapedabsorption line centered at an energy of sim300 eV and with σwidth of sim100 eV although even broader lines at energies downto 100 eV or several unresolved lines can not be excluded Thedepth of the line relative to the continuum (the equivalent widtheqw) was measured to minus150 eV (we use negative values to indi-cate that the line is in absorption) the deepest absorption lineseen from the M7 Moreover pulse-phase spectroscopy revealedthe line to vary in strength with a full amplitude of sim40 eV inequivalent width (Schwope et al 2005) The line is deepest at theintensity maxima of the double-peaked pulse profile and shal-lowest at the minima

A similar behavior was found for RX J07204minus3125 Haberlet al (2004b) reported a phase-dependent absorption line in thespectrum which varies in depth with pulse phase This line isbroad (sim64 eV 1σ width when modeled with a Gaussian profile)and centered at sim300 eV (Haberl et al 2004b 2006) The equiva-lent width varies with pulse phase from minus31 eV around intensitymaximum and minus58 eV at the declining part of the pulse Whilethe line is much weaker on average the full amplitude varia-tion with pulse phase is almost as large as for RX J13086+2127Additionally the line depth was found to change on timescalesof years Parallel to the increase in temperature with a maxi-mum seen in May 2004 the line depth also increased from eqw =minus40 eV to minus74 eV in the phase-averaged spectra (Haberl et al2006 Hohle et al 2012a) It is remarkable that the amplitude inthe variations with pulse phase stayed constant at sim40 eV (Hohleet al 2009)

While for RX J13086+2127 and RX J07204minus3125 the vari-ability of the absorption lines with pulse-phase excludes all pos-sible doubt that they are real spectral features the detection ofa broad absorption line in the high resolution X-ray spectra of

RX J16053+3249 obtained by the RGS instruments of XMM-Newton constrains the width of the line Relative to CCD detec-tors the superior energy resolution of the RGS revealed that thedeviation from a blackbody spectrum can be well modeled with asingle broad absorption line centered at 450 eV with a 1σ widthof 59 eV (van Kerkwijk et al 2004) On the other hand the highstatistical quality of the EPIC-pn spectra of RX J16053+3249revealed strong evidence for the existence of multiple lines Anacceptable fit was only reached when including three Gaussianabsorption lines at energies of E1 = 403plusmn 2 eV E2 = 589plusmn 4 eVand E3 = 780plusmn 24 (Haberl 2007) It is remarkable that the ratiosof the line energies are consistent with 1152 The existing dataat the time of that work did not allow the fitting of the widthof the lines individually and a single common fit parameter wasderived with σ of 87 eV Including the spectra from new XMM-Newton observations required an even more complex modelingwith two blackbody components for the continuum (a cool onewith kT around 30 eV and the dominant hot one with kT sim

110 eV) and three absorption lines (Pires et al 2014) From RGSspectra these authors determined E1 = 443+13

minus20 eV (σ1 = 74+13minus11 eV

and eqw = minus31 eV) and E2 = 828 plusmn 5 eV (σ2 = 15+minus4 eV andeqw minus13 eV) A somewhat narrower line with central energy ofE = 576plusmn8 eV and Gaussian width σ = 16+7

minus5 eV (eqw = minus5 eV)was already reported by van Kerkwijk et al (2004) and might beexplained by the presence of highly ionized oxygen (O vii) in theinterstellar medium andor absorption in the neutron star atmo-sphere by O viii gravitationally red-shifted (Hohle et al 2012b)A narrow line at similar energy (569 eV) was also reported fromRX J07204minus3125 (Hambaryan et al 2009 Hohle et al 2012b)and at 535 eV from RX J13086+2127 (Hohle et al 2012b) Thenew RGS results for the lines at 576 eV and 828 eV makes itless clear if they are related to the broad absorption featureat 440 eV

The properties of absorption features in the spectra ofRX J21430+0654 and RX J08064minus4123 are less clear A featurefound in the first XMM-Newton observation of RX J21430+0654was reported by Zane et al (2005) at an energy of 700 eV(when modeled with an absorption edge) or 750 eV (multiplica-tive Gaussian line) New XMM-Newton observations with a factorof 25 more exposure confirmed this and Kaplan amp van Kerkwijk(2009b) inferred a significant improvement in fit quality whenincluding a multiplicative Gaussian line with a width of 73 eVcentered at 756 eV in the spectral model This is the highest energymeasured for an M 7 star and yields a magnetic field strengthmore than a factor of seven higher than the field strength inferredfrom the dipole model while for the other M 7 stars this factoris more typical 12 to 4 Also for RX J08064minus4123 the spec-tral modeling is formally improved when considering an absorp-tion line Fixing the σ width of the line at 70 eV Haberl et al(2004a) derive line parameters of 460plusmn 15 eV for the central lineenergy and eqw =minus33plusmn6 eV from the merged EPIC-pn spectrumof two XMM-Newton observations For the corresponding RGSspectra the authors report 413 plusmn 19 eV and minus56 plusmn 13 eV respec-tively With the errors at 90 confidence level the parameters areformally inconsistent and indicate large systematic uncertaintiesMoreover Kaplan amp van Kerkwijk (2009a) report a line energyof 486plusmn 5 eV from EPIC-pn observations performed in 2008 and2009 (a factor of four more exposure than available from the olderobservations) These authors also find further improvement in fitquality when using two Gaussian lines (E1 = 460plusmn 5 eV eqw1 =minus89 eV E2 = 693plusmn12 eV eqw2 =minus55 eV) It should be noted thatthey also fix all line widths at the same value (85 eV) while experi-ence with RX J16053+3249 shows that they can be considerablydifferent

A61 page 20 of 30

Table 3 The Magnificent Seven ndash cyclotron lines

Object Broad lines Narrow linesEcyc eqwcyc

a Bcyc Ecyc eqwcyc Bcyc

(eV) (eV) (1013 G) (eV) (eV) (1013 G)

RX J04200minus5022b 329c minus43 65RX J07204minus3125 300 minus10 to minus75 (plusmn20) 60 750 simminus30 149RX J08064minus4123 410ndash490 simminus45 81-97RX J13086+2127 300 minus150 (plusmn20) 60 750 simminus15 149RX J16053+3249 443828 minus31minus13 88164RX J18565minus3754 250 or amp800 50 or amp159RX J21430+0654 750 minus25 149

Notes B is calculated as B(1013 G) = (1 + z)E(63 eV) with (1 + z) = (1 minus 2GMRc2)minus12 assumed as 125 (eg Zane et al 2001) (a)Equivalentwidth of broad absorption line Numbers in parentheses indicate variations with pulse phase (b)Line parameters subject to possible large systematicuncertainties (see text) (c)The colon indicates that the parameters are subject to larger calibration uncertainties (see text)

