gamma Cas stars: Normal Be stars with disks impacted by the wind of a helium-star companion?
N. Langer, D. Baade, J. Bodensteiner, J. Greiner, Th. Rivinius, Ch. Martayan, C.C. Borre
AAstronomy & Astrophysics manuscript no. gCas-resub c (cid:13)
ESO 2019November 18, 2019 γ Cas stars: Normal Be stars with disks impacted bythe wind of a helium-star companion?
N. Langer , , D. Baade , J. Bodensteiner , J. Greiner , Th. Rivinius , Ch. Martayan , and C.C. Borre Argelander Institut für Astronomie der Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germanye-mail: [email protected] Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany European Organisation for Astronomical Research in the Southern Hemisphere (ESO), Karl-Schwarzschild-Str. 2, 85748 Garchingb. München, Germanye-mail: [email protected] Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, Bus 2401, 3001 Leuven, Belgiume-mail: [email protected] Max-Planck-Institut für extraterrestrische Physik, Giessenbachstr. 1, 85748 Garching b. Münchene-mail: [email protected] European Organisation for Astronomical Research in the Southern Hemisphere (ESO), Casilla 19001, Santiago, Chilee-mail: [email protected], [email protected] Stellar Astrophysics Centre, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmarke-mail: [email protected]
Received; accepted
ABSTRACT γ Cas stars are a ∼
1% minority among classical Be stars with hard ( ≥ ff ect, or by accretion onto a white dwarf (WD)companion. In view of the growing number of identified γ Cas stars and the only imperfect matches between these suggestions and theobservations, alternative models should be pursued. Two of the three best-observed γ Cas stars, γ Cas itself and π Aqr, have a low-masscompanion with low optical flux; interferometry of BZ Cru is inconclusive. Binary-evolution models are examined for their abilityto produce such systems. The OB + He-star stage of post-mass transfer binaries, which is otherwise observationally unaccounted, canpotentially reproduce many observed properties of γ Cas stars. The interaction of the fast wind of helium stars with the circumstellardisk and / or with the wind of Be stars may give rise to the production of hard X-rays. While not modelling this process, it is shownthat the energy budget is favourable, and that the wind velocities may lead to hard X-rays as observed in γ Cas stars. Furthermore,the observed number of these objects appears to be consistent with the evolutionary models. Within the Be + He-star binary model,the Be stars in γ -Cas stars are conventional classical Be stars. They are encompassed by O-star + Wolf-Rayet systems towards highermass, where no stable Be decretion disks exist, and by Be + sdO systems at lower mass where the sdO winds may be too weak to causethe γ Cas phenomenon. In decreasing order of the helium-star mass, the descendants could be Be + black-hole, Be + NS or Be + WDbinaries. The interaction between the helium-star wind and the disk may provide new diagnostics of the outer disk.
Key words.
Stars: emission-line, Be – stars: circumstellar matter – stars: evolution – binaries: general – X-rays: stars – stars -individual: γ Cas, BZ Cru, π Aqr
1. Introduction
Many of the most rapidly rotating non-supergiant B, late O, andearly A stars exhibit H α line emission (Zorec & Briot 1997;Yudin 2001). Typically, the emission lines form in a Keple-rian disk and the central stars rotate at very roughly 80% ofthe critical velocity (Meilland et al. 2012). Stars with theseproperties are commonly called (classical) Be stars which werebroadly reviewed by Rivinius et al. (2013). The Be Star Spectradatabase (BeSS, Neiner et al. 2011) lists nearly 250 Be starswith v ≤ ffi cient initial supply (as found by Martayan et al. 2007),could eventually lead to critical rotation (Granada et al. 2013;Brott et al. 2011). As explained by Rímulo et al. (2018, theirSect. 5.2.5 and references therein), Be stars can avert the possiblepermanent angular-momentum crisis by the viscous decretion ofmatter and associated angular momentum. Viscosity can enablethe formation of a Keplerian disk by redistributing the specificangular momentum of ejected matter such that a ∼
1% fractionreaches Keplerian velocities and the rest falls back to the star(Lee et al. 1991). The variability of the mass content of the diskmay provide a means to estimate the amount of angular momen-tum lost along with the matter (Ghoreyshi et al. 2018; Rímuloet al. 2018).
Article number, page 1 of 16 a r X i v : . [ a s t r o - ph . S R ] N ov & A proofs: manuscript no. gCas-resub
An obvious alternative mechanism to spin up Be stars is masstransfer in a binary. In fact, in some classical Be stars hot sublu-minous companions have been found (Peters et al. 2016; Wanget al. 2018, for other examples see below) so that the high spinrate of the B star may be the result of mass transfer from thecompanion, which initially was the more massive star. The ef-fectiveness of viscous decretion to build Keplerian disks is un-a ff ected by su ffi ciently distant companion stars. Therefore, vis-cous decretion is thought to be a universal property of Be starsbecause Be stars with known short orbital periods are very rare(however, it is well possible that the frequency of such systems isreduced if the formation of stable decretion disks is hindered bythe companion). For viscous decretion being able to form Keple-rian disks, it must be supplied with matter by a stellar mass-lossprocess. The ubiquity of nonradial pulsations (NRPs) in Be stars(Rivinius et al. 2013; Baade et al. 2017; Semaan et al. 2018)and the co-phasing of apparent mass-loss events with maxima ofthe vectorial amplitude sum of multiple pulsation modes (Baadeet al. 2018) suggest strongly to search for the root of the massloss in multi-mode NRPs in single as well as binary Be stars.Most probably, single- as well binary-star formation channelsof Be stars are also realised by nature, either alone or in com-bination. This paper considers the binary channel only, withoutimplication for the single-star channel.Since the X-ray luminosity of OB stars is proportional totheir bolometric luminosity (Güdel & Nazé 2009), X-rays dueto shocks in the winds are not an important property of isolatedBe stars (Cohen et al. 1997). A possible small X-ray excess in Bestars w.r.t. normal B stars (Cohen 2000) may be due to additionalshocks in the interface region between wind and disk. However,some binary Be stars do reveal themselves through prominent,often strongly modulated X-ray emission. In the vast majorityof these Be X-ray binaries (BeXRBs, Reig 2011), a neutron staraccretes matter when it passes through or close to the Be star’scircumstellar disk, and part of the gravitational energy releasedin the accretion process is emitted in the X-ray domain. Whilethe X-ray flux of all BeXRB detected in early surveys is pulsed,systematic searches in nearby galaxies are beginning to identifysources without short periods (Haberl & Sturm 2016); either theyare genuinely aperiodic, or the periods were not found becausethey are too long to be easily determined.A second subclass, which accounts for ∼
1% of all classicalBe stars, is also identified on the basis of X-ray properties (Smithet al. 2016a; Nazé & Motch 2018). These stars emit unusuallyhard ( ≥ γ Cas. Accordingly, the other members are often called γ Casstars. γ Cas is also the first Be star that was discovered (Secchi1866). For this reason, γ Cas is considered by some as the pro-totype of Be stars (for instance the General Catalog of VariableStars, Samus’ et al. 2017, calls all Be stars ‘GCAS’ (or ’BE’)stars). However, γ Cas has a number of observed properties thatonly few Be stars share (Harmanec 2002) although it is not clearto what extent this is due to the particularly rich database. Themost important di ff erence is the mentioned X-ray flux.Because the X-ray properties of γ Cas do not match any con-ventional category of X-ray sources in early-type stars, Smithand collaborators (see Smith et al. 2016a, for references) have,in a long series of papers, developed the unconventional notionthat the X-rays from γ Cas result from the interplay between twomagnetic fields, one at the stellar surface and the other in the disk. Both are said to be not observationally detectable becauseof their small spatial scales. Nevertheless, there seems to be theassociated hope (Motch et al. 2015) that this model, which in thefollowing will be called the magnetic model for short, may even-tually explain Be stars at large. Because of the small fraction ofBe stars with γ Cas-like X-ray properties and the elusiveness ofdirect observational evidence for the suggested magnetic fields,it is important that no mistake is made with any extrapolatinggeneralisation.This paper will develop a completely di ff erent concept to ex-plain γ Cas stars which has little implication for the majority ofBe stars. It incorporates without restriction the general picturethat has been sketched above of classical Be stars so that γ Casstars are ordinary Be stars with some additional properties. Theproposed main di ff erence is the response of the circumstellarBe disk and / or the Be wind to the impact of a fast wind froma helium-star companion.For a better understanding, the key properties of the cur-rently most prominent γ Cas stars, namely γ Cas itself, π Aqr,and BZ Cru, are recalled in Sect. 2. Section 3 describes the mag-netic model in more detail as well as the white-dwarf (Tsuji-moto et al. 2018) and the magnetic-neutron-star propeller model(Postnov et al. 2017) that were recently proposed as alternatives.Because γ Cas and π Aqr are binaries, the role of binarity in Bestars is reviewed in the context of extent observations (Sect. 4)and evolutionary models (Sect. 5). The conclusions are bundledin Sect. 6.
2. Observed properties of γ Cas stars
At this moment, a Be star is admitted to the γ Cas family onthe basis of its X-ray flux if the latter is hard (L(2-10 keV) / L(0.5-2 keV) > X / L bol ) ∼ –6), andthermal (Nazé & Motch 2018). These selection criteria havemostly identified stars in the narrow spectral-type range of B0.5to B1.5 (with luminosity classes V-III), although some excep-tions are beginning to be reported (Nazé & Motch 2018). The0.1-10 keV X-ray luminosity is intermediate between noninter-acting Be stars and BeXRBs. Table 1 reproduces the main prop-erties of the ∼
15 currently known γ Cas stars as compiled byNazé & Motch (2018). A very useful account of the X-ray prop-erties of γ Cas stars and possibly related objects is available fromTsujimoto et al. (2018).The individual characteristics of the three best-observed rep-resentatives are outlined in the following subsections. γ Cas
After the first detection of X-rays from γ Cas (Jernigan 1976),there was not much of an alternative to a classification as aBeXRB. However, the lack of pulsing (Parmar et al. 1993)and regularly repeating X-ray outbursts when a putative com-pact companion would in its (eccentric) orbit accrete mat-ter from the Be disk (Okazaki & Negueruela 2001) castdoubts on the origin of the X-rays, and the nature of γ Cas( = HR 264 = HD 5394 = HIP 4427) has been controversial eversince. γ Cas was also one of the first Be stars in which discrete ab-sorption components (DACs) of UV resonance lines were dis-covered (Henrichs et al. 1983). DACs are nearly universal in lu-minous OB stars (Howarth & Prinja 1989) and usually attributedto corotating interaction regions in the wind that originate from
Article number, page 2 of 16. Langer et al.: γ Cas stars: Normal Be stars with disks impacted by the wind of a helium-star companion?
Table 1.
Key observational data for the known γ Cas stars taken from Nazé & Motch (2018, their Table 5). Soft and hard X-ray fluxes refer to the0.5-2.0 keV and 2.0-10.0 keV intervals, respectively.
