Serb. Astron. J. } 194 (2017), 1 - 21 UDC 524.386 + 524.387DOI: https://doi.org/10.2298/SAJ1794001M Invited review

LONG PHOTOMETRIC CYCLES IN HOT ALGOLS

R. E. Mennickent

Universidad de Concepción, Departamento de Astronomı́a, Casilla 160-C, Concepción, ChileE–mail: rmennick@udec.cl

(Received: May 15, 2017; Accepted: May 15, 2017)

SUMMARY: We summarize the development of the field of Double PeriodicVariables (DPVs, Mennickent et al. 2003) during the last fourteen years, placingthese objects in the context of intermediate-mass close interacting binaries similarto β Persei (Algol) and β Lyrae (Sheliak) which are generally called Algols. DPVsshow enigmatic long photometric cycles lasting on average about 33 times the orbitalperiod, and have physical properties resembling, in some aspects, β Lyrae. About200 of these objects have been found in the Galaxy and the Magellanic Clouds.Light curve models and orbitally resolved spectroscopy indicate that DPVs aresemi-detached interacting binaries consisting of a near main-sequence B-type staraccreting matter from a cooler giant and surrounded by an optically thick disc. Thisdisc contributes a significant fraction of the system luminosity and its luminosityis larger than expected from the phenomenon of mass accretion alone. In somesystems, an optically thin disc component is observed in well developed Balmeremission lines. The optically thick disc shows bright zones up to tens percent hotterthan the disc, probably indicating shocks resulting from the gas and disc streamdynamics. We conjecture that a hotspot wind might be one of the channels for amild systemic mass loss, since evidence for jets, winds or general mass loss has beenfound in β Lyrae, AUMon, HD170582, OGLE05155332-6925581 and V 393 Sco.Also, theoretical work by Van Rensbergen et al. (2008) and Deschamps et al.(2013) suggests that hotspot could drive mass loss from Algols. We give specialconsideration to the recently published hypothesis for the long-cycle, consisting ofvariable mass transfer driven by a magnetic dynamo (Schleicher and Mennickent2017). The Applegate (1992) mechanism should modify cyclically the equatorialradius of the chromospherically active donor producing cycles of enhanced massloss through the inner Lagrangian point. Chromospheric emission in V 393 Sco, anoptically thicker hotspot in the high-state of HD170582 and evidence for magneticfields in many Algols are observational facts supporting this picture. One of theopen questions for this scenario is why, among the Algols showing evidence formagnetic fields, the DPV long-cycle is present only under some combinations ofstellar parameters, particularly those including the B-type gainers. Other openquestions are what are the descendants of these interesting binaries, how muchmass contain the discs around the likely rapidly rotating gainers, and the role playedby the outflows through the Lagrangian L2 and L3 points reported in a couple ofsystems.

Key words. binaries: close – Stars: evolution – Stars: mass-loss

1. INTRODUCING ALGOLS

In this section we provide a brief introductionto the class of close binaries named Algols, startingwith a review of the importance of binaries in gen-eral.

1.1. The importance of binary stars

A large fraction of the stars in the Universe arebinaries or members of multiple systems bounded bygravity. The multiplicity frequency of main sequencestars is a steep function of the stellar mass, increa-

c© 2017 The Author(s). Published by Astronomical Observatory of Belgrade and Faculty of Mathematics, University ofBelgrade. This open access article is distributed under CC BY-NC-ND 4.0 International licence.

1

R. E. MENNICKENT

sing toward earlier spectral types (Duchêne andKraus 2013). Binaries are specially useful astronomi-cal tools, since they provide a direct way of weightingthe stars, and deriving fundamental parameters likemass and radius (Andersen 1991). The first list ofwell observed binaries is provided by Popper (1980).Harmanec (1988) collects and analyzes data on abso-lute dimensions of eclipsing binaries and derives ap-proximation formulae relating the effective temper-ature with mass, radius and bolometric magnitude.Torres et al. (2010) present and discuss a criticalcompilation of accurate, fundamental determinationsof stellar masses and radii based on data for 95 de-tached binary systems containing 190 stars. It shouldbe noticed that for eclipsing binaries and multicolorcalibrated light curves, it is possible to get relative lu-minosities and effective temperatures of componentsand thus good distance estimates, something espe-cially important for binaries in foreign galaxies. Ac-tually, binaries provide valuable tools to study ourUniverse even beyond the Milky Way (Guinan 2004,Ribas 2004).

Binaries tends to interact at some stages oftheir lifetime, especially the massive ones. Accordingto Sana et al. (2012), more than 70% of all massivestars will exchange mass with a companion, leadingto a binary merger in one-third of the cases. Assum-ing constant star formation, de Mink et al. (2014)find that 8+9−4% of a sample of early-type stars arethe products of a merger resulting from a close bi-nary system. They report that 30+10−15% of massivemain-sequence stars are the products of binary inter-action. These considerations suggest that the studyof binary interaction is relevant to understand theevolutionary paths of massive stars. Actually, binaryinteraction has been claimed to be relevant even tounderstand the multiple stellar populations detectedin some globular clusters (Jiang et al. 2014, Carraroand Benvenuto 2017). Understanding binary inter-action will help us to understand how they arrive totheir late evolutionary stages, and in the case of themore massive binaries, how they give rise to the mostenergetic phenomena in the universe as supernovae,gamma ray bursts or even the merger of binary blackholes triggering gravitational waves (Abbott et al.2016 a,b).

1.2. Some basic theoretical concepts

The basic physical picture for binary interac-tion and evolution can be described in terms of theRoche model for binary systems (Roche 1873, Kopal1959). In this model the stars are treated as pointmasses and an effective potential is defined includ-ing the stellar gravitational potentials and the cen-trifugal potential due to binary motion. A specificequipotential curve defines the Roche lobes or regionsof gravitational bounding of each star. When onestar evolves until filling this volume, a semi-detachedsystem is formed, and under certain conditions partof its atmosphere starts to be transferred onto theother star through the inner Lagrangian point L1,the common point of both Roche lobes. Depending

on the mass ratio and the size of the primary, the gasstream hits directly the gainer or turns around form-ing an accretion disc (Lubow and Shu 1975); hencetwo kinds of semi-detached systems can be found,disc and impact systems. The Lubow and Shu (1975)critical radius can be approximated by (Hessman andHopp 1990):

rca

= 0.0859q−0.426 for 0.05 < q < 1. (1)

where q is the mass ratio M2/M1 and the formulais accurate to 1%. This radius is usually taken asthe maximum possible radius of the primary allow-ing disc formation. A particle orbiting at this ra-dius has the same specific angular momentum as aparticle released at the inner Lagrangian point L1,therefore, the radius corresponds to the radial exten-sion of a ring of matter formed by mass loss due tothe Roche lobe overflow, just before viscosity startsspreading it into a disc. Therefore, a primary whoseradius is larger than the critical radius (R1 > rc)is an impact-system where the gas stream hits thestar and disc formation is unlikely. Actually, due tothe finite stream size, it is still possible that the outerstream orbits avoid the impact, the respective radiusrmax is a bit larger than rc and also a function of themass ratio (Lubow and Shu 1975).

The observational signatures of these semi-detached systems in the high-energy range criticallydepend on presence of a compact object; cataclysmicvariables containing a white dwarf, high-mass X-raybinaries containing a neutron star are some examplesof systems emitting strongly in UV and X-rays due tomass accretion in deep gravitational potential wells.However, in this review we consider semidetachedbinaries of intermediate mass containing no compactobject. These binaries emit mostly in optical and in-frared wavelengths and besides the spectral contribu-tions of both stars, those of disc and stream must beoccasionally included. Even with the main sequenceor giant components, the real situation can involvedistortion of stars by rapid rotation, which shouldmodify the equipotential surfaces, the irradiation ofone star by the other (Claret and Gimenez 1992), theexistence of hot regions in the disc due to energy dis-sipation by dynamical shocks, the existence of discjets and magnetic spots, among other phenomena(Nazarenko and Glazunova 2006a,b, 2013).

