Radius, rotational period and inclination of the Be stars in the Be/gamma-ray binaries MWC 148 and MWC 656
R. K. Zamanov, K. A. Stoyanov, J. Marti, V. D. Marchev, Y. M. Nikolov
aa r X i v : . [ a s t r o - ph . S R ] F e b Astronomische Nachrichten, 4 February 2021
Radius, rotational period and inclination of the Be stars in theBe / gamma-ray binaries MWC 148 and MWC 656 ⋆ R. K. Zamanov ,⋆⋆ , K. A. Stoyanov , J. Mart´ı , V. D. Marchev , and Y. M. Nikolov Institute of Astronomy and National Astronomical Observatory, Bulgarian Academy of Sciences,Tsarigradsko Shose 72, BG-1784 Sofia, Bulgaria Departamento de F´ısica, Escuela Polit´ecnica Superior de Ja´en, Universidad de Ja´en, Campus Las Lagunillas, A3,23071, Ja´en, SpainReceived 2020 November 3, accepted 2020 February 3Published online ...
Key words
Stars: emission-line, Be – binaries: spectroscopic – Gamma rays: stars – Stars: individual: MWC 148,MWC 656Using TESS photometry and Rozhen spectra of the Be / γ -ray binaries MWC 148 and MWC 656, we estimate the projectedrotational velocity ( v sin i ), the rotational period (P rot ), radius (R ), and inclination ( i ) of the mass donor. For MWC 148we derive P rot = . ± .
03 d, R = . ± . ⊙ , i = ◦ ± ◦ , and v sin i = ± − . For MWC 656 we obtainP rot = . ± .
03 d, R = . ± . ⊙ , i = ◦ ± ◦ , and v sin i = ± − . For MWC 656 we also find that therotation of the mass donor is coplanar with the orbital plane. Copyright line will be provided by the publisher
The γ -ray binaries are a recently established and rare sub-class of the high-mass X-ray binaries with most of their lu-minosity output being radiated above 1 MeV (Dubus 2013;Chernyakova & Malyshev 2020). They are composed ofan OBe donor star and a neutron star or a black hole(Mirabel 2012). The mechanism responsible for the high-energy emission in these systems is still a subject of debate.The γ -rays could be produced either by accretion-drivenjets, or by the rotation-powered strong pulsar winds inter-acting with the nearby medium (Dubus 2006; Romero et al.2007; Massi & Jaron 2013), and / or by a neutron star in thepropeller regime (Wang & Robertson 1985).So far, seven systems have been confirmed as γ -ray bi-naries - PSR B1259-63 (Aharonian et al. 2005a), LS 5039(Aharonian et al. 2005b), LS I +
61 303 (Albert et al. 2006),HESS J0632 +
057 (Aharonian et al. 2007), 1FGL J1018.6-5856 (Corbet et al. 2011), PSR J2032 + + γ -ray binaries are pro-posed. The first subgroup harbours an O-type donor star andshows a single-peak profile in their γ -ray light-curve. Thesecond subgroup contains an OBe star and shows severalpeaks in their light-curves, occasionally correlated with the ⋆ Data from TESS and Rozhen ⋆⋆ Corresponding author: [email protected] times when the compact object crosses and in some casestruncates the circumstellar disc of the donor star (Paredes &Bordas 2019).MWC 148 (HD 259440) was identified as the opticalcounterpart of the variable TeV source HESS J0632 + orb = + − d (Aliu et al. 2014).MWC 656 (HD 215227) is the suspected optical coun-terpart of the γ -ray source AGL J2241 + AGILE satellite above 100 MeV (Lucarelli et al. 2010;Williams et al. 2010). It is the first discovered binary con-taining a black hole as a companion of a Be star (Casareset al. 2014). MWC 656 was only occasionally detected atGeV energies (Aleksi´c et al. 2015). The black hole natureof the compact object renders it similar to the typical γ -raybinaries. The orbital period of the system, obtained by opti-cal photometry and later confirmed by radial velocity mea-surements, is P orb = . ± .
04 d (Williams et al. 2010;Casares et al. 2014).Here, using photometric and spectral observations, weestimate the rotational period, the radius and the inclinationof the mass donors in the Be / γ -ray binaries MWC 148 andMWC 656. We use both space photometry and ground-based spectra.