No. Name Spectral Type log( L X / L bol ) L X L X , hard hardness ratio kT v sin i erg / s 10 erg / s keV km / s1 γ Cas B0IV-Vpe -5.39 85.0 65.1 3.25 14–25 2953 V782 Cas B2.5III:[n]e + -5.25 30.3 29.9 63.1 717 PZ Gem(high) O9pe -6.14 9.66 7.87 4.32 16 26526 HD90563 B2Ve -5.85 32.034 BZ Cru B0.5IVpe -5.69 27.6 20.3 2.81 13 33837 HD119682 B0Ve -5.63 66.7 47.9 2.55 8-17 20039 V767 Cen B2Ve -5.37 26.2 17.4 1.97 6 10040 CQ Cir B1Ve -4.30 175 147 5.26 9 33547 V759 Ara B2Vne -5.29 41.9 31.9 3.21 10 27751 V3892 Sgr Oe -5.78 30.8 21.2 2.24 7-14 26053 V771 Sgr B3 / π Aqr B1Ve -5.59 7.44 5.80 3.56 12 24383 V810 Cas B1npe -5.14 48.4 41.1 5.58 64 422the high intrinsic instability of the wind, perhaps triggered byphotospheric inhomogeneities (Cranmer & Owocki 1996). Theazimuthal propagation of the interaction regions may lead to amodulation of X-ray flux resulting from shocks in the wind (Os-kinova et al. 2001). Because of their ubiquity in luminous starswith radiatively driven winds, the DACs in γ Cas do not revealanything specific about the properties of this star, except that itsmass-loss process and wind are perfectly normal for an early-type Be star.Four periods have been reported for γ Cas and used in var-ious attempts to identify the nature of this star’s X-ray activity.The orbital period of ∼ ∼ α emission-line profiles (Miroshnichenko et al. 2002;Nemravová et al. 2012). Although major long-term correctionsare required and the radial velocity of the disk is not the same asthat of one of the two stars, neither the value of the period nor itsnature are disputed. The orbital period was also found in the tem-porarily flat top of the H α emission-line profile (Borre et al., inprep.), which is probably orbitally modulated by the interactionof the companion with the (spiral) disk structure (cf. Panoglouet al. 2018). Harmanec et al. (2000) propose a likely mass rangeof the primary between 13 and 18 M (cid:12) .The nature of the companion is not well constrained. Themass is about one solar unit, and Nemravová et al. (2012) sug-gested that it might be a helium star. Miroshnichenko et al.(2002) find inhomogeneities in the disk and consider as one pos-sible explanation that H α -emitting material is associated withthe secondary. In search for a spectral signature of the secondary,Wang et al. (2017) cross-correlated the UV spectrum with modelsdO spectra. However, this e ff ort failed because the very hot pri-mary dominated the cross-correlation function which, moreover,is very broad due to the rapid rotation of the B-star primary.Probably because of the unfavourable magnitude di ff erence atthe wavelengths used, long-baseline H α (Tycner et al. 2006) andK-band (Gies et al. 2007) interferometry has not detected thecompanion either. However, the circumstellar disk was resolvedand and the derived inclination angles of 55 ◦ and 51 ◦ , respec-tively, are in very good agreement. With primary, we designate the brighter of the two stars in a binary.
For 15 years, a 1.216-d period was seen in single-site ground-based photometry (Henry & Smith 2012) but eventually droppedbelow the detection threshold of very few mmag. Both the fre-quency and the decay in amplitude of this second periodic vari-ability were also found in SMEI space photometry (Borre etal., in prep.). Later space photometry with BRITE-Constellationconfirmed the absence of the 1.216-d period at the 2-3-mmaglevel (Baade et al. 2017, Borre et al., in prep.). Instead, BRITEdetected a very nearly, but probably not perfectly, three timesshorter third period at 0.403 d (frequency: 2.48 c / d) with a peak-to-peak amplitude slowly varying between ∼ ∼ / d in the SMEI observations (Borre et al.,in prep.). An attempt was made to use Doppler shifts of the 2.5-c / d frequency to locate the site of the variability in the system.However, the time baseline of the BRITE data was too short,and the systematic noise of the SMEI observations was too large(Borre et al., in prep.).The long-term constancy of the three short periods implieseither rotation or pulsation as their origin. Rotationally inducedvariability with period P would require some physical propertyto vary along the star’s circumference with an azimuthal scale of( P / P rot ) × π . For instance, temperature, abundances or magneticstructures. There is no such report for γ Cas (apart from the opti-cal broad-band flux). Radial pulsations are not known in Be starsbut both short periods are well within the range of NRPs foundin other Be stars (Rivinius et al. 2016; Baade et al. 2017; Semaanet al. 2018). Since the 1.216 d variability faded while the 0.403 dvariability rose, it is plausible to believe that both are of the samenature, which can, then, only be NRPs. In fact, space photometry(Rivinius et al. 2016; Baade et al. 2017; Semaan et al. 2018) hasdetected multiple low-order NRP modes in many Be stars overthe full range of B-type stars.Ongoing and forthcoming large-scale photometric surveysfrom space will show how typical (multi-mode) NRP is for Bestars. If the pulsation properties of Be stars are di ff erent fromthose of Bn stars (very rapidly rotating B-type stars identifiedthrough their equator-on orientation but not known to have ex-hibited emission lines, i.e., not possessing a circumstellar disk),this would be a strong indicator that NRPs are a defining prop-erty of Be stars, probably through their involvement in mass-lossevents feeding the disk. Article number, page 3 of 16 & A proofs: manuscript no. gCas-resub
Additional periods may be hidden in complex spectroscopicline-profile variability. In agreement with quite similar observa-tions in other early-type stars, Yang et al. (1988) and Horaguchiet al. (1994) attributed such variability in optical absorption linesalso of γ Cas to high-order NRP. Intermediate- to higher-orderNRP modes were also deduced from long series of spectra ofother Be stars (e.g., Reid et al. 1993; Kambe et al. 1997), includ-ing π Aqr (Peters & Gies 2005). Smith et al. (2016a) rejected theNRP hypothesis for γ Cas because they found the variations ofUV lines to be erratic and each migrating subfeature in the lineprofiles to maintain its identity for no more than very few hours.However, the 30 hours, i.e. only about one rotational pe-riod, of HST spectroscopy considered by Smith et al. (2016a)are without doubt insu ffi cient for the proper tracking of featureswith similar but di ff erent propagation rates and for the determi-nation of their periods. Accordingly, the suggestion by Smithet al. (1998) that the subfeatures are only rotationally advectedis lacking a solid observational foundation. By contrast, Walkeret al. (2005) observed ζ Oph (O9.5 Ve) for 24 days with the
MOST space photometer and during 17 of these 24 days withthree spectrographs at di ff erent geographical longitudes. Theydetected at least a dozen photometric and eight spectroscopicperiods. Six periods were in common to both datasets and in-terpreted as intermediate-order NRPs. An obvious rotation pe-riod was not identified, and the multi-periodicity of the migratingsubfeatures rules out the rotational hypothesis for them.In addition to the three genuine periods in γ Cas, thereare also cyclic optical broad-band flux variations on seasonallychanging timescales around 70 d with a total range of 50-91 d.The peak-to-peak amplitude of ∼ .
02 mag is not too far from thesensitivity threshold to so slow variations of single-site ground-based photometry. Robinson et al. (2002) combined the earliercycles into a single sinusoid with adaptive period and comparedthis variable-stretch pseudo-sine curve of optical light to the X-ray flux. They derived a correlation in the variability of the twodomains using only two photometric seasons and just six epochsof X-ray data. Since the pseudo-sine curve interpolates the lightcurve, the e ff ective comparison is between seasonally fragmen-tary optical-flux and very patchy X-ray observations. There is noassurance that such a data treatment can lead to a stress-resistantconclusion.From just one day of simultaneous X-ray and UV observa-tions, Smith and collaborators (for references see Smith et al.2016a) inferred correlations between X-ray flux on the one handand UV flux, UV spectral lines, etc. on the other. However, itis not clear that coincidences of two features each in two shortdatasets can carry high weight in an object that in all observedwavelength regions is variable on all timescales. More signifi-cant is the correlation over 15 years between X-ray and opticalflux reported by Motch et al. (2015) although it is not clear whiche ff ect the choice of the time windows has. From their compari-son, these authors conclude that the X-rays lag the optical fluxby no more than a month. Because the radial drift velocity ofmatter in Be disks is only of the order of a few km / s (Riviniuset al. 1999), the time delay of X-ray emission due to accretionby a companion at an au-scale distance would be much longer.By contrast, a lag by only a month is more plausible if it takesa month for the disk to build up and the interaction between thetwo postulated magnetic fields to commence.However, in the cross-correlation function, there is a broadand not well separated peak near three years. In view of this net-work of claimed correlations, it surprises that the purported rota-tion period has not been seen modulating any observable (otherthan the optical flux). Lopes de Oliveira et al. (2010) emphasised the need formulti-component fits of the continuum X-ray flux distribution.From high-spectral-resolution XMM-Newton observations witha complex emission-line spectrum, they derived optically thinthermal emissions at four discrete temperatures, namely 12-14 keV, perhaps at 2.4 keV, and with confidence at 0.6 and0.11 keV. From observations between 0.6 and 100 keV, Shraderet al. (2015) firmly rule out any power-law component andthereby confirm the thermal nature of the X-ray flux. Smith et al.(2012b) report that after an apparent mass-loss event (ejectionof matter into the disk), an absorbing layer developed temporar-ily, indicating the presence of additional matter along the line ofsight. Temperature contrasts are also evidenced by spectral lines(Lopes de Oliveira et al. 2010; Smith et al. 2012b).Using independent observations, Tsujimoto et al. (2018) ba-sically agree with the stated decomposition of the X-ray con-tinuum. They also confirm that changes in the hardness ratioare only weakly coupled to flux variations, which mainly oc-cur in the hottest plasma above 4 keV while the softer X-rays aremore stable and are most of the time only negligibly absorbed.A new finding though are dips in softness, especially of the ratio[0.5-2 keV] / [4-9 keV], which last a few ks. Because these dipsare unrelated to flux increases in the hard band, Tsujimoto et al.(2018) conclude that these fadings are caused by absorption intemporarily intervening matter. This is consistent with the sim-ilar picture derived by Smith et al. (2012b) from X-ray obser-vations during an outburst of the B star. Adopting the outburstinterpretation, it seems plausible that the X-ray-emitting volumewas (partly) located behind the ejecta. The implied proximity tothe B star would argue, as may be deduced from the time delaysbetween optical and X-ray fluxes, against the X-rays formingnear a companion star at an au-scale distance.In the latest of his papers on γ Cas, Smith (2019) discussesvarious observations once again, o ff ering basically the same in-terpretations. It seems useful to point out that all the old observa-tions were obtained with instruments not employing solid-statedetectors. In those detectors, photons do not merely excite elec-trons (internal photoelectric e ff ect) but lead to the physical emis-sion of electrons (external photoelectric e ff ect), which are sub-sequently amplified and measured. As the result, measurementscan in some cases deviate more from unbiased photon statis-tics than is typical of solid-state detectors. Moreover, physicallyemitted electrons are more susceptible to subtle external pertur-bations. π Aqr
On the basis of its X-ray properties, Nazé et al. (2017) re-cently classified π Aqr ( = HR 8539 = HD 212571 = HIP 110672)as another γ Cas star. The similarity concerns not only the X-ray flux and hardness but also the variability. During the 50 ksobservations with XMM-Newton, several brightenings with abase width of 1-2 ks occurred with pronounced peaks reachingroughly thrice the previous or subsequent level. As in γ Cas, noBeXRB-like outbursts have been observed.After γ Cas itself and BZ Cru (Sect. 2.4), π Aqr became thethird γ Cas star in the Bright Star Catalog (and is moreover equa-torial) so that also for π Aqr a good record of its general prop-erties and variability in other wavelength regions is available.Wisniewski et al. (2010) documented the long-term stability ofthe disk orientation in space by spectropolarimetry. The decreas-ing H α emission strength traced the dissipation of the disk overnearly a decade. Variations in H α equivalent width and contin-uum polarisation also caught a number of outbursts (Wisniewski Article number, page 4 of 16. Langer et al.: γ Cas stars: Normal Be stars with disks impacted by the wind of a helium-star companion? et al. 2010) which are quite typical especially of early-type Bestars (Labadie-Bartz et al. 2018; Bernhard et al. 2018). The oc-currence of DACs in UV wind lines (Smith 2006) is also com-mon among Be stars (Grady et al. 1989).Bjorkman et al. (2002) found that π Aqr is an 84.1-d binary.The mass ratio is about 6:1, which should be more favourable forthe detection of the companion than the ∼ γ Cas. De-pending on the inclination angle, the mass of the secondary maybe between 2.2 and 4.5 M (cid:12) . The orbital motion of the secondarywas derived from a ’travelling emission component’, which theauthors attributed to a gaseous envelope surrounding the sec-ondary. From H α profiles covering ∼
40 orbits, Zharikov et al.(2013) extracted the same period for the violet-to-red ratio V / R of the two emission peaks. Accordingly, the disk structure isphase-locked to the position of the companion. The power spec-trum plotted by Zharikov et al. (2013) does not include the firstharmonic. If this omission is justified, it would mean that anytwo-armed spiral structure (Panoglou et al. 2018) is not axisym-metric, perhaps because one arm strongly dominates (or the twoarms are not 180 degrees apart in disk azimuth). In fact, thestudy identifies an extended region of enhanced H α line emis-sion between the two stars. The strength of this emission followsthe long-term variability of the overall emission strength. As for γ Cas, the cross-correlation technique of Wang et al. (2017) didnot detect the companion to this hot and broad-lined star.Nazé et al. (2017) put forward the argument that the sec-ondary in the π Aqr system is not a compact object itself andthat no such third body is likely to be in a closer orbit than thesecondary. Therefore, they conclude that the X-ray properties of π Aqr and, by implication, γ Cas stars in general are not causedby a compact companion. However, if the interaction of the com-panion with the disk leads to additional H α emission (see alsoBjorkman et al. 2002), more power seems required than is avail-able from an intermediate-mass main-sequence star.As in γ Cas and several other Be stars, NRPs of intermediatedegree ( m =
5) have been deduced from the photospheric line-profile variability of π Aqr (Peters & Gies 2005). Rivinius et al.(2003) observed low-order line-profile variability not matchingthe quadrupole NRP patterns typically seen in Be stars.
