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Subsections

3 Results

Synthetic magnitudes of MR Vel resulted in J = 13.05, J-H = 0.76 and H-K = 0.53, with probable uncertainties of 0.1 mag. When using a colour excess of E(B-V) = 1.94 (Matsumoto & Mennickent 2000), we find unreddened colours of J-H = 0.15and H-K = 0.17, comparable to those observed in the SSS QR And (RX J0019.8+2156, Fender & Burnell 1996). Our finding likely indicates the presence of absorbing circumstellar material or a late-type companion. To our knowledge, these are the first infrared magnitudes and colours obtained for MR Vel ever. Therefore, it would be interesting to compare these magnitudes with future data in order to search for variability.

3.1 Spectrum description

The combined spectrum reveals a steep blue continuum and weak emission lines (Fig. 1). A straight-line fit to the continuum in this region results in a slope of $-1.1 \times 10^{-15}$ ergs s-1 cm-2 Å-1/$\mu$m, which is incompatible with a power law. After a close inspection of the normalized spectrum (Fig. 2), we identified lines of neutral hydrogen (Paschen and Bracket), single ionized helium and highly ionized oxygen. These lines are listed in Table 1 along with relevant spectroscopic data. No evidence of a transient emission-line jet like those observed in H$\alpha$ by Motch (1998) was detected. No photospheric absorptions, such as CO bands, are observed in the spectra. One interesting feature is the P-Cygni profile observed in the Paschen $\beta $ and Bracket $\gamma $lines (Fig. 3). The velocities found in the corresponding blueshifted absorption wings, relative to the emission maximum, reach up to -3000 (-1500) km s-1, being the absorption minimum at -755 (-680) km s-1, for Paschen $\beta $(Brackett $\gamma $). After inspection of the data, we realized that the difference between the maximum absorption velocity of these lines are real, and they cannot be due to an error in the continuum normalization.


  \begin{figure}
\par\includegraphics[width=7cm,clip]{rxj0925.eps} \end{figure} Figure 1: Flux calibrated spectrum of MR Vel. The vertical scale has been normalized to 2.03E-15 erg cm-2 s-1 Å-1.


  \begin{figure}
\par\includegraphics[height=9cm,width=16.7cm,clip]{combined.eps} \end{figure} Figure 2: From up to down, J-band, K-band and H-band continuum normalized spectra for MR Vel. Emission lines are labeled.

3.2 SED modeling

In the picture of the steady nuclear-burning white dwarf model, the mass accretion rate is limited in the narrow region around ${\sim}10^{-7}$  $M_{\odot}~{\rm yr^{-1}}$. Since the critical accretion rate of the white dwarf ( $\dot{M}_{\rm crit}$) is

\begin{displaymath}\dot{M}_{\rm crit} \equiv \frac{L_{\rm E}}{\eta c^{2}} = 2.2 ...
...10^{-3}}\right)^{-1}
\frac{M}{M_\odot} M_\odot~{\rm yr}^{-1},
\end{displaymath} (1)

where $L_{\rm E}$ ( $= 1.25 \times 10^{38}~ M/M_\odot~ {\rm erg~s}^{-1}$) is the Eddington luminosity considering electron scattering and $\eta$ is the efficiency, the unstable mass transfer rate expected for semi-detached systems with q > 1 is comparable to the critical mass accretion rate $\dot{M}_{\rm crit}$.
  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{pcygni.eps} \end{figure} Figure 3: A zoom around the P-Cygni profiles of Paschen $\beta $ and Brackett $\gamma $.


 
Table 1: Spectroscopic information of emission lines. The peak intensity is given in units of 10-15 erg s-1cm-2Å-1. N/A means not available.
Line Intensity EW (Å) FWHM (km s-1)
       

O II 11334-38

2.2 -2 N/A
He II 11628-77 2.3 -2 N/A
O VI 12617 2.0 N/A N/A
O III 12692 2.2 N/A N/A
Pa$\beta $ 2.4 -5 367

Br$\iota$

1.7 -3 555
Br$\theta$ 1.6 -2 627
Br$\eta$ 1.5 -2 560
He II 16926 1.5 -1 540
Br$\zeta$ 1.5 -4 440

O I 19463

1.3 -9 564
He II 19548 1.2 -3 520
Br$\gamma $ 1.0 -9 473
He II 21891 0.9 -4 740
He II 23480 0.7 N/A N/A


A model of an accretion disk with a supercritical accretion rate was originally proposed by Abramowicz et al. (1988), as an optically thick and geometrically thick disk (e.g., Kato et al. 1998 for a review). Abramowicz et al. (1988) called the model a slim disk because of its medium thickness between a thin disk and a thick one. We refer it as a supercritical accretion disk, based on a physical viewpoint of the supercritical accretion rate.

