The many lives of magnetized neutron stars

Astron. Nachr. /AN 335, No. 6/7, 715 – 720 (2014) / DOI 10.1002/asna.201412098

The many lives of magnetized neutron stars

R. Perna1,�, J. A. Pons2, D. Vigano3, and N. Rea3

1. Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY, 11794, USA2. Departament de Fısica Aplicada, Universitat d’Alacant, Ap. Correus 99, 03080 Alacant, Spain3. Institute of Space Sciences (CSIC–IEEC), Campus UAB, Faculty of Science, Torre C5-parell, E-08193 Barcelona,Spain

Received 2014 Apr 30, accepted 2014 May 13Published online 2014 Aug 01

Key words pulsars: general – stars: magnetic fields – stars: magnetars – stars: neutron – X-rays: stars

The magnetic field strength at birth is arguably one of the most important properties to determine the evolutionary path ofa neutron star. Objects with very high fields, collectively known as magnetars, are characterized by high X-ray quiescentluminosities, occurrence of outbursts, and, for some of them, sporadic giant flares. While the magnetic field strength isbelieved to drive their collective behaviour, however, the diversity of their properties, and, especially, the observation ofmagnetar-like bursts from “low-field” pulsars, has been a theoretical puzzle. In this review, we discuss results of long-termsimulations following the coupled evolution of the X-ray luminosity and the timing properties for a large, homogeneoussample of X-ray emitting isolated neutron stars, accounting for a range of initial magnetic field strengths, envelope compo-sitions, and neutron star masses. In addition, by following the evolution of magnetic stresses within the neutron star crust,we can also relate the observed magnetar phenomenology to the physical properties of neutron stars, and in particular totheir age and magnetic field strength and topology. The dichotomy of “high-B” field pulsars versus magnetars is naturallyexplained, and occasional outbursts from old, low B-field neutron stars are predicted. We conclude by speculating on thefate of old magnetars, and by presenting observational diagnostics of the neutron star crustal field topology.

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1 Introduction

Isolated neutron stars (NSs) are characterized by a bewil-dering variety of astrophysical properties. The bulk of theseobjects manifests themselves as radio pulsars, and is char-acterized by a rather steady spin down, occasionally inter-rupted by glitches (discontinuities in the period derivative).These NSs have an estimated magnetic field in the ∼10

12–10

13 G range. Another, distinctive class of NSs is character-ized by large surface temperatures for their ages, occasionalX-ray bursts, and, in some cases, even giant γ-ray flares. Es-timated magnetic field strengths for these objects are verylarge, ∼10

14–1015 G. Other NSs, at the opposite end of the

spectrum, are very quiet and their surface emission is gen-erally consistent with arising from the entire surface of thestar. These objects, also known as Central Compact Objects(CCOs), have been proposed as NSs with very low magneticfield strengths, B <

∼ 108–10

9 G, either by birth, or as theresult of field screening by fallback accreted matter (Mus-limov & Page 1995; Young & Chanmugam 1995; Vigano &Pons 2012).

Evidently, the magnetic field strength of a NS plays afundamental role in its observational appearance, and in itsevolutionary path. Indeed, a large number of investigations

� Corresponding author: [email protected]

over several decades have been aimed at understanding howthe B-field shapes the NS life and properties as we see them.However, despite significant progress, new observations inthe last few years have brought in more questions than an-swers. Neutron stars with similar measured magnetic fieldstrengths (as inferred from timing measurements, i.e. fromP and P ), appear to “behave” very differently (details inSect. 3), calling for a re-evaluation of our global under-standing of the relation between the measured B-field andthe appearance of a NS (e.g. Kaspi 2010).

In this review, we summarize recent work from ourgroup aimed at developing a unified theoretical modelwhich can naturally account for the varied NS observationalphenomenology. In particular, we describe results from longterm simulations which follow the coupled temperature andmagnetic field evolution within the NS crust, while alsotracking the evolution of the relative magnitude of magneticstresses and the breaking strain the crust. As a result, we canpredict, for an initial magnetic field configuration at birth,the evolution of the surface temperature (and hence X-rayluminosity), of the timing parameters P and P , and of theoutburst frequency, strength, and distribution on the NS sur-face.

