A possible nonthermal X-ray emission from γ Cas analogues stars


 We analyze the archival XMM-Newton X-ray observations of 15 γ Cas analogue stars and two candidates for such objects. The EPIC spectra of the considered stars in the range of 0.2-8 keV were extracted and fitted by different models. Our estimates show that assuming the X-ray emission from γ Cas analogues to be totally thermal, their model plasma temperatures can reach anomalously high values. However including an additional power components to the model spectra leads to significant decreasing of the plasma temperatures. The spectral index of the power component is about 1.5, and the fraction of this in the total model flux is rather large (50-90%). Moreover, it decreases with expanding temperature of the X-ray emitting plasma as compared to typical OB stars. We conclude that γ Cas analogues can produce nonthermal X-ray emission within the framework of the Chen & White (1991) model, while if the nonthermal X-rays from typical OB stars exists, they should be generated by different processes.


Introduction
The γ Cas analogues are enigmatic Oe and Be stars with very strong X-ray emission and X-ray luminosities up to L X ∼ 10 32 erg s −1 . Supposing that the X-ray emitting plasma is thermal, its temperature can reach 10-20 keV and more. These values are higher than those for typical OB stars but smaller than typical temperatures for High Mass X-ray Binaries (HMXB). Such stars demonstrate variations of their X-ray emission on a timescale from a few minutes to a few years. The γ Cas analogues are supposed to have the circumstellar Keplerian decretion disks that manifest themselves via strong emission lines in the optical spectra (Naze et al., 2020).
The phenomenon of γ Cas analogues still remains debated. The large-scale magnetic field of stars is unlikely to be responsible for the γ Cas analogue X-rays, because the formation of Keplerian decretion disks is incompatible with the presence of a strong dipolar magnetic fields (Grunhut et al., 2012;ud-Doula et al., 2018). But localized small-scale magnetic fields can interact with instability-generated fields of the disk, leading to flaring X-ray emission (Robinson et al., 2002).
According to Hamaguchi et al. (2016) and Postnov et al. (2017) the X-rays from these enigmatic stars can be generated due to the accretion onto a compact companion. Smith et al. (2016) also consider an interaction of the star and disk magnetic fields as a possible source of X-rays. Later Ryspaeva & Kholtygin (2020) proposed that γ Cas analogues can be the sources of nonthermal X-rays, which are formed in a framework of Chen & White (1991) theory. In such case X-ray emission is "produced through the inverse Compton mechanism when the stellar UV photons are scattered by relativistic electrons accelerated by shocks in the stellar wind near the star"¹.
In the present paper we test and develop the results by Ryspaeva & Kholtygin (2020) analyzing a more extended sample of objects. The paper is organized by the following manner. Section 2 describes the observations used and their reduction. The applied X-ray models are described in Section 3. Results of spectral fits are presented in Section 4. A comparison of the X-ray spectra of γ Cas analogues with those of typical OB stars is given in Section 5. The general conclusions are given in Section 6.

Observations and data reduction
We reanalyzed the archival XMM-Newton X-ray observations of 15 γ Cas analogues and two candidates for such objects HD 42054 and HD 120678. The log of observations is presented in Table 1. We extracted and analyzed the low-resolution stellar spectra from the EPIC ("European Photon Imaging Camera") images. The data reduction was performed using the SAS 19.0 software following the recommendation of the SAS team².
First of all we made the preliminary pipeline of observation data files by the emproc script for EPIC-MOS1/EPIC-MOS2 data, and by the epproc script for EPIC-PN data. The filtration of the EPIC-images from background flares was performed with the tabgtigen and esfilter tasks. The stellar spectra were extracted from the "clean" images by the evselect, arfgen, and rmfgen procedures. The spectra of sources were obtained from the circle region with a radius of not less than 15 ′ centered on the stellar coordinates. They were taken from the SIMBAD³ database and corrected by the images. The background spectra were obtained from the regions of the same size in the places free of other bright 2 www.cosmos.esa.int/web/xmm-newton 3 http://simbad.u-strasbg.fr/Simbad sources. The background spectral correction was performed using the specgroup task.
For each star from our sample we have got three lowresolution spectra extracted from the EPIC-PN, EPIC-MOS1, EPIC-MOS2 images. The EPIC-PN, EPIC-MOS1, and EPIC-MOS2 spectra obtained on different dates were merged using the epicspeccombine command. The stars HD 161103 and HD 316568 were observed twice and their spectra obtained on different dates were also merged.
Futhermore, we extracted light curves with a 200 s step from the EPIC images in the energy bands of 0.2-8 keV and 2-8 keV. Stellar and background light curves were extracted from the same regions as stellar and background spectra using the evselect procedure. Background light curves were substracted by the epiclccorr task. A visual inspection of light curves did not showed fast changes of count rate during the observations.