It is interesting that no definitive prescrip-tion exists for some kinds of binary interaction inspite of being a critical stage where the future out-come of the binary is defined. Many evolutionarymodels deal with our ignorance through ad-hoc pa-rameterizations. For instance, the α parameter in-troduced during common envelope phase (Livio andSoker 1998) represents the amount of energy that isremoved from the orbit and is transferred to the cir-cumstellar gas, its value determines how much theorbit of the binary shrinks during dissipation of thecommon envelope and it is critical to understand thepopulation of cataclysmic variables (Zorotovik et al.2010). Also, the mass transferred onto the gainerduring the stage of Roche overflow is not well con-strained since a fraction can be lost into the circum-

2

LONG PHOTOMETRIC CYCLES IN HOT ALGOLS

stellar medium through equatorial outflows or discwinds; this uncertainty is represented by the param-eter β determining the fraction of transferred massthat is lost from the system (e.g. de Mink et al.2014). None of these parameters is well constrainedand population synthesis models must rest on edu-cated assumptions.

Another uncertainty present in impact sys-tems is the amount of matter the star can accretefrom the disc once reached the critical velocity.Petrovic et al. (2005) and de Mink et al. (2009)assume that accretion ceases when the mass-gainingstar reaches Keplerian rotation, while Popham andNarayan (1991) argue that a star near critical ro-tation can sustain accretion due to viscous couplingbetween the star and the disc.

The above scenarios are illustrated in theAlgol-type variables, a class of semi-detached bina-ries with intermediate mass components, where theless massive star is more evolved that the gainermore massive star, something that can be under-stood only if the donor was once the more massivestar of the system, evolved first, and then lost afraction of its mass through the Roche lobe overflowonto the gainer. This evolutionary sequence was firstexplained by Crawford (1955) and later confirmedvia evolutionary calculations by Kippenhahn andWeigert (1967) and Eggleton and Kisseleva-Eggleton(2006). The Roche lobe overflow can happen during(Kippenhahn and Weigert 1967): the donor main se-quence stage (case-A), during the transition to (orin) the red-giant phase (case-B) or during the super-giant phase (case-C).

1.3. Historical perspective

Goodricke discovered the 2.867 day period inthe eclipses of the prototype Algol (β Per) in the year1783 (Goodricke 1783). However, the star has beenknow as a variable since ancient times; evidence hasbeen found indicating that the period of Algol was2.850 days three millennia ago as recorded by an-cient Egyptians (Jetsu et al. 2013). Algol is actuallya triple-star system: the eclipsing binary pair con-sisting of a B8V and a K0III star separated by 0.062astronomical units (AU) from each other, whereasthe third star is at an average distance of 2.69 AUfrom the pair, and the mutual orbital period of thetrio is 681 Earth days. The total mass of the systemis about 5.7 solar masses (Kolbas et al. 2015 andreferences therein).

A related system is the widely studied β Lyrae(its arabic name is Sheliak) whose proximity effectsare noticed in the rounded shape of the light curvebetween eclipses, a signature of a gravitationally dis-torted star. β Lyrae consists of a B8 II star and amore massive primary of probably also B-type. Themore massive star is surrounded by an optically thickand geometrically thick disc (Wilson 1974) and a jethas beed detected emerging from the region of in-teraction between the disc and the gas stream (Har-manec et al. 1996, Ak et al. 2007). The first di-rect detection of photospheric tidal distortion due to

the Roche lobe filling was presented by Zhao et al.(2008) in β Lyrae, based on the CHARA interfer-ometry. These authors also detected the thick disksurrounding the mass gainer at resolved H-band im-ages. The level of activity in β Lyrae is larger thanin ordinary Algols, as revealed by variable eclipseshapes, super-orbital photometric cycles and orbitalperiod changes (see below). β Lyr was the secondvariable star in being discovered, after Algol, andthe history of earlier investigations of this fascinat-ing star is skillfully presented by Sahade (1980) andHarmanec (2002).

1.4. Some words about Algols as aclassification scheme

The traditional classification of eclipsing bi-naries in terms of their light curve morphology isEA (flat between eclipses), EB (rounded betweeneclipses) and EW (no clear distinction when oneeclipse ends and the other starts). These systemswere also named in terms of famous cases as Algolsystems (EA light curve), β Lyrae type systems (EB)and W UMa type systems (EW). Later investigationson the evolution of close binaries yielded to under-stand β Lyrae as a close binary in a stage of masstransfer and the Roche lobe overflow, while Algolwas understood as a system that already underwenta major episode of mass transfer in the past, and nowis ongoing very small mass transfer. For this reasonit was popular to name Algols also those systems un-dergoing the Roche lobe overflow. In this scheme βLyrae is an Algol, although it is not from the point ofview of the scheme of light curve classification alone.In this review we consider Algols the whole class ofintermediate mass close binary systems independentof their evolutionary stage or light curve morphology,including in this way β Lyrae and Algol itself.

1.5. Variability in Algols

Orbital period changes have been reported ina couple of Algols; they can be interpreted as sig-nature of mass loss as expected from basic laws ofenergy and angular momentum conservation (Eggle-ton 2006). However, the orbital period can also varyin a monotonic way in the conservative case due tosimple mass transfer among the stars. In the case ofβ Lyrae, the orbital period of 12.9 days increases ata rate of 19 s/yr (Harmanec and Scholz 1993) andthis is usually interpreted as due to the effect of amass transfer rate of 2.2 × 10−5 M�/yr (Hubenyand Plavec 1991, Harmanec and Scholz 1993). Theorbital period of Algols can also vary cyclically by thelight-time effect due to unseen components aroundthe system (e.g. Hoffmann et al. 2006, Soydugan2008). Another interpretation for these cyclic orbitalperiod changes is magnetic cycles in the cool com-ponent producing variations in its quadrupole mo-mentum yielding changes in the angular momentumdistribution and therefore in the orbital period (Ap-plegate 1992). From the above, the changes in theorbital period have not an unique interpretation, and

3

R. E. MENNICKENT

must be studied in a case by case basis. In this reviewwe focus on a class of Algols where long super-orbitalphotometric periods are detected. These long cyclesare rare in classical Algols, they usually appear inabsence of clear orbital period changes, and mightbe related to magnetic activity of the donor star aswe will show later.

Episodes of systemic mass loss are needed toexplain the current population of Algols. For in-stance, Massevitch and Yungelson (1975) state thatit is necessary that in Algols about 40% to 50% ofthe matter lost by the primary is lost by the sys-tem. Sarna (1993) determines that β Per (Algol)loses about 15% of its initial total mass and 30% ofits initial total angular momentum during evolution.However, intents to detect where the mass lost byAlgols has gone have been unsuccessful (Deschampset al. 2015).

It is possible that magnetic activity plays arole in the observational signatures of Algols. Therelation between Algols and chromospherically activeRS CVn binaries was explored by Hall (1989). In-deed, magnetic variability, like those observed in theRS CVn binaries, has been inferred from radio ob-servations (Lefevre et al. 1994 a,b), X-rays (Singh etal. 1995, 1996), Doppler tomography of the Hα line(Richards and Albright 1993, Richards et al. 2012)and starspots (Zhang et al. 2014). Algol itself showsa cycle of 32 years (Soderhjelm 1980) whose connec-tion with magnetic activity has been confirmed byradio observations by Peterson et al. (2010). Thepossibility of tracing dynamo action in mass-losingstars that are components of Algol-type binaries hasbeen examined by Sarna et al. (1997) and recentlyexplored by Schleicher and Mennickent (2017) in thecontext of long-cycles of hot Algols, as we will showlater in this review. It must be stated that the roleplayed by magnetism in the overall evolution of Al-gols (and also massive stars) remains to be estab-lished.

1.6. Long cycles in Algols

The existence of long cycles is known sincea long time ago in a handful of Algols; Gaposchkin(1944) reported a long cycle of 517.6 days in RX Cas,Lorenzi (1980) showed the presence of a 411 day longcycle in AU Mon, Guinan (1989) inferred a 275 dayperiod for β Lyr, Hill et al. (1997) reported a longcycle of 322.24 days for V360 Lac and Koubsky etal. (1998) reported a long cycle of few hundred daysin CX Dra. The exact long period for this interest-ing system is not well determined. From a studyof infrared images, Mayer et al. (2016) determinedthat CX Dra shows an irregular circumstellar envi-ronment morphology which might somehow be re-lated to systemic mass loss. More recently, a periodof 253.4 days was reported for V 393 Sco (Pilecki andSzczyygiel 2007).