The review is organized as follows: Section 2 briefly de-scribes the magnetothermal code used for the calculations,and summarizes the main results for the timing and temper-

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716 R. Perna et al.: The many lives of magnetized neutron stars

Fig. 1 Left panel: comparison between the thermal luminosity measured in a large sample of NSs, and theoretical cooling curves fordifferent magnetic field strengths. Right panel: evolutionary tracks in the P -P diagram for a range of initial (poloidal) magnetic fieldstrengths. The asterisks indicate the real ages t = 10

3, 104, 105, 5×105 yr, while the dashed lines mark the tracks followed in absence

of field decay. Figure adapted from Vigano et al. (2013).

ature evolution of the NS population. Section 3 discussesthe theoretically predicted outburst properties as a functionof NS age, and initial magnetic field strength and configu-ration. Observational tests of the internal field configurationare described in Sect. 4, and we summarize in Sect. 5.

2 Unifying the apparent diversity ofmagnetized neutron stars: thermal and timingproperties

The evolution of the magnetic field in NSs has been stud-ied extensively by a number of authors (e.g. Goldreich& Reisenegger 1992; Geppert & Rheinhardt 2002; Cum-ming et al. 2004; Pons et al. 2007; Pons & Geppert 2007;Glampedakis et al. 2011). In the solid crust of the NS, thefield evolves under the combined influence of the Lorentzforce (causing the Hall drift) and the Joule effect (respon-sible for Ohmic dissipation). Coupling of the magneticevolution with the temperature evolution was introducedwith simplifying assumptions by Pons & Geppert (2007)and Aguilera et al. (2008). The first 2D simulations ofthe fully coupled magneto-thermal evolution were eventu-ally performed by Pons et al. (2009), but included onlyOhmic dissipation, due to the numerical difficulties in thetreatment of the important Hall term for large magneticfields. Very recently, Vigano et al. (2012) presented the firstfinite-difference, 2D magneto-thermal code able to man-age arbitrarily large magnetic field intensities while self-consistently including the Hall term throughout the entiremagneto-thermal evolution. This code has provided a fun-damental step in order to model the long-term evolution ofmagnetized NSs, and hence being able to understand timingand spectral properties of isolated NSs as a function of theirage.

In order to perform a meaningful comparison betweentheoretical modeling and observations, Vigano et al. (2013)gathered and thoroughly re-analyzed (using the same meth-ods for the entire sample) the best data available to date onisolated, thermally emitting neutron stars. The sample con-sisted of 40 sources, ranging from magnetars, to X-ray dimisolated NSs, to high-B pulsars, to rotation-powered pul-sars, to the central compact objects. The thermal luminositywas estimated for each of them, using the best estimated dis-tance. The data points are displayed, as a function of age,in the left panel of Fig. 1. Ages are estimated from kine-matic measurements when available, otherwise from timingmeasurements. Together with the data points, the left panelof Fig. 1 shows several cooling curves for magnetic fieldsin the range of 3×10

14 – 3×1015 G, and for two envelope

compositions: hydrogen and iron. Note that for the samemagnetic field strength and age, light-elements envelopesare able to maintain a higher luminosity (up to an order ofmagnitude) than iron envelopes.

The comparison between a range of theoretical mod-els and the observations has shown that, for the weaklymagnetised NSs (Bp

<∼ 10

14 G in the P -P diagram), themagnetic field has little effect on the luminosity. These ob-jects, of which the radio pulsars are the most notable rep-resentatives, have luminosities which are compatible withthose predicted by standard cooling models. Overall, themagnetothermal simulations can broadly reproduce the ob-served X-ray luminosities for a range of initial magneticfield strengths, envelope compositions, and NS masses.

