143 Acta Polytechnica CTU Proceedings 2(1): 143–147, 2015 143 doi: 10.14311/APP.2015.02.0143 Model Atmosphere Spectrum Fit to the Soft X-Ray Outburst Spectrum of SS Cyg V. F. Suleimanov1,2, C. W. Mauche3, R. Ya. Zhuchkov2, K. Werner1 1Institute for Astronomy and Astrophysics, Kepler Center for Astro and Particle Physics, Eberhard Karls University, Sand 1, 72076 Tübingen, Germany 2Kazan (Volga region) Federal University, Kremlevskaya str. 18, 42008 Kazan, Russia 3Lawrence Livermore National Laboratory, L-473, 7000 East Ave., Livermore, CA 94550, USA Corresponding author: suleimanov@astro.uni-tuebingen.de Abstract The X-ray spectrum of SS Cyg in outburst has a very soft component that can be interpreted as the fast-rotating optically thick boundary layer on the white dwarf surface. This component was carefully investigated by Mauche (2004) using the Chandra LETG spectrum of this object in outburst. The spectrum shows broad (≈ 5 Å) spectral features that have been interpreted as a large number of absorption lines on a blackbody continuum with a temperature of ≈ 250 kK. Because the spectrum resembles the photospheric spectra of super-soft X-ray sources, we tried to fit it with high gravity hot LTE stellar model atmospheres with solar chemical composition, specially computed for this purpose. We obtained a reasonably good fit to the 60–125 Å spectrum with the following parameters: Teff = 190 kK, log g = 6.2, and NH = 8 · 1019 cm−2, although at shorter wavelengths the observed spectrum has a much higher flux. The reasons for this are discussed. The hypothesis of a fast rotating boundary layer is supported by the derived low surface gravity. Keywords: cataclysmic variables - dwarf novae - radiation transfer - X-rays - individual: SS Cyg ≡ BD+42◦ 4189a. 1 Introduction SS Cyg is one of the brightest cataclysmic variables (CVs), one of the best-studied dwarf nova stars (Warner 1995), and was the first CV discovered in X-ray radi- ation (Rappaport et al. 1974). The properties of the X-ray radiation of this close binary system have been extensively investigated, and are observed to be dra- matically different in quiescence and in outburst. In quiescence, the X-ray spectrum is hard and can be de- scribed by an optically thin hot (kT ≈ 20 keV) plasma with an observed flux ≈ 2 · 10−10 erg s−1 cm−2. In out- burst, this hard component decreases by a factor of ten, the plasma temperature is reduced to ∼ 6–8 keV, and an additional soft component appears with a blackbody temperature ≈ 200–300 kK (Córdova et al. 1980; Mc- Gowan et al. 2004; Ishida et al. 2009). It is commonly accepted that the X-ray radiation of non-magnetic CVs arises in the boundary layer (BL) between the white dwarf (WD) and the accretion disc (Pringle & Savonije 1979; Tylenda 1981; Patterson & Raymond 1985a, b; Kley 1991), which are optically thick at high accretion rates (Ṁ > 1016 g s−1) and optically thin at lower ac- cretion rates. The soft X-ray spectrum of SS Cyg in outburst was carefully investigated by Mauche (2004) using a high- resolution spectrum obtained with the Chandra LETG. He phenomenologically described the observed 40–130 Å spectrum by a blackbody with temperature T ≈ 250 kK and numerous broad absorption features of ions of cosmically abundant O, Ne, Mg, Si, S, and Fe. The BL luminosity and WD spin were also evaluated in this work. On the other hand, this spectrum looks like the photospheric spectra of super-soft X-ray sources (Lanz et al. 2005; Rauch et al. 2010; van Rossum 2012), so it probably could be described using the spectra of hot stellar model atmospheres. Boundary layers pos- sibly rotate with almost Keplerian velocities and could have reduced (in comparison with WD) surface gravi- ties close to the local Eddington limit. Therefore, we consider close to Eddington limit models in the present work. Here we present our attempt to fit the