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Astron. Astrophys. 338, 465-478 (1998)

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5. Low resolution spectroscopy

From our low resolution spectroscopy we derived light curves (see Fig. 12) by folding the spectra with synthetic bandpasses representing BVR standard filters. Despite the fact that non-photometric conditions might account for some of the variability (e.g. due to slit losses), it is clear that the simple smooth variation seen in the regular mode is not observed. Instead the light curves suggest that the system was accreting already in the irregular mode, as it was clearly the case two months later during our photometry run (although then the photometric minimum occured later in phase at [FORMULA]).

[FIGURE] Fig. 12. Variation of the V and R magnitude (upper panels) and of the strength of flux deficit of the TiO-band [FORMULA]6195 (lower panel) during the low resolution spectroscopy run August 20/21 1992. The flux deficit is given in units of 10-15erg cm-2 s-1. Different symbols indicate data obtained at different nights. Photometric phase zero occurs at spectroscopic phase [FORMULA].

5.1. The secondary star

The red and near-infrared parts of the spectra shown in Figs. 8 and 13 exhibit low-frequency intensity modulations which we identify as TiO absorptions bands ([FORMULA]6195, 6322, 6651, 7053 and 7666 Å) of the late type companion. In addition the NaI doublet at [FORMULA]8183 and 8194 appears as an unresolved dip bluewards to HeII emission line at [FORMULA]8205. Following the methods of Young & Schneider (1981) and Wade & Horne (1988) we tried to use the strength of the TiO-bands in order to quantify the contribution of the companion to the total flux and it's spectral type.

Consequently the flux density deficits [FORMULA] of all suitable TiO-bands ([FORMULA]6195, 6651, 7053 and 7666 Å) were calculated for each individual spectrum of RX J0203 and a set of single M dwarf (M0-M6) spectra for comparison. This was done by first defining a reference continuum (fitting a straight line between two continuum bands bridging a TiO trough) and then averaging the flux in the TiO trough over an appropriate wavelength range (free of emission lines or residual atmospheric absorption).

The strength of the TiO-bands show a remarkably strong modulation with the orbital phase. As an example the flux deficit of the TiO-band [FORMULA]6195 (Fig. 14, lower panel) is shown, whose strength is obviously reduced around phase [FORMULA] when that side of the secondary is seen which is exposed to radiation from the primary star. Such a behaviour cannot be explained by gravity darkening of the secondary star, which would in contrary enhance the flux deficit. It is most likely caused by the strong X-ray/EUV irradiation from the accretion region on the white dwarf. A similar variation of the flux deficit caused by irradiation has also been found in Z Cha (Wade & Horne 1988) and QQ Vul (Schwope et al. 1998) and is in agreement with model-atmosphere calculations (Brett & Smith 1993) which predict a reduced flux deficit of both TiO and Na absorption features for an irradiated M dwarf.

The ratio of the flux deficit of TiO-bands is a function of the effective temperature of a M-dwarf and hence an indicator of its spectral type. In Fig. 14 we show the ratio of the bands TiO ([FORMULA] 6195)/TiO([FORMULA] 7666) for a sequence of M-dwarfs, which is compared with the mean value and standard deviation obtained for RX J0203 in the phase interval [FORMULA] = 0.8-1.1, when the undisturbed backside of the secondary is seen and the ratio is well defined. Taking this and the results of the other bands (marked in Fig. 13) together we deduce that the companion has a spectral type M2.5 with an estimated uncertainty of about one subclass.

[FIGURE] Fig. 13. Continuum subtracted faint phase spectrum of RX J0203 together with a scaled spectrum of a M 2 dwarf (Gliese 393). The continuum has been estimated as a power law and was adapted to the blue spectral range. The TiO-bands used for determination of band strengths are marked.

[FIGURE] Fig. 14. The ratio of the flux deficit of the TiO-bands [FORMULA] and [FORMULA] as a function of spectral subclass for a sequence of M dwarfs. From the mean value obtained for RX J0203 faint phase spectrum and its standard deviation (horizontal bars) we deduce that the spectral type of its secondary is M 2.5[FORMULA].