The X-ray similarity to γ Cas of BZ Cru( = HR 4830 = HD 110432 = HIP 62027) was established bySmith et al. (2012a). In six visits by the
Rossi X-ray TimingExplorer (RXTE) , each collecting 8-9 hours of observations withthe Proportional Counter Array (Jahoda et al. 1996), well over1000 flares were seen by the authors. With 5-s binning, theycould be as short 2.5 bins and lasted up to more than a minutewith an average rate of about one flare in twenty 5-s bins, i.e.,not far from the confusion limit. As in γ Cas, most of the time,the hardness ratio did not change during the flaring. On twooccasions, the X-ray emission subsided for a few hours. The sixdatasets span only 155 days; yet, the authors derived a ’period’of 226 days. Tsujimoto et al. (2018) applied their models also toBZ Cru. As in the case of γ Cas, they achieved satisfactory fitsof the X-ray flux distribution but could not distinguish betweena nonmagnetic and a magnetic white dwarf.As most other Be and supergiant OB stars with stellar winds,BZ Cru exhibits variable DACs (Smith et al. 2012a). The sameauthors also found intermittent migrating subfeatures in stellarline profiles that, in other OB and Be stars, were attributed tononradial pulsation, but did not report periods. They speculatedabout “magnetically confined clouds” but admitted that this is “not proven”. As mentioned above (Sect. 2.2), such speculationswere disproven in the case of ζ Oph (O9.5 Ve, Walker et al.2005).Smith & Balona (2006) also noted that, if BZ Cru is a mem-ber of NGC 4609, it would be a blue straggler. From a dedi-cated interferometric search, Stee et al. (2013) only derived up-per detection limits for a companion star. The disk had a stronglyasymmetric structure the nature of which could not be firmly es-tablished. Wang et al. (2018) did not detect the signature of ansdO companion in
International Ultraviolet Explorer ( IUE ) UVspectra.
Any attempt to extract commonalities from a sample of justthree, albeit well-studied, representatives must appear presump-tuous. However, relying on Nazé & Motch (2018) for the X-rayproperties of γ Cas stars, the following working description isperhaps broadly agreeable:– Typical spectral subtypes fall into the range B0.5 to B1.5.– The X-ray flux is hard (L(2-10 keV) / L(0.5-2 keV) > X / L bol ) ∼ –5.5), and thermal.– The X-ray flux is variable on timescales from seconds toyears.– Variations in the X-ray hardness ratio are small and mainlydue to the hard component.– There are occasional reductions in the soft X-ray flux, con-sistent with intervening absorbers.– At least on long timescales, X-ray and optical flux variationstrack each other.– There is a lower-mass and optically faint companion (maynot be the case for BZ Cru).– The companion interacts with the Be disk. (The not finallyexplained strong asymmetry of the disk of BZ Cru may becaused by a not otherwise detected companion.)– Intervening absorbers ejected by the B star may localise theX-ray-forming region near the B star, not around the com-panion.
3. Current models for γ Cas stars
In addition to most of the observed properties listed in Sect. 2.5,the magnetic model rests on the assumptions that (i) the 1.216-d period of γ Cas is the rotation period of the B star, (ii) thereis a correlation without major relative shift in time between X-ray and optical flux, (iii) there is a correlation, without o ff sets intime, between X-ray flux and spectral UV features, (iv) the mi-grating subfeatures in spectroscopic line profiles are not causedby nonradial pulsation, and (v) companion stars are irrelevantfor the understanding of γ Cas stars. As seen in Sect. 2, all ofthese assumptions meet with various degrees of doubt and can-not be proved or disproved using currently available observa-tions of γ Cas stars.The magnetic model casts these assumptions into the no-tion of magnetic fields as the common umbrella. Two kinds ofmagnetic field are envisioned. One resides in the star and issaid to arise from sub-surface convection zones (Cantiello &Braithwaite 2011). The other one is pictured to result from theamplification by magneto-rotational instability (MRI; e.g., Sanoet al. 2000) of seed fields in the disk. Circumstellar and stel-lar magnetic field lines are assumed to temporarily connect viafingers extending from the disk towards the star. Because of
Article number, page 5 of 16 & A proofs: manuscript no. gCas-resub the di ff erent rotation rates of star and disk, the field lines arethought to be stretched, eventually disrupted and finally recon-nected. The snapping back of the field lines is suggested to ac-celerate charged particles to high energies dissipated as X-rayswhen they hit the star. Disk instabilities and mass injections fromthe star are seen as the origin of the assumed correlation, with-out much delay, between optical and X-ray flux on the variable70-d timescale. Migrating subfeatures in absorption lines are at-tributed to superphotospheric cloudlets forced into corotation bythe putative magnetic field (Smith et al. 1998). As discussed inSect. 2.2, the empirical basis for this latter belief is deficient.According to Smith et al. (2017), neither the stellar nor thedisk magnetic field postulated by them is directly observable be-cause their structures are thought to be too tangled and small-scale. Therefore, the magnetic model is not a priori in directconflict with a survey of 85 Be stars (incl. γ Cas, π Aqr, andBZ Cru Wade et al. 2016, , Neiner et al., in prep.) which didnot find one star with a large-scale magnetic field whereas fornon-Be early-type stars in the same survey the typical fractionof magnetic stars is about 5-10% (Wade et al. 2016). (A possibleexplanation of this negative result is that a magnetic field woulddestroy a Keplerian disk (ud-Doula et al. 2018) so that magneticBe stars cannot exist. By contrast, rapid rotation and a magneticfield are not strongly mutually exclusive for B0.5 to B1.5 starsnear the zero age main sequence.) In spite of the lack of detectedlarge-scale magnetic fields in Be stars, the stellar magnetic fieldin γ Cas stars is believed to be also responsible for the claimedrotational modulation with extremely constant period of the opti-cal broad-band flux (Smith et al. 2016b), which requires a large-scale structure that does not migrate in the co-rotating frame.The magnetic model does not address this obvious tension otherthan by hypothesising that the non-detection of a magnetic fieldis related to the disappearance of the photometric 1.215-d vari-ability and due to the decay of the stellar magnetic field (Smith2019). If so, γ Cas would, during the presence of the 1.215-d pe-riod, have possessed a large-scale magnetic structure not seen inany other Be star.The two magnetic constructs are imported from other con-texts. Convective sub-surface dynamos might produce variableinhomogeneous surface brightness distributions which other-wise, in purely radiative atmospheres, lack a simple explana-tion. MRI is broadly invoked to produce the level of viscosityneeded to bring the timescales of accretion processes into agree-ment with observational constraints (Martin et al. 2019). (It isuseful to note that also the viscous-decretion-disk model for Bestars [cf. Sect. 1] merely assumes viscosity but does not explainit.) However, to date, neither magnetic-field-producing mecha-nism seems to have found direct observational confirmation evenin the domains they were designed for. This motivates searchesfor alternate explanations of the γ Cas stars.The magnetic model was conceived before the (optically)faint and low-mass companion star of γ Cas was discovered. Themodel has evolved over the years. However, also in its currentversion it does not foresee any role for the companion to con-tribute to the observed phenomena. This attitude is seeminglyreinforced by the fact that BeXRBs, where compact compan-ions are the main X-ray actors, and γ Cas stars are clearly dis-tinguished populations. If faint low-mass companions in low-eccentricity orbits are characteristic of γ Cas stars, a large di ff er-ence in the X-ray properties of BeXRBs and γ Cas stars may beexpected because in near-circular orbits the Be disk is stronglytruncated. As the result, the disk remains well within the B star’sRoche lobe so that major X-ray outbursts with the orbital periodare unlikely (Okazaki & Negueruela 2001). Therefore, accreting binary models of γ Cas stars need to be powered by the B star’smass loss.
One way of avoiding the overproduction in γ Cas stars of X-raysat the level of BeXRBs is to assume a white dwarf (WD) as theaccreting body because it has a shallower gravitational poten-tial than that of a neutron star or a black hole. This was firstproposed by Haberl (1995). In fact, accreting white dwarfs innovae and symbiotic stars are X-ray sources of roughly compa-rable properties. Contrary to the purely parametric formalismsof most earlier studies, Tsujimoto et al. (2018) employed mod-els specifically designed for white dwarfs accreting matter froma cool companion as in novae or symbiotic stars and included re-flection by the white dwarf of X-rays as well as absorption. Theyachieved reasonable fits of the X-ray flux distributions of both γ Cas and BZ Cru. However, the models could not conclusivelydiscriminate between magnetic (as in polars or intermediate po-lars) and non-magnetic (as in [dwarf] novae) WD companions.Hamaguchi et al. (2016) o ff ered the interesting idea that thecooler X-ray emitting plasma “probably originates from the Beprimary stellar wind, while the hot component may originatefrom the head-on collision of either the Be or WD wind withthe Be disk”. In a di ff erent context, it has, in fact, been shownthat Be disks are probably subject to ablation by the B star’s ra-diation (Kee et al. 2018, and references therein). However, if aninteraction between the wind from a Be star with the disk wereat the origin of the hard X-rays from γ Cas, more than just ∼ γ Cas stars. A variant of the suggestionof a collision with a wind from a companion will be developedin Sect. 5.The mass estimate for the companion to γ Cas of one solarmass is at the high end of WDs. However, if the range of 2.2 to4.5 M (cid:12) for the secondary star in π Aqr (Bjorkman et al. 2002) iscorrect, the WD model would not be applicable. Depending onhow much mass is transferred back to a WD companion duringthe later evolution of the B-type primary and when this happens,such systems might even be progenitors of a thermonuclear TypeIa supernova explosion of the WD and a core-collapse Type IIsupernova of the B star.