Chandra LETG spectrum of SS Cyg using such model spectra. We also make estimates of the BL parameters in the context of our model fits. 2 Model Atmospheres The version of the LTE computer code ATLAS (Ku- rucz 1970; 1993), modified by us to deal with high temperatures (Ibragimov et al. 2003; Suleimanov & Werner 2007), was used to model high temperature at- 143 http://dx.doi.org/10.14311/APP.2015.02.0143 V. F. Suleimanov et al. mospheres. In this code, local thermodynamic equilib- rium (LTE) is assumed and the pressure ionization ef- fects using the occupation probability formalism (Hum- mer & Mihalas 1988) as described by Hubeny et al. (1994) are taken into account. Coherent electron scat- tering together with the free-free and bound-free tran- sitions of all ions of the 15 most abundant elements us- ing cross-sections from Verner & Yakovlev (1995) were adopted for the continuum opacity. Line blanketing is also included using ∼ 25000 spectral lines from the CHI- ANTI, Version 3.0, atomic database (Dere et al. 1997). 140 160 180 200 220 240 260 5.6 5.8 6.0 6.2 6.4 6.6 6.8 g < g Edd lo g g T Eff , kK 10-5 10-4 10-3 10-2 10-1 1 10 102 0 1 2 3 4 5 6 7 8 9 10 11 12 g r ad / g Column density, g cm-2 T Eff = 200 kK, log g = log g Edd + 0.2 = 6.28 T Eff = 200 kK, log g = log g Edd + 0.4 = 6.48 T Eff = 250 kK, log g = log g Edd + 0.2 = 6.67 Figure 1: Top panel: Positions of the computed model atmospheres in the Teff –log g plane. The dashed curve demarcates the Eddington limit (log g = log gEdd). Bot- tom panel: The relative radiation force vs. depth for various model atmospheres. Twenty-two model atmospheres with solar chemical composition were computed using the described code. The effective temperatures of the models range between 150 kK and 250 kK with a step of 10 kK. Two values of the surface gravity for each effective temperature, namely log g = log gEdd + 0.2 and log g = log gEdd + 0.4, were used. Here log gEdd = log(σe σSBT 4 eff/c) = 4.88 + 4 log(Teff/10 5 K) is the surface gravity that has an equal radiation pressure force for a given Teff , and σe ≈ 0.34 cm2 g−1 is the electron scattering opacity for the as- sumed solar chemical composition. The positions of the computed models on the Teff –log g plane are shown in Fig. 1 (top panel). For the considered model atmo- spheres, a radiation pressure force grad due to spectral lines becomes larger than the surface gravity at the up- per atmospheric layers (see Fig. 1, bottom panel). To enforce hydrostatic equilibrium, we took a gas pressure equal to 10% of the total pressure (Pgas = 0.1Ptot) at all atmospheric layers where grad > g. As shown in Fig. 2, the computed emergent spec- tra are dominated by a forest of absorption lines, and have to be convolved with the LETG spectral resolution and the interstellar gas transmission to be compared with the observed spectrum of SS Cyg (see Fig. 3). The spectra of models with different surface gravities are sufficiently different to discriminate them from a com- parison with the observed spectrum (see Fig. 2, bottom panel). 40 60 80 100 1011 1012 1013 1014 1015 1016 1011 1012 1013 1014 1015 1016 log g = log g Edd + 0.2 = 6.28 log g = log g Edd + 0.4 = 6.48 T Eff = 200 kK H , er g cm -2 s -1 A -1 Wavelength, A T Eff = 150, 200, 250 kK log g = log g Edd + 0.2 H , er g cm -2 s -1 A -1 Figure 2: Top Panel: Emergent spectra of three model atmospheres with the same log g = log gEdd + 0.2 and various effective temperatures: 150 kK (solid curves), 200 kK (dashed curves), and 250 kK (dotted curves). Bottom panel: Emergent spectra of two model atmo- spheres with the same effective temperature (200 kK) and different log g. 3 Results The model spectra convolved with the Chandra LETG spectral resolution ∆λ = 0.05 Å were used to fit the observed soft X-ray spectrum of SS Cyg. The interstel- lar absorption (with the hydrogen column number den- 144 