The interpretation of the long cycles has re-mained controversial. Kalv (1979) interpreted the516-day periodicity of RX Cas as pulsation of theRoche lobe filling star. Pulsation is also suggestedby Guinan (1989) for the B8 II component of β Lyrae

although he also mentioned possible changes in thestructure of the disc. Peters (1994) suggests that inAU Mon the changes are due to cyclic pulsations ofthe donor but without any explanation of how thiscould be possible. Studying β Lyrae, Harmanec et al.(1996) considered the 282 day cycle as a possible beatbetween the orbital period and the 4.7 day periodthey detected in spectroscopy. They also noticed thesimilarity of β Lyrae with V 1343 (SS 433), a massiveX-ray binary of orbital period 13.08 days and bipo-lar jets. Posteriorly, Wilson and van Hamme (1999)concluded that neither apsidal advance nor preces-sion can account for the 282-day light variation inβ Lyrae, but they were unable to exclude disc pul-sations as the origin. Later, Desmet et al. (2010)study very accurate the CoRoT space photometry,past the Johnson V photoelectric photometry andhigh-resolution echelle spectra of AU Mon and con-clude that the long term photometric variations aredue to light attenuation by variable amounts of cir-cumbinary matter. This conclusion is mainly basedon the constancy of the light curve shape during thelong-cycle.

2. DOUBLE PERIODIC VARIABLES

In year 2003 an announcement of the discov-ery of a group of stars in the Magellanic Clouds waspublished, showing two linked periodicities, a short-one lasting a couple of days and a longer one last-ing hundreds of days; both periodicities were cou-pled through the relation Pl = 35.2 ± 0.8 Po (Men-nickent et al. 2003). The typical amplitude of thelong variability is 0.1-0.2 mag in the I-band and thelight curve shape sometimes sinusoidal and some-times double-hump (e.g. Poleski et al. 2010). Theabove relation and the existence of two periods havegiven rise to the name of Double-Periodic Variables(DPVs). An example of the DPV light curve isshown in Fig. 1.

Since the beginning it was clear that theseobjects were binaries, since the short-term lightcurves revealed ellipsoidal or eclipsing type variabil-ity. Their position in the Hertzsprung Russell di-agram was above the main sequence in the V − Icolor region corresponding to B/A-type stars, actu-ally, they were found during a search of emission lineobjects of the Be-type. At the beginning their re-lationship to Algols was not clear and the nature ofthe long cycles remained unknown. Mennickent et al.(2003) explored hypothesis in terms of disc preces-sion but later observations of V 393 Sco were incom-patible with this idea (Mennickent et al. 2012a,b).In year 2005, the first spectra of DPVs in the Mag-ellanic Clouds were published, and the view of lowmass ratio binaries containing B-type componentswas strengthened (Mennickent et al. 2005a). SomeBalmer lines in the spectra were filled by emission,pointing to the presence of circumstellar matter.

In the above study, the systemOGLE05200407-6936391 presented a remarkableshortening of the long-cycle from 340d to 270d ina couple of cycles. The non-constancy of the long-cycle in many DPVs was confirmed by Mennickent

4

LONG PHOTOMETRIC CYCLES IN HOT ALGOLS

et al. (2005b). In addition, it was clear that the longcycle produces photometric variability of larger am-plitude in redder bands (Michalska et al. 2010). Thepresence of Hα emission in a couple of DPVs wasreported by Mennickent et al. (2011) for a sampleof 8 DPVs, illustrating their complex nature, andconfirming the presence of circumstellar matter inmost of these systems.

The connection with β Lyrae was evident withthe study of OGLE 05155332-6925581 (Mennickentet al. 2008). This object turned out to be a rela-tively massive semi-detached binary of orbital periodof 7.284297 days resembling β Lyrae in some aspects;a luminous accretion disc surrounds a hidden B-typestar. After 12 relatively stable cycles, the systemshows a remarkable long period change from 188 to172 days. This period shortening lasts for at least 10cycles. Interestingly, the star follows a loop in thecolor-magnitude diagram during the long cycle, be-ing bluer during the rising phase and redder duringdecline. This was interpreted by the authors as ev-idence of mass loss, following a similar phenomenondetected in Be stars by de Wit et al. (2006). Addi-tional evidence for mass loss came from the behaviorof discrete absorption components detected in theinfrared HI lines; their strength and radial velocitiesfollow a saw-teeth pattern during the orbital cycleconsistent with equatorial outflows. Mennickent etal. (2008) proposed cycles of mass loss feeding acircumbinary disc as explanation for the long pho-tometric cycle, the color-magnitude loop and for theorbital behavior of the discrete absorption featuresdetected in infrared H I lines.

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 00 . 20 . 10 . 0

- 0 . 1- 0 . 2

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 00 . 80 . 60 . 40 . 20 . 0

- 0 . 2

l o n g - c y c l e p h a s e

∆V (m

ag)

∆V (m

ag)

o r b i t a l p h a s e

Fig. 1. Disentangled light curve for V495Cen, theorbital period is 33.49 days and long period 1283 days(Mennickent and Rosales 2014).

Further analysis of the system yielded a com-parison of the orbital and stellar parameters withthose provided by the grid of synthetic binary starmodels by Van Rensbergen et al. (2008) includingepochs of non-conservative mass transfer. The bestmulti-parametric fit is obtained with a model in aconservative case-B mass-exchange with a relativelylarge mass transfer rate of Ṁ = 3.1 × 10−6 M�/yr(Garrido et al. 2012). However, contrary to the ex-

pectation for a conservative high-mass transfer ratesystem, the orbital period remained relatively sta-ble during 15 years. A complex picture of balancedand opposite effects of mass transfer and mass lossis offered by these authors to account for the ab-sence of orbital period variations. In this picture,outflows through the Lagrangian L2 and L3 pointscould bring enough angular momentum of the systemto keep constant the orbital period.

The definitive connection of DPVs with Al-gols appeared in 2012 when the first catalogueof Galactic DPVs was released (Mennickent et al.2012a). Some of them were known Algols: AU Mon,V 393 Sco, LP Ara, DQ Vel, and GK Nor. Amongthese, only AU Mon was known to show a long pe-riodicity. These objects (except for LP Ara) are stillmiss-classified as detached binaries in the SIMBADdatabase.

The fact that the long cycles last hundredsof days conspired against an early detection of theseGalactic DPVs; only all-sky patrol programs and sur-vey data, especially ASAS, along with scarce long-term monitoring of specific objects, provided thedata with enough time coverage to reveal them.

Catalogues of DPVs have been published inthe Galaxy (Mennickent et al. 2012a, Mennickent etal. 2016a), the Large Magellanic Clouds (Poleski etal. 2010), the Small Magellanic Cloud (Pawlak etal. 2013) and in the direction of the Galactic Bulge(Soszynski et al. 2016). The current census gives 137DPVs in the LMC (125 from Poleski et al. 2010 plus12 found during our own unpublished research), 55DPVs in the SMC (Mennickent et al. 2003, 2005,Pawlak et al. 2013 and our own unpublished re-search) and 21 DPVs in the Galaxy (Mennickent etal. 2016a), but see the update at the end of this sec-tion. The number of DPVs in the Soszynski et al.catalogue remains to be determined. For compari-son, the more recent catalogue of Algols by Buddinget al. (2004) lists 411 Algol-type semi-detached bi-nary stars. In the meantime, new samples of similarbinaries with long-cycles were released by Desmet etal. (2010) and Harmanec et al. (2015). The abovenumbers suggest that the DPV phenomenon tracesa relatively long-lasting stage in the lifetime of a bi-nary. About 3% of the DPVs have been studied spec-troscopically, about 30% of the DPVs are eclipsing.

DPVs have been found in three galaxies, theMagellanic Clouds and the Milky Way; in all cases arelationship:

Pcycle = f × Porb, (2)

has been found between the long cycle length andthe orbital period, with f ≈ 33 but with single val-ues for the period ratio typically between 27 and 39(e.g. Mennickent et al. 2016a).

In the past, there was some reluctance in in-cluding β Lyrae and RX Cas among DPVs since theyshowed, contrary to known DPVs, variable orbitallight curves and variable orbital periods. TYC 7398-2542-1 (ASAS J182841-3314.6) was also excluded be-cause of showing an Algol-type (EA) light curve typ-ical of a detached system, not as almost all known

5

R. E. MENNICKENT

1 1 0 1 0 0

0 . 1

1

1 0

1 1 0 1 0 0

1 0

1 0 0

P cycle

(yea

rs)

P cycle

/P orb

P o r b ( d a y s )

L M C D P V s S M C D P V s G a l a c t i c D P V s

Fig. 2. Long versus orbital period for Double Periodic Variables. Data are from Poleski et al. (2010),Pawlak et al. (2013), Mennickent et al. (2016a), our own SMC DPV studies (Mennickent and Kolaczkowski,unpublished, 55 objects), and we also have included β Lyrae, RXCas, TYC 7398-2542-1 and DD CMa. Areference line has been traced at the period ratio Pcycle/Porb = 33.

