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

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4. The emission lines

In Fig. 8 we show the mean, low-resolution spectrum of RX J0203 . it exhibits strong emission lines of the H-Balmer (H[FORMULA] - H11) and H-Paschen series (P8 - P18), those of neutral (e.g. HeI [FORMULA] 3936, 4026, 4387, 4471, 5875) and ionized Helium (e.g. HeII [FORMULA] 4541, 4686, 5411) and of highly excited metals like CII [FORMULA]4267 or CIII/NIII at [FORMULA]4635-4650. the Balmer lines appear with an inverted Balmer-decrement of [FORMULA]H[FORMULA]H[FORMULA] indicating that effects of optical thickness and collisional excitation play an important role. This together with the relative strength of HeII compared to H[FORMULA] is typical for a magnetic CV in a high accretion state.

[FIGURE] Fig. 8. top: Average low-resolution spectrum of RX J0203 obtained on August 20/21, 1992. The effective exposure time is 5.3 hours. The main emission and absorption lines are indicated. bottom: The same spectrum as above after subtraction of a continuum with [FORMULA].

4.1. Emission line profiles

The emission line profiles observed in RX J0203 show a complex intrinsic structure which could be resolved by the 27 high-resolution spectra (FWHM[FORMULA] Å) obtained in August and October 1993. All available emission lines (H[FORMULA], HeI [FORMULA]4471, HeII[FORMULA] and H[FORMULA]) show the same general behaviour in terms of radial velocity and intensity variation, but for the following analysis, however, we restrict ourselves to the HeII [FORMULA] line, which is intrinsically sharpest. The trailed high-resolution spectrogram of RX J0203 (Fig. 9) is surprisingly similar to that of HU Aqr (Schwope et al. 1997). We can clearly discriminate between three components with different widths and different intensity and radial velocity variations: an unresolved narrow emission line (NEL) with [FORMULA]2 Å FWHM showing maximum intensity at [FORMULA], a medium width component (MWC) with [FORMULA]6 Å FWHM best visible between [FORMULA] while rapidly moving from large redshifts to large blueshifts, and a fainter, underlying broad base component (BBC) with [FORMULA]14Å FWHM. The phase convention [FORMULA] used here refers to the blue-to-red zero crossing of the NEL as derived below.

[FIGURE] Fig. 9a and b. left: Grey-scale representation of phase-resolved continuum-subtracted, high-resolution spectra of the HeII [FORMULA] emission line obtained on October 21, 1993. Phase runs from bottom to top and is plotted twice for clarity. right: Doppler map of the same line computed by filtered backprojection of the spectra obtained in August and October 1993. the overlay shows the shape of the secondary star and the accretion stream in Doppler coordinates for a mass ratio of [FORMULA] and [FORMULA] km s-1 as resulting from our illumination model. the lines in the lower left quadrant mark the trajectories of the magnetic controlled stream assuming threadening at three different radii.

In order to estimate radial velocities and intensities of the different components we deconvolved the line profile with three Gaussians. In a first step we fitted the line keeping the width of each component as a free parameter. While the NEL appeared unresolved at our spectral resolution and the widths of the broad components showed only little intrinsic scatter (1-2 Å) we kept them fix at values mentioned above in order to improve the fit in a second iteration.

In Fig. 10  (upper panel) we present the heliocentric corrected radial velocities of all components of the HeII [FORMULA] (including the spectra of August 1993).

[FIGURE] Fig. 10. Upper panel: Radial velocities of the subcomponents of the HeII [FORMULA] line: The NEL (filled symbols), the MWC (grey symbols) and the BBC (open symbols). The different data sets are marked as circles (August 1993) and squares (October 1993). Middel panel: The data of the NEL plotted at a larger scale together with the sine fit. Filled symbols mark points which entered the fit. Lower panel: Intensity of the NEL as derived from the gaussian fits together with model light curves of an illuminated hemisphere calculated for inclinations of [FORMULA] (dotted line), [FORMULA] (dashed line) and [FORMULA] (dashed-dotted line).