Recently, Postnov et al. (2017) advanced the so-called propellermodel, which employs a neutron star but reduces the X-ray fluxfrom direct accretion as in BeXRBs by letting the magnetic fieldand rapid rotation of the neutron star suitably moderate the ac-cretion rate. Moreover, because the X-ray emission is from a hothalo, it is not rotationally pulsed (as observed). This constructwould seem to eliminate the discrepancy in the X-ray domainbetween γ Cas stars and BeXRBs. However, Smith et al. (2017)have nevertheless vehemently rejected the propeller model. Inparticular, they argue that the X-rays form close to the B star, notnear the companion at au-scale distances, because of intermittentX-ray attenuations by cold plasma, ejected by the B star, be-tween the X-ray-emitting region and the observer. Furthermore,they insist that the density of the X-ray emitting plasma is of or-der 10 cm − , i.e., at a photospheric level, while the propellermodel yields values near the inner radius of the magnetospherethat are 1-2 orders of magnitude lower.In addition, the assumption of neutron-star companions to γ Cas and π Aqr is not straightforward. Because BeXRBs can ex-
Article number, page 6 of 16. Langer et al.: γ Cas stars: Normal Be stars with disks impacted by the wind of a helium-star companion?
Fig. 1.
WISE 24 µ m image of γ Cas. The black line at the center illus-trates the 10,000-year proper motion (corrected for Galactic rotation) asmeasured by Hipparcos ( γ Cas is too bright for Gaia DR2). ist for a few 10 years after the supernova explosion that formedthe neutron star whereas the remnant nebulae merge with the in-terstellar medium within a few 10 years, the absence of suchnebulae around these stars is not an obstacle to the neutron-starhypothesis. Better indicators are, however, their orbital eccen-tricity and the space velocity both of which may be significantlymodified by a supernova explosion. This is briefly discussed inthe following two subsections. If a star exploding in a binary experiences a significant kick, theeccentricity of the orbit grows, and the plane of the orbit mayget tilted with respect to the equatorial plane of the previousmass gainer, which in the case of Be stars is also the plane ofthe disk. The details depend very much on the direction of thekick (Renzo et al. 2019). These expectations find their confirma-tion in many observed BeXRBs (Reig 2011). They do not appearto be satisfied in γ Cas (Gies et al. 2007) and π Aqr (Bjorkmanet al. 2002; Zharikov et al. 2013) the orbits of which seem nearlycircular. Postnov et al. (2017) invoke an electron-capture super-nova explosion for the progenitor of the assumed neutron star.Such explosions are thought to impart a low kick on the rem-nant. However, about 10% of the rest mass of the exploding staris lost as neutrinos. Even if this mass loss is symmetric w.r.t. thecenter of gravity of the exploding star, it is asymmetric about thebinary’s center of gravity and so imposes some orbital eccentric-ity on binaries that remain bound.
If a supernova explosion increases the velocity of a binary rela-tive to the ambient interstellar medium (ISM), a bow shock maydevelop when a stellar wind impacts the ISM. A prototypicalcase is the O9.5 Ve runaway star ζ Oph (del Valle & Romero2012, and references therein). However, as Renzo et al. (2019)explain, most surviving systems are not expected to be acceler-ated by more than ∼
30 km / s. Fig. 2.
Ditto as Fig. 1 except for π Aqr and a combination of the Hippar-cos and Gaia proper-motion measurements.
Bodensteiner et al. (2018) have inspected and classifiedWISE (Wright et al. 2010) 24 µ m images of all OBA stars inthe Bright Star Catalog (Ho ffl eit & Jaschek 1991), including γ Cas and π Aqr. WISE images of the regions around γ Cas and π Aqr are reproduced in Figs. 1 and 2. The superimposed proper-motion vectors illustrate the classifications by Bodensteiner et al.(2018) for γ Cas and π Aqr, respectively. A bow shock can beseen to be associated with π Aqr (see also Mayer et al. 2016).However, the apex of the nebula is not aligned with the proper-motion vector. Accordingly, the relative velocity of π Aqr and theambient interstellar medium is not dominated by the stellar mo-tion. γ Cas is also surrounded by a nebula, which may be relatedto the star. But the morphological evidence is weak so that theentry in Bodensteiner et al. (2018) is “not classified”. Neverthe-less, the peculiar space velocities are close to ( π Aqr: 21 km / s) oreven well within ( γ Cas: 38 km / s, Bodensteiner et al. 2018) thedomain of single run-away stars (Renzo et al. 2019).The environments of the other γ Cas stars in Table 1 werealso inspected in the WISE 24 µ m atlas. However, no convincingassociation of any of these stars with a nebula was found. In mostcases, the most likely explanation is the much larger distanceimplied by the much lower optical brightness. The field aroundBZ Cru has a very patchy background, with no structure centeredon the star standing out.In summary, there is only mild dynamic or kinematic supportof the neutron-star hypothesis for the companions to γ Cas and π Aqr. This makes it useful to study in more depth the role ofbinarity at large in the genesis of Be stars from an observational(Sect. 4) as well theoretical (Sect. 5) perspective.
4. Observations of binary Be stars
It is not known whether all γ Cas stars are binaries. In viewof the strongly rotationally broadened spectral lines of Be starsand the large mass and (optical) luminosity di ff erence betweenearly-type B stars and highly evolved companion stars, attemptsto prove definitively that a given Be star does not have such acompanion appear illusionary. More quantitative statistical con-straints, especially for less evolved systems, may result from Article number, page 7 of 16 & A proofs: manuscript no. gCas-resub possible discoveries of eclipsing systems by large-scale photo-metric monitoring surveys such as OGLE (Soszynski et al. 2005)or with TESS (Ricker et al. 2016). In any event, the assumptionof a binary nature of γ Cas stars is not currently in obvious con-flict with the available observational evidence.Early suggestions for a possible binary origin of Be starswere made by Kˇríž & Harmanec (1975) and Pols et al. (1991),triggering various observational searches. The former work as-sumed that the Be disks are accretion disks. However, owing tothe lack of accreting classical Be stars, the observational supportis at best weak. Since a decretion disk can only be observed afterthe mass transfer, Be stars formed by mass transfer should havestripped companions that cannot fill their Roche lobes, or theircompact remnants.Sometimes it is even asked whether all Be stars have highlyevolved companions (e.g., Wang et al. 2017), making their Be-typical rapid rotation the result of mass transfer from their pro-genitors (cf. Introduction). Certainly, the scarcity of Be starswith main-sequence companions shows that, if a Be star is dou-ble, its companion very probably is highly evolved. From a veryelaborate study based on the comparison of kinematic data fromGaia for a large sample of Be stars and detailed modelling, Bou-bert & Evans (2018) infer that the 13.1% fraction of runawaystars found by them is probably su ffi cient to conclude that allBe stars are post-mass-transfer binaries. However, the apparentpreference for lower-mass and highly evolved companions maybias the result if Be stars with relatively close and / or more mas-sive companions cannot maintain a major stable disk.In analyses of observations of individual Be stars, neutron-star, WD and sdO companions have up to now been consideredalmost exclusively. The results are briefly summarised in the nextthree subsections. This overview may soon require completionfor helium stars (see Sect. 5). The first to propose that the remains of the mass donors in Be-star-forming binaries are WDs were Waters et al. (1989) and Polset al. (1991). Theoretical estimates of the fraction of Be starswith a WD companion reach at least 70% (Raguzova 2001).Several surveys have been conducted but no positive detectionwas made (Meurs et al. 1992), with some authors consider-ing γ Cas as the best candidate. Perhaps, a formal non-Be star,namely Regulus, currently comes closest to such systems, con-sidering the late spectral subtype (B7V) and the intermittency ofBe phases especially among late-type Be stars. Regulus rotatesabout 86% critically (McAlister et al. 2005) and has a WD com-panion (Gies et al. 2008). Rappaport et al. (2009) trace out thepast and future evolution of this system and find that the B starmay evolve into an sdB star. In addition, Cracco et al. (2018)recently identified some supersoft X-ray sources with Be starsin the Magellanic Clouds. These sources are often intermittentand may be massive WDs occasionally igniting accreted matter,for example from a Be disk. Apparently, unlike in BeXRBs, therelease of gravitational energy does not play a major role in suchsystems.
Two of the first Be stars initially suspected and later demon-strated to be orbited by a low-mass star strongly interactingwith the Be disk were HR 2142 (Peters et al. 2016) and φ Per (Mourard et al. 2015). In UV spectra (mostly from
IUE ) withsu ffi cient orbital phase coverage, spectral lines can be clearlyseen with a much larger velocity swing than that of the B-typeprimary (Thaller et al. 1995). Numerous narrow Fe IV, V, andVI lines as well as the He II λ ff ective for broad-lined early-type Be stars,i.e., many γ Cas stars. The relatively low detection rate is proba-bly also due to the low S / N ratio of
IUE spectra. The total num-ber of Be stars with a detected or likely sdO companion is about15 (Wang et al. 2018).
Systems with neutron-star and black-hole companions (cur-rently, only one Be system with a black hole seems to be knownCasares et al. 2014), i.e. BeXRBs are omitted from the discus-sion because, as outlined above, the X-ray properties of γ Casstars seem incompatible with those of BeXRBs and there is noconvincing evidence that the companions of γ Cas and π Aqr areneutron stars or even black holes. However, the immediate pro-genitors of BeXRBs, namely Be stars with a helium-star com-panion have not yet been placed into a close perspective with theformation of Be stars; this will be done in Sect. 5.
5. Binary stellar evolution models
Since stars, during their evolution, tend to increase their radii bylarge factors, most close binary systems will experience trans-fer of mass between the two stars. For the closest binaries, i.e.for orbital periods typically below ∼
10 d, mass transfer startswhile both stars undergo core hydrogen burning (Case A; Pols& Marinus 1994; Pols 1994; Wellstein et al. 2001). In this case,the mass transfer is divided into three distinct phases: a thermal-timescale mass transfer (fast Case A), which is succeeded by anuclear-timescale mass transfer phase during which the mass ra-tio is inverted (slow Case A or Algol phase), followed by anotherthermal-timescale mass-transfer once the donor star ends corehydrogen burning (Case AB). In wider binary systems, the post-main sequence expansion of the initially more massive star leadsto thermal-timescale mass transfer, while the companion is gen-erally still burning hydrogen (Case B). In both cases, the masstransfer may become unstable, with the likely consequence of amerger of both stars (de Mink et al. 2014). However, if a mergeris avoided, the mass donor – the initially more massive star –loses almost its entire hydrogen-rich envelop due to mass trans-fer, while the mass gainer is accreting all or only part of it. Theratio of the number of mergers and the number of stable mass-transfer systems, and the mass-transfer e ffi ciency, are uncertain(Langer 2012).Struve (1963) and Huang (1966) realised that the accretionof mass from a companion star can lead to an increase of thestar’s specific angular momentum, with the consequence thatmass gainers may spin supersynchronously w.r.t. the orbital rota-tion. This e ff ect is observationally well documented for massiveAlgol systems (e.g., Howarth et al. 2015, Mahy et al., submit- Article number, page 8 of 16. Langer et al.: γ Cas stars: Normal Be stars with disks impacted by the wind of a helium-star companion?
Table 2.