DPVs (EB-type). However, in this review they areincluded as possible DPVs, since we don’t know a pri-ori if the same mechanism triggering the long DPVcycle operates in them. All DPV periods are shownin Fig. 2. It is interesting that there is a group ofsystems with orbital period around 1 day, especiallyconsidering the relatively small room available for apotential disc; they certainly need more investiga-tion. For Algols TT Hya and SX Cas, presence of along cycle is unclear, so they were not included inthe list of 26 Galactic DPVs presented in Table 1.

3. NOTES ON METHODOLOGY

DPVs have been studied with conventionalspectroscopic and photometric techniques often ap-plied to binary stars. In particular, we briefly men-tion in this section the methodology of spectral disen-tangling, light curve modeling, Doppler Tomographyand χ2 minimization, the later between multiple ob-served parameters and those predicted by syntheticevolutionary tracks of binary stars. This section isstrongly biased by the experience of the author, whileother techniques used in some DPVs by other groupsare probably not described in detail.

Spectral disentangling allows separation ofspectral components in the binary. This is especiallyneeded due to the multiple-component structure ofthe DPV spectra where stars, disc, gas stream andwind significantly contribute to the radiative flux.

A method for spectral disentangling is pro-vided by the program KOREL developed by PetrHadrava at Ondrejov Observatory. It is based onthe Fourier Transform; it allows to decouple until5 different spectral components assuming their con-stancy in flux contribution during the orbital cycle(Hadrava 1995, 1997). Other method is describedby Gonzales and Levato (2006); it consists in trans-lating spectra in the velocity space according to theorbital motion of one of the components, and thensum the resulting spectra removing at first order onecomponent. This procedure is repeated in successiveiterative steps until getting a spectrum relatively freeof the flux constribution of one of the components.Another method consists in that, after knowing thespectral characteristics of the donor, its orbital mo-tion and their contribution to the total flux, a syn-thetic spectrum of the same characteristics can beremoved from each observed spectrum to get residu-als spectra that can be investigated furthermore (e.g.Mennickent et al. 2012b). The advantage of thismethod is to avoid the assumption of constancy ofthe fractional light contribution of the donor duringthe orbital cycle but, on the other hand, it demandsadequate a-priori knowledge on the system. Addi-tional disentangling techniques include direct sub-traction (Ferluga et al. 1997), tomographic separa-tion (Bagnuolo and Gies, 1991) and wavelength do-main (Simon and Sturm, 1994). All these methodscan in principle be applied to disentangle DPV

6

LONG PHOTOMETRIC CYCLES IN HOT ALGOLS

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7

R. E. MENNICKENT

spectra, but taking special care of emit-ting/absorbing structures which might have differentvisibility at different orbital phases.

The light-curve fitting has been performed us-ing the inverse-problem solving method based on thesimplex algorithm, and the model of a binary systemwith a disc (Djurašević 1992a,b). The Nelder-Meadsimplex algorithm (see e.g. Press et al. 1992) hasbeen used with optimizations described by Dennisand Torczon (1991). While the direct problem com-prises the calculation of the light curve from modelparameters given a priori, the inverse problem is pro-cess of finding the set of parameters that will opti-mally fit the synthetic light curve to the observa-tions. The method has been successfully applied toDPVs and revealed the basic properties of the ac-cretion discs (temperature, radii, vertical extension)and incidentally the presence of bright regions, whichare discussed later in this review. Other light-curvefit algorithms applied to Algols with discs are thoseby Zola (1995) who pointed out the importance ofincluding the disc in the model to avoid spurious con-tact configurations, and Wilson and Caldwell (1978)who modeled V 356 Sgr.

Doppler tomography was introduced as a toolfor the study of accretion discs by Marsh and Horne(1988). This method is now a widespread procedurein the study of emission lines in Algols (Richards2004, Richards et al. 2012), and provides a quantita-tive mapping of optically thin line forming regions inthe velocity space. The underlying assumptions in-clude an optically thin emitting disc in the binary or-bital plane. Even when severe self-absorption and/orintrinsic line broadening are present, the tomogramsprovide at least a concise and convenient way ofdisplaying phase-resolved line profile measurements.The Doppler reconstructions are computed using thefiltered back-projection method (Rosenfeld and Kak1982), the Maximum Entropy Method (Marsh andHorne 1988, Spruit 1998) or the Total Variation Min-imization (Uemura et al. 2015). When interpretingDoppler maps, one should keep in mind the diffi-culty in representation of optically thick structuresand components above or below the orbital plane.Doppler tomography allows the study of the discemissivity and chromospheric emission sites in Al-gols and DPVs (Richards et al. 2012, Mennickentet al. 2012b, 2016b). While Doppler tomographyis usually sensible to line emission, the light curvemodel is more sensible to continuum emission andoptically thick regions of the disc. This might, inprinciple, produce differences in the estimated discsize in both methods. A good example of this mis-match is the radius of the disc of AU Mon. WhileAtwood et al. (2012) determine 23 R� with a tech-nique sensible to optically thin line emitting regions,Djurašević et al. (2010) found 13 R� with a methodsensible to flux emitted in the continuum, i.e. ininner, denser and hotter regions of the disc.

Another method used to reconstruct the im-age of the disc is eclipse mapping. This technique,developed by Horne (1985), consists in the analy-sis of multi-wavelength photometry during eclipse toreconstruct the radial brightness distribution of the

disc in a close binary, using the maximum entropyapproach. The method has been successfully appliedto cataclysmic variables (e.g. Baptista 2001) and alsoto some Algols with discs.

For instance, Pavloski et al. (2006) studied 7-color photometric observations in the Geneva systemof the active Algol W Cru, covering several cycles ofthis long-period (198.5 days) eclipsing binary. Theyused a modified Rutten’s approach to the eclipse-mapping and the optimization of the system’s pa-rameters and the recovery of the disk intensity dis-tribution was performed using a genetic algorithm.These authors confirm the presence of a thick discaround the gainer extending 80% of the gainer’s crit-ical lobe. The reconstructed image reveal a ratherclumpy and nonuniform brightness distribution ofthe accretion disk rim in this system. Accordingto these authors, this clumpiness accounts for lightcurve distortions and asymmetries, as well as forsecular changes. Afterwards, Mimica and Pavloski(2012), using the same methodology of eclipse map-ping, reconstruct the accretion disk image of AUMon from CoRoT Photometry. They found a clumpydisk structure similar to those detected in W Cru.

In order to study the evolutionary stage ofDPVs we have used predicted evolutionary tracksof a sample of binaries by Van Rensbergen et al.(2008) to perform a χ2 minimization procedure be-tween the observed parameters of a system and thoseof a grid of models. The best fit is obtained for asystem characterized by a given combination of ini-tial masses, radii, temperatures, orbital period andthe corresponding set of parameters at the currentage. The system age and stellar core metallicitiesare also provided by this methodology (e.g. Men-nickent et al. 2012a). The methodology is limitedby the discrete grid of parameters of the syntheticmodels and also for the ad-hoc prescriptions aboutmass loss in the same models (Van Rensbergen et al.2008). In spite of these limitations, the method hasprovided age and mass transfer rate for β Lyrae con-sistent with earlier investigations (Mennickent andDjurašević 2013), and for the first time for severalsystems, all of them were found inside or very closeto a burst of the Case-B mass transfer (Mennickentet al. 2016a and references therein).