RX J04200minus5022 is the X-ray faintest of the M7 and exhibitsthe softest spectrum which makes it difficult to confirm the exis-tence of absorption features due to possible systematic calibra-tion uncertainties caused by insufficient energy resolution at lowenergies (lt300 eV) in modern CCD detectors Formally the fit tothe EPIC-pn phase-averaged spectra improves when a Gaussianabsorption line is added to the absorbed blackbody model (Haberlet al 2004a) Because the line parameters are subject to larger cal-ibration uncertainties we list them in Table 3 with colon

The discovery of a second strongly phase-variable narrowabsorption feature at sim750 eV was recently reported forRX J07204minus3125 and RX J13086+2127 (Borghese et al 20152017) The fact that the features are significantly detected foronly sim20 of the pulsar rotation suggests that they are formedvery close to the neutron starrsquos surface

83 Origin of proton cyclotron lines

The absence of non-thermal emission components in the X-rayspectra of the M7 no confirmed radio detection and their insuffi-cient spin-down energy losses to power the X-ray emission leadto the generally accepted picture of cooling isolated neutron starsThe M7 provide the unique opportunity to obtain informationabout their magnetic fields in two independent ways One methodis based on the measurement of the spin down rate and assumesmagnetic dipole breaking according to the model of a magneticdipole rotating in vacuum A more direct determination of themagnetic field strength is possible when cyclotron resonance linescan be observed in the X-ray spectra Unlike for accreting X-raypulsars the absorption features observed from M 7 stars can not becaused by electrons because the inferred magnetic field strength isby far incompatible with that derived from magnetic dipole break-ing For protons the derived field strengths are generally higher butmore consistent with the dipole model However which particlescontribute is also a matter of the composition of the neutron staratmosphere Moreover bound-bound and bound-free transitionsof neutral hydrogen are also expected at similar energies for mag-netic fields above 1013 G (see Fig 7 in van Kerkwijk amp Kaplan2007)

However whether or not transitions of free protons or mag-netized hydrogen atoms contribute to the observed lines is amatter of the temperature distribution in the neutron star atmo-sphere According to Fig 1 in Ho et al (2003) the atomic frac-tion of hydrogen at temperatures of kT = 50minus100 eV typical forthe M7 is rather low (lt=03 ) As a consequence the protoncyclotron lines dominate the spectrum (Figs 2 and 3 of Ho et al

2003) while atomic hydrogen transitions may produce addi-tional features That may explain some of the observed multiplelines In view of the limited significance of the line detections itappears difficult to make specific assignments

Another way to explain multiple lines is to invoke ndash beyondthe radiation from the hot cap at the magnetic dipole ndash sepa-rate hot spots on the stellar surface having higher multipolarmagnetic fields The first strong evidence for this comes fromthe discovery of strongly phase-variable absorption lines whichare visible only for about 20 of the neutron star rotation Thelines were detected in the X-ray spectra of RX J07204minus3125and RX J13086+2127 (Borghese et al 2015 2017 respectively)and have energies a factor of sim25 higher than the broad lines(Table 3) Such multipole fields must be quite young comparedto the age of the NS They may be formed by extracting mag-netic energy from the toroidal field that resides in deep crustallayers via Hall drift (eg Geppert amp Viganograve 2014)

We conclude that proton cyclotron lines produced in strongmagnetic fields of isolated neutron stars can explain theabsorption-type features observed in the soft X-ray spectra ofyoung isolated neutron stars of the M7 class More accurate mea-surements in the future in combination with further theoreticalwork on magnetized atmospheres and the magneto-thermal evo-lution of neutron stars are required to make further progress inthis exciting field

9 SummaryWith this contribution we attempt to provide a review on thecurrent state of our knowledge about X-ray sources that showcyclotron line features in their spectra ndash both for electroncyclotron lines (this is by far the larger part) and for protoncyclotron lines We concentrate on the observational aspectsproviding a number of Tables that contain detailed informa-tions on all sources that we consider reasonably well securedregarding the existence of cyclotron lines In the case of elec-tron cyclotron lines ndash observed from binary X-ray pulsars highlymagnetized accreting neutron stars in binaries ndash we also give aTable with candidate sources mostly objects for which a detec-tion of a cyclotron line was claimed some time ago but hadnot been confirmed in subsequent observations or sources thatwere observed rather recently but only once and with somewhatpeculiar properties On the other hand for some of the objectslisted in the main Tables the existence of a cyclotron line stillneeds confirmation (or not) through re-measurements (with afinite probability that they have to be moved into the candidates

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category) We try to address the basic physics underlying thecyclotron line phenomenon including a large number of refer-ences to theoretical work with some coverage of specific theo-retical modeling

Since the discovery of the first CRSF in Her X-1 in 1976a new field of Cyclotron Line Research has evolved With therather fast confirmation of the line in Her X-1 after 1977 by anumber of different instruments and the detection of the samephenomenon in other X-ray binary pulsars an impressive waveof theoretical work was initiated leading to a basic understand-ing of the underlying physics Observational activities have leadto the discovery of many more objects until today (at an approx-imate mean rate of one per year) In the meantime the empha-sis has however shifted from a pure discovery of new cyclotronline objects to the investigation of physical details like the widthdepth line profile phase dependence etc of the lines and tonew associated phenomena like the dependence of the cyclotronline energy on luminosity or its long-term decay (so far foundin only two sources) This has been possible through moderninstruments (like NuSTAR) with good energy resolution broadspectral coverage and low background and high sensitivity Onthe theoretical front progress has been made in the understand-ing and modeling of the phenomenon leading for example to aprocedure to fit observed spectra to theoretical spectra that aregenerated by highly complex Monte Carlo modeling allowingus to find solid physical parameters Overall however our feel-ing is that theoretical work is somewhat lagging behind observa-tions and that there are many open questions to be answered

Acknowledgements We thank the anonymous referee for very useful com-ments that allowed us to improve the text

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2018 MNRAS 476 2110Rodriguez J Tomsick J A Bodaghee A et al 2009 AampA 508 889Romanova M M Kulkarni A K amp Lovelace R V E 2008 ApJ 673 L171Rosenberg F D Eyles C J Skinner G K amp Willmore A P 1975 Nature

256 628Rothschild R Markowitz A Hemphill P et al 2013 ApJ 770 19Rothschild R E Kuumlhnel M Britton Hemphill P et al 2016 AASHigh

Energy Astrophys Div 15 12021Rothschild R E Kuumlhnel M Pottschmidt K et al 2017 MNRAS 466