Key data of selected massive binary evolution models from Wellstein & Langer (1999) and Wellstein et al. (2001). Besides the initialbinary parameters, i.e., the initial masses of the mass donor ( M , i ) and the mass gainer ( M , i ), and the initial orbital period P orb , i , we give parametersof the binary and its component stars at the time where the mass donor has a central helium mass fraction of 0.8 during core helium burning, i.e.,the orbital period P He + OB , both stellar masses during that stage, the corresponding luminosities and e ff ective temperatures, and the expected stellarwind mass loss rate, velocity and mechanical wind energy production rate according to Vink (2017). No. M , i M , i P orb , i P He + OB M He M OB L He L OB T He T OB log ˙ M He (cid:51) esc , He L wind , He M (cid:12) M (cid:12) d d M (cid:12) M (cid:12) L (cid:12) L (cid:12) kK kK M (cid:12) / yr km / s L (cid:12) ffi cient, does one expect the spin-up processto drive the mass gainer towards critical rotation, since the orbitsbecome wide enough to render tides negligible. It was shownanalytically by Packet (1981), and later through detailed modelsby Petrovic et al. (2005), that a mass increase by only 10% canbe su ffi cient to spin up a star to its critical rotation. The problemwith this situation is that after Case AB or Case B mass transfer,the envelope mass of the donor has become very small such thatthe donor is hotter than a main sequence star, and thus remainsvery faint in optical light. Furthermore, its remaining lifetime ismuch shorter than that of its spun-up companion. This means, itwill rapidly evolve into a compact object, which, in case a neu-tron star or black hole is formed, may lead to the disruption ofthe binary by the supernova explosion. As a consequence, mostpost Case AB or Case B systems may not be recognised as such(de Mink et al. 2014).In the following, it will be assumed that the mass gainersof Case AB or Case B are in fact spun up such that they appearas Oe / Be stars after the mass transfer. This idea is, of course,strongly supported by the large number of classical BeXRBs,which are explained as such post-Case AB or Case B binarieswhere the donor star evolved into a neutron star without breakingup the binary (Tauris & van den Heuvel 2006). In these systems,the nature of the companion is revealed by the copious X-rayemission which is produced when the neutron star crosses or ap-proaches the Be disk in its tilted and / or elliptical orbit, whichleads to mass accretion onto the neutron star. As seen in Sect. 4,there is also a smaller number of Be stars with known or sus-pected BH, WD or sdO companions, which all fit into the post-mass transfer scenario.It is worth pointing out that rotating, non-magnetic stars canspin down due to stellar-wind mass loss (Langer 1998). For themost massive main sequence stars, which lose a significant frac-tion of their initial mass through a wind, this process may bee ffi cient, and observational evidence for this exists in GalacticO stars (Markova et al. 2018). It explains also the fast but sub-critical rotation of the O stars in Galactic WR + O-star binaries(Vanbeveren et al. 2018), in which the WR star was likely themass donor in a mass transfer process (Petrovic et al. 2005).However, γ Cas stars are Be / Oe stars which do not spin down.This is consistent with the expectation that the main sequencemass loss in Galactic stars is below 10% for stars with an initialmass below 28 M (cid:12) (Brott et al. 2011; Langer 2012). γ Cas stars as Be + helium-star binaries(BeHeBs)
According to the above considerations, an Oe / Be star, when it isformed as such in a binary system, has a helium star companion.The corresponding Be + helium-star binaries will below be calledBeHeBs for short. While the helium star evolves faster than theBe star, the lifetime of this BeHeB stage – the helium burningtimescale of the helium star – is long enough to expect that someof the observed Be binaries are in this stage (cf. Sect. 5.1.3).The following will discuss the hypothesis that γ Cas stars areBeHeBs, based on binary evolution models computed by Well-stein & Langer (1999) and Wellstein et al. (2001). Whereas thesemodels do not include rotation, they assume conservative masstransfer, which implies that the mass increase is su ffi cient to spinup the mass gainer to critical rotation. Table 2 gives an overviewof the initial parameters of these models, and those during theBeHeB stage. These were chosen such that the masses of theformed helium stars (1 . − . (cid:12) ) cover the plausible massrange of such objects in γ Cas stars. That is, more massive he-lium stars would likely form optically thick winds, which wouldmake them easily identifiable as Wolf-Rayet stars (Langer 1989).And helium stars significantly below 1M (cid:12) even require progeni-tors of so low initial mass that the mass gainer could not evolveinto a B star of the earliest spectral type.Figure 3 gives an overview of the evolution of both compo-nents of the binary models in the Hertzsprung-Russell diagram.The tracks of the pairs of stars start on the zero-age main se-quence. Whereas otherwise these evolutionary tracks show thetypical pattern of Case A and B binary models (cf. Wellsteinet al. 2001), the thick-drawn part of the lines focuses on the Be-HeB stage, i.e., on the time period during which the mass donorevolves through core helium burning.As the mass gainers – the presumed later Be stars – hardlyevolve during this time, the thick-drawn stretch of their evolu-tionary tracks is very short. For the mass donors, however, thereis significant evolution. In any case, it is important to realise thatthe donors move fast along the horizontal parts of the evolution-ary tracks. The thick dots on their tracks mark a central heliummass fraction of Y c = .
8, and core helium exhaustion is signi-fied by the end of the thick-drawn part of the track. Therefore,the time-averaged properties of the helium stars are well repre-sented by their properties at Y c = ffi cult to observe, in the optical and at longer wavelengths,next to the much brighter Be star (Götberg et al. 2018). How-ever, with luminosities of 500 to 50,000 L (cid:12) , helium stars arestill luminous stars, and as such they are expected to emit aradiation-driven wind. Observational evidence for this is found Article number, page 9 of 16 & A proofs: manuscript no. gCas-resub
Fig. 3.
Evolutionary tracks of both, the mass donors (dotted lines) and the mass gainers (solid lines) of the analysed six binary models in theHertzsprung-Russell diagram. Pairs of tracks with the same colour belong to the same binary system. The thick gray line marks the zero-age mainsequence for the initial mass range of our models (i.e., from 8 to 25 M (cid:12) ). The thick solid drawn parts of the mass gainers’ tracks marks the phaseduring which the companion is a He star (starting from a core helium mass fraction of Y c = .
95 during core helium burning). The correspondingarea in the HR diagram is coloured light blue and labelled “Be stars”. On the tracks of the mass donors, dots are placed every 10 yr during corehelium burning, and a star symbol marks the time at which their core helium mass fraction is Y c = .
80. The tracks end during the phase of shellhelium burning with a small remaining lifetime of the He stars, except for the System No. 1, which ends at Y c = .
7. The area in the HR diagramin which the He star models spend most of their lifetime is coloured in pink and labelled “He stars”. The tracks correspond to the binary modelsNos. 1 to 6 (Tab. 2) in the order of increasing helium-star luminosity (as marked by the star symbols). in the UV spectra of the rare so-called extreme helium stars (Jef-fery & Hamann 2010). While helium-star wind mass loss basedon Hamann et al. (1982) is included in the presented binary evo-lution models, the present study uses the recent theoretical mass-loss rates by Vink (2017), which reproduce the empirical rates ofHamann et al. reasonably well, but also provide a smooth transi-tion to the mass-loss properties of the more massive Wolf-Rayetstars. As the total amount of mass lost during core helium burn-ing is mostly very small, this does not introduce any significantinconsistency.The models provide guidance in answering the questionwhether the presence of a wind emanating from the helium starcould give rise to an observable X-ray signal in BeHeBs. As thehelium stars are compact, and their winds fast, the models leadto the expectation of X-ray emission from two potential interac-tion regions. The first candidate zone is where the wind of theHe star encounters the disk of the Be star, and the second one re- sides where the He-star wind meets the – also present – ordinaryradiation-driven wind of the Be star. The following subsectionsexamine these two cases.
If the He star had no wind, the Be disk might well extend to theHe star companion or even engulf it. This is so by analogy tothe BeXRBs, where a neutron star, i.e., the descendant of a he-lium star in a BeHeB, emits X-rays when it crosses the equatorialplane of the Be star. Since He stars possess a strong wind, theywill blow a cavity into the Be disk, whose size may be deter-mined by the balance of the wind ram pressure and the thermaland turbulent pressure of the gas in the Be disk. The cavity maybe elongated in the direction of the orbital motion, and its ver-tical size will depend on the thickness and vertical structure ofthe Be disk. Truncation by the companion of the disk (Panoglou
Article number, page 10 of 16. Langer et al.: γ Cas stars: Normal Be stars with disks impacted by the wind of a helium-star companion?
Fig. 4.
Time evolution of the mechanical luminosity of the donor star’swind during its helium-star stage, for the six binary models during corehelium burning of the donor star. The colour coding is the same as inFig. 3, and the tracks belong to binary models Nos. 1 to 6 (Table 2) inincreasing order of their wind luminosity. et al. 2018) could lead to still other geometries. Some fraction ofthe He-star wind could escape without interacting with the disk.In any case, the interaction shock front will likely have acomplex three-dimensional structure, and may develop turbu-lence and magnetic fields, which would all a ff ect the emissionof energetic photons. In a first simple step, the next paragraphsattempt to derive upper limits on the X-ray luminosity and thephoton temperature from predictions of stellar-evolution andradiation-driven-wind physics.Figure 4 illustrates the time dependence of the helium star’smechanical wind luminosity L wind , He = ˙ M He (cid:51) , He for the sixevolutionary models in Table 2. Here, ˙ M He is the mass loss ratepredicted by Vink (2017), and (cid:51) wind , He is the terminal wind ve-locity, for which Vink showed that it exceeds the escape speedof the helium stars by about a factor of three. It is, therefore,assumed here that (cid:51) wind , He = √ GM He / R He .Figure 4 also provides an upper limit to the X-ray luminosityproduced by the wind-disk interaction because only a fractionof the kinetic energy can be converted to X-rays. As the figureshows the wind kinetic-energy fluxes are of the order of a fewhundred L (cid:12) for the massive helium stars ( M (cid:39) (cid:12) ) down tofractions of L (cid:12) at lower masses ( M (cid:39) (cid:12) ). These numbersshould only be taken as order-of-magnitude indicators since, inhis pioneering study, Vink (2017) adopted a fixed e ff ective tem-perature of 50 000 K (log T e ff (cid:39) .
7; cf. Fig. 3) while the tem-perature dependence of these winds is not yet well understood.Clearly, even lower wind luminosities will occur in systems withmasses below the range considered here. However, as potentiallyobservable e ff ects will become correspondingly weaker, they arenot considered here. More massive systems, on the other hand,might contain O stars whose strong winds would – at least atGalactic metallicities – spin down the stars, such that they wouldnot be Oe / Be stars for long. Potentially, they would also destroyany circumstellar disk.As for the X-ray luminosity, the given models only place anupper limit on the temperature of the hot gas which is producedby the shock front where the He-star wind hits the Be disk. Withescape speeds of the helium stars in the range 1100-1800 km / s,the terminal wind speeds of the He star are of the order of 3000- Fig. 5.