4. DPV PHYSICAL CHARACTERISTICS

The first comprehensive study of physical datafor a sample of DPVs was published by Mennickentet al. (2016a). They find that DPVs are mostlytangential-impact systems, i.e. their primaries haveradii barely larger than the critical Lubow-Shu ra-dius. In principle, these systems are expected toshow transient discs, but Mennickent et al. (2016a)find that they host stable discs with radii smallerthan the tidal radius. We notice here that this lastresult might be influenced by the method that wasused to determine the disc radii in several systems,which is very sensitive to the continuum radiation,i.e. it traces the innermost and hottest regions of thedisc. Therefore, the results might indicate that the

8

LONG PHOTOMETRIC CYCLES IN HOT ALGOLS

optically thick disc is confined very inside the tidalradius, whereas optically thin outer regions reacheslarger radii. The existence of optically thin disc re-gions is evident in some systems with well developeddouble emission lines as AU Mon (e.g. Atwood et al.2012). In addition, other result of the above paperis that, among tangential-impact systems includingDPVs and semi-detached Algols, those systems withprimaries with masses between 7 and 10M� (corre-sponding to B-type spectra types) are always (in thesmall studied sample) DPVs. This suggests a spe-cial role of B-type gainers in the DPV phenomenon.Furthermore, Mennickent et al. (2016a) find thatDPVs are in a mass transfer stage, with donor massesusually between 1 and 2 M�. The same authorsanalyze infrared photometry of 2MASS and WISEsatellites revealing significant color excesses in manyDPVs, which suggests variable amounts of circum-stellar matter.

Studies of DPVs suggest that they are foundin the Case-B mass transfer, i.e. the donor has al-most exhausted hydrogen in its core (Mennickent etal. 2016a). The comparison with synthetic evolu-tionary tracks for binary stars indicates that DPVsborn as close binaries with similar stars of few solarmasses and orbital periods of few days, say 2 or 3days, and then evolve to the stage of longer periods

because of mass transfer when the more massive starevolves filling its Roche lobe (Van Rensbergen et al.2008).

It is instructive to see the positions of thegainer and donor in the luminosity-temperatureand luminosity-mass diagrams in comparison withsemidetached Algols (Fig. 3). We observe the DPVgainers near the main sequence and closely follow-ing the L-M relationship for these stars. However,the donors appear much evolved above the main se-quence and detached from the L-M relation for mainsequence stars. This is undoubtedly the result of thedonor size inflation by nuclear evolution and massloss onto the gainer, as has been recognized also forsemi-detached Algols (circles in Fig. 3, Dervişoǧluet al. 2010). It is also evident that DPV gainers anddonors are in the upper range of masses and tempera-tures of semidetached Algols. We can say that DPVsare found inside the population of hot and massiveAlgols.

From the DPV light curve analysis it is clearthat the accretion disc is optically thick, at least theregion closer to the star and to the orbital plane. Thestability of this region in most DPVs is remarkable,as revealed by the unperturbed light curve shape dur-ing the long cycle, except for β Lyrae and few otherhighly active systems. Fig. 4 shows diagrams with

4 . 6 4 . 4 4 . 2 4 . 0 3 . 8 3 . 6 3 . 4- 1

0

1

2

3

4

5

6

- 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5- 1

0

1

2

3

4

5

6

2 0 . 0

1 0 . 0

5 . 0

3 . 0

2 . 0

log L/

L O

l o g T e

1 . 0

l o g M / M OFig. 3. Comparison of physical data for semi-detached Algols from Dervişoǧlu et al. (2010, primaries bluecircles and secondaries red circles) and DPVs (primaries blue crosses and secondaries red squares). Thezero-age main sequence for Z = 0.02 is plotted with a solid black line and evolutionary tracks for single starswith initial masses (in solar masses) labeled at the track footprints are also shown (Pols et al. 1998). Thebest evolutionary tracks for the primary and secondary of HD170582 are also plotted by two solid lines inthe left panel (adapted from Mennickent et al. 2016a).

9

R. E. MENNICKENT

ß Lyrae

40

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Fig. 4. Some Double Periodic Variables. The units of the vertical and horizontal axis are solar radii. Disc,Roche lobes and stars are shown with the same scale factor. The center of mass is indicated by a solid circle.Data are taken from Mennickent et al. (2016a, and references therein). Plots courtesy of Mauricio Cabezas.

10

LONG PHOTOMETRIC CYCLES IN HOT ALGOLS

the geometry of some DPVs and their discs. Thefractional radius of DPV gainers and discs are shownin Fig. 5. This figure illustrates that DPVs are con-strained to the mass ratio M2/M1 = 0.15−0.35 andare mostly ”impact-systems”, i.e. they are in a re-gion where the stream impact should spin-up thegainer very efficiently.

0 . 1 10 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

Fractio

nal ra

dius

q ( M 2 / M 1 )

r t i d a l / a

r m a x / ar c / a

Fig. 5. The fractional radius for the primary(R1/a; circles) and disc (Rd/a, triangles) of DPVs.Symbol size for stellar radii is proportional to thesystem total mass. Below the circularization radiusshown by the solid black line a disc should be formedand below the dash-point a disc might be formed. Thetidal radius indicates the maximum possible disc ex-tension (upper dashed line). Semi-detached Algolprimaries from Dervişoǧlu et al. (2010) are alsoshown as black points. Adapted from Mennickent etal. (2016a).

Table 2. Longitude (λ) and temperature ofhotspots, relative to the external-edge disc tempera-ture, in some DPVs. Longitudes are measured fromthe line joining the star centers counter rotation.References are given in Mennickent et al. (2016a)except for V 495 Cen (one hotspot, Rosales et al. inpreparation).

System λ (◦) Tspot/Tdisc Tdisc (K)HD 170582 332 ± 6 1.7 ± 0.1 5700 ± 200V 393 Sco 324 ± 6 1.2 ± 0.1 8600 ± 600

β Lyr 325 ± 7 1.2 ± 0.1 8200 ± 400DQ Vel 329 ± 7 1.4 ± 0.1 6580 ± 300iDPV 324 ± 5 1.1 ± 0.1 12600 ± 600

V 495 Cen 338 ± 9 1.11 ± 0.03 4040 ± 200HD 170582 141 ± 5 1.4 ± 0.1 5700 ± 200V 393 Sco 162 ± 9 1.2 ± 0.1 8600 ± 600

β Lyr 107 ± 9 1.1 ± 0.1 8200 ± 400DQ Vel 143 ± 9 1.4 ± 0.1 6580 ± 300iDPV 130 ± 13 1.2 ± 0.1 12600 ± 600

5. EVIDENCE OF MASS LOSSAND HOTSPOT WIND

An improvement in the knowledge of theAU Mon system was made by Desmet et al. (2010),who analyzed very accurate CoRoT space photome-try, Johnson V photoelectric photometry and high-resolution echelle spectra. They show that the long-term variation must be due to attenuation of thetotal light by some variable circumbinary material.The fact that the shape of the orbital light curveis the same at high and low state of the long-cycleindicates that the origin of the long-cycle is not in-side the stars but comes from circumbinary matter.They find new ephemerides and orbital/system solu-tions, deriving a mass ratio M2/M1 = 0.17 ± 0.03based on the assumption that the G-type secondaryfills its Roche lobe and rotates synchronously. Fur-thermore, they demonstrate that the Balmer/Heliumlines may not be of photospheric origin but be formedin a pseudo-photosphere around the gainer. This re-search reinforces the idea of variable circumstellarmatter as the origin of the long-cycle, as claimedfor OGLE 05155332-6925581 by Mennickent et al.(2008).

Later, the system V 393 Sco was studied in de-tail in a series of papers by Mennickent et al. (2010,2012a,b). They discuss the evolutionary stage of thesystem finding the best match with one of the evo-lutionary models of Van Rensbergen et al. (2008).According to this model, the system is found after anepisode of fast mass exchange that transferred 4 M�from the donor to the gainer in a period of 400 000years. Mennickent et al. (2012b) found that theline emission is larger during main eclipse and alsoduring the maximum of the long-cycle. Also, theyfind chromospheric emission in the lines Mg II 4481and C I 6588, revealed in Doppler maps. Again inV 393 Sco, as happens in AU Mon, the stability ofthe orbital light curve suggests that the stellar plusdisc configuration remains stable during the long cy-cle. Therefore, the long cycle should be producedby an additional variable and not-eclipsed emittingstructure. The broad emission lines are not com-patible with circumbinary disc emission in this case.They conclude explaining the long photometric cy-cle in terms of variable strength of a bipolar diskwind. We notice that the extra line emission duringthe maximum of the long-cycle was also observed inDQ Vel (Barŕıa et al. 2014) and AU Mon (Barŕıa andMennickent 2011). All these findings bring similari-ties with the case of β Lyrae.