2752Roy J Choudhury M amp Agrawal P C 2017 ApJ 848 124Rutledge R E Fox D W Bogosavljevic M amp Mahabal A 2003 ApJ 598

458Santangelo A del Sordo S Segreto A et al 1998 AampA 340 L55

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Santangelo A Segreto A Giarrusso S et al 1999 ApJ 523 L85Sartore N Jourdain E amp Roques J P 2015 ApJ 806 193Sasano M Makishima K Sakurai S Zhang Z amp Enoto T 2014 PASJ 66

35Schoumlnherr G Wilms J Kretschmar P et al 2007 AampA 472 353Schoumlnherr G Schwarm F-W Falkner S et al 2014 AampA 564 L8Schurch M P E Coe M J McBride V A et al 2011 MNRAS 412

391Schwarm F-W Ballhausen R Falkner S et al 2017a AampA 601 A99Schwarm F-W Schoumlnherr G Falkner S et al 2017b AampA 597 A3Schwope A D Hasinger G Schwarz R Haberl F amp Schmidt M 1999

AampA 341 L51Schwope A Hasinger G Lehmann I et al 2000 Astron Nachr 321 1Schwope A D Hambaryan V Haberl F amp Motch C 2005 AampA 441

597Schwope A D Hambaryan V Haberl F amp Motch C 2007 ApampSS 308

619Shakura N Postnov K Kochetkova A amp Hjalmarsdotter L 2012 MNRAS

420 216Shapiro S L amp Salpeter E E 1975 ApJ 198 671Shi C-S Zhang S-N amp Li X-D 2015 ApJ 813 91Shrader C R Sutaria F K Singh K P amp Macomb D J 1999 ApJ 512

920Shtykovsky A E Lutovinov A A Tsygankov S S amp Molkov S V 2019

MNRAS 482 L14Soong Y Gruber D E Peterson L E amp Rothschild R E 1990 ApJ 348

641Staubert R 2003 Chin J Astron Astrophys 3 S270Staubert R 2014 PoS(INTEGRAL2014)024Staubert R Kendziorra E Pietsch W et al 1980 ApJ 239 1010Staubert R Shakura N I Postnov K et al 2007 AampA 465 L25Staubert R Klochkov D Postnov K et al 2009 AampA 494 1025Staubert R Klochkov D Vasco D amp Wilms J 2010a in Proceedings

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Staubert R Klochkov D Postnov K et al 2010b X-ray Astronomy 2009Present Status Multi-Wavelength Approachand Future Perspectives 1248209

Staubert R Klochkov D Vasco D amp Wilms J 2010c in Proceedingsof the 8th INTEGRAL Workshop ldquoThe Restless Gamma-ray Universerdquo(INTEGRAL 2010) September 27ndash30 2010 Dublin Castle Dublin Irelandhttppossissaitcgi-binreaderconfcgiconfid=115 48

Staubert R Pottschmidt K Doroshenko V et al 2011 AampA 527 A7Staubert R Klochkov D Vasco D et al 2013 AampA 550 A110Staubert R Klochkov D Wilms J et al 2014 AampA 572 A119Staubert R Klochkov D Vybornov V Wilms J amp Harrison F A 2016

AampA 590 A91Staubert R Klochkov D Fuumlrst F et al 2017 AampA 606 L13Steele I A Negueruela I Coe M J amp Roche P 1998 MNRAS 297 L5Stella L White N E Davelaar J et al 1985 ApJ 288 L45Stella L White N E amp Rosner R 1986 ApJ 308 669Stoyanov K A Zamanov R K Latev G Y Abedin A Y amp Tomov N A

2014 Astron Nachr 335 1060Suchy S Pottschmidt K Wilms J et al 2008 ApJ 675 1487Suchy S Pottschmidt K Rothschild R E et al 2011 ApJ 733 15Suchy S Fuumlrst F Pottschmidt K et al 2012 ApJ 745 124Sugizaki M Yamamoto T Mihara T Nakajima M amp Makishima K 2015

PASJ 67 73Takagi T Mihara T Sugizaki M Makishima K amp Morii M 2016 PASJ

68 S13Takeshima T Dotani T Mitsuda K amp Nagase F 1994 ApJ 436 871Tanaka Y 1983 IAU Circ 3891 00Tanaka Y 1986 Lect Notes Phys 255 198Tananbaum H Gursky H Kellogg E M et al 1972 ApJ 174 L143Tendulkar S P Fuumlrst F Pottschmidt K et al 2014 ApJ 795 154Terada Y Mihara T Nakajima M et al 2006 ApJ 648 L139Terada Y Mihara T Nagase F et al 2007 Adv in Space Res 40 1485Terrell J amp Priedhorsky W C 1983 BAAS 15 979Terrell J amp Priedhorsky W C 1984 ApJ 285 L15Tetzlaff N Neuhaumluser R Hohle M M amp Maciejewski G 2010 MNRAS

402 2369Tetzlaff N Eisenbeiss T Neuhaumluser R amp Hohle M M 2011 MNRAS 417

617Tetzlaff N Schmidt J G Hohle M M amp Neuhaumluser R 2012 PASA 29

98Tiengo A amp Mereghetti S 2007 ApJ 657 L101Torii K Kohmura T Yokogawa J amp Koyama K 2000 IAU Circ 7441

Torrejoacuten J M Kreykenbohm I Orr A Titarchuk L amp Negueruela I 2004AampA 423 301

Torrejoacuten J M Negueruela I Smith D M amp Harrison T E 2010 AampA 510A61

Torrejon JM Reig P Fuumlrst F et al 2018 MNRAS 479 3366Townsend L J Coe M J Corbet R H D amp Hill A B 2011 MNRAS 416

1556Truumlmper J Pietsch W Reppin C et al 1977 Ann NY Acad Sci 302 538Truumlmper J Pietsch W Reppin C et al 1978 ApJ 219 L105Truumlmper J Kahabka P Oegelman H Pietsch W amp Voges W 1986 ApJ

300 L63Tsygankov S S amp Lutovinov A A 2005 Astron Lett 31 88Tsygankov S S Lutovinov A A Churazov E M amp Sunyaev R A 2006

MNRAS 371 19Tsygankov S S Lutovinov A A Churazov E M amp Sunyaev R A 2007

Astron Lett 33 368Tsygankov S S Lutovinov A A amp Serber A V 2010 MNRAS 401 1628Tsygankov S S Krivonos R A amp Lutovinov A A 2012 MNRAS 421 2407Tsygankov S S Mushtukov A A Suleimanov V F amp Poutanen J 2016a