4.2. The NEL: Location of the secondary star and the white dwarf 's mass

The radial velocity amplitude of the NEL is comparatively small suggesting that it is indeed associated with the illuminated side of the secondary. For a circular orbit the motion of the secondarys center of mass is given by:

[EQUATION]

where [FORMULA] is the systemic velocity, [FORMULA] the projected velocity amplitude of the secondary and [FORMULA] is the phase angle with [FORMULA]0 at inferior conjunction. The orbit of a close binary is thought to be highly circular due to the strong tidal forces, but effects of illumination and geometrical distortion can lead to an apparent eccentricity causing deviations from a pure sinusoidal variation of the radial velocity curve. Close inspection at a larger scale (Fig. 10, middle panel) reveals that the RV variation of the NEL does not follow a sinusoid. Instead one finds that its motion alters abruptly from moving bluewards to moving redwards at [FORMULA]. While this deflection could be caused by illumination effects, we rather interpret this behaviour as resulting from the influence of a narrow, faint component associated with parts of the accretion flow. We therefore included only those RVs where the NEL is bright and can be unambiguously identified ([FORMULA]). A fit according to Eq. 2yielded, [FORMULA] km s-1 , [FORMULA] km s-1 , and a blue-to-red zero crossing at [FORMULA]. The latter value corresponds to [FORMULA] and was used to define the spectroscopic ephemeris used throughout this paper as

[EQUATION]

The errors quoted above are only formal fit errors and do not include systematic uncertainties introduced by the (somewhat arbitrary) selection of input data. Additional confirmation of the correct phasing of the NEL comes from the Doppler-tomography (Fig. 9, right). The NEL is transformed to a small spot at [FORMULA] km s-1 in the Doppler-map (where the emission from the heated side of secondary is expected) if the ephemeris of Eq. 3 is applied.

We can utilize the observed [FORMULA]-velocity as an estimator of the white dwarf 's mass [FORMULA]. Since this velocity is likely to represent the motion of the center of light [FORMULA] and not that of the center of mass [FORMULA], it has to be corrected by a factor [FORMULA]. We calculated a grid of synthetical values of [FORMULA] as a function of [FORMULA] and i on the basis of the illumination model described in Beuermann & Thomas (1990). The result of this calculation, for which we assumed a secondary mass [FORMULA] found according to a ZAMS mass-radius relationship (see Sect. 5.1), is shown in Fig. 11. The contours represent the observed [FORMULA] and its 3[FORMULA] errors. Additionally plotted in the figure is the corresponding mass of the white dwarf. Assuming an upper limit of the system's inclination of [FORMULA], a lower limit of [FORMULA] M[FORMULA] is given. On the other hand inclinations [FORMULA] imply masses of the white dwarf greater than 1.44 M[FORMULA] and can therefore be rejected.

[FIGURE] Fig. 11. Isovelocity lines of the reprocessed emission line from the secondary star as a function of the inclination i and the mass ratio [FORMULA] as calculated by our illumination model. The contours shown represent the observed [FORMULA] velocity amplitude and its 3[FORMULA] error. After fixing the mass ratio, the white dwarf mass can be estimated using its (almost linear) dependence on Q, which is plotted as a straight line from bottom left to top right (scale to the right of the graph).

The light curve of the NEL as derived from the gaussian fits is plotted in Fig. 10, lower panel. The NEL is strongest around phase [FORMULA], but hardly recognizable between phase [FORMULA] (Note that the flux attributed to the NEL at its faint phase may probably also arise from the accretion stream, as already mentioned). We compared the observed flux variation with that expected from the illuminated hemisphere of the secondary assuming different inclinations. Our model light curves which were computed for a homogeneously illuminated companion star (shown also in Fig. 10) suggest that the system's inclination has to be larger than 40o to explain the deep minimum of the NEL. In that case, the mass of the white dwarf is less than 1M[FORMULA]. However, none of the model curves gives a convincing fit to the data. The NEL clearly seems to be brighter during the first half of the orbital cycle. This was seen also in HU Aqr (Schwope et al. 1997) and undoubtedly ascribed to reduced illumination of the leading side of the companion star by an accretion curtain between the two stars. The asymmetric shape of the NELs light curve suggests a similar phenomenon to be present in RX J0203 , but the phase resolution of the present data is not high enough to study this in detail here. If, however, the light curve of the NEL is affected by shielding, lower inclination angles than 40o are possible.