X-rays spectral models
We fit stellar spectra in the 0.2-8 keV energy band by different models within the "XSPEC 12.10.0"⁴ package. The EPIC-PN, EPIC-MOS1, EPIC-MOS2 spectra are fitted simultaneously. First we approximate spectra by the sums of models APEC (Astrophysical Plasma Emission Code by Smith et al. (2001)) or MEKAL (Mewe et al., 1985(Mewe et al., , 1986Liedahl et al., 1995)⁵ Both models describe the X-ray emission from hot gas with the atoms ionized by electron impact. These models are characterized by the following parameters: -kT is the plasma temperature in keV; norm is the normalized parameter that depends on the emission measure EM and determines a fraction of plasma with the temperature kT: where the emission measure Here d is the distance to the source (in cm), ne and n H are the electron and hydrogen number densities (in cm −3 ) respectively. -Abundance is the metal abundance parameter in X-ray emitted plasma in solar units based on data from the list of Anders & Grevesse (1989), we used this parameter as common in sums of all models for a given star.
Also we use the model of plane-parallel post-shock wave PSHOCK of Borkowski et al. (2001). This model describes nonstationary thermal X-ray emission from the hot plasma heated by shock waves. This model is characterized by the same parameters as the APEC/MEKAL and the additional ionization timescale parameter τu (in s cm −3 ). The parameter τu = T char · ne (s · cm −3 ).
where ne is the postshock electron number density and T char is the characteristic time. In the original model PSHOCK of Borkowski et al. (2001) developed for the supernova remnants T char is the remnant's age t 0 . For the stellar winds we can specify the value of T char to be equal to the plasma cooling time. For all combinations of the considered models we estimated the average plasma temperature Here T i is the temperature of the hot plasma for the contributed model with the number i, n is the number of the model, and norm i is the normalized parameter (1) for the corresponding plasma component. Average plasma temperatures ⟨kT⟩ for γ Cas analogues are close to the highest temperature in the case of a two-temperature model. To search for the possible nonthermal contributions to the common X-ray fluxes in the spectra of γ Cas analogues we fit their X-ray spectra by sums of the APEC, MEKAL or PSHOCK models with the addition of a power law (PL) component. Last model describes nonthermal emission. Together with the spectral index G and the amplitude norm PL of the PL we calculated a fraction of the power component in the whole model flux H total (0.2-8 keV) in the 0.2-8 keV range: where H PL (0.2-8 keV) is the model flux for the PL component only. Likewise we test whether the hypothesis of Chen & White (1991) is valid for the γ Cas analogues. Chen & White supposed that the nonthermal X-rays from the stars should be described by the power law with the spectral index G = 1.5. For this reason we considered the models with both fixed and free parameter G.
To take into account interstellar absorption and possible circumstellar absorption of X-rays, the sums of additive models were multiplied on the TBABS model of Wilms et al. (2000). Last model presents the cross section for X-ray absorption by the interstellar medium (ISM) as a sum of cross sections for X-ray absorption by the gas, grains, and molecules in the ISM. The TBABS model is characterized by the single parameter of hydrogen column density N H in 10 22 cm −2 . To estimate a value of the possible local X-ray absorption by the circumstellar disk or/and stellar wind we subtracted from our N H parameters the interstellar values, which are calculated via the expression of Gudennavar et al. (2012): .12 · 10 21 cm 2 .
In the cases when the hydrogen column density N H determined in our fitting appeared to be less than the value of N G H calculated from Eq. 6 we fixed N H = N G H and multiplied the sum of models by the additional photoelectric absorption model PHABS of Balucinska-Church & McCammon (1992) to determine the local column density N local H .
Besides we calculated three model independent characteristics of the studied spectra: -absorbed X-ray luminosities in intervals 0.2-8 keV and 2-8 keV and -hardness ratio (e.g. Naze et al., 2014) -fraction of hard luminosity 4 Fitting X-ray spectra A list of the considered stars along with their spectral types, distances, color excesses E(B-V) and the above model independent parameters of X-rays is given in Normalized flux, Counts/s/keV spectrum Whole model APEC kT=0.5-7.5 keV APEC kT=17-59 keV HD162718 Figure 1. The best fits of stellar spectra by thermal models. The contributions of individual components into the total model Xray spectra are shown by color lines. For the model spectrum of HD 162718 (bottom panel), confidence ranges of plasma temperature are presented. (Capitanio et al., 2017), but E(B-V) for HD 316568 is taken from Marshall et al. (2006). The results of our spectral fitting are presented in Tables 3-7. Table 3 shows the results of the model fits for combinations of two thermal models APEC or MEKAL. For stars marked with † we are unable to estimate N local H . For these stars the interstellar value N H obtained within the TBABS model given in the table. A value of 1.0 for the Abundance means that this parameters are fixed in one solar unit. A reduced χ 2 /n statistics and degrees of freedom (in brackets) are given in the last column of table. Figure 1 provides the fits of X-rays by thermal models for the selected γ Cas analogues with the labeled contributions of the components with different temperatures. As can be seen from the figure and from data in Table 3 it is mandatory to use high plasma temperature, since an excess of X-ray radiation in the 2-8 keV range can be reproduced only for extremely high plasma temperatures up to kT ∼ 40 keV. HD162718 Figure 4. The same as in Figure 1 but for APEC/MEKAL+PL models with fixed spectral index G = 1.5. Table 4 shows the results of the model fits for combinations of both one of the thermal models APEC/MEKAL and the PSHOCK. The ionization parameter τu is tabulated in Column 7 of the table. Figure 2 demonstrates the fits of X-rays by the APEC/MEKAL+PSHOCK models for the same objects as in Figure 1 excluding HD 44458. Analyzing this figure and the data of Table 4 one can conclude that as for the purely thermal APEC/MEKAL model combinations high temperatures of the shocked plasma are mandatory for most stars. As such temperatures for shocks in the stellar winds of OB stars are hardly achievable we can suggest that the applicability of the combination of APEC/MEKAL+PSHOCK models for describing X-ray spectra of all γ Cas analogues is doubtful.
The results of our spectral fitting by two PSHOCK models only are given in Table 5. Such approximation can be used only for 6 stars. Moreover in this approach similar to the APEC/MEKAL+PSHOCK model combination too high plasma temperatures kT shock are needed. It means that PSHOCK+PSHOCK model is also hardly applicable to describe the X-ray spectra of γ Cas analogues.
Parameters of the spectral fit for the thermal models with a contribution of the PL component are given in Table 6. In this table asterisks indicates spectral fits when the Fe 6.4 keV Kα line is absent in the model spectrum. Analyzing the data of Table 6 we can conclude that the fixation of the G value leads to decreasing fraction of the power component F PL in the total X-ray model flux.      Table 3 but for by PSHOCK+PL models.
Energy, keV  Figure 5. The same as in Figure 1 but for PSHOCK+PL models. Figure 3 shows the examples of the fits of X-ray spectra by APEC/MEKAL+PL model. The analogical fits of spectra of the same stars but with the fixed value G = 1.5 are presented in Figure 4. Analyzing these figures, one can conclude that an additional PL component makes it possible to describe the X-ray spectra of γ Cas analogues with acceptable temperatures of hot plasma.
Parameters of the fit for the model combination PSHOCK+PL are given in Table 7. Both free and fixed values of the spectral index G= 1.5 are used. For all the stars excluding HD 157832 we use fixed Abundance = 1.0. For HD 157832 we accept the parameter Abundance = 0.54 ± 0.25. Also as for the APEC/MEKAL+PL combination the models with the PL component allows us to decrease the plasma temperatures to the acceptable temperatures. Figure 5 demonstrates the fits of X-ray spectra by APEC/MEKAL+PL model with parameters given in Table 7. We are not able to fit spectra of V 2156 Cyg and HD 316568 stars because these spectra are very faint and noisy. We calculate only model independent characteristics of X-rays from these objects.