In fact, Harmanec et al. (1996) and Hoffmanet al. (1998) independently discovered the presenceof bipolar jets in β Lyr from optical interferometryand from spectropolarimetry, respectively. A theo-retical justification for the presence of bipolar jetswas suggested by Bisikalo et al. (2000), who in theirgas dynamical model identified the roots of the jetsin the disc/stream interaction region as the zone oflarger rate of energy release. Since the collimatedcharacter of the jets in β Lyrae has not been proved,we suspect they are of the same nature that the winddetected in V 393 Sco.

11

R. E. MENNICKENT

The idea of jets or polar winds in Algols is notlimited to β Lyrae. Plavec (1992) already suggestedthat a stellar wind induced by the accretion processmight explain the emission observed in ultravioletlines of Si IV, C IV and N V in some systems, espe-cially those he called W Serpentis stars. Peters andPolidan (2004) interpreted the very little variationin profile, strength, and velocity of the OVI emis-sion line observed in V356 Sgr, TT Hya, and RY Peras evidence of ”material that has a substantial flowperpendicular to the orbital plane (perhaps a bipolarjet)”. We notice that none of these systems is a DPV.In addition, a recent polarization study of V 356 Sgrby Lomax et al. (2017) reports a large intrinsic po-larization signature arising from electron scatteringthat is not eclipsed.The authors suggest that lightscattering in a circumbinary disc or bipolar outflowcan be responsible for the constant flux polarization.

The finding of a bipolar wind in V 393 Sco mo-tivated the study of HD 170582, a non-eclipsing DPVseen at intermediate latitudes, where the wind, ifpresent, should show up in spectral signatures. Thestudy by Mennickent et al. (2015) indicates that thesystem consists of a cool evolved star of M2 = 1.9 ±0.1 M�, T2 = 8000 ± 100 K and R2 = 15.6 ± 0.2R� and an early B-type dwarf of M1 = 9.0 ± 0.2M�. The B-type star is surrounded by a geometri-cally and optically thick disc of radial extension 20.8± 0.3 R� contributing about 35% to the system lu-minosity at the V -band. Two extended regions lo-cated at opposite sides of the disc rim, and hotterthan the disc by 67% and 46%, fit the light-curveasymmetries. Especially interesting is the doubleline nature of He I 5875; two absorption componentsmove in antiphase during the orbital cycle; they canbe associated with the shock regions revealed by thelight curve models constructed by the same authors(Fig. 6). The radial velocity of one of the He I 5875components closely follows the donor radial velocity,suggesting that the line is formed in a region near thestream-disc interaction region. It is possible that thewind emerging from the hotspot located in the 1stquadrant is the region where this line is produced(Mennickent et al. 2015).

Further analysis of HD 170582 revealed addi-tional details on its interesting nature. The Dopplermaps constructed with the Hα emission at highand low state of the long cycle showed interest-ing changes: increased emission is observed in thehotspot region during the low state (Fig. 7). Thisfinding strengthen the idea that the long cycle rep-resents the variability of a hotspot bipolar wind, asreported for V 393 Sco.

It should be noticed that due to the presenceof the disc, the gas stream cannot hit directly thestar, but hits the disc at its outer edge, producinga hotspot or hotline, which is revealed in light curvemodels (Mennickent and Djurašević 2013) and hy-drodynamical simulations (Bisikalo et al. 1998, 1999,2003). The idea of mass loss driven by radiation pres-sure produced in the hotspot was explored theoret-ically by Van Rensbergen et al. (2008). This stageoccurs when the mass transfer rate exceeds a criticalvalue and the gainer cannot accrete more material,according to these authors.

Fig. 6. Observed (LCO) and synthetic (LCC)light-curves of HD170582 obtained by analyzing V -band photometric observations; final O-C residualsbetween the observed and optimum synthetic lightcurves; fluxes of donor, gainer and of the accretiondisk, normalized to the donor flux at phase 0.25; theviews of the optimal model at orbital phases 0.20,0.50 and 0.80, obtained with parameters estimatedby the light curve analysis. From Mennickent et al.2015.

12

LONG PHOTOMETRIC CYCLES IN HOT ALGOLS

-500 0 500V(km/s)

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Low state

High state

Fig. 7. Phased time series observed and reconstructed spectra around the Hα line folded with the orbitalperiod of the system and corresponding Doppler maps. Most spectra at the high (low) stage are in 0.7 <Φl < 1.0 (0.4 < Φl < 0.6). The orbital period of Porb = 16.87 days, the primary mass of M1 = 9.0 M�,inclination angle 67 .◦4 and the mass ratio of q = 0.21 from Mennickent et al. (2015) are used to overlaypositions of the stellar components on the Doppler maps. Φ = 0.0 corresponds to the inferior conjunctionof the donor. The loci for the center of mass for both stellar components, the theoretical ballistic gas streamand the Keplerian velocity at the stream are marked on the tomograms. The circle represents the Keplerianvelocity of the disc outer radial edge as inferred from the light curve model (Mennickent et al. 2015). Thefilling of missing phases in the folded spectra is used for best presentation. From Mennickent et al. (2016b.)

Accretion discs with hotspots have been re-ported in Algols with long cycles as β Lyrae,AU Mon, DQ Vel, V 393 Sco and HD 170582 butalso in classical Algols with discs (Richards 2014,Richards et al. 2012). The evidence comes from discemissivity maps constructed from light curve mod-els and also from Doppler tomography of emissionlines. Bright zones are found at the first and fourthquadrants (Table 2). The first of these regions is usu-ally associated to the site of interaction between thestream and the disc, a region of intense dissipation

of kinetic energy. We notice that the first quad-rant hotspot is strongly constrained to (average) λ =327 .◦7 ± 5 .◦6 (std). These regions are hotter than therest of the disc and the temperature could maintain ahotspot wind, as described by Van Rensbergen et al(2008). An indicator of mass loss should be circum-stellar matter producing appreciable reddening. Ac-tually, DPVs indeed show reddening in infrared col-ors, however not so pronounced as in W Serpentids(Mennickent et al. 2016a) or FS CMa stars (Men-nickent 2017, in press). As mentioned earlier, evi-

13

R. E. MENNICKENT

dence for large-scale gas envelopes, relics of violentmass-loss events, have not been detected in Algols(Deschamps et al. 2015).

One of the undetermined parameters is themass of the disc. Since the spin-up of the gainer is arelatively rapid process (e.g. Dervişoǧlu et al. 2010,Packet 1981), and assuming that tidal forces are notso effective to break this rotation, and also consid-ering that the DPV mass loss is a smooth process,we can conjecture that a significant fraction of thetransferred mass remains in the disc. This could ex-plain the mentioned lack of nebulosity around thesesystems (Deschamps et al. 2015). More work is nec-essary to confirm this suggestion.

Following these ideas, Mennickent et al.(2012a) argue that a significant fraction of the trans-ferred mass has not been accreted by the gainer inV 393 Sco but remains in an optically thick massive(about 2 M�) disc-like pseudo-photosphere whoseluminosity is not driven by viscosity but probablyby reprocessed stellar radiation. Although the massof the disc has not been confirmed (and it shouldproduce an interesting challenge for the dynamicalmodel of the system), the result regarding the na-ture of the disk radiation is important since it con-tradicts earlier assumptions that the disk luminosityof Algols is accretion-driven (Smak 1989, Plavec andHubeny 1994). This result is later confirmed andgeneralized to a sample of DPVs by Mennickent etal. (2016a) based on calculations for the disc lumi-nosity arising from light curve models (Fig. 8), andconfirmed by theoretical and numerical simulationsfor Algols with disks by Van Rensbergen and Greve(2016). In other words, accretion is not enough tosustain the observed luminosity of the disks in thesesystems.

7.0 7.5 8.0 8.5 9.0 9.5100

1000

7.0 7.5 8.0 8.5 9.0 9.5

0.1

1

10

100

1000

iDP

V

HD

170

582

V39

3 S

co

DQ

Vel

AU

Mon

L d(L

sun)

L da c

c (L

sun)

Mh(Msun)

Fig. 8. The bottom panel shows the accretion lumi-nosity for DPVs, as derived from the mass transferrate of the best binary model for the present systemand stellar parameters. The upper panel shows thedisc luminosity inferred from the light curve analysis.iDPV stands for OGLE05155332-6925581. FromMennickent et al. (2015).