4.3. The broad lines

Broad emission line components in AM Herculis stars are believed to arise in the accretion stream. Not only the large widths, but also the results of the sine fits are in general agreement with that picture: The measured amplitudes are high [FORMULA] km s-1 and [FORMULA] km s-1 . The broad components are shifted in phase with respect to the NEL by [FORMULA]155 and [FORMULA]115o, respectively. Thus maximum redshift occurs at [FORMULA] for the MWC and at [FORMULA] for the BBC. The latter value is near to the phase of the optical minimum [FORMULA] and indicates that we are looking along the stream and most directly from above the accretion region. The orbital minimum is then explained by cyclotron beaming.

The observed [FORMULA]-values are [FORMULA] km s-1 and [FORMULA] km s-1. These numbers can be used in order to derive constraints about the [FORMULA] component of the velocity vector and the location of the emitting regions as has been demonstrated e.g. by Rosen et al. (1987) or Thomas et al. (1996) for the cases of V834 Cen or RX J1957.1-5738. If we adopt the measured [FORMULA] km s-1 as the true systemic velocity then the positive [FORMULA]-shift of the BBC would indicate that it is emitted by gas moving away from the orbital plane or from above the plane towards the white dwarf. The colatitude [FORMULA] of that velocity vector with respect to the rotation axis, however, is rather large. If one adopts the relation between velocity amplitude [FORMULA], relative [FORMULA], orbital inclination i and [FORMULA] by Thomas et al. (1996), [FORMULA], one arrives at [FORMULA] between 90o and 100o for [FORMULA]. The almost zero [FORMULA]-shift of the MWC relative to [FORMULA] suggests that this component originates from a region with [FORMULA] km s-1 , most likely the horizontal stream.

In the Doppler-map (Fig. 9, right) the accretion flow manifests itself by the enhanced emission at negative [FORMULA] velocities. The resolution of the map is poor (mainly due to the low phase resolution of the input data) so that features especially at high velocities are smeared out. In the figure we also show three trajectories with different coupling radii of the accretion stream. They correspond to azimuthal angles of [FORMULA] and are thus in the typical range found for a number of polars (Cropper 1988). With the limited resolution of our Doppler-map we can not constrain the location of the coupling region with high accuracy. However, the detection of the MWC and the general distribution of emission in the [FORMULA]-[FORMULA] plane suggest the existence of a ballistically falling stream which is redirected at [FORMULA]. The field strength of the undisturbed field in that region is of the order of [FORMULA] kG.

4.4. The spectroscopic period

In the previous section we regarded the spectroscopic and photometric period to be equal. To uncover even a small degree of asynchronism we analysed the radial velocity variation of the combined low and high resolution data sets, which span a baseline of [FORMULA]1 year. In order to do so, the high resolution spectra had to be degraded to the resolution of the low resolution spectra of [FORMULA]7 Å beforehand. At that resolution the emission line profile is smeared into two components which we deconvolved by two Gaussian: one appears quasi-stationary over the orbit, while the other displays quasi-sinusoidal variation with an amplitude of [FORMULA]500 km s-1 . The latter was used for a period search following the analysis-of-variance (AoV) method (see Sect. 3.2). In the corresponding periodogram (Fig. 5, lower panel) we find a probable period of 16567 sec close to that derived from photometry, although a number of alias periods are also present. At the basis of the presently available data RX J0203 indeed appears to be synchronized. The width of the peak in the periodogram of [FORMULA]2 sec sets a firm upper limit for the degree of synchronization in the order of [FORMULA]10-4.

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© European Southern Observatory (ESO) 1998

Online publication: September 14, 1998
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