MNRAS 457 1101Tsygankov S S Lutovinov A A Krivonos R A et al 2016b MNRAS 457

258Tsygankov S S Lutovinov A A Doroshenko V et al 2016c AampA 593

A16Tsygankov S S Doroshenko V Mushtukov A A Lutovinov A A amp

Poutanen J 2019 AampA 621 A134Tuerler M Chenevez J Bozzo E et al 2012 ATel 3947 00Ulmer M P Baity W A Wheaton W A amp Peterson L E 1973 ApJ 184

L117van Kerkwijk M H amp Kaplan D L 2007 ApampSS 308 191van Kerkwijk M H amp Kaplan D L 2008 ApJ 673 L163van Kerkwijk M H Kaplan D L Durant M Kulkarni S R amp Paerels F

2004 ApJ 608 432Vasco D Staubert R Klochkov D et al 2013 AampA 550 A111Vasilopoulos G Haberl F Carpano S amp Maitra C 2018 AampA 620 L12Ventura J Nagel W amp Meszaros P 1979 ApJ 233 L125Viganograve D Perna R Rea N amp Pons J A 2014 MNRAS 443 31Voges W Pietsch W Reppin C et al 1982 ApJ 263 803Vurgun E Chakraborty M Guumlver T amp Goumlguumls E 2019 New Astron 67 45Vybornov V Klochkov D Gornostaev M et al 2017 AampA 601 A126Vybornov V Doroshenko V Staubert R amp Santangelo A 2018 AampA 610

A88Walter F M 2001 ApJ 549 433Walter F M Wolk S J amp Neuhaumluser R 1996 Nature 379 233Walter F M Eisenbeiszlig T Lattimer J M et al 2010 ApJ 724 669Walton D J Bachetti M Fuumlrst F et al 2018 ApJ 857 L3Wang Y-M 1981 AampA 102 36Wang Y-M 1987 AampA 183 257Wang W 2009 MNRAS 398 1428Wang W 2013 MNRAS 432 954Wang Y-M amp Frank J 1981 AampA 93 255Wang Y-M amp Welter G L 1981 AampA 102 97Wang J C L Wasserman I M amp Salpeter E E 1988 ApJS 68 735Wasserman I amp Salpeter E 1980 ApJ 241 1107Wheaton W A Doty J P Primini F A et al 1979 Nature 282 240White N E Swank J H amp Holt S S 1983 ApJ 270 711Wilms J 2012 Proc 39th COSPAR Sci Assembly 39 2159Wilson C A Finger M H Coe M J Laycock S amp Fabregat J 2002 ApJ

570 287Wilson C A Fabregat J amp Coburn W 2005 ApJ 620 L99Wolff M T Becker P A Gottlieb A M et al 2016 ApJ 831 194Yahel R Z 1979a ApJ 229 L73Yahel R Z 1979b AampA 78 136Yahel R Z 1980a AampA 90 26Yahel R Z 1980b ApJ 236 911Yamamoto T Sugizaki M Mihara T et al 2011 PASJ 63 751Yamamoto T Mihara T Sugizaki M et al 2014 PASJ 66 59Yan J Zurita Heras J A Chaty S Li H amp Liu Q 2012 ApJ 753 73Yan J Zhang P Liu W amp Liu Q 2016 AJ 151 104Yokogawa J Torii K Kohmura T amp Koyama K 2001 PASJ 53 227Younes G Kouveliotou C Grefenstette B W et al 2015 ApJ 804 43Zampieri L Campana S Turolla R et al 2001 AampA 378 L5Zane S Turolla R Stella L amp Treves A 2001 ApJ 560 384Zane S Haberl F Cropper M et al 2002 MNRAS 334 345Zane S Cropper M Turolla R et al 2005 ApJ 627 397Zelrsquodovich Y B amp Shakura N I 1969 Sov Astron 13 175Zhang S Qu J-L Song L-M amp Torres D F 2005 ApJ 630 L65Zheleznyakov V V 1996 Astrophys Space Sci Lib 204

A61 page 25 of 30

AampA 622 A61 (2019)

Appendix A Additional tables

Table A1 Cyclotron line sources (listed first in alphabetical order then according to right ascension)

System Typec Pspin Porb Ecl Ecyc Instr of Ref Line Other(s) (days) (keV) 1st Det 1st Det conf Refs

Cen X-3 HMXBb 484 209 Yes 28 BeppoSAX 3 Yes 4950186Cep X-4 Be trans 66 2085 No 30 Ginga 1446 Yese 48 2845 Suzaku 47 Yes 48130162 3055 NuSTAR 130 Yes 130GX 301-2 HMXB 681 415 Near 3750 GingaNuSh 710223 Yes 5152GX 304-1 Be trans 275 1322 No 54 RXTE 20 Yes 232428213214Her X-1 LMXBa 12377 170 Yes 37 Balloon 1 Yes 25-27186NGC300 ULX1 Be HMXB 20 ndash No 13 NuSTAR 190 No 191228SMC X-2 HM trans 237 184 No 27 NuSTAR 91 No 149155SXP 153 Be trans 152 No 5ndash8 AstroSatNuSh 215 (Yes) RX J00521-7319Vela X-1 HMXB 283 896 Yes 2553 Mir-HEXE 967 Yes 1473270186X Persei Be XRB 837 2503 No 29 RXTE 16 Yes 360115+63 (4U) Be trans 361 243 No 122436 HEAO-1 2 Yes 1484142118 4862 RXTESAX f 3940 Yes 68186