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Zamanov et al.: The Be / gamma ray binaries MWC 148 and MWC 656 Table 1
Spectroscopic observations of MWC 148 and MWC 656. In the table are given the date of observations,UT start, exposure time in seconds, signal-to-noise ratio at about 6600 Å, EW(H α ), FWHM( H α ), EW(FeII5316), andFWZI(FeII5316). Object Date-obs exp-time S / N EW(H α ) FWHM(H α ) EW(FeII5316) FWZI(FeII)yyyy-mm-dd:hh:mm [sec] [Å] [km s − ] [Å] [km s − ]MWC 148 2019-02-20T18:45 2400 75 -46.9 411 -0.59 672MWC 148 2019-12-06T01:45 2400 95 -46.4 405 -0.60 711MWC 148 2020-01-16T21:16 3600 70 -44.8 418 -0.59 683MWC 148 2020-09-06T02:01 1800 60 -43.7 412 -0.57 709MWC 656 2019-08-22T20:10 3600 90 -20.9 493 -0.48 705MWC 656 2019-12-05T17:48 2400 100 -21.6 491 -0.54 722MWC 656 2020-09-05T21:50 3600 64 -21.7 490 -0.60 700 Fig. 1
The emission lines H α and FeII 5316 in the spectra of MWC 148 (left panel) and MWC 656 (right panel). The
Transiting Exoplanet Survey Satellite ( TESS , Rickeret al. 2015) is a space-based optical telescope launched in2018 with the primary mission to perform an all-sky sur-vey to search for transiting exoplanets. In order to fulfill themission, the sky is divided into a number of sectors , each ofwhich corresponds to the total field of view of all four cam-eras of the telescope – 24 ◦ × ◦ . Each sector is observedfor approximately 27 days at a cadence of 2 minutes. Sim-ple aperture photometry is applied to each of the data files toobtain a barycentered light curve file of the selected object.The bandpass of TESS is centered on the classical I c filter,but it is wider and spans from 6000 Å to 10 000 Å, in otherwords the telescope observes the red and the near-infraredemissions of the stars. The light curves of MWC 656 andMWC 148 were downloaded from the Mikulski Archive forSpace Telescopes archives . https: // archive.stsci.edu / tess / The spectral observations were obtained with the ESPEROspectrograph of the 2.0m RCC telescope at Rozhen NationalAstronomical Observatory located in Rhodope Mountain,Bulgaria. ESPERO is a fiber-fed Echelle spectrograph giv-ing a dispersion of 0.06 Å px − and resolving power ∼ α ) and the full width at half maximum (FWHM) ofthe H α emission line, equivalent width EW(5316) and thefull width at zero intensity (FWZI) of the FeII 5316 Å line.FWZI is the full width of the emission line at the continuumlevel. Examples of the emission lines are presented in Fig. 1.They are normalized to the local continuum. The typical er-rors of our measurements are ±
5% in EW(H α ), ± − in FWHM(H α ), ±
10% in EW(FeII5316), ±
40 km s − inFWZI(FeII). The log of observations is given in Table 1. Copyright line will be provided by the publisher sna header will be provided by the publisher 3
Traces of residual wings due to photospheric absorp-tion were not detected and the interpolated continuum wastaken as the baseline during the measurements of EW andFWHM. The equivalent width is measured using splot rou-tine in IRAF by marking two continuum points around theline to be measured. The linear continuum is subtracted andthe flux is determined by simply summing the pixels withpartial pixels at the ends. The method calculates the areaunder the profile irrespective of its shape (e.g. Mathew &Subramaniam 2011). The FWHM is measured by identify-ing the points of the emission line profile where the intensityis equal to one half of the peak intensity, as shown in Fig. 1of Glebocki et al. (1986). The horizontal distance betweenthis two points was measured. This measurement also doesnot depend on the profile shape.
In this section we give the equations connecting the relevantparameters of the primary components on which our esti-mates are based. For the Be stars, Hanuschik (1989) givesa relation between projected rotational velocity ( v sin i ),FWHM(H α ), and EW(H α ). We use his relation in the form v sin i = .
813 (FWHM 10 .
08 log EW(H α ) − . − , (1)where FWHM and v sin i are measured in km s − ; EW(H α )is in Å.The Fe II lines are optically thin and their profiles re-flect the Keplerian rotation in the innermost part of the Bedisc (Hanuschik 1996). The inclination of the Be star is con-nected with the full width at zero intensity of the FeII linesand its radius:FWZI2 sin i = GM (1 + ǫ )R ! / , (2)where G is the gravitational constant, M is the mass of theBe star, R is its radius, i is the inclination of the Be star tothe line of sight, ǫ is a dimensionless parameter, ǫ ≥
0. Eq. 2represents the Keplerian motion in the disc and is a modifi-cation of that used in Sect. 6.1 of Casares et al. (2012). Theregion where the Fe II lines are produced can be extendeddown to the very surface of the Be star or close to it. Theparameter ǫ , for which we adopt 0 ≤ ǫ < .