Time evolution of the ratio η of the wind momentum of the donorstar to that of the mass gainer for the six binary models (see Table 2)during core helium burning of the donor star. The colour coding is thesame as in Fig. 3. / s (see above). For an adiabatic shock, these numberstranslate to temperatures of about 5 · K to 15 · K , or 50to 130 keV, assuming T = m p (cid:51) , He / (2 k ), where m p is the massof the proton. On the other hand, at su ffi ciently high densities,the shock may be non-adiabatic so that the achieved temperaturecan be much smaller. Hydrodynamic instabilities, clumping, orentrainment of cold gas may as well lead to smaller tempera-tures. However, this is challenging to estimate quantitatively, andbeyond the scope of the present work. As mentioned above, a fraction f < f ∗ f of the He-star wind leaves the systemwithout any interaction at all. Here, f < ffi ciency of colliding wind systemsis the wind momentum ratio η = ˙ M He (cid:51) He / ˙ M OB (cid:51) OB , where ˙ M and (cid:51) denote the mass-loss rates and terminal wind velocitiesof both stars, respectively. The interaction fraction and the X-ray production e ffi ciency are largest for η = η for theselected binary-model sequences during the stage of core He-burning of the helium star. The underlying mass-loss rates andterminal wind velocities are those proposed by Krtiˇcka (2014)for ordinary B main-sequence stars. As the terminal wind speedsof Krtiˇcka’s wind models are roughly three times the correspond-ing escape speed from the star, the escape speed of the modelsin Table 2 was multiplied by a factor of three to compute theirterminal wind speeds. This neglects the possibility that in veryclose systems, or for values of η far from unity, one or both windsmight not quite have attained their terminal speeds when reach-ing the interaction point.Figure 5 demonstrates that, in the considered binary models,quite diverse situations may prevail. In some systems (typicallythe more massive ones) the He-star wind momentum is larger by Article number, page 11 of 16 & A proofs: manuscript no. gCas-resub more than an order of magnitude, in some other systems (typi-cally the less massive ones) the B-star wind is stronger by a sim-ilar factor, and in still others the wind momentum ratio is closeto unity. This occurs because both the wind velocities and themass-loss rates of He- and B-stars are not too di ff erent.Similar to the wind-disk interaction, it is di ffi cult to providefirm predictions for the X-ray emission produced by the wind-wind interaction. The upper limits to the X-ray flux and plasmatemperature are similar to those of the wind-disk interaction,since the wind velocities and mass-loss rates are also similar.On the other hand, the conditions in the wind-wind interactionregion will be di ff erent from those in the wind-disk case, since,e.g., the matter density in the Be disk will be larger than that inthe Be star wind. It is therefore possible that X-ray emission willbe composed of more than one discrete component.Observations of colliding-wind binaries show that the X-rayflux in massive He-star + -O-star binaries can reach about 100 L (cid:12) and temperatures up to 100 MK (Gagné et al. 2012). The mass-loss rates in these systems are several orders of magnitude abovethose in BeHeBs, but the wind velocities are comparable. Pit-tard & Dawson (2018) find from hydrodynamical simulationsthat the expected X-ray emission decreases roughly linearly withthe weaker-to-stronger wind-momentum ratio. Moreover, in Be-HeBs, the wind-wind interaction is restricted to higher latitudes,as the equatorial regime is blocked by the Be disk. Nevertheless,while there are several factors which may reduce the X-ray emis-sion, a detectable X-ray flux from the wind-wind interaction isnot excluded, especially not for BeHeBs with a wind momentumratio near unity, which is achieved by the majority of the modelsconsidered (Table 2). The BeHeB phase is a short intermediate evolutionary phase ofmassive binary systems, for which direct observational evidenceis still lacking. This phase is defined by the core helium-burningstage of the mass donor. It is often disregarded in comparisonwith observations, because its duration is mostly shorter than thatof the foregoing Algol phase (if any), but also shorter than thesubsequent BeXRB or Be + WD phase.The binary evolution models of Wellstein et al. (2001) cangive an estimate of the number of BeHeBs relative to BeXRBor Be + WD systems. The stripped core helium-burning compan-ions to B-star mass gainers are very hot ( T e ff ∼ > kK ) and sub-luminous (cf. Fig. 3), leading to no realistically observable sig-nal in the optical regime which is dominated by the B star. Thelifetime of the faint, hot helium star is the nuclear timescale ofcore helium burning, which is of the order a few Myr for heliumstars in the mass range 1 . − (cid:12) (Woosley 2019). Comparedto the hydrogen-burning lifetimes of the rejuvenated B-star massgainers of 10 to 30 Myr, this is about 10% or less. Therefore,among the Be stars that have emerged from this binary evolu-tion channel, a comparable fraction, i.e., up to 10%, could havea helium-star companion.For an accurate prediction of the number of γ Cas binariesexpected from the ansatz pursued above a population-synthesisstudy will probably be required. Clearly, the estimate of ∼ + WD systems) can serve as anupper limit. However, direct empirical comparisons will su ff erfrom a strong observational bias. γ Cas binaries would be iden-tified on account of their X-ray properties while only γ Cas bi-naries with su ffi ciently massive helium-star companions are pre-dicted to have detectable X-ray fluxes. The latter subpopulation Fig. 6.
Mechanical luminosities of the donor star winds versus the massgainer’s bolometric luminosity for the six binary models (cf. Table 2),during core helium of the donor star. The colour coding is the same asin Fig. 3, and the tracks belong to binary models Nos. 1 to 6 (Table 2)in increasing order of their wind luminosity. Also plotted are the X-ray luminosities of the γ Cas stars versus their bolometric luminosities,according to Nazé & Motch (2018, see also Table 1). may roughly consist of those systems in which the helium starsend their evolution as neutron stars. The expected fraction of ob-served γ Cas binaries would be 10% of the BeXRBs, multipliedby the luminosity bias factor, and divided by the break-up frac-tion, f breakup of Be binaries at neutron-star formation in a super-nova explosion. Both factors are quite uncertain, but a fractionof about 10% of all BeXRBs (i.e., of all progenitor systems notdisrupted by a supernova explosion) does not seem impossible. As seen above, some fraction of the Be-star binaries (the Be-HeBs) are expected to contain a core helium-burning star. TheHe star is not likely to be readily observable as it is bolometri-cally much dimmer than the B star. Because the He star is muchhotter than the Be star, the contrast problem is lowest in the UV.The previous section considered corresponding binary-evolutionand stellar-wind models, with the idea in mind that the presenceof a helium star may give rise to observable X-ray emission. Thefollowing discusses to what extent the γ Cas stars and their pe-culiar X-ray properties (cf. Sect. 2.5) might correspond to theBeHeBs. To this e ff ect, the recent compilation of γ Cas stars byNazé & Motch (2018) is used, from which the quantities in Ta-ble 1 were drawn.Firstly, it should be noted that, in BeHeBs, there may beother sources of X-rays than those which are induced by the fastwind of the helium star. In particular, the helium star itself canbe so hot that it emits X-rays. E.g., for T e ff =
100 000 K, thePlanck function peaks at 0.3 keV. As this is the hottest tempera-ture expected for BeHeBs, it follows that only very soft X-rayscan be produced in this way. This holds similarly for the ther-mal emission of hot pre-white dwarfs, as well as for accretingwhite dwarfs (cf. Cracco et al. 2018). As the X-rays measuredin γ Cas stars are much harder (cf. Sect. 2), they are unlikely tobe produced in stellar photospheres.Secondly, in Fig. 6, the mechanical luminosities of thehelium-star winds as a function of the OB star’s bolometric
Article number, page 12 of 16. Langer et al.: γ Cas stars: Normal Be stars with disks impacted by the wind of a helium-star companion? luminosity for the six model systems (Table 2) are plotted to-gether with the observed X-ray luminosities of the γ Cas starsand their respective bolometric luminosities. Here, it should bestressed that both, predicted (cf., Sects. 5.1.1 and 5.1.2) and ob-served quantities (Table 1) have large uncertainties. In particu-lar the bolometric luminosities of the Be stars could be wrong afactor of 2 −
3, since their luminosity classes are only adopted,individual extinction corrections have not been determined, andthe rapid rotation of the Be stars leads to an anisotropy of thephoton emission (von Zeipel 1924) which is unaccounted.There is some overlap in the areas populated by models andobservations in Fig. 6. Also, the bolometric luminosities of bothsamples span about a factor of 20, and the ordinate range of mod-els and observations span 2 − ff sets in both coordinates between the two datasets, namelyby about a factor of 3 in L bol , OB , and a factor of 100 comparing L wind , He and L X .Specifically considering the ordinate of Fig. 6, the di ff erencemay arise because the conversion of mechanical wind energy toX-rays in γ Cas binaries is an ine ffi cient process. In fact, thisseems to be generally the case for colliding-wind binaries as dis-cussed above, in particular when the wind momentum ratio isfar from unity. The conversion e ffi ciency in the wind-disk inter-action case is less clear owing to the lack of comparable casesin other systems. However, we can conclude that the mechanicalwind energy of the helium stars is su ffi cient to account for theobserved energy in X-rays in γ Cas stars.The range in OB-star bolometric luminosities (the abscissain Fig. 6) should be more directly comparable, in spite of thecaveats mentioned above. In L bol , OB , the overlap between mod-els and observations is larger, but the models are generally moreluminous. One reason for the di ff erence is the inclusion of afairly massive model (No. 6 in Table1), mostly for illustrativepurposes, as this may correspond better to WR + O-star binariesinstead of BeHeBs. Certainly, at 36 M (cid:12) the mass gainer in thismodel becomes so massive that its wind will spin it down quickly(Brott et al. 2011) so that its lifetime as Oe star would be veryshort. However, it is also important to consider that the modelsof Wellstein et al. (2001) are mass conserving, which means thatthe entire mass lost from the donor is accreted onto the massgainer. Recent evidence shows, however, that mass transfer inmassive close binaries may well be non-conservative on average(de Mink et al. 2007; Langer 2012). Because non-conservativeevolution does not lead to a di ff erent evolution for the donorstars, the He-star properties of Wellstein et al. (2001) would re-main about the same in the non-conservative case. However, themass gainers, which are mostly in the late O-star regime in themodels analysed above, would be significantly less massive, andthus less luminous. That is, the tracks of the models shown inFig. 6 would move to the left at constant ordinate. In extremecases, the mass gainer’s mass would just be about half of what itbecomes in the conservative model, thereby decreasing log L / L (cid:12) by about 0.9 dex.It seems unlikely that models and data could be broughtinto agreement by considering binary models with smaller ini-tial masses. As seen in Fig. 6, models and data might overlapwell if the downward trend of wind luminosity with bolometricluminosity continued. However, if the observed sample of γ Casstars is merely the peak of a distribution which extends to lowerX-ray luminosities, the known γ Cas stars should correspond tothe most luminous models that predict the γ Cas phenomenon.This range is obviously covered by the chosen theoretical tracks.In summary, if γ Cas stars are binaries with core helium-burning helium stars, Fig. 6 suggests that (a) the mass transfer
Fig. 7.
Mechanical luminosities of the donor-star winds versus the5 keV / / γ Casstars versus their bolometric luminosities, according to Nazé & Motch(2018) (cf. Table 1). e ffi ciency during the preceding mass transfer phases was about0.5 (since the model tracks would have to be shifted to the leftby about 0.4 dex to match the data) and (b) about 1% of the windluminosity would be converted into X-rays.Figure 7 compares the (mechanical) He-star wind luminosi-ties and the 5 keV / γ Cas stars from Nazé & Motch (2018).Taken at face value, the X-ray luminosities as well as the adi-abatic flux ratios derived from the models (Table 2) are muchtoo high compared to the observed X-ray luminosity and hard-ness ratio. However, as discussed above, only about 1% of themechanical wind luminosity needs to be converted to X-rays,thereby drastically reducing the apparent mismatch. At the sametime, the flux ratio is predicted one order of magnitude too high,which means that the temperature needs to come down from ∼
500 MK ( ∼
40 keV) to ∼
15 MK ( ∼ γ Cas (Miroshnichenko et al. 2002) and π Aqr(Bjorkman et al. 2002) also support the notion of an interactionbetween the companion stars and the disks of the Be stars, al-though it is not clear whether this interaction is radiative, gravi-tational or both. The asymmetric structure in the disk of BZ Cru(Stee et al. 2013) may have the same origin.The BeHeB model reproduces also other observed proper-ties of the γ Cas stars. (i) Any interaction between He-star windand Be disk will lead to a correlation between X-ray and opti-cal continuum as well as H α line-emission flux. (ii) An inter-action between He-star wind and Be disk will also often placethe X-ray-emitting region closer to the B star than accreting-companion models would. (iii) Injection of new matter into thedisk can easily lead to increased line-of-sight column densities ofX-ray-attenuating matter. (iv) Collision of the He-star wind witha Be-star wind strongly structured by co-rotating interaction re-gions and / or with an azimuthally inhomogeneous Be disk often Article number, page 13 of 16 & A proofs: manuscript no. gCas-resub fed by discrete stellar mass-loss events may lead to variable X-ray flux on a broad range of time scales. Furthermore, the X-rayemission that may arise from two distinct regions in the BeHeBmodel may well relate to the multi-temperature nature of the ob-served X-ray continuum in some γ Cas stars (Sect. 2); a similardi ff erentiation was already proposed by Hamaguchi et al. (2016). As discussed in Sect. 3.3, the supernova explosions that ulti-mately transform BeHeBs with massive helium-star componentsinto BeXRBs lead to an increase in orbital eccentricity. By con-trast, in the progenitors of BeXRBs, namely the BeHeBs, theprevious mass-transfer evolution should reduce any earlier ec-centricity to zero, and align the Be spin and the orbital angular-momentum vector. Therefore, the orbit of the helium star aroundthe Be stars is expected to be circular and coplanar with theBe disk. Instead of being strongly orbitally modulated, as inBeXRBs (Okazaki & Negueruela 2001), the X-ray productionin BeHeB should thus be more continuous (but variable due tomass-loss events from the Be star). The truncation by the com-panion of the disk (Okazaki & Negueruela 2001) would placethe locus of formation of the X-rays slightly closer to the B starthan to the helium star.Other predictions resulting from the given ansatz are that γ Cas stars might have rather massive helium-star companions.For most of the γ Cas stars, it is not known whether they are bi-naries, let alone the masses of any companions. However, Nem-ravová et al. (2012) proposed that the secondary in γ Cas is a he-lium star with a mass of about one 1 M (cid:12) , and π Aqr seems to havea companion mass that does not fit a white dwarf or a neutron star(2.2-4.5 M (cid:12)
Bjorkman et al. 2002). Nazé et al. (2017) suggestedthat the companion may be a main sequence star. However, thiswould not explain the Be nature of the primary, nor the level ofthe observed X-ray emission. Furthermore, as π Aqr would be awide pre-interaction binary in this case, a circular orbit would bevery unlikely. By contrast, the masses of many other sdO starsreported for Be stars are far below one solar mass, which may bea challenge as explained above.The He-star wind may blow a significant cavity or even ahole into the Be disk. While model predictions of this are beyondthe scope of this study, it is noteworthy that asymmetries seemto have been observed in some cases, for instance in BZ Cru(Sect. 2.4). Furthermore, the hot helium star can locally changethe ionisation structure of the disk, leading to periodic orbitalmodulations as already observed in some Be binaries (Riviniuset al. 2004). Direct detection of the hot helium stars would bestbe attempted by orbital-phase-resolved UV spectroscopy (cf. Pe-ters et al. 2013).