The standard model for SSS indicates that we should consider a nearly critical accretion in SSS systems instead of the standard accretion disk (Shakura & Sunyaev 1973). It is also expected that a very luminous white dwarf in SSS strongly irradiates the accretion disk and eventually the companion (e.g.  Popham & Di Stefano 1996; Schandl et al. 1997; Meyer-Hofmeister et al. 1997; Matsumoto & Fukue 1998; Meyer-Hofmeister et al. 1998). These effects in SSS were investigated by Fukue & Matsumoto (2001). In this work, we have calculated the spectral energy distribution (SED) for MR Vel, including the supercritical accretion disk and the irradiation effect, and have compared it with the observed spectrum in the range of optical-IR region after dereddening with E(B-V)= 1.94 (i.e. AV $\approx$5.9, Matsumoto & Mennickent 2000). The concept and formulation of the numerical model are described in Fukue & Matsumoto (2001), and we basically conform the manner in calculations to Fukue & Matsumoto (2001) in this paper.

The inferred intrinsic X-ray luminosity highly depends on the model-atmosphere and gravity used in the fitting process, but in any case, X-ray observations and theoretical models have suggested that the white dwarf should be extremely massive (Shimura 2000; Ebisawa et al. 2001), although recent NLTE models of hot white dwarf atmospheres fail to represent the complex X-ray spectrum (Motch et al. 2002). In the following, as a working hypothesis, we assume a blackbody SED for the central source associated with a ${\sim}1.4~M_{\odot}$ white dwarf. This means that we choose the WD luminosity matching thecore-mass-luminosity relationship derived by Iben & Tutukov (1996) for cold WDs accreting hydrogen:

$\displaystyle \frac{L}{L_{\odot}} \approx 4.6 \times {10 }^{4 } \left(\frac{M_{\rm core }}{M_{\odot}} - 0.26\right).$     (2)

This relationship is similar to those regulating the luminosity of asymptotic giant branch stars (Paczynski 1971a). Due to the Roche lobe-filling requirement, the contribution from the SED of the companion depends on the inclination angle of the binary system. The apparent variations in both of the light curve and radial velocity reject very-low inclinations, and no eclipse also indicates $i\le65^{\circ}$ (Motch et al. 1994; Matsumoto & Mennickent 2000; Schmidtke et al. 2000). Thus an inclination angle range of 45-65$^{\circ }$ seems to be plausible. Using the mass function derived by Matsumoto & Mennickent (2000) and the fixed mass of the white dwarf, the mass of the secondary star was derived for a set of allowed inclination angles. The stellar radii followed from the relationships for Roche-lobe filling secondaries in binary systems (Paczynski 1971b). The effective temperature for each mass-radius combination was calculated from the stellar evolutionary tracks by Claret & Gimenez (1989). Then we estimated the SED for these possible configurations assuming the secondary star partially shielded from the white dwarf by the disk rim. So the shielding by the disk is partial and a part of the companion is irradiated, as shown in e.g. Schandl et al. (1997). The magnitude of the irradiation was estimated considering the vertical scale height of the disk. In these calculations we neglected any possible contribution of irradiation by the hotspot.

An extremely small opening angle of the supercritical accretion disk ($\delta$) corresponds to a thin standard accretion disk. According to Hanamoto et al. (2001), $\delta$ is required to be more than 0.3$^{\circ }$ for a mass-accretion rate of ${\ge}10^{-7}~M_{\odot}~{\rm yr^{-1}}$ expected for SSS. On the other hand, larger $\delta$ brings no significant increase of the luminosity in Rayleigh-Jeans tail of the SED. This can constrain upper and lower limits for the distance.

For an inclination angle in the range from 45$^{\circ }$ to 65$^{\circ }$, we found that the calculated SED based on the supercritical model described above suggests a distance to the source between 2 and 4 kpc for a wide range of $\delta$ (0.3-5). Even in the unlikely case of $\delta= 20$, the distance is constrained to $d\sim$ 5-6 kpc. A representative fitting is shown in Fig. 4, which is calculated for a case of $i=50^{\circ }$ (corresponding to $M_{2} = 3.21~ M_{\odot}$, $R_{2} = 7.6~ R_{\odot}$, T= 7200 K) and $\delta = 0.3-5$. Besides the approximations and assumptions of our disk models, the differences between observed and theoretical spectra can be explained by a small error in the dereddening and/or the flux calibration for the optical NTT data, by photometric orbital variability or by the use of non-simultaneous optical-infrared data. From the above considerations we conclude that the distance for the source probably lies between 2 and 5 kpc.


  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{model.EPS} \end{figure} Figure 4: A representative SED model of MR Vel calculated for the supercritical accretion case with an inclination angle of $i=50^{\circ }$. Two solid lines denote the contributions by the white dwarf (right) and the companion (left). Total contribution from the white dwarf, companion, and supercritical accretion disk are shown by five dashed lines, which correspond to $\delta =$ 5$^{\circ }$, 3$^{\circ }$, 1$^{\circ }$, 0.5$^{\circ }$, and 0.3$^{\circ }$, from top to bottom. The de-reddened observed spectrum is over-plotted on the model SEDs by filled circles considering the best fitted case of d = 3 kpc. Optical data is from Matsumoto & Mennickent (2000) and infrared data is from this paper.


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