1, representshow close to the surface of star the emission at FWZI of theFeII lines is formed.The rotational period of the Be star is also connectedwith the above parameters:P rot = π R v sin i sin i . (3)The rotational periodicity is probably due to the interactionbetween the magnetic field of the Be star and its circum-stellar disc or the presence of some physical feature, suchas a spot or cloud, co-rotating with the star (Smith, Henry& Vishniac 2006). The rotational periods in the Be / γ -raybinaries are expected to be of order 1 day (Zamanov et al.2016).The applied methodology involves the following steps: 1. A periodogram analysis of the TESS data is performedto estimate P rot ;2. The parameter v sin i is estimated using Eq. 1 and thedata in Table 1;3. A mass value for the Be star is adopted according to itsspectral type;4. Using Eq. 2 and Eq. 3, the values of R and i are calcu-lated for the primaries of MWC 148 and MWC 656.The period-search methods applied to the TESS photometrywere the phase dispersion minimization, PDM (Stellingwerf1978) and the CLEAN algorithm (Roberts, Lehar & Dreher1987). TESS photometry for MWC 148, in the intervalJD 2451468.2 – JD 2451490.0, can be accessed underInput Catalogue ID 234929785 and is plotted in Fig. 2. Theperiodogram analysis is presented in the left panel of Fig. 3,where the PDM statistic (theta) and the CLEAN componentamplitude are plotted. Over the entire data set, the analysisyields P rot = . ± . − ± .
03 days, in the interval 1468– 1477 a clear period of 1.131 ± .
025 days, and in theinterval 1478 – 1490 a clear period of 1.075 ± .
025 days.A visual inspection of the data gives us the possibility toselect the parts of the light curve where this periodicityis most clearly visible. Using days 1468 – 1474, we find1.156 d, and for days 1479 – 1487 we find 1.101 d. Thelight curve for days 1468 – 1474 is plotted in the right panelof Fig. 3. We consider that the rotational period of the Bestar in MWC 148 is in the range 1 . ≤ P rot < .
16 d.Using Eq. 1 and the values given in Table 1, we find v sin i = ± − . Casares et al. (2012) give a spec-tral type B0Vpe. A B0V star is expected to have on aver-age mass M = . ± . ⊙ (Hohle et al. 2010). ForMWC 148, Aragona et al. (2010) derived M = . − . ⊙ from spectral model fits, which is in agreementwith the adopted M = . ⊙ . Adopting FWZI( λ ≈
694 km s − , and v sin i =
272 km s − , we find i = ◦ ± ◦ and R = . ± . ⊙ .It is worth noting for comparison that (i) a B0V star isexpected to have R = . R ⊙ (Straizys & Kuriliene 1981);(ii) Casares et al. (2012) give FWZI( λ ∼ − and v sin i =
373 km s − ; (iii) v sin i =
430 km s − (Guti´errez-Soto et al. 2007) and v sin i =
500 km s − (Arag-ona et al. 2010) are reported for this object. TESS photometry for MWC 656 (HD 215227), in the in-terval JD 2451738 – 2451763, can be accessed under In-
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Zamanov et al.: The Be / gamma ray binaries MWC 148 and MWC 656 Fig. 2
TESS light curve of MWC 148.
Fig. 3
Left panel: periodogram analysis for MWC 148 – theta and power versus period. The right panel represents thelight curve during 1468 - 1474 folded with a 1.156 d period.
Fig. 4
TESS light curve of MWC 656.
Fig. 5
Left panel: periodogram analysis for MWC 148. The most significant period is 0.559 days. The right panel rep-resents the light curve during 1751 - 1763 folded with a 1.117 d period, which is probably the rotational period of the Bstar.
Copyright line will be provided by the publisher sna header will be provided by the publisher 5 put Catalogue ID 153880067 (Fig. 4). The data gap is dueto the telescope being repointed to transfer data to Earthat this time. The periodogram analysis is shown in the leftpanel of Fig. 5 with the same kind of plots as for the pre-vious source. Over the entire data set, the analysis yieldsP rot = . ± . − ± .
025 days is detected. Looking at the in-terval 1760-1763 days, we see that there is a repetition ofstrong and weak maxima, which probably means that therotational period is doubled P rot = .
117 d.For the primary, Williams et al. (2010) estimated T e ff = ± g = . ± .