Comparison with typical OB stars
As it follows from the previous section, X-ray spectra of γ Cas analogues can be described by thermal models with anomalously high plasma temperatures. Meanwhile the spectra of 10 stars can be fitted by the APEC/MEKAL+PSHOCK models, spectra of 6 stars can be fitted by the PSHOCK+PSHOCK models.
In model spectra with the PSHOCK component, plasma temperature can also reach great values ∼20 keV. It means that using the PSHOCK model only or in combination with the thermal models hardly allows to describe the X-ray spec-tra with acceptable for OB stars plasma temperature about 1 keV for γ Cas analogues. Instead adding the power component PL to the sums of thermal models significantly reduced plasma temperature for most of considered stars. In many such approximations kT not more than 10 keV. According to Vink et al. (2009) terminal wind velocity of HD 45314 v∞ = 2410 km s −1 . Hence the upper limit of plasma temperature for this star should be about 7 keV. Therefore, if other γ Cas analogues have similar v∞, than kT < 10 keV can be acceptable for such objects.
Spectra of 13 stars in the APEC/MEKAL+PL model have a power component with the spectral index G~1-2, 14 spectra can be fitted by thermal models with a PL component with the fixed G = 1.5. In both cases F PL ∼ 50 − 90%. In many model spectra fluxes described by the PL component at energies of more 2 keV are higher than the corresponding fluxes for the APEC/MEKAL or PSHOCK model. Adding the PL component to the model spectra reduces plasma temperature to values below 1 keV for some γ Cas analogues. This value is typical for OB stars. But model spectra with such temperatures do not contain the Fe Kα line at 6.4 keV, which is presents in X-ray spectra of γ Cas analogues. Spectra of 7 stars can be fitted by the PSHOCK+PL model. In the recent cases the ionization timescale τu ∼ 10 12 − 10 13 s cm −3 , this is higher by one order than that for typical OB stars (Ryspaeva & Kholtygin, in prep).
To check the possibility of generation of nonthermal X-rays by γ Cas analogues and other mechanisms of origin of their X-rays, we trace possible correlations between the defined characteristics of target stars' spectra. We compare the obtained dependences with similar ones for typical OB stars considered by Ryspaeva & Kholtygin (in prep.). The results of our regression analysis are presented in Table 8. The best correlations are shown in Figures 6-9.
A fraction of hard luminosity F HL for γ Cas analogues increases with HR. This correlation continues the similar dependence for typical OB stars as it is shown in the bottom panel of Figure 6.
Given the whole X-ray emission from γ Cas analogues is thermal, their plasma temperature from the APEC/MEKAL model also increases with a hardness ratio. The correlation coefficient of such dependence is similar to that for typical OB stars (Ryspaeva & Kholtygin, in prep.) but approximation parameters are different.
The bottom panel of Figure 7 demonstrates the fits of dependencies kT vs HR both for typical OB stars and γ Cas analogues and dependence between the lowest model kT in the two-temperature model spectra of γ Cas analogues (squared markers). Approximation of the dependence kT vs. HR for OB type stars is not correct for the lowest model temperature of γ Cas analogues.
At the same time no dependences between HR and plasma temperature from thermal models with the added PL or PSHOCK component from the PSHOCK+PSHOCK model are found. Thus the X-ray emission from γ Cas analogues can be principally thermal but it should be formed by another way than X-rays for typical hot stars.
For the APEC/MEKAL model with additional PL component F PL grows with extending of F HL if the spectral index is fixed at G = 1.5. Top panel of Figure 8 illustrates this dependence. In the same time such dependence is a continuation of similar correlation for model spectra of typical OB stars, but with free parameter G⁸. The approximation parameters of both dependences are very close. Herewith 8 We were unable to fit X-ray spectra of typical OB stars by thermal or/and PSHOCK models with additional power component with fixed G=1.5 (Ryspaeva & Kholtygin, in prep.)   the dependence F PL vs. F HL for model spectra of OB stars and γ Cas analogues combined with free spectra index G takes place too. Furthermore, we revealed a decreases of the fraction of power components F PL of the model spectra of γ Cas analogues with growing plasma temperature unlike for typical OB stars (Ryspaeva & Kholtygin, 2020). This can be seen in Figure 9 (top panel). Whereas F PL of γ Cas analogues grows with the hardness ratio HR if spectral index is fixed at G=1.5. F PL in spectra of typical OB stars is unlike to depend on HR since the correlation coefficient R∼0.4 (Ryspaeva & Kholtygin, in prep.) is low. We can propose, that if the nonthermal X-rays from γ Cas analogues and from typical OB stars exist, they should be generated by different mechanisms.