6. Summary and conclusions
Occam’s razor o ff ers the insight that the credibility of a proposedsolution to a problem increases with the simplicity of the solu-tion, where simplicity is often understood as the usage of estab-lished knowledge modules. While the existence and e ff ects ofcompanion stars can be addressed observationally (albeit onlyvery tediously for any given individual Be system), the two mag-netic fields of the magnetic model proposed for γ Cas stars can-not by construction. Moreover, helium stars are known to ex-ist whereas magnetic fields caused by subsurface convection orMRI are still awaiting observational confirmation even in objectsthey were originally designed for. On this ground, Occam wouldadvise to first exhaust the explanatory power of binary models. Previous binary models tried to explain the defining X-rayproperties of γ Cas stars in terms of accretion to white dwarfs orneutron stars. However, they are struggling in various ways toreproduce the observations fully. A generic objection apparentlyfuelled by the available observations could be that the releaseof gravitational energy that powers such systems can only takeplace close to these compact companions, i.e., far away from theB star. Therefore, the present study has explored a di ff erent typeof companion, namely the short-lived phase of B stars with ahelium-star companion, BeHeBs, which are the progenitors ofBeXRBs, Be + WD or Be + sdO systems, depending on the massof the helium star.The collision in BeHeBs of a fast stellar wind from a com-panion with the Be disk and / or the Be wind as a di ff erent con-cept has a well-proven analog in the colliding winds of the twocomponents of massive binary systems. The discovery of BHeBstars, i.e. of ’normal’ B stars with a helium-star companion butwithout circumstellar disk and without γ Cas-like X-ray prop-erties, would favour the wind-disk collision part of the BeHeBmodel. A specific variant of this idea, namely the interaction ofa WD wind with the Be disk, was first proposed by Hamaguchiet al. (2016). Because the X-rays do not have to be generated inthe immediate vicinity of the companion, prospects are much im-proved that detailed modelling can achieve good agreement witha wide range of observations. Closer to the B star and its mass-loss activity, the door is much wider open towards reproducinglong-term but only little delayed correlations between variationsin X-rays, optical flux, and UV spectral lines. In particular, out-bursts may well supply the variable amounts of line-of-sight mat-ter to explain the observed intermittent attenuations of the softX-ray flux.If γ Cas stars do have a companion with such e ff ects, it isclear that these stars must be of relatively low mass and low op-tical luminosity. With the additional restriction to stars with astrong wind, only helium stars and WDs remain as candidates.The helium-star wind model has the potential to place the hard-ness and flux of thermal X-rays from γ Cas stars in the observeddomains. More γ Cas stars should be carefully screened for hotsubluminous companions. The most conclusive results can beexpected from UV spectroscopy.There is no observational evidence of systematic di ff erencesother than the X-ray properties between γ Cas stars and the gen-eral population of classical Be stars of the same spectral type.This agrees with our model which is not dependent on any spe-cial assumptions about the Be stars themselves other than theirrapid rotation. A full reunification of γ Cas and classical Be starscan be expected from a spectroscopic study of a representa-tive γ Cas star like that performed by Walker et al. (2005) for ζ Oph. First positive diagnoses of multimode NRP exist alreadyfor γ Cas (Sect. 2.2) and π Aqr (Sect. 2.3). Such work may alsolead to coarse predictions of mass-loss outbursts of the B star(Rivinius et al. 1998; Baade et al. 2018) and thereby facilitateparallel optical and X-ray spectroscopy when the wind of thehelium star interacts with ejecta from the B star. A first esti-mate of the relative X-ray contributions by interactions betweenthe He-star wind and the Be disk or the Be wind, respectively,may also result. Combined spectroscopy and photometry mayprovide valuable diagnostics of disk regions not well probed byother observations which are mostly biased to the denser parts.Because it is di ffi cult to find Be stars that do not pulsate, itmay be feasible (certainly is attractive) to search for any statis-tical di ff erences between the pulsation properties of bona fide single Be stars and Be stars with di ff erent kinds of companion(neutron stars, WDs, sdO stars, main-sequence stars): Can such Article number, page 14 of 16. Langer et al.: γ Cas stars: Normal Be stars with disks impacted by the wind of a helium-star companion? a first crude step towards asteroseismology of Be stars distin-guish formation channels of Be stars?Furthermore, BeHeB stars should be valuable academies ofthe short-lived helium stars and their role in the evolution of mas-sive binaries. An identification of γ Cas stars with these objectswould provide the missing link between the unevolved main-sequence binaries and Be binaries with compact companions.
Acknowledgements.
We thank the referee, Dr. Georges Meynet, for useful com-ments and suggestions. J.B. acknowledges support from the FWO Odysseusprogram under project G0F8H6N. This publication makes use of data productsfrom the Wide-field Infrared Survey Explorer (WISE), which is a joint projectof the University of California, Los Angeles, and the Jet Propulsion Labora-tory / California Institute of Technology, funded by the National Aeronautics andSpace Administration. This research has made use of the SIMBAD database(Wenger et al. 2000) and the VizieR catalog access tool (Ochsenbein et al. 2000),both operated at CDS, Strasbourg, France. This research has made use of NASA’sAstrophysics Data System (ADS).
References
Baade, D., Rivinius, T., Pigulski, A., et al. 2017, in Second BRITE-ConstellationScience Conf.: Small satellites – big science, Proc. Polish Astron. Soc., Vol. 5,eds. K. Zwintz and E. Poretti, 196–205Baade, D., Rivinius, T., Pigulski, A., et al. 2018, in 3rd BRITE Science Confer-ence, ed. G. A. Wade, D. Baade, J. A. Guzik, & R. Smolec, Vol. 8, 69–76Bernhard, K., Otero, S., Hümmerich, S., et al. 2018, MNRAS, 479, 2909Bjorkman, K. S., Miroshnichenko, A. S., McDavid, D., & Pogrosheva, T. M.2002, ApJ, 573, 812Bodensteiner, J., Baade, D., Greiner, J., & Langer, N. 2018, A&A, 618, A110Boubert, D. & Evans, N. W. 2018, MNRAS, 477, 5261Brott, I., de Mink, S. E., Cantiello, M., et al. 2011, A&A, 530, A115Cantiello, M. & Braithwaite, J. 2011, A&A, 534, A140Casares, J., Negueruela, I., Ribó, M., et al. 2014, Nature, 505, 378Cohen, D. H. 2000, in Astronomical Society of the Pacific Conference Series,Vol. 214, IAU Colloq. 175: The Be Phenomenon in Early-Type Stars, ed.M. A. Smith, H. F. Henrichs, & J. Fabregat, 156Cohen, D. H., Cassinelli, J. P., & MacFarlane, J. J. 1997, ApJ, 487, 867Cracco, V., Orio, M., Ciroi, S., et al. 2018, ApJ, 862, 167Cranmer, S. R. & Owocki, S. P. 1996, ApJ, 462, 469de Mink, S. E., Langer, N., Izzard, R. G., Sana, H., & de Koter, A. 2013, ApJ,764, 166de Mink, S. E., Pols, O. R., & Hilditch, R. W. 2007, A&A, 467, 1181de Mink, S. E., Sana, H., Langer, N., Izzard, R. G., & Schneider, F. R. N. 2014,ApJ, 782, 7del Valle, M. V. & Romero, G. E. 2012, A&A, 543, A56Gagné, M., Fehon, G., Savoy, M. R., et al. 2012, in Astronomical Society ofthe Pacific Conference Series, Vol. 465, Proceedings of a Scientific Meetingin Honor of Anthony F. J. Mo ff at, ed. L. Drissen, C. Robert, N. St-Louis, &A. F. J. Mo ff at, 301Ghoreyshi, M. R., Carciofi, A. C., Rímulo, L. R., et al. 2018, MNRAS, 479, 2214Gies, D. R., Bagnuolo, Jr., W. G., Baines, E. K., et al. 2007, ApJ, 654, 527Gies, D. R., Bagnuolo, Jr., W. G., Ferrara, E. C., et al. 1998, ApJ, 493, 440Gies, D. R., Dieterich, S., Richardson, N. D., et al. 2008, ApJ, 682, L117Götberg, Y., de Mink, S. E., Groh, J. H., et al. 2018, A&A, 615, A78Grady, C. A., Bjorkman, K. S., Snow, T. P., et al. 1989, ApJ, 339, 403Granada, A., Ekström, S., Georgy, C., et al. 2013, A&A, 553, A25Güdel, M. & Nazé, Y. 2009, A&A Rev., 17, 309Haberl, F. 1995, A&A, 296, 685Haberl, F. & Sturm, R. 2016, A&A, 586, A81Hamaguchi, K., Oskinova, L., Russell, C. M. P., et al. 2016, ApJ, 832, 140Hamann, W.