Notes (a)Low mass X-ray binary (b)High mass X-ray binary (c)a more specific definition of Type is given in Table A3 (d)still questionable (e)butsee Ref 117 ( f )read BeppoSAX (g)read INTEGRAL (h)read NuSTARReferences 1 Truumlmper et al (1978) 2 Wheaton et al (1979) 3 Santangelo et al (1998) 4 Orlandini et al (1998) 5 Heindl et al (2001) 6Kretschmar et al (1996) 7 Makishima amp Mihara (1992) 8 Clark et al (1990) 9 Kendziorra et al (1992) 10 Mihara (1995) 11 Kendziorraet al (1994) 12 Grove et al (1995) 13 Makishima et al (1990a) 14 Mihara et al (1991) 15 DeCesar et al (2013) 16 Coburn et al (2001) 17Tsygankov et al (2012) 18 Heindl et al (2003) 19 Doroshenko et al (2010) 20 Yamamoto et al (2011) 21 Jaisawal et al (2013) 22 Bhaleraoet al (2015) 23 Klochkov et al (2012) 24 Malacaria et al (2015) 25 Staubert et al (2007) 26 Staubert et al (2014) 27 Staubert et al (2016)28 Rothschild et al (2016) 29 Bodaghee et al (2016) 30 DrsquoAigrave et al (2011) 31 Tendulkar et al (2014) 32 Fuumlrst et al (2014b) 33 Vasco et al(2013) 34 Torrejoacuten et al (2004) 35 Masetti et al (2004) 36 Lutovinov et al (2012) 37 Bonning amp Falanga (2005) 38 Farrell et al (2008) 39Heindl et al (1999) 40 Santangelo et al (1999) 41 Iyer et al (2015) 42 Muumlller et al (2013a) 43 Maitra et al (2012) 44 Staubert et al (2011)45 Suchy et al (2011) 46 McBride et al (2007) 47 Jaisawal amp Naik (2015a) 48 Fuumlrst et al (2015) 49 Burderi et al (2000) 50 Suchy et al(2008) 51 Kreykenbohm et al (2004) 52 Suchy et al (2012) 53 La Barbera et al (2005) 54 Jaisawal et al (2016) 55 Rothschild et al (2017)56 Klochkov et al (2011) 57 Nakajima et al (2006) 58 Tsygankov et al (2007) 59 Postnov et al (2015) 60 McBride et al (2006) 61 Yan et al(2012) 62 Tsygankov et al (2006) 63 Cusumano et al (2016) 64Mowlavi et al (2006) 65 Pottschmidt et al (2005) 66 Mihara et al (2004)67 Lutovinov et al (2015) 68 Li et al (2012a) 69 Maitra amp Paul (2013b) 70 Kreykenbohm et al (2002) 71 La Barbera et al (2003) 72 Maitraamp Paul (2013a) 73 Caballero et al (2007) 74 Sartore et al (2015) 75 Muumlller et al (2013b) 76 Shrader et al (1999) 77 Yamamoto et al (2014)78 Bellm et al (2014) 79 Orlandini et al (2012) 80 Rodes-Roca et al (2009) 81 Hemphill et al (2016) 82 Tsygankov et al (2016b) 83 Iwakiriet al (2012) 84 Coburn et al (2006) 85 Iaria et al (2015) 86 Sasano et al (2014) 87 Hemphill et al (2013) 88 Fuumlrst et al (2014a) 89 Reig ampCoe (1999) 90 Klochkov et al (2008a) 91 Jaisawal amp Naik (2016) 92 Mason et al (1978) 93 Parkes et al (1980) 94 Caballero et al (2013b)95 Camero-Arranz et al (2012b) 96 Pearlman et al (2013) 97 Marcu-Cheatham et al (2015) 98 Ballhausen et al (2016) 99 Doroshenko et al(2017) 100 Ferrigno et al (2016b) 101 McBride et al (2008) 102 Motch et al (1997) 103 Reig et al (2005) 104 Rawls et al (2011) 105Kaper et al (2006) 106 DrsquoAigrave et al (2015) 107 Doroshenko et al (2015) 108 Masetti et al (2014) 109 Younes et al (2015) 110 Degenaar et al(2014) 111 Tuerler et al (2012) 112 Halpern (2012) 113 Li et al (2012b) 114 Nowak et al (2012) 115 La Parola et al (2016) 116 Mason ampCordova (1982) 117 Doroshenko et al (2012) 118 Ferrigno et al (2011) 119 Ikhsanov amp Beskrovnaya (2013) 120 Makishima et al (1990b)121 Kreykenbohm et al (2005) 122Negueruela et al (1999) 123 Tsygankov et al (2010) 124 Haigh et al (2004) 125 Coe et al (2007) 126Maisack et al (1996) 127 Naik et al (2008) 128 Coburn et al (2002) 129 Pellizza et al (2006) 130 Vybornov et al (2017) 131 Janot-Pachecoet al (1981) 132 Levine et al (1988) 133 Reig amp Nespoli (2013) 134 Wilson et al (2002) 135 Reynolds et al (1997) 136 Klochkov et al(2008b) 137 Fuumlrst et al (2013) 138 Kuumlhnel et al (2013) 139 Hemphill et al (2014) 140 Reig amp Milonaki (2016) 141 Galloway et al (2005)142 Lutovinov et al (2017a) 143 Torrejoacuten et al (2010) 144 Augello et al (2003) 145 Martiacutenez-Nuacutentildeez et al (2015) 146 Lutovinov et al (2016)147 Kretschmar et al (1997) 148 Nagase et al (1991) 149 Lutovinov et al (2017b) 150 Ghosh amp Lamb (1979a) 151 Wang (1987) 152 Wang(1981) 153 Wang amp Welter (1981) 154 Staubert et al (1980) 155 Klus et al (2014) 156 Lipunov (1992) 157 Jain et al (2010) 158 Chou et al(2016) 159 Takagi et al (2016) 160 Lin et al (2010) 161 DrsquoAigrave et al (2017) 162 Jaisawal amp Naik (2017) 163 Mihara et al (1995) 164 Pirainoet al (2000) 165 Markwardt et al (2007) 166 Manousakis et al (2009) 167 Ferrigno et al (2007) 168 Orlandini et al (1999) 169 Barnstedt et al(2008) 170 Jaisawal amp Naik (2015b) 171 La Barbera et al (2001) 172 Rivers et al (2010) 173 Fuumlrst et al (2011) 174 Fuumlrst et al (2012) 175Blay et al (2005) 176 Blay et al (2006) 177 Reig et al (2016) 178 Wang (2009) 179 Wang (2013) 180 Corbet et al (2007) 181 Stoyanov et al(2014) 182 Reig et al (2016) 183 Naik et al (2006) 184 Tsygankov amp Lutovinov (2005) 185 Epili et al (2016) 186 Doroshenko (2017) 187Staubert et al (2017) 188 Torrejon et al (2018) 189 Vybornov et al (2018) 190 Walton et al (2018) 191 Carpano et al (2018) 192 Cusumanoet al (2010) 193 Corbet et al (2010a) 194 Corbet et al (2010b) 195 Pearlman et al (2011) 196 Bodaghee et al (2006) 197 Roy et al (2017)198 Tsygankov et al (2019) 199 Crampton et al (1985) 200 Farrell et al (2006) 201 Masetti et al (2006) 202 den Hartog et al (2006) 203Bozzo et al (2011) 204 Rodriguez et al (2009) 205 Corbet amp Krimm (2009) 206 Rodes-Roca et al (2018) 207 Brumback et al (2018) 208Hulleman et al (1998) 209 Reig (2004) 210 Baykal et al (2007) 211 Baykal et al (2000) 212 Yan et al (2016) 213 Sugizaki et al (2015)214 McClintock et al (1977) 215 Maitra et al (2018) 216 Corbet et al (2018) 217 Brightman et al (2018) 218 Liu amp Mirabel (2005) 219Ibrahim et al (2002) 220 Ibrahim et al (2003) 221 Alford amp Halpern (2016) 222 Vurgun et al (2019) 223 Fuerst et al (2018) 224 Shtykovskyet al (2019) 225 Halpern amp Gotthelf (2007) 226 Antoniou et al (2018) 227 Maravelias et al (2018) 228 Vasilopoulos et al (2018)