Discussion and conclusion
On basis of our analysis of the EPIC-spectra of 15 stars of enigmatic class of γ Cas analogues we can made the following essential conclusions.
Assuming the purely thermal origin of X-ray emission from the studied objects we need the extremely hot plasma. At the same time in the model spectra with an additional power component the spectral index G∼1-2, the PL component dominates at hard energies (more 2 keV). This can be interpreted that the X-ray spectra of γ Cas analogues have the nonthermal component produced through the inverse Compton scattering of UV-photons by relativistic electrons in an agreement with the hypothesis of Chen & White (1991).
But since in the 2-8 keV energy region in spectra of γ Cas analogues there can be present a few spectral lines, the thermal contribution to X-rays for these energies may be important. In the cases of the presence of both PL and thermal components with a plasma temperature of about a few keV in the model spectrum we can propose that thermal X-rays are produced in the framework of the models of Hiller et al. (1993), Feldmeier et al. (1997 or due to hybrid model of Cassinelli & Swank (1983), Waldron & Cassinelli (2009). X-ray emission from γ Cas analogues can not be formed according to MCWS model (Babel & Montmerle, 1997;ud-Doula & Owocki, 2002), because they unlike to have strong large-scale magnetic fields.
In our sample there are two candidates for γ Cas analogues HD 42054 and HD 120678. We estimated the characteristics of their X-ray spectra to be similar to those for γ Cas analogues. Therefore, we suggest these stars to be the members of this group of enigmatic objects.

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