-R., Schoenberner, D., & Heber, U. 1982, A&A, 116, 273Harmanec, P. 2002, in Astron. Soc. Pacific Conf. Ser., Vol. 279, Exotic Stars asChallenges to Evolution, ed. C. A. Tout & W. van Hamme, 221Harmanec, P., Habuda, P., Štefl, S., et al. 2000, A&A, 364, L85Henrichs, H. F., Hammerschlag-Hensberge, G., Howarth, I. D., & Barr, P. 1983,ApJ, 268, 807Henry, G. W. & Smith, M. A. 2012, ApJ, 760, 10Ho ffl eit, D. & Jaschek, C. 1991, The Bright Star CatalogueHoraguchi, T., Kogure, T., Hirata, R., et al. 1994, PASJ, 46, 9Howarth, I. D., Dufton, P. L., Dunstall, P. R., et al. 2015, A&A, 582, A73Howarth, I. D. & Prinja, R. K. 1989, ApJS, 69, 527Huang, S.-S. 1966, ARA&A, 4, 35Jahoda, K., Swank, J. H., Giles, A. B., et al. 1996, in Proc. SPIE, Vol. 2808,EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VII, ed. O. H.Siegmund & M. A. Gummin, 59–70 Je ff ery, C. S. & Hamann, W. R. 2010, MNRAS, 404, 1698Jernigan, J. G. 1976, IAU Circ., 2900Kambe, E., Hirata, R., Ando, H., et al. 1997, ApJ, 481, 406Kee, N. D., Owocki, S., & Kuiper, R. 2018, MNRAS, 474, 847Krtiˇcka, J. 2014, A&A, 564, A70Kˇríž, S. & Harmanec, P. 1975, Bulletin of the Astronomical Institutes ofCzechoslovakia, 26, 65Labadie-Bartz, J., Chojnowski, S. D., Whelan, D. G., et al. 2018, AJ, 155, 53Langer, N. 1989, A&A, 210, 93Langer, N. 1998, A&A, 329, 551Langer, N. 2012, ARA&A, 50, 107Lee, U., Osaki, Y., & Saio, H. 1991, MNRAS, 250, 432Lopes de Oliveira, R., Smith, M. A., & Motch, C. 2010, A&A, 512, A22Markova, N., Puls, J., & Langer, N. 2018, A&A, 613, A12Martayan, C., Frémat, Y., Hubert, A.-M., et al. 2007, A&A, 462, 683Martin, R. G., Nixon, C. J., Pringle, J. E., & Livio, M. 2019, arXiv e-prints[ arXiv:1901.01580 ]Mayer, A., Deschamps, R., & Jorissen, A. 2016, A&A, 587, A30McAlister, H. A., ten Brummelaar, T. A., Gies, D. R., et al. 2005, ApJ, 628, 439Meilland, A., Millour, F., Kanaan, S., et al. 2012, A&A, 538, A110Meurs, E. J. A., Piters, A. J. M., Pols, O. R., et al. 1992, A&A, 265, L41Miroshnichenko, A. S., Bjorkman, K. S., & Krugov, V. D. 2002, PASP, 114, 1226Motch, C., Lopes de Oliveira, R., & Smith, M. A. 2015, ApJ, 806, 177Mourard, D., Monnier, J. D., Meilland, A., et al. 2015, A&A, 577, A51Nazé, Y. & Motch, C. 2018, A&A, 619, A148Nazé, Y., Rauw, G., & Cazorla, C. 2017, A&A, 602, L5Neiner, C., de Batz, B., Cochard, F., et al. 2011, AJ, 142, 149Nemravová, J., Harmanec, P., Koubský, P., et al. 2012, A&A, 537, A59Ochsenbein, F., Bauer, P., & Marcout, J. 2000, A&AS, 143, 23Okazaki, A. T. & Negueruela, I. 2001, A&A, 377, 161Oskinova, L. M., Clarke, D., & Pollock, A. M. T. 2001, A&A, 378, L21Packet, W. 1981, A&A, 102, 17Panoglou, D., Faes, D. M., Carciofi, A. C., et al. 2018, MNRAS, 473, 3039Parmar, A. N., Israel, G. L., Stella, L., & White, N. E. 1993, A&A, 275, 227Peters, G. J. & Gies, D. R. 2005, in Astronomical Society of the Pacific Confer-ence Series, Vol. 337, The Nature and Evolution of Disks Around Hot Stars,ed. R. Ignace & K. G. Gayley, 294Peters, G. J., Pewett, T. D., Gies, D. R., Touhami, Y. N., & Grundstrom, E. D.2013, ApJ, 765, 2Peters, G. J., Wang, L., Gies, D. R., & Grundstrom, E. D. 2016, ApJ, 828, 47Petrovic, J., Langer, N., & van der Hucht, K. A. 2005, A&A, 435, 1013Pittard, J. M. & Dawson, B. 2018, MNRAS, 477, 5640Pols, O. R. 1994, A&A, 290, 119Pols, O. R., Cote, J., Waters, L. B. F. M., & Heise, J. 1991, A&A, 241, 419Pols, O. R. & Marinus, M. 1994, A&A, 288, 475Postnov, K., Oskinova, L., & Torrejón, J. M. 2017, MNRAS, 465, L119Raguzova, N. V. 2001, A&A, 367, 848Rappaport, S., Podsiadlowski, P., & Horev, I. 2009, ApJ, 698, 666Reid, A. H. N., Bolton, C. T., Crowe, R. A., et al. 1993, ApJ, 417, 320Reig, P. 2011, Ap&SS, 332, 1Renzo, M., Zapartas, E., de Mink, S. E., et al. 2019, A&A, 624, A66Ricker, G. R., Vanderspek, R., Winn, J., et al. 2016, in Society of Photo-OpticalInstrumentation Engineers (SPIE) Conference Series, Vol. 9904, Proc. SPIE,99042BRímulo, L. R., Carciofi, A. C., Vieira, R. G., et al. 2018, MNRAS, 476, 3555Rivinius, T., Baade, D., & Carciofi, A. C. 2016, A&A, 593, A106Rivinius, T., Baade, D., Stefl, S., et al. 1998, in Astronomical Society of thePacific Conference Series, Vol. 135, A Half Century of Stellar Pulsation In-terpretation, ed. P. A. Bradley & J. A. Guzik, 343Rivinius, T., Baade, D., & Štefl, S. 2003, A&A, 411, 229Rivinius, T., Carciofi, A. C., & Martayan, C. 2013, A&A Rev., 21, 69Rivinius, T., Štefl, S., & Baade, D. 1999, A&A, 348, 831Rivinius, T., Štefl, S., Maintz, M., Stahl, O., & Baade, D. 2004, A&A, 427, 307Robinson, R. D., Smith, M. A., & Henry, G. W. 2002, ApJ, 575, 435Samus’, N. N., Kazarovets, E. V., Durlevich, O. V., Kireeva, N. N., & Pas-tukhova, E. N. 2017, Astronomy Reports, 61, 80Sano, T., Miyama, S. M., Umebayashi, T., & Nakano, T. 2000, ApJ, 543, 486Secchi, A. 1866, Astronomische Nachrichten, 68, 63Semaan, T., Hubert, A. M., Zorec, J., et al. 2018, A&A, 613, A70Shrader, C. R., Hamaguchi, K., Sturner, S. J., et al. 2015, ApJ, 799, 84Smith, M. A. 2006, A&A, 459, 215Smith, M. A. 2019, PASP, 131, 044201Smith, M. A. & Balona, L. 2006, ApJ, 640, 491Smith, M. A., Lopes de Oliveira, R., & Motch, C. 2012a, ApJ, 755, 64Smith, M. A., Lopes de Oliveira, R., & Motch, C. 2016a, Advances in SpaceResearch, 58, 782Smith, M. A., Lopes de Oliveira, R., & Motch, C. 2016b, in Astronomical Soci-ety of the Pacific Conference Series, Vol. 506, Bright Emissaries: Be Stars asMessengers of Star-Disk Physics, ed. T. A. A. Sigut & C. E. Jones, 215Smith, M. A., Lopes de Oliveira, R., & Motch, C. 2017, MNRAS, 469, 1502 Article number, page 15 of 16 & A proofs: manuscript no. gCas-resub
Smith, M. A., Lopes de Oliveira, R., Motch, C., et al. 2012b, A&A, 540, A53Smith, M. A., Robinson, R. D., & Hatzes, A. P. 1998, ApJ, 507, 945Soszynski, I., Udalski, A., Kubiak, M., et al. 2005, Acta Astron., 55, 331Stee, P., Meilland, A., Bendjoya, P., et al. 2013, A&A, 550, A65Struve, O. 1931, ApJ, 73, 94Struve, O. 1963, PASP, 75, 207Tauris, T. M. & van den Heuvel, E. P. J. 2006, Formation and evolution of com-pact stellar X-ray sources, Vol. 39, 623–665Thaller, M. L., Bagnuolo, Jr., W. G., Gies, D. R., & Penny, L. R. 1995, ApJ, 448,878Tsujimoto, M., Morihana, K., Hayashi, T., & Kitaguchi, T. 2018, PASJ, 70, 109Tycner, C., Gilbreath, G. C., Zavala, R. T., et al. 2006, AJ, 131, 2710ud-Doula, A., Owocki, S. P., & Kee, N. D. 2018, MNRAS, 478, 3049Vanbeveren, D., Mennekens, N., Shara, M. M., & Mo ff at, A. F. J. 2018, A&A,615, A65Vink, J. S. 2017, A&A, 607, L8von Zeipel, H. 1924, MNRAS, 84, 665Wade, G. A., Petit, V., Grunhut, J. H., Neiner, C., & MiMeS Collaboration. 2016,in Astron. Soc. Pacific Conf. Ser., Vol. 506, Bright Emissaries: Be Stars asMessengers of Star-Disk Physics, ed. T. A. A. Sigut & C. E. Jones, 207Walker, G. A. H., Kuschnig, R., Matthews, J. M., et al. 2005, ApJ, 623, L145Wang, L., Gies, D. R., & Peters, G. J. 2017, ApJ, 843, 60Wang, L., Gies, D. R., & Peters, G. J. 2018, ApJ, 853, 156Waters, L. B. F. M., Pols, O. R., Hogeveen, S. J., Cote, J., & van den Heuvel,E. P. J. 1989, A&A, 220, L1Wellstein, S. & Langer, N. 1999, A&A, 350, 148Wellstein, S., Langer, N., & Braun, H. 2001, A&A, 369, 939Wenger, M., Ochsenbein, F., Egret, D., et al. 2000, A&AS, 143, 9Wisniewski, J. P., Draper, Z. H., Bjorkman, K. S., et al. 2010, ApJ, 709, 1306Woosley, S. E. 2019, ApJ, 878, 49Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868Yang, S., Ninkov, Z., & Walker, G. A. H. 1988, PASP, 100, 233Yudin, R. V. 2001, A&A, 368, 912Zharikov, S. V., Miroshnichenko, A. S., Pollmann, E., et al. 2013, A&A, 560,A30Zorec, J. & Briot, D. 1997, A&A, 318, 443at, A. F. J. 2018, A&A,615, A65Vink, J. S. 2017, A&A, 607, L8von Zeipel, H. 1924, MNRAS, 84, 665Wade, G. A., Petit, V., Grunhut, J. H., Neiner, C., & MiMeS Collaboration. 2016,in Astron. Soc. Pacific Conf. Ser., Vol. 506, Bright Emissaries: Be Stars asMessengers of Star-Disk Physics, ed. T. A. A. Sigut & C. E. Jones, 207Walker, G. A. H., Kuschnig, R., Matthews, J. M., et al. 2005, ApJ, 623, L145Wang, L., Gies, D. R., & Peters, G. J. 2017, ApJ, 843, 60Wang, L., Gies, D. R., & Peters, G. J. 2018, ApJ, 853, 156Waters, L. B. F. M., Pols, O. R., Hogeveen, S. J., Cote, J., & van den Heuvel,E. P. J. 1989, A&A, 220, L1Wellstein, S. & Langer, N. 1999, A&A, 350, 148Wellstein, S., Langer, N., & Braun, H. 2001, A&A, 369, 939Wenger, M., Ochsenbein, F., Egret, D., et al. 2000, A&AS, 143, 9Wisniewski, J. P., Draper, Z. H., Bjorkman, K. S., et al. 2010, ApJ, 709, 1306Woosley, S. E. 2019, ApJ, 878, 49Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868Yang, S., Ninkov, Z., & Walker, G. A. H. 1988, PASP, 100, 233Yudin, R. V. 2001, A&A, 368, 912Zharikov, S. V., Miroshnichenko, A. S., Pollmann, E., et al. 2013, A&A, 560,A30Zorec, J. & Briot, D. 1997, A&A, 318, 443