As the NSs age and their luminosity drop as a result offield decay and cooling, they also slow down, primarily dueto dipolar radiation losses. In the absence of field decay, NSsfollow linear tracks in the P -P diagram (see dashed linesin the right upper panel of Fig. 1). However, when mag-netic field dissipation is taken into account into the mag-netothermal evolution, it causes the tracks in the P -P dia-

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Astron. Nachr. /AN 335, No. 6/7 (2014) 717

Fig. 2 Outburst properties of an NS with initial magnetic field components Bp = 8×1014 G and Bt = 2×10

15 G during three differentperiods of its lifetime: 0.4–1.6 kyr (labeled “SGR”), 7–10 kyr (labeled as “AXP”), and 60–100 kry (labeled as “old AXP”). Figure fromPerna & Pons (2011).

gram to bend down (see solid lines in the upper right panelof Fig. 1). Inspection of these evolutionary track shows thatobjects like the traditional rotation-powered radio pulsarswere born with magnetic fields in the range of a few 10

12

to a few 1013 G. When these NSs cool and slow down, they

become invisible in both the radio and the X-rays, and hencethey have no observable descendants. On the other hand, afraction of the magnetars, born with initial dipolar fields ofabout a few 10

14 G, will have as descendants the objectsknown as X-ray dim isolated NSs. These simulations allowto uncover tracks connecting apparently disparate groups ofNSs; these are simply the same kind of objects observed atdifferent evolutionary stages of their life.

3 Unifying the apparent diversity ofmagnetized neutron stars: outburst properties

According to the highly successful model developed byThompson & Duncan (1995, 2001), the Anomalous X-rayPulsars (AXPs) and the Soft γ-ray Repeaters (SGRs), col-lectively known as magnetars, undergo outbursts when, dur-ing the evolution of the strong internal field, local magneticstresses occasionally become too strong to be balanced bythe elastic strength of the crust, which hence breaks, and theextra stored magnetic/elastic energy becomes available forpowering the bursts and flares.

Despite the success of the magnetar model in explainingsome general features of the triggering mechanism of burstsand flares, some major questions have been left unanswered.In particular, if the magnetic field is the main driver of theoutbursts, then how can one explain the recent observationsof outbursts from “low-B” NSs (Gavriil et al 2008; Rea etal. 2010, 2012, 2013a,b), with dipolar magnetic fields in the

7×1012 – 5×10

13 G range, well below what believed to benecessary for magnetar activity? Similarly, how can it bethat NSs with almost identical dipolar field (as measuredform P and P ) behave very differently? For example, theradio pulsar PSR J1814-1744, and the AXP 1E 2259+586,both of which have a dipolar field ∼6×10

13 G, but verydifferent observational properties, the former behaving as alow-luminosity, quiet radio pulsar, while the latter as a verybright and active magnetar.

To address these questions, and to gain a global under-standing of the varied phenomenology of the highly mag-netized NSs, Perna & Pons (2011) performed long-term 2Dsimulations that follow the evolution of the relative magni-tude of the magnetic and the breaking stresses in the crust,hence allowing them to estimate the outburst frequency, en-ergetics and location on the NS surface.

Sample results for the outburst properties for a particularinitial magnetic field configuration (with Bp = 8×10

14 Gand Bt = 2×10

15 G at maximum) are shown in Fig. 2. Theevolution is followed for 10

5 years, and three representa-tive periods were selected, each involving the same num-ber of events (1000 in this particular case). The youngestgroup is labeled “SGR” and spans the interval between 400and 1600 yr. The second is indicated as “AXP” and cov-ers the age period ∼ 7–10 kyr, while the third period is la-beled “old AXP” and corresponds to the events recordedfrom 60 to 100 kyr. Inspection of the figure shows that thereis a significant difference in the energetics and recurrencetime as the star evolves. This is because the crustal magneticfield evolves more rapidly initially due to the fact that it isstronger (and the star is hotter), while at late times the rateof dissipation decreases and hence the evolution becomesslower. These simulations show that there is no fundamentaldifference between objects classified as “AXPs” or “SGRs”;

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generally speaking, objects with a stronger initial field willbe more active at the same age, while for a given initial mag-netic field configuration, older objects tend to be quieter.