Once the idea of a hotspot wind was settleddown, it was necessary to look for a mechanism ableto modulate the strength of this wind. This leadus to the study of magnetic dynamos as possiblecause for such a variability. But before going tothis mechanism, let’s put face to face the modu-lated bipolar wind (e.g. Mennickent et al. 2012bfor V 393 Sco) and the occultation by a circumbinarydisc (e.g. Desmet et al. 2010 for AU Mon) as com-petent hypotheses to explain the long cycle.

6. EQUATORIAL OUTFLOWSAND CIRCUMBINARY DISC

In the above Section we have presented a solidevidence for the existence of circumbinary matter inthe form of bipolar outflows in some Algols. How-ever, evidence for equatorial outflows has also beenreported in the literature. Especially interesting arethe reports of material escaping through the La-grangian L2 and L3 points (see Flora and Hack(1975) for evidence of L2 outflows in β Lyrae andPeters (1989) for evidence of L3 outflows in severalsystems). These outflows are also expected fromnumerical simulations (Bisikalo et al. 1998, 1999,2000, 2003). Mennickent et al. (2010) report ul-traviolet and high-resolution infrared spectroscopyof V 393 Sco; they observe lines asymmetries at sec-ondary eclipse during long cycle minimum compati-ble with large mass loss through the L3 point. Ac-cording to these authors, the large asymmetries ob-served in the He I 1083 nm line at orbital phases 0.54and 0.94 cannot be explained by blends with donorfeatures, but require other explanation, possibly anequatorial outflow (Fig. 9). Since these asymmetriesonly appear in infrared lines not in super-ionized ul-traviolet lines, these authors suggest that the ultra-violet lines form in a wind above the orbital plane,consistent with the bipolar wind scenario discussed inthe above section. A similar outflow signature nearphase 0.5 was observed in the Si IV line by Peters(1994) in AU Mon.

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1081 1082 1083 1084 1085 1086

norm

aliz

ed fl

ux +

con

stant

wavelength (nm)

0.54

0.94

Fig. 9. The asymmetries observed in the He I 1083nm line of V 393 Sco at orbital phases 0.54 and 0.94cannot be explained only by blending with donor fea-tures (dashed lines). Mass flows are a possible inter-pretation. From Mennickent et al. (2010).

14

LONG PHOTOMETRIC CYCLES IN HOT ALGOLS

Desmet et al. (2010) propose that a dustycircumbinary disc occults AU Mon during the mini-mum of the long-cycle and argue that this scenarioexplains the equal depth of main minima at max-imum and minimum of the long-cycle. We notice,however, that it hardly explains the larger Hα emis-sion observed during the maximum of the long-cycle,when the circumbinary disk is expected to disappear(Barŕıa and Mennickent 2011). In general terms, oc-cultation by a circumbinary disc does not explain thedeeper primary minima observed during the long cy-cle minimum in a couple of LMC DPVs by Poleskiet al. (2010). These observations are compatiblewith clearing of the system at minimum, and an ex-tra light during maximum, as should happen with anenhanced bipolar wind at maximum. The large andbroad emission lines observed during the secondaryeclipse in V 393 Sco were attributed to such a wind(Fig. 10), and it is difficult to image how they couldbe produced by a circumbinary disc.

We conjecture that equatorial outflows reallyoccur in some systems, but are of second order ofimportance compared with the outflows related tothe hotspot. An artistic view of a Double PeriodicVariable is shown in Fig. 11.

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

-1000 -500 0 500 1000

norm

aliz

ed fl

ux

velocity (km/s)

0.45, 0.07, 30.55, 0.25, 2

0.49-0.54, 0.34, 110.48, 0.65, 30.50, 0.77, 3

vsini = 415 km/s

Fig. 10. Donor-subtracted Hα profiles of V 393 Sconear the secondary eclipse at different long-cyclephases. The labels indicate, from left to right, theorbital phase, long-cycle phase and number of spec-tra averaged. A synthetic profile of the gainer also isshown. X-axis velocities are with respect to the sys-tem centre of mass. From Mennickent et al. (2012b).

Fig. 11. Artistic view of a Double Periodic Variable (credits Cristobal Sandoval).

15

R. E. MENNICKENT

7. MAGNETIC DYNAMOS IN DPVs

Recently, a model for the DPV long cycle hasbeen proposed by Schleicher and Mennickent (2017)based on Applegate‘s (1992) mechanism. Apple-gate’s mechanism considers torques produced by thestar magnetic field into the outer stellar layers, pro-ducing a change in the star’s oblateness with a conse-quence on the distribution of its angular momentum.This affects the overall angular momentum of the bi-nary, producing a change in the orbital period of theorder of ∆P/P ∼ 10−5. Hence, the magnetic cyclein a chromospherically active donor produces struc-tural changes in the star, especially its quadrupolemomentum, yielding larger size in the direction of theinner Lagrangian point at some epochs, and eventu-ally producing larger mass transfer rates if the binaryis semidetached, and this is possibly observable bychanges in the system luminosity. Actually, a poten-tial impact of magnetic activity on mass transfer hasalready been discussed by Bolton (1989) and Mein-tjes (2004) for Algol-type binary systems. Indirectevidence for the Applegate mechanism in binary sys-tems includes the fact that orbital period variationsonly occur in late-type stars, as originally found byHall (1989) and the relation between activity cyclesand O-C modulation periods, as inferred by Lanzaand Rodono (2004) and Lanza et al. (2001).

The work presented by Schleicher and Men-nickent (2017) is largely inspired in the discovery ofa potential relationship between the dynamo num-ber and the rotational velocity of chromosphericallyactive stars. The dynamo number is a parametercentral to stellar dynamo theory and it is definedas D = α∆Ωd3/η2, where α is a measure of helic-ity, ∆Ω the large-scale differential rotation, d thecharacteristic length scale of convection and η theturbulent magnetic diffusivity in the star. In thecontext of dynamo models, the dynamo cycle Pcycleis related to the rotation period Prot via a relationof the form (Soon et al. 1993, Baliunas et al. 1996):

Pcycle = DαProt, (3)

with D the dynamo number and α a power-law in-dex, with typical values of α between ∼ 13 and ∼

56 .

Similar phenomenological relations were reported forsingle stars (e.g. Saar and Brandenburg 1999).

Assuming synchronous rotation of the donorstar in a close binary, Schleicher and Mennickent(2017) derive a similar relationship between the dy-namo cycle and the orbital period of the binary:

Pcycle = ηPorb, (4)

with η a factor involving physical parameter of thedonor as luminosity, mass, radius, pressure scaleheight and mixing length. Then they propose thatthe long cycle length of DPVs corresponds to adynamo cycle. Furthermore, they calculate theexpected mass transfer rate changes due to stel-lar quadrupole moment as predicted in Applegate’smodel, specifically employing the framework outlined

by Völschow (2016). This mechanism thus corre-sponds to a modulation of the mass transfer rateand can give rise to a cyclic variation of the sys-tem luminosity. Comparison with observed valuesof Pcycle/Porb gives acceptable results (Fig. 12) andthey conclude that a magnetic dynamo in the donorcan potentially explain the long-term variability ob-served in DPVs (Schleicher and Mennickent 2017).

10

20

30

40

50 60 70 80

100

150

3 4 5 6 7 8 9 10 15 20 30 40

Ratio long to o

rbital period

Orbital period [days]

modelobserved

Fig. 12. Ratio of the long to the orbital periodas a function of the orbital period based on observa-tions and the dynamo model. From Schleicher andMennickent (2017).

8. POORLY STUDIED PHENOMENA

Here we provide a brief introduction for someinteresting and still unexplained phenomena ob-served in DPVs. Certainly, they deserve further at-tention, both from the observational as well as theo-retical point of view.

8.1. Loop in the color-magnitude (CM)diagram

After disentangling the long and short pho-tometric cycles a loop in the CM diagram is ob-served during the long cycle of OGLE05155332-692558; the star rises to the maximum through theblue branch and descends to the minimum throughthe red branch; this was interpreted in terms ofmass loss cycles (Mennickent et al. 2008). Ex-tensive and multi-wavelength photometric coverageof several targets is essential to clarify this phe-nomenon. This CM loop has only been documentedin one DPV, but the whole OGLE database mightbe scanned to study further this phenomenon thatmimics the loops observed in the eruptive cycles ofsome Be stars (de Wit et al. 2006). Color informa-tion for the LMC and SMC DPVs can be provided bythe MACHO and EROS projects. Multi-band pho-tometric monitoring of bright Galactic DPVs can bedone even with small size telescopes.