Using the spectrum of the single M-star Gliese 393 (M2) as a template for the secondary in RX J0203 and adapting it to the average spectrum of RX J0203 ([FORMULA] = 0.8-1.1), we find that the secondary in RX J0203 has [FORMULA]. Hence it contributes [FORMULA]4% to the total flux at 7000 Å. The optimally adapted spectrum of Gl 393 is included in Fig. 13. It is demonstrated clearly in the figure, that most of the spectral features in the near infra-red may readily be ascribed to the late type companion. However there remains a significant flux excess around 8200 Å independently of the spectral type (M1 to M4) of the template M-star. This might possibly be a single cyclotron line of a second accretion region (with the next higher harmonic being too faint to be detected and the next lower harmonic lying outside our spectral window). We note, that in addition the Paschen jump in emission (8204 Å) might contribute to that feature.

The secondary in RX J0203 fills its Roche lobe and is therefore likely to have a mean density of [FORMULA] g cm-3 for the observed period and a wide range of mass ratios ([FORMULA]). If we assume that it is on the main-sequence and adopt a mass-radius relationship (e.g. Patterson 1984) it should have a mass of 0.46 M[FORMULA] and a radius of 0.5 R[FORMULA]. Using the mass-spectral-type relationship of Kirkpatrick & McCarthy (1994) we find a corresponding spectral type of M2.7[FORMULA], where the uncertainty is mainly due to the rms-scatter of their relation. Since this equals the value deduced using the TiO-band strengths we conclude that the secondary is indeed on the main-sequence and has an appropriate radius for its mass.

5.2. A distance estimate

Armed with the spectral type and magnitude of the secondary we are now able to derive the distance of the system. Assuming a colour [FORMULA] mag for a M 2.5 dwarf (Kirkpatrick & McCarthy 1994) and using the improved colour-surface brightness relationship of Ramseyer (1994) the surface brightness is [FORMULA]. Together with the secondary's radius as derived above we can now adapt the method of Bailey (1981) and find a distance [FORMULA] pc. The uncertainty accounts for the photometric accuracy of our spectra ([FORMULA]30%), the scatter of Ramseyer's calibration (0.13 mag) and the uncertainty of the secondary's radius ([FORMULA]5%).

5.3. The magnetic field of the white dwarf

For further investigation we calculated average faint ([FORMULA] = 0.7-1.1) and bright ([FORMULA] = 0.2-0.6) phase spectra. Since the system appeared to be intrinsically brighter on August 20, 1992 we averaged the spectra of both nights separately. The contributions of the emission lines and of the secondary were removed beforehand. In order to not over- or undersubtract the M-star, our template had to be scaled for each individual spectrum according to the TiO flux deficit observed.

Both, the faint and bright phase spectrum, are dominated by a blue continuum with [FORMULA] to which mainly three components may contribute: optically thick cyclotron radiation from the accretion spot, photospheric radiation of the white dwarf and probably to a large amount reprocessed continuum radiation from line emitting regions.

We can separate the two latter components by subtracting the faint from the bright phase spectrum. The resulting difference spectra shown in Fig. 15 are deeply modulated and likely to be of pure cyclotron origin. We can identify the prominent humps at [FORMULA] 7600, 6200 and 5300 Å as the 4[FORMULA], 5[FORMULA] and 6[FORMULA] harmonics. Their separation suggest a magnetic field strength B of about 40 MG.

[FIGURE] Fig. 15. Difference of the bright and faint phase average spectra. Contributions of the emission lines and the M-star have been subtracted beforehand. The spectra of the individual nights have been treated separately, because the system appeared intrinsically brighter on August 20 (upper graph). The prominent 4[FORMULA], 5[FORMULA] and 6[FORMULA] harmonics are marked. The smooth curves overlayed represent a cyclotron model for [FORMULA] MG (see text for details).

We try to further constrain B, the temperature T and the viewing angle [FORMULA] by adapting a simple isothermal, homogeneous cyclotron model (Barrett & Chanmugam 1985) to the data. An excellent agreement could be achieved with [FORMULA] MG, [FORMULA]20 keV and [FORMULA]70o , with an estimated uncertainty for B of 2 MG. For both nights slightly different depth parameters [FORMULA] of 2.5 and 2.2 have been used and the model had to be shifted by an extra amount of flux to match the spectrum of August 20, 1992.

A rough estimate of the cyclotron luminosity measured at August 20, 1992, can be derived by integrating the spectrum shown in Fig. 15 and accounting for a factor 2 for radiation outside our spectral window and assuming isotropic radiation, hence [FORMULA] erg s-1. This is only [FORMULA]25% of total visual light observed in the high-state, and, as a result we suspect that a larger fraction of optically thick cyclotron radiation might be hidden in the blue continuum.

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© European Southern Observatory (ESO) 1998

Online publication: September 14, 1998