To further address the issue of the varied observed phe-nomenology, and in particular the observations of objectswith similar inferred dipolar fields but very different be-haviours with respect to the quiescent X-ray luminosity andoutburst properties (see above), Pons & Perna (2011) ran asuite of simulations with varying relative intensities of theinitial poloidal (Bp) and toroidal (Bt) components of themagnetic field. In fact, while the inferred B field from tim-ing measurements only constrains the dipolar component,there could be a hidden, much stronger toroidal componentwhich can only be inferred through more indirect observa-tions (see Sect. 4). Their numerical exploration showed that,for a given poloidal field, the luminosity of objects withstrong internal toroidal components is systematically higherthan that of objects without toroidal fields, due to the ad-ditional energy reservoir stored in the toroidal field, whichis gradually released as the field dissipates. Therefore, twoNSs with similar poloidal field could have a significantlydifferent X-ray luminosity if the field of one of them (thebrightest of course) is largely dominated by a strong toroidalcomponent. Similarly, the outburst rate is found to dependon the presence and intensity of the internal toroidal field inaddition to the poloidal one. At fixed Bp, the dependence onthe toroidal field is found to be very weak until Bt ∼ Bp,but then the outburst rate increases rapidly with increasingvalues of Bt > Bp (Pons & Perna 2011).

These numerical investigations led to the conclusionthat the apparent dichotomy between quiet, high-B radiopulsars and active magnetars is not real. There is a contin-uum of possibilities, and all types of sources can potentiallyshow some unusual activity. The continuing discovery ofnew magnetar outbursts from “low-B” NSs provides sup-port to this unified picture.

4 Observational tests of the crustal fieldtopology

The previous sections, and in particular Sect. 3, have high-lighted the potential importance of the (crustal) toroidalfield in determining the appearance of an NS, especiallyso when the toroidal component is much stronger than thepoloidal one. While the timing parameters of an NS directlyyield an estimate of the dipolar component, the toroidalfield remains hidden to timing measurements. In the follow-ing, we discuss how the X-ray spectra and light curves ofthe NSs bear valuable information about the presence of astrong toroidal field embedded in the their crust.

We begin by reminding that, for strong magnetic fieldsB >

∼ 1013 G, anisotropies are expected as a result of

anisotropic heat conduction coupled with the blanketingeffect of the envelope. In the region where the magneticfield is radial, the heat is transported much more efficiently,hence the surface is thermally connected to the inner crust

and the core. On the other hand, the regions with nearly tan-gential magnetic field are insulated and disconnected fromthe hot core. Therefore, in the outer crust and in the envelopeof NSs, the magnetic field geometry drives the preferred di-rection for the heat conduction, acting in some regions as athermal insulator.

Given the above, it is evident that the temperature dis-tribution on the surface of an NS constitutes a powerful di-agnostics of its magnetic field topology. In order to identifyobservational features that could signal the presence of astrong toroidal field component, Perna et al. (2013) ran asuite of magneto-thermal evolutionary models, some witha purely poloidal (dipolar for simplicity) field, and otherswhich, in addition, had a strong dipolar toroidal compo-nent.1 Some sample results for the temperature distributionare shown in the upper panels of Fig. 3. When only the dipo-lar component is present (upper left panel, Bp = 10

13 G),the initial symmetry with respect to the equator is main-tained throughout the evolution. However, when a strongtoroidal component is present and dominating, such as inthe case of the upper left panel of Fig. 3 (with Bp = 10

13 G,Bt = 10

15 G), then the equatorial symmetry is broken dur-ing the evolution; this is the result of the Hall term in the in-duction equation, which leads to a complex field geometrywith asymmetric north and south hemispheres. The degreeof anisotropy strongly depends on the initial strength of thetoroidal field. For a given initial magnetic field configura-tion at birth, the degree of anisotropy generally increaseswith the age of the star. For old NSs (t>∼ a few 10

5 yr) withstrong toroidal fields, the anisotropy can generate hotter re-gions (“hot spots”) which are significantly smaller than theNS surface. When fitted with a single blackbody and a highabsorption (which hides the cooler component), these con-figurations can yield effective blackbody radii which can be1–2 km in size (Perna et al. 2013).