Model Atmosphere Spectrum Fit to the Soft X-Ray Outburst Spectrum of SS Cyg sity NH as a fitting parameter) was also taken into ac- count. The observed spectrum was fitted in the 60–125 Å wavelength range because at the shorter wavelengths our model spectra could be incorrect (see next sec- tion). The best-fit model parameters are Teff = 190 kK, NH = 8·1019 cm−2, and normalization K = 7.82·10−26, and correspond to the models with the lower surface gravity log g = log gEdd + 0.2. The reduced χ 2 = 3.9 is relatively large, hence the formal parameter errors are large, too, and we have not attempted to deter- mine them. The best-fit model spectrum together with the observed spectrum is shown in Fig. 3. The con- tours of χ2 on the Teff –log NH parameter plane are shown in Fig. 4. The normalization can be expressed as K = fR2WD/d 2 where d is the distance to SS Cyg and f is the WD fractional area occupied by the BL, which can be expressed as the relative BL extension along the WD surface f ≈ (2πRWD 2HBL)/(4πR2WD) = HBL/RWD. The basic properties of the BL can be derived from the obtained fit parameters. Using the same sys- tem and WD parameters as used by Mauche (2004) — MWD = 1 M�, RWD = 5.5 · 108 cm (therefore, model log g = 8.46), d = 160 pc, and an accretion disk bolometric luminosity in outburst LDisk = 10 35 erg s−1 — we obtain the fractional area of the BL f = 6.3 · 10−2 (5 · 10−3), the bolometric BL luminosity LBL = 1.8 · 1034 (5 · 1033) erg s−1, and the relative BL luminosity LBL/LDisk = 0.18 (0.05), where the best-fit parameter values obtained by Mauche (2004) are shown in parentheses for comparison. The spin period of the WD in SS Cyg is 12 (9) s as inferred using the relation between the BL and accre- tion disk luminosities (Kluźniak 1987; Kley1991) LBL/LDisk = [1 − ΩWD/ΩK(RWD)]2, (1) where ΩK(RWD) is the Kepler angular velocity at the WD radius. The accepted model gravity on the WD surface in SS Cyg (log gWD = 8.46) is more than two orders of magnitude higher than the obtained BL effective sur- face gravity log geff = 6.2. The surface gravity of the BL can be reduced only by fast rotation of the accreting matter geff = gWD − Ω2BLRWD (2) = gWD (1 − [ΩBL/ΩK(RWD)]2). Therefore, a relative BL angular velocity ΩBL/ΩK(RWD) ≈ 0.98 was obtained using this rela- tion. Figure 3: The Chandra LETG spectrum of SS Cyg in outburst (thick black curve) and the best-fit model atmosphere spectrum with Teff = 190 kK, log g = 6.2, and log NH = 19.9 (thin red curve). The fitting was per- formed in the 60–125 Å wavelength range. The model spectrum at shorter wavelengths is shown by the dashed red curve. Figure 4: Position of the best-fit model in the Teff –log NH parameter plane and contours of χ 2 = [1.5, 3, 6] χ2min. 4 Discussion and Conclusion We present here the results of fitting the SS Cyg Chan- dra LETG spectrum in outburst with model atmo- sphere spectra. The obtained best fit model spectrum does not describe the observed spectrum at short wave- lengths (< 60 Å) and in the 82–90 Å wavelength re- gion and, therefore, it is not statistically acceptable (χ2/dof = 3.9). These deficiencies can be connected with model shortcomings: the most important ignored effect is atmosphere expansion due to a spectral line- driven stellar wind. This expansion can be significant 145 V. F. Suleimanov et al. because grad > g at the outer layers of our model at- mospheres (see also van Rossum 2012). In addition, non-LTE effects could be important (see, e.g., Rauch et al. 2010), the chemical composition may differ from solar, and, finally, the atomic data are almost certainly neither complete nor entirely accurate. The second important shortcoming is connected with a likely complicated BL structure with a distri- bution of effective temperatures and surface gravities over its surface. Therefore, a simple one-zone BL model presented here is most