16

LONG PHOTOMETRIC CYCLES IN HOT ALGOLS

8.2. Discrete absorption components(DACs)

They were reported in HI infrared lines ofOGLE05155332-6925581 following some orbital pat-terns (Mennickent et al. 2008) and also in somemetallic lines of V 393 Sco (Mennickent et al. 2012b).In V 393 Sco a forest of blue-shifted and red-shiftedDACs at the O I 7773 and Si II 6347 lines roughly fol-lows the donor RV during the orbital cycle whilea few of them remain stationary. DACs sometimesdrops 5% below the continuum and are better visiblein the first part of the orbital cycle. It is not clearhow general this phenomenon is among DPVs neitherits origin. High signal to noise spectra sampling theorbital cycle are needed to clarify this phenomenon.

8.3. Chromospheric emission

Chromospheric emission was detected inV 393 Scorpii from Doppler maps of Mg II 4482 andC I 6588 (Mennickent et al. 2012b). Spectra withhigh signal to noise ratio and good disentangling ofadditional spectral features (e.g. those of the hotstar and the circumprimary disk) are needed to re-veal these lines. It is not clear what is the incidenceof chromospheric emission in DPVs but seems to bea relatively common phenomenon in Algols (Sarna etal. 1998, Richards et al. 2012). If the hypothesis ofmagnetic cycles mentioned in Section 7 is true, thenwe should expect chromospheric emission in manyDPVs.

8.4. Weird light curves

OGLE-LMC-DPV-097 shows deeper primaryeclipses and the disappearance of secondary eclipsesduring long cycle minimum (Poleski et al. 2010).OGLE-LMC-DPV-065 shows a decline of the longcycle length from 280 to 215 days in 4200 days(Poleski et al. 2010). As mentioned previously,OGLE05155332-6925581 also shows a remarkableslow shortening of the long cycle from 188 to 172days lasting about 1800 days, and this shorteningoccurs after 12 relatively stable oscillations. Thesestill unexplained phenomena are rare in DPVs, butcould place constrains on competing models for thelong cycle.

8.5. Additional frequencies

The existence of multiple frequencies in theLMC DPVs was reported by Buchler et al. (2009).They re-investigated the MACHO photometry for 30DPVs selected by Mennickent et al. (2003) and re-vealed that in 11 of these objects, besides the twomost prominent frequencies also a sum of these fre-quencies f1 + f2 is significant in the time series anal-ysis. They found a linear relation among the threedominant frequencies. According to these authors,an explanation of this relation requires an interplaybetween the binary motion and that of a third ob-ject. However, spectroscopic monitoring of several

DPVs does not reveal a third body (e.g. Desmet etal. 2010, Mennickent et al. 2012a). From 125 LMCDPVs, Poleski et al. (2010) found combination fre-quencies (not only the most common combinationf1 + f2) in 36 cases (29% of the sample). They alsoconfirmed 5 of the 10 LMC DPVs reported with sumfrequencies by Buchler et al. (2009). They note thatthe detected combination frequency can be sensitiveto pre-whitening frequency, period uncertainty andnumber of harmonics used.

A short periodicity of 5.26 days was also foundin the residuals of the V -band light curve of DQ Velby Barŕıa et al. (2013) who interpreted it as a pul-sation of a slowly pulsating B-type (SPB) gainer.Desmet et al. (2010) discovered rapid and peri-odic light changes visible in the high-quality residualCoRoT light curves of AU Mon, at sub-orbital fre-quencies of 10.4 and 8.3 c/d. They state that the os-cillations are probably due to a non-uniform bright-ness distribution seated in the accretion disc. Out-side the primary minima of the CoRoT light curve,they detected signals in the expected frequency do-main of B-stars. According to these authors, bothcombination frequencies as well as sub-orbital peri-odicities have an uncertain origin. At present, it isnot clear if these frequencies are related to the long-cycle phenomenon or are independent signatures re-lated to other cause.

9. EVOLUTIONARY ASPECTS

If DPVs are near impact systems, the gainershould be rotating near the critical velocity, since thisspin-up process seems to occurs rapidly (Dervişoǧluet al. 2010, Packet 1981). If the gainer cannotaccrete more material the presence of the disk isexplained. The DPV phenomenon, interpreted ascyclic mass loss from the system (Mennickent etal. 2008) is hence consistent with the incapacity ofthe gainer of accreting more material. Evolutionarytracks for the masses of the donor and gainer andfor the orbital period are illustrated in Fig. 13. It isinteresting to notice that after the DPV phase thedonor will decrease its mass (and luminosity), theorbital period will increase and the system will con-sist of a rapidly rotating B-type gainer and a low-mass secondary star. Therefore, it is possible thatsome Be stars have passed through this evolution-ary route, accelerating the gainer in a past processof mass transfer. This does not necessarily meansthat the Be star disc is a remanent of the interact-ing phase, since formation and ejection of envelopesis usual in Be stars, but the scenario could in prin-ciple explain the stellar rapid rotation. Spin-up ofgainers in the Roche lobe overflow binaries as ori-gin of Be stars was proposed by Pols et al. (1991)and discussed by Gies (2007). Whereas not all Bestars show signs of binarity until now (Rivinius et al.2013), more and more Be stars are suspected to be bi-naries with faint companions (Klement et al. 2017).DPVs might be the progenitors of at least some ofthe Be stars, but more work is necessary to clarifythe true descendants of the DPV phenomenon.

17

R. E. MENNICKENT

10. FUTURE RESEARCH

A future line of research is to investigate thepresence of magnetic fields in DPVs. Under the viewof the dynamo model, one should expect modula-tions in field strength through the cycles, revealedfor instance in changes in the strength of chromo-spherically excited emission lines or in the degreeof polarization of the light or in the intensity ofchromospheric radio emission. To search for corre-lations of these parameters with the long cycle is apossible route of future investigation. Some openquestions are: if the Applegate mechanism acts inDPVs producing long cycles does it also operate inother Algols, and are there observational manifes-tations? What are the conditions for the dynamomechanism to operate? We conjecture that duringthe mass transfer stage, typically lasting ∼ 10.000years, changes of donor inner structure are enough totrigger the Applegate dynamo only at certain epochs;this should explain why some semidetached Algolsdo not show long-cycles. Are there other evolution-ary stages where the dynamo and/or the Applegatemechanism are effectively hidden, due to a mass ac-cretion rate that is too small to still observe its mod-ulation? What is the role played by the opticallythick disc and the tangential impact condition of thegainer in the DPV phenomenon?

6 0 7 0 8 0 9 0

123456789

d o n o rg a i n e r P O

A g e ( M y r )

Mass

(Msu

n)

B e s t a r ?

D P VV 3 9 3 S c o

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

P O (d

ays)

Fig. 13. Evolutionary tracks for V 393 Scorpii(Mennickent et al. 2012a) resulting of a search inthe grid of synthetic models of Van Rensbergen et al.(2008). The vertical dashed line represents the cur-rent state of V 393 Scorpii. Episodes of rapid masstransfer are characterized by rapid changes in stellarmasses. In the future, V 393 Scorpii might look like aclassical Be star, with a hidden low-mass companion.From Mennickent (2012).

Acknowledgements – My research on DPVs has beenpossible due to the appreciated contribution of manycollaborators during the years, but is not possible toname all of them here. I especially acknowledge Go-jko Djurašević for his hospitality in Belgrade and formodeling the DPV light curves. I also thank Zbig-niew Kolaczkowski for his hospitality in Wroclawand valuable help with data reduction and analy-

sis. I thank hospitality and scientific discussions withPavel Koubsky and Petr Harmanec during my stayin Prague. I also thank Dominik Schleicher for hiscontribution with theoretical aspects of Double Pe-riodic Variables. Thanks to Gojko Djurašević, PetrHarmanec, Geraldine Peters and Dominik Schleicherfor reading a first version of this manuscript and forproviding comments that helped to improve this pa-per. Any remaining error or omission in the text isof my exclusive responsibility. Thanks to MauricioCabezas for making Fig. 4 and Cristobal Sandovalfor the artistic illustration shown in Fig. 11. I alsoacknowledge support by the BASAL Centro de As-trof́ısica y Tecnoloǵıas Afines (CATA) PFB–06/2007and VRID-Enlace 216.016.002-1.0.

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