A61 page 26 of 30

Table A1 continued

0332+53 (V) Be trans 438 34 No 28 TenmaGinga 12013 Yes 636465 Be pers 5174 GingaRXTE 1362 Yes 9910012104409+4431 (RX) Be trans 203 155 No 32 RXTE 17 No05205-6932 (RX) Be (LMC) 803 239 No 31 NuSTAR 31 No0535+26 (A) Be trans 104 1106 No 50 Mir-HEXE 11 Yes 6727394 110 OSSE 12 Yes 74750658-073 (XTE) Be trans 161 101 No 33 RXTE 18 Yes 60611008-57 (GRO) Be trans 935 2495 No 78 GROSuzaku 7677 Yes 781118-616 (1A) Be trans 407 24 No 55 110 RXTE 1945 Yes 43441409-619 (MAXI) HMXB 500 No 4473128 BeppoSAX 79 No1538-52 (4U) HMXB 526 373 Yes 22 Ginga 8 Yes 8187186 47 RXTEINT 80 Yes 81871553-542 (2S) Be trans 928 306 ndash 23ndash27 NuSTAR 82 No1626-67 (4U) LMXB 767 00289 No 3761 BeppoSAX 4161 YN 839518616266-5156 (Swift) Be pers 1536 1329 No 1018 RXTE 8415 No 1516393-4643 (IGR) HMXB 904 42 No 29 NuSTAR 29 No 19419519616493-4348 (IGR) SG HMXB 1093 678 Yes 31 SwiftBAT 30 No 96192193 Suzaku ndash1744-28 (GRO) LMXB 0467 1183 No 47 XMM 106 Yes 107186 104158 INTEGRAL No 108ndash11017544-2619 (IGR) Be trans 715d 493 No 1733 NuSTAR 22 No18027-2016 (IGR) HMXB 1399 46 No 24 NuSTAR 142 No18179-1621 (IGR) HMXB 1182 21 INTEGRAL 111 Yes 112ndash1141822-371 (4UX) LMXB 0592 0232 Yes 0733 XMMSuzaku 8586 No1829-098 (XTE) Be trans 784 246 No 15 NuShRXTE 224 Yes 2251907+09 (4U) HMXB 440 837 Near 1836 Ginga 7 Yes 877217219294+1816 (IGR) Be trans 124 117 No (36)43 (RXTE)NuSh (197)198 (Yes) 203ndash2061946+274 (XTE) Be trans 1583 1692 No 36 RXTE 5 Yes 72971861947+300 (KS) Be trans 187 404 No 12 NuSTAR 88 No 98183185

Table A2 Candidate cyclotron line sources cyclotron line(s) claimed but doubtful andor not confirmed

System Typec Pspin Porb Ecl Ecyc Instr of Refe Line Other(s) (days) (keV) 1st Det 1st Det conf Refe

GX 1+4 LMXBa 304 138 No 34 INTEGRAL 167 No ndash 1161M51 ULX8 f ULX ndash ndash No 45 Chandra 217 No 218LMC X-4 HMXBb 14 135 No 100 BeppoSAX 171 No ndash0052-723 (XTE J) Be XRB 478 ndash 102 NuSTAR 226 No 2270114+650 (3A2S) B SG XRB 9520 116 No 22 44 INTh 37 No 38199ndash202 super-orbit 3075 d0541347-682550 HMXB 80 62 No 1020 RXTE 165 No 166 (XMMU) ndash1657-415 (OAO) HMXB 104 38 Yes 36 BeppoSAX 168 No 1691700-37 (4U) HMXB 34 Yes 39 Suzaku 170 No ndash1806-20 (SGR) f SGR 747 ndash No sim5 RXTE 219 No 2201810-197 (XTE J) f AXP trans 554 ndash No 11 ChandraXMM 221 Yes 2221843+009 (GS) Be XRB 295 No 20 Ginga 163 No 1641901+03 (4U) Be trans 276 226 No 10 RXTE 140 No ndash1908+075 (4U) HMXB 604 44 44 Suzaku 21 No 1731741862030+375 (EXO) Be trans 414 46 No 3663 RXTEINTd 8990 No ndash21035+4545 (SAX J) Be XRB 359 127 No 12 NuSTAR 207 No 208ndash2112206+54 (4U) HMXB 5570 957 No 29ndash35 RXTESAX f 3435 YN 35119188 1925 INTEGRAL 175 178179

Notes (a)Low mass X-ray binary (b)High mass X-ray binary (c)a more specific definition of Type is given in Table A3 (d)read INTEGRAL(e)References see Table A1 ( f )candidates for a possible proton cyclotron line (see also Sect 8)

A61 page 27 of 30

AampA 622 A61 (2019)

Table A3 Additional information about the sources

System Typea RAb Decb Optical Spectral Mass Mass Dist Refc

(J 2000) (J 2000) compa Type compan NS (Gaia)e

(h m sec) ( prime primeprime) nion (M) (M) (kpc)