probably insufficient and more sophisticated BL models have to be considered. Nevertheless, the spectral modeling presented here supports a BL in SS Cyg that is, to first approximation, a hot (≈ 190 kK), fast rotating [ΩBL ≈ 0.98 ΩK(RWD)], narrow (HBL ≈ 0.063 RWD) belt on the WD surface. Acknowledgement This work is supported by the DFG SFB / Transregio 7 “Gravitational Wave Astronomy” (V.S.) and the Rus- sian Foundation for Basic Research (grant 12-02-97006- r-povolzhe-a) (R.Zh.). C.W.M.’s contribution to this work was performed under the auspices of the U.S. De- partment of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. References [1] Córdova, F. A., Chester, T. J., Tuohy, I. R., & Garmire, G. P. 1980, ApJ, 235, 163 [2] Dere, K. P., Landi, E., Mason, H. E., Monsignori Fossi, B. C., & Young, P. R. 1997, A&ASS, 125, 149 [3] Hubeny, I., Hummer, D. G., & Lanz, T. 1994, A&A, 282, 151 [4] Hummer, D. G., & Mihalas, D. 1988, ApJ, 331, 794 doi:10.1086/166600 [5] Ibragimov, A. A., Suleimanov, V. F., Vikhlinin, A., & Sakhibullin, N. A. 2003, Astronomy Reports, 47, 186 doi:10.1134/1.1562213 [6] Ishida, M., Okada, S., Hayashi, T., Nakamura, R., Terada, Y., Mukai, K., & Hamaguchi, K. 2009, PASJ, 61, 77 [7] Kley, W. 1991, A&A, 247, 95 [8] Kluźniak, W. 1987, Ph.D. thesis, Stanford Univ. [9] Kurucz, R. L. 1970, SAO Special Report, 309 [10] Mauche, C. W. 2004, ApJ, 610, 422 [11] McGowan, K. E., Priedhorsky, W. C., & Trudolyubov, S. P. 2004, ApJ, 601, 1100 doi:10.1086/380758 [12] Patterson, J., & Raymond, J. C. 1985a, ApJ, 292, 535 doi:10.1086/163187 [13] Patterson, J., & Raymond, J. C. 1985b, ApJ, 292, 550 doi:10.1086/163188 [14] Pringle, J. E., & Savonije, G. J. 1979, MNRAS, 187, 777 doi:10.1093/mnras/187.4.777 [15] Rauch, T., Orio, M., Gonzales-Riestra, R., Nelson, T., Still, M., Werner, K., & Wilms, J. 2010, ApJ, 717, 363 doi:10.1088/0004-637X/717/1/363 [16] Rappaport, S., Cash, W., Doxsey, R., McClintock, J., & Moore, G. 1974, ApJ, 187, L5 doi:10.1086/181378 [17] Suleimanov, V., & Werner, K. 2007, A&A, 466, 661 [18] Tylenda, R. 1981, Acta Astr., 31, 267 [19] van Rossum, D. R. 2012, ApJ, 756, 43 [20] Verner, D. A., & Yakovlev, D. G. 1995, A&ASS, 109, 125 [21] Warner, B. 1995, Cambridge Astrophysics Series, 28 DISCUSSION DMITRY KONONOV: What is a reason to initially use the solar chemical composition instead of chemical compositions for stars of later spectral type? VALERY SULEIMANOV: Unfortunately, we do not know the chemical composition of the secondary in SS Cyg. Therefore, we started from the most conser- vative case, which is the solar chemical composition. JAN-UWE NESS: The assumed WD mass in the model (1 M�) seems discrepant from the mass given in the introduction (0.55 M�), a factor 2. This suggest that all parameters of the model may be discrepant from reality, so what do we learn? VALERY SULEIMANOV: Sorry, you mixed up the white dwarf mass with the mass of the secondary (0.55 M�). DMITRY BISIKALO: How can you discriminate be- tween a boundary layer and a pseudo-photosphere or a hot disk halo? 146 http://dx.doi.org/10.1086/166600 http://dx.doi.org/10.1134/1.1562213 http://dx.doi.org/10.1086/380758 http://dx.doi.org/10.1086/163187 http://dx.doi.org/10.1086/163188 http://dx.doi.org/10.1093/mnras/187.4.777 http://dx.doi.org/10.1088/0004-637X/717/1/363 http://dx.doi.org/10.1086/181378 Model Atmosphere Spectrum Fit to the Soft X-Ray Outburst Spectrum of SS Cyg VALERY SULEIMANOV: The observed soft X- ray luminosity is a discrimination factor. Any pseudo- photosphere or an optically thick hot disk halo with this low surface gravity (log g ≈ 6.2) and the derived effec- tive temperature (≈ 190 kK) would have a radius that is tens of times larger than the white dwarf radius, and the luminosity would be hundreds of times larger than the observed luminosity. 147 Introduction Model Atmospheres Results Discussion and Conclusion