2, M = . ± . ⊙ ,and R = . ± . ⊙ . Casares et al. (2014) found that themass donor is a giant (B1.5-2 III) and gave a mass range10–16 M ⊙ . From the results of Hohle et al. (2010), such astar is expected to have 8 . < M < . ⊙ .Using the relation between v sin i , FWHM( H α ), andEW(H α ) (Eq. 1), and our values (see Table 1), we find v sin i = ± − , which is similar to the values330 ±
30 km s − (Casares et al. 2014), 262 ±
26 km s − (Yudin 2001), and 330 ±
50 km s − (Williams et al. 2010).We measure FWZI(FeII 5316) = = ±
12 km s − , which is below the value FWZI(FeII 5018) ∼ − (Casares et al. 2012).Adopting M = . ± . ⊙ , v sin i =
313 km s − ,and FWZI ( FeII ) =
709 km s − , the system of Eqs. 2 and3 can be solved. As a result, we find R = . ± . ⊙ and i = ◦ ± ◦ . The obtained value of R agrees with theestimates of the average radius for a B1.5-2 III star (8 . − . ⊙ , Straizys & Kuriliene 1981).For MWC 656, from the radial velocity measurements,Casares et al. (2014) obtained M sin i orb = . ± . =
10 M ⊙ , this gives 53 ◦ < i orb < ◦ . It appears thatthe orbital plane and the equatorial plane of the Be star arepractically coplanar within ± ◦ . In Be / X-ray binaries the primary is a rapidly rotating Be starwith mass ∼
10 M ⊙ and the secondary is a neutron star ora black hole. The secondary mass is expected to be ∼ ⊙ for a neutron star, and ∼ ⊙ in the case of black hole.The orbital periods are in the range 10 – 400 d (Reig 2011).The Be / γ -ray binaries are a subgroup of the Be / X-ray bina-ries and should have similar binary parameters. They are aproduct of the evolution of a binary containing two moder-ately massive stars, which undergoes mass transfer from theoriginally more massive star towards its companion (Pols etal. 1991; Negueruela 2007). The eccentricities in these sys-tems are caused by a kick to the compact object during thesupernova explosion that formed it (e.g. Martin et al. 2009).HESS J0632 +
057 (MWC 148) produces non-thermalradio, X-ray, GeV and very high-energy gamma-ray emis-sion. The non-thermal emission is modulated with the 315 days orbital period and has a a peculiar light curve contain-ing two peaks, separated by a dip – a sharp peak with a shortdecay before the apastron passage and a broad (several tensof days) secondary peak after the apastron passage in X-raysand TeV (Aliu et al. 2014, Archer et al. 2020). The non-thermal activity before and around apastron can be linkedto (i) the accumulation of non-thermal particles in the vicin-ity of the binary, and the sudden drop of the emission be-fore apastron is produced by the disruption of the two-windinteraction structure, allowing these particles to escape e ffi -ciently (Bosch-Ramon et al. 2017) or (ii) an accumulationof hot shocked plasma in the inner spiral arm, later releasedwhen the spiral arm is disrupted in the periastron-apastrondirection (Barkov & Bosch-Ramon 2018).For MWC 148, two solutions for the orbit indicate thatit is highly eccentric: e = . ± .
08 (Casares et al. 2012)and e = . ± .
29 (Moritani et al. 2018). In our previouspaper (Zamanov et al. 2017), we assumed the value of i , onthe basis of the strong resemblance of the optical emissionlines between MWC 148 and the bright Be star γ Cas (Za-manov, Stoyanov & Mart´ı 2016), for which the inclination is i = ◦ ± ◦ (Poeckert & Marlborough 1978; Clarke 1990).Our result here for MWC 148 ( i = ◦ ± ◦ ) confirms theassumption that one of the reasons for this similarity is theinclination.MWC 656 is faint in X-rays and it reaches the faintestX-ray luminosities ever detected in stellar-mass black holes(Rib´o et al. 2017). It may not continuously emit in γ -rays(Alexander & McSwain 2016). For this binary, Casares et al.(2014) found that the mass of the black hole is in the range3.8 – 6.9 M ⊙ . The orbital eccentricity is e = ± ff ects –it renders the orbit eccentric and it misaligns the orbit withrespect to the spin axis of the Be star. In systems that ex-perience low velocity kicks, the misalignments tend to besmall (Martin et al. 2011). The low orbital eccentricity andthe alignment between the spin axis of the primary and theaxis of the binary orbit, indicates that the compact object inMWC 656 was born with low kick velocity. We evaluated some parameters for the mass donor starsin the Be / γ -ray binaries MWC 148 and MWC 656. ForMWC 148, we estimate v sin i = ± − , P rot = . ± .
03 d, R = . ± . ⊙ , and i = ◦ ± ◦ . ForMWC 656, we obtain v sin i = ± − , P rot = . ± .
03 d, R = . ± . ⊙ , and i = ◦ ± ◦ . Theseparameters should be useful for future accurate modeling ofthese systems. Copyright line will be provided by the publisher
Zamanov et al.: The Be / gamma ray binaries MWC 148 and MWC 656 Acknowledgements.
This work is supported by Bulgarian Na-tional Science Fund – project K Π -06-H28 / / AEI / / / References