Cen X-3 1263 11 21 1578 minus60 37 227 V779 Cen O65 II-III 221 plusmn 14 149 plusmn 008 8 (64) 50104Cep X-4 1316 21 39 3060 +56 59 129 V490 Cep B1-B2Ve ndash ndash 38 (102) 48GX 301-2 1211 12 26 3756 minus62 46 132 WRAY 977 B15 Ia 43 plusmn 10 19 plusmn 06 3 (35) 105GX 304-1 1316 13 01 1710 minus61 36 066 V850 Cen B2Vne ndash ndash 24 (20) 9293Her X-1 1413 16 57 4981 +35 20 326 HZ Her B0Ve-F5e 20 plusmn 04 11 plusmn 04 66 (50) 104135NGC 300 1340 00 55 0485 minus37 41 435 SN ndash ndash 14 1880 190191ULX1SMC X-2 1216 00 54 3343 minus73 41 013 star 5 O95III-V ndash ndash 60 101SXP 153 1310 00 50 3023 minus73 35 3628 Be star O95IIIe ndash ndash 60 215Vela X-1 1312 09 02 069 minus40 33 169 HD 77581 B05 Ib 24 plusmn 04 177 plusmn 008 20 (24) 104X Per 1310 03 55 230 +31 02 590 X Per B0Ve ndash ndash 07 (079)0115+63 1386 01 18 319 +63 44 240 V635 Cas B02Ve ndash ndash 7 (72)0332+53 1366 03 34 599 +53 10 233 BQ Cam O85Ve ge20 144 75 (51) 12204409+4431 1310 04 40 5932 +44 31 4927 LSV +44 17 B0e ndash 33 (32) 10210321205205-6932 1316 05 20 3090 minus69 31 550 LMC8 O8-9Ve ndash ndash 50 310535+26 1366 05 38 5460 +26 18 568 V725 Tau O97IIIe 22 plusmn 3 ndash 2 (21) 1240658-073 1341 06 58 1730 minus07 12 353 M81-I33 O97Ve ndash ndash 39 (51) 601008-57 1316 10 09 440 minus58 17 420 ndash B0 IIIVe 15 ndash sim5 1251118-61 1366 11 20 5718 minus61 55 002 Hen 3-640 O95Ve ndash ndash 5 (29) 1311409-619 1310 14 08 0256 minus61 59 003 2MASS OB ndash ndash 145 791538-52 1213 15 42 233 minus52 23 100 QV Nor B0 Iab 141 plusmn 28 10 plusmn 01 64 1041553-542 1316 15 57 483 minus54 24 531 VVV star B1-2V ndash ndash 20 plusmn 4 821461626-67 1410 16 32 1679 minus67 27 393 KZ TrA ndash 003-009 ndash 5-13 132416266-5156 1366 16 26 3624 minus51 56 335 2MASSJ B0-2Ve ndash ndash ndash16393-4643 1220 16 39 0547 minus46 41 130 B giant B giant ge7 ndash ndash 2916493-4348 1220 16 49 2692 minus43 49 0896 2MASS B05 Ib ndash ndash ndash 301744-28 1495 17 44 3309 minus28 44 270 star a G4 III 02-07 14-2 75 10610817544-2619 17 54 257 minus26 19 58 GSC 6849 O9Ib 25-28 ndash 2-4 (26) 12918027-2016 1360 18 02 399 minus20 17 135 ndash B1Ib ge11 ndash 124 14314418179-1621 1311 18 17 5218 minus16 21 3168 2MASS (IR) ndash 1141822-371 1417 18 25 4681 minus37 06 186 V691 Cra ndash 046 plusmn 002 ndash 25 1161829-098 1310 18 29 4398 minus09 51 23 ndash OB ndash ndash sim10 2251907+09 1216 19 09 393 +09 49 450 O8-9 Ia sim27 sim14 5 (44) 10519294+1816 1311 19 29 559 +18 18 384 2MASS B1 Ve ndash ndash 11 203ndash2061946+274 19 45 3930 +27 21 554 ndash B01-IVVe 1947+300 1316 19 49 3549 +3012 318 2MASS B0Ve gt34 14d 95 183184

Notes (a)The type of object is according to HEASARC coding httpheasarcgsfcnasagovW3Browseclass_helphtml1000 - X-ray binary1100 - HMXRB mdashmdashmdashmdashmdashmdashmdash- 10 - X-ray pulsar mdashmdashmdash 1 - flares1200 - HMXRB supergiant mdashmdashmdash 20 - burster mdashmdashmdashmdashmdash- 2 - jets1300 - HMXRB mdashmdashmdashmdashmdashmdashmdash- 30 - black hole mdashmdashmdashmdash 3 - eclipsing1300 - HMXRB Be star mdashmdashmdashmdash- 40 - QPO mdashmdashmdashmdashmdashmdash 4 - ultra-soft trans1400 - LMXRB mdashmdashmdashmdashmdashmdashmdash- 50 - QPO + black hole mdash 5 - soft transient1400 - LMXRB mdashmdashmdashmdashmdashmdashmdash- 60 - QPO + pulsar mdashmdashndash 6 - hard transient1500 - LMXRB Globular cluster ndash 70 - QPO + bursts mdashmdashmdash 7 - eclipsing dippermdashmdashmdashmdashmdashmdashmdashmdashmdashmdashmdashmdashmdashmdash 80 - QPOpulsarbursts mdash 8 - eclipsing ADCmdashmdashmdashmdashmdashmdashmdashmdashmdashmdashmdashmdashmdashmdash 90 - pulsar + bursts mdashmdash- 9 - dipper(b)Coordinates from SIMBAD (c)References see Table A1 (d)assumed (e)distances from Gaia DR2 in parenthesis (Bailer-Jones et al 2018)(see also Treuz et al in prep)

A61 page 28 of 30

Table A4 Changes of cyclotron line energy Ecyc with pulse phase and luminosity corresponding changes in photon index Γ with luminosity

System Ecycphase Ref EcycLx Change For factor Refd ΓLx Refd(maxndashmin) correl in Ecyc in Lx correlmean

Cen X-3 sim30 4950 ndash ndash ndash ndash ndash ndashCep X-4 15 (at 28 keV) 47 posa +3 for Factor 3 46 Yes 4648 20 (at 45 keV) 47 ndash ndash ndash ndash ndash ndash ndash ndash pos linb ndash ndash 189 Yes ndashGX 301-2 25ndash30 5152 posc ndash ndash 5352 ndash ndashGX 304-1 sim20 54 posa +10 for Factor 10 2023 Yes 2359133 ndash ndash pos flatten +20 for Factor 3 55 Yes 55Her X-1 25 3326 pos lina +5 for Factor 2 2527 Yes 56 ndash ndash pos linb +4 for Factor 2 56 Yes 56NGC300 ULX1 ndash ndash ndash ndash ndash ndash ndash ndashSMC X-2 20 91 negc Not signif ndash 91 Yesc 91SXP 153 50 215 ndash ndash ndash ndash ndash ndashVela X-1 25 69 pos flat +4 Factor 5 32 Yes 32 15ndash20 7071 ndash ndash ndash ndash ndash ndash pos flat +8 Factor 7 115 ndash ndashX Per 40 16 No ndash ndash ndash No ndash0115+63 20 1st har 1990 66 neg linac minus40 for Factor 4 5758 Yes 59133 35 2nd har 1990 66 neg linbc minus11 for Factor 2 56 ndash ndash 25 1st har 1991 66 No ndash ndash 42 ndash ndash ndash ndash No ndash ndash 41 ndash ndash0332+53 Small (sim5) 65 neg lina minus20 for Factor 10 62 Yes 5964133 2ndash6 (Lx dep) 67 neg linb simminus2 for Factor 17 56 ndash pos linb sim12 for Factor 35 189 9904409+4431 ndash ndash ndash ndash ndash ndash ndash05205-6932 20 31 Not signif lt+06 Factor 109 31 ndash ndash0535+26 15 1172 No ndash ndash 73 Yes 59133 pos lin 10 for Factor 5 74 Yes 74940658-073 No 6061 No ndash ndash ndash YesNo 59601331008-57 sim10 77 No ndash ndash ndash Yes 1331381118-61 20 43 No ndash ndash ndash Yes 1331409-619 ndash ndash ndash ndash ndash ndash ndash ndash1538-52 10 8187 No ndash ndash 8187 Yes 1391553-542 20 82 No ndash ndash ndash Yes 821626-67 sim20 83 ndash ndash ndash ndash No 8316266-5156 25 15 pos lin sim8 for Factor 6 15 Yes 1516393-4643 le3 29 No ndash ndash ndash ndash ndash16493-4348 ndash ndash ndash ndash ndash ndash ndash ndash1744-28 ndash ndash ndash ndash ndash ndash ndash ndash17544-2619 ndash ndash ndash ndash ndash ndash ndash ndash18027-2016 25 142 ndash ndash ndash ndash ndash ndash18179-1621 1822-371 ndash ndash ndash ndash ndash ndash ndash ndash1829-098 sim9 224 ndash ndash ndash ndash ndash ndash1907+09 25 72 posc 87 ndash ndash19294+1816 ndash ndash ndash ndash ndash ndash ndash ndash1946+274 30 72 No 1947+300 Not signif 88 ndash ndash ndash ndash ndash ndash