From an observational point of view, temperatureanisotropies are revealed by means of pulsed profiles ofthe X-ray radiation. The pulsed profiles for the represen-tative temperature distributions of the upper two panels ofFig. 3 are correspondingly shown in the lower two pan-els for a star with gravitational redshift z = 0.8, and lo-cal isotropic (blackbody) emission. Those two representa-tive models capture the most important differences betweena purely dipolar field, and a field dominated by a toroidalcomponent. In the former case, the profile is double peaked,and perfectly symmetric for an orthogonal rotator. Pulsedfractions are very low, below the 10 % level. In contrast, themodel with a strong toroidal component generally displaysa single peak, and the pulsed fraction can exceed the 50 %level as the star ages. These differences are very importantas potential diagnostics of the internal field topology. Wenote that objects with a single peaked pulse profile (often ac-companied by high pulsed fractions and small inferred emit-

1 Note that it is important that the toroidal component is dipolar anddominant over the poloidal one. If the toroidal component were, e.g.,quadrupolar, much smaller effects would be seen in the resulting tempera-ture distribution and hence the pulsed profiles.


Astron. Nachr. /AN 335, No. 6/7 (2014) 719

Fig. 3 Top panels: temperature distribution on the surface of the NS, for a case with a purely poloidal field at birth (left), and anotherwith the same poloidal field, but in addition a much stronger toroidal component (right). The temperature is shown at different ages ofthe NS. Bottom panels: pulse profiles for an orthogonal rotator with the temperature distributions of the upper panels. The differencebetween the pulse profiles in NSs with purely dipolar fields (double peaked, always low pulsation) and the profiles of NSs with strongtoroidal fields (which can be single peaked and have a high modulation level) is apparent. Figure adapted from Perna et al. (2013).

ting areas) are rather common among magnetars (e.g. Tamet al. 2008; Bernardini et al. 2009, 2011; Halpern & Gotthelf2011; Dib et al. 2012) and some of the central compact ob-jects (e.g. Gotthelf et al 2013), suggesting a strong internaltoroidal field in these objects. For the magnetars in partic-ular, which are young objects, a strong toroidal field willincrease the outburst frequencies as discussed in Sect. 3.

5 Summary

Numerical simulations of the magneto-thermal evolution ofisolated, magnetized neutron stars have begun to paint aunified picture of their variety of observational properties,and evolutionary paths. The initial magnetic field configu-ration plays an important role in determining the observedphenomenology of the NSs. In particular, the presence ofa strong toroidal field breaks the symmetry with respect tothe equator that characterizes a purely dipolar field, result-ing in a warmer hemisphere. As a result, NSs with strong

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toroidal fields can display single-peaked pulse profiles, withpulsation levels which can reach the ∼ 50–60% level. Cor-respondingly, the inferred blackbody radii that would be in-ferred through spectral fitting can be much smaller than theNS radius.

A toroidal field which is much stronger than the poloidalfield can further help explain the apparent dichotomy ofNSs having a similar value of the dipolar field (as inferredthrough timing measurements), but apparently different be-haviour, and, correspondingly the presence of “high-B”NSs behaving like regular radio pulsars, while some “low-B” NSs exhibit a magnetar-type behaviour.

For a given magnetic field configuration at birth, the ap-pearance of an NS (and the way we classify it) will evolvewith time. Younger objects are brighter and more active(more likely classified as “SGRs”), while the “middle-aged”ones are less active and more likely classified as “AXPs”.As the field decays and the outburst occurrence rate persource becomes much too sporadic to be observed in ourlifetime, the thermal and timing properties of the magnetars(as determined through our magneto-thermal simulations)evolve and become consistent with those of the X-ray dimisolated NSs (e.g. Turolla 2009), hence suggesting that thelatter might be the descendants of magnetars.

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The many lives of magnetized neutron stars