Notes (a)On long timescales (b)On timescales of pulse period (ldquopulse amplitude selectedrdquo) (c)Questionableto be confirmed (d)References seeTable A1

A61 page 29 of 30

AampA 622 A61 (2019)

Table A5 Further details on cyclotron lines centroid energy (from Table A1) line width σ central line depth D (the normalization constant ofthe line component often called the ldquostrengthrdquo of the line) ldquooptical depthrdquo τ of the line (with ldquostrengthrdquo D = τσcyc

radic2π) X-ray luminosity Lx

References and additional notes

System Ecyc Width ldquostrengthrdquo Optical Lx Refc Notesσ (gabs) depth (1036 ldquotbcrdquo = to be confirmed

(keV) (keV) D τ ergss)

Cen X-3 3028 78 ndash 1108 ndash 128186a

29 46 25 067073 54 4950Cep X-4 30 5849 20166 ndash 1455 48 Lx dependent 2845 6ndash9sim11 ndash ndash 14 47GX 301-2 42 8 ndash 05 ndash 128a

35 7434 ndash 106014 3910 5251GX 304-1 5660 1019 ndash 09 ndash 55 43ndash58 4ndash12 ndash 06ndash09 17ndash380 55 Lx dependent 50ndash59 5ndash11 81 07 2ndash16 2454Her X-1 4042 6465 95 066074 ndash 128186a Lx dependent 37 sim6 ndash 06ndash10 30 136137 super-orbit 3485 dNGC 300 ULX1 13 sim35 sim55 ndash 100ndash3000 190 tbcSMC X-2 27 64ndash72 ndash 6ndash9 180ndash550 91 tbc Lx dependentSXP 153 5ndash8 ndash ndash 04 20ndash100 215 tbcVela X-1 2425 0947 ndash 016026 ndash 128186a Lx dependent 26553 357 sim15 sim04ndash ndash 32X Persei 164134 3627 ndash 078036 ndash 128186a

0332+53 2726 7654 ndash 1819 375341 65123 Lx dependent 275ndash305 5ndash7 ndash 18 9ndash160 99 5150 8999 ndash 2221 375341 65123 7472 45101 ndash 3313 375341 6512304409+4431 32 6(fix) ndash ndash ndash 17 tbc05205-6932 31 59 ndash 06 370-400 31 tbc0535+26 50 sim10 sim0116 05 ndash02 1273127 see also 7594 44-50 9ndash11 3-13 6ndash49 74 Lx dependent 110 10ndash15 116 73126 see also 740658-073 33 sim12 ndash 04 ndash 60 same as MX 0656-0721008-57 78 sim11 ndash ndash 05ndash100 77 781118-616 55 110 sim14 60 ndash 9 451409-619 44 4(fix) ndash 16+14minus7 007 79 tbc1538-52 21 2ndash3 ndash sim05 35ndash9 88081216 super-orbit 1492 d1553-542 2327 108644 ndash828 ndash 76 82 tbc1626-67 3938 6643 ndash 2114 ndash 128186a

sim38 sim5 ndash sim20 15ndash100 8316266-5156 1018 06ndash13 ndash 01ndash03 sim30 15 tbc Lx dependent16393-4643 29 4 ndash 04 ndash 29 tbc16493-4348 31 10 fixed sim06b ndash ndash 3096 tbc super-orbit 2007 d1744-28 43 12 ndash 012 100 186 tbc Bursting Pulsar17544-2619 1733 3066 ndash 05309 004 22 tbc18027-2016 24 sim5 ndash 02ndash05 31 142 tbc18179-1621 21 1822-371 07 014 ndash 003 180ndash250 85 tbc 33 sim5 ndash ndash ndash 861829-098 15 23 ndash 052 sim43 224 assumed D = 10 kpc1907+09 18 1619 ndash 026026 ndash 128186a Lx dependent 40 306 ndash 23 18619294+1816 43 54 ndash 12 a few 198 tbc1946+274 3539 489 ndash 02511 ndash 128186b

1947+300 12 25 036ndash048 (007) ndash 8898 tbc

Notes (a)Using the systematic studies by RXTE Coburn et al (2002 Ref 128) and BeppoSAX Doroshenko (2017 Ref 186) (b)using cyclabsfor the description of the cyclotron line (see Sect 3) (c)References see Table A1

A61 page 30 of 30

Introduction

Collection of cyclotron line sources

Spectral fitting

Observed variations in cyclotron line energy

Cyclotron line parameters as function of pulse phase

Cyclotron line parameters as function of luminosity

EcycLx correlations on different timescales and line-continuum correlation

Long-term variations of the cyclotron line energy

Correlations between Ecyc and other spectral parameters

Individual sources

Physics of the accretion column

Accretion regimes

Scaling CRSF relations in collisionless shock regime

Scaling CRSF relations in radiative shock regime

Cyclotron line modeling

Empirical knowledge of the magnetic field strength of a neutron star

Statistical analysis

Proton cyclotron lines

The Magnificent Seven

Proton absorption features

Origin of proton cyclotron lines

Summary

References

Additional tables