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Astron. Astrophys. 338, 933-946 (1998)

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4. Discussion

4.1. The temperature structure of the heated atmosphere

A major difficulty in the interpretation of the origin of the UV and EUV continuum of AM Her in its high state has been the absence and/or weakness of the absorption features expected from a hot high gravity atmosphere. The ORFEUS-I spectra of AM Her in high state do not show any evidence for [FORMULA] or [FORMULA] absorption (Raymond et al. 1995), the EUVE spectrum does show weak edges of Ne VI, VIII, but lacks the expected strong O VI 2s, 2p edges (Paerels et al. 1995). The common answer to that riddle is that heating the white dwarf by irradiation from the post-shock plasma causes a flatter temperature gradient in the atmosphere, weakening absorption features which form at Rosseland optical depths [FORMULA]. Only a limited number of irradiated white dwarf model atmospheres exist in the literature, e.g. Williams et al. (1987) and van Teeseling et al. (1994). Other instructive papers, even though treating irradiation of the secondary star in accreting binaries, are Anderson (1981) and Brett & Smith (1993). The theoretical temperature structures show mainly two features: a thin, hot, corona-like layer at the outer boundary of the atmosphere and a flat, sometimes completely isothermal temperature structure at larger optical depths. For optical depths [FORMULA], the temperature structure usually approaches that of the undisturbed atmosphere.

A fully self-consistent model for irradiated white dwarf model atmospheres is beyond the scope of the present paper, but we have computed two sets of "poor man's models" in order to illustrate the main observational effects that can be expected. As input, we use the temperature structure [FORMULA] of an undisturbed 20 000 K white dwarf, which was computed with the code described in Paper 1. This temperature structure was modified in two different ways.

(a) [FORMULA] was set to a constant value [FORMULA], from the outer boundary of the atmosphere down to an optical depth [FORMULA] where the temperature of the undisturbed white dwarf equals [FORMULA]. For optical depths larger than [FORMULA], [FORMULA] of the undisturbed white dwarf was adopted. Fig. 12a shows the temperature structures for several values of [FORMULA]. This modification mimics an isothermal regime in the heated atmosphere.

[FIGURE] Fig. 12a-d. "A poor man's model of the heated atmosphere". a and b Temperature structures modified as described in the text. c and d Model spectra computed from the temperature structures a and b , respectively. The line types of the individual spectra correspond to those used for the temperature structures. The solid curves show the temperature structure, (a ) and (b ), and the spectrum, (c ) and (d ), of the undisturbed [FORMULA] K white dwarf.

(b) The temperature was set to a constant [FORMULA], from the outer boundary of the atmosphere down to an optical depth [FORMULA] where it is smoothly changed into the temperature run of the undisturbed atmosphere. Fig. 12b shows the temperature structures for different values of [FORMULA]. This modification mimics the presence of a hot corona with a temperature inversion.

From these modified temperature structures, we synthesised model spectra by solving the hydrostatic equation, computing the ionization equilibrium, occupation numbers and the absorption coefficients, and solving the radiative transfer. The resulting spectra are shown in Fig. 12c,d. In the isothermal case (Fig. 12a,c), the absorption lines become weaker with increasing [FORMULA], and, thereby, also increasing [FORMULA], and the continuum approaches the slope of a blackbody. If a hot layer extends deeper than to Rosseland optical depths [FORMULA], strong emission of [FORMULA] is produced (Fig. 12b,c). This is in contrast to the observations of AM Her, which show no emission of [FORMULA] during the bright phase, i.e. when the heated region has its maximal projected area (Fig. 1). During the faint phase, i.e. when the spot is mostly eclipsed by the white dwarf, broad but weak [FORMULA] emission is present. This emission presumably originates in the accretion stream, or in the outer edges of the hot spot. In any case, there is no strong emission of [FORMULA] at any orbital phase in our GHRS spectra and no emission of [FORMULA], [FORMULA] in the ORFEUS-I spectra (Raymond et al. 1995). This indicates that any hot corona is limited to an outermost thin layer of the atmosphere.

With the results from our simple models in mind, we attempted a crude two-component fit to a combined FUV/UV spectrum of AM Her, constructed from the ORFEUS-I spectrum taken at [FORMULA] (Raymond et al. 1995) and GHRS data selected from the same phase interval. Even though AM Her was optically fainter by 0.3 mag during the ORFEUS-I observations, the two spectra match quite well in absolute flux. Fig. 13 shows the observations along with our two components, a model spectrum for the undisturbed white dwarf as observed during the low state and an "irradiated" model spectrum as in Fig. 12a-c, scaled appropriately. The sum of the two components quantitatively describes the observations for an assumed size of the heated spot of [FORMULA]. This spot is uncomfortably large, but, as discussed in Sect. 3, the accretion stream might contribute somewhat to the observed UV continuum.

[FIGURE] Fig. 13. Combined ORFEUS-I (900-1150 Å) and HST/GHRS (1150-1435 Å) spectrum of AM Her in high state at [FORMULA]. For comparison, a low state faint-phase IUE spectrum of AM Her is plotted (1225-1435Å). Shown as dashed lines are the best-fit model for the unheated backside of the white dwarf and the contribution of the heated spot according to Sect. 4.1. The solid line is the sum of the two model components. The emission of [FORMULA] is of geocoronal origin.

Thus, it appears that the heated regions of the white dwarf in AM Her emit a blackbody-like spectrum without noticeable emission or absorption features. This is in agreement with the EUV and soft X-ray data, which gave only marginal evidence for absorption/emission edges.

A fully satisfactory model for the phase-dependent emission of the accretion heated white dwarf has to overcome two hurdles. (a) It is necessary to compute self-consistent white dwarf model atmospheres which include irradiation by thermal bremsstrahlung and cyclotron radiation. (b) The flux and shape of the irradiating spectrum has to be estimated as a function of the location on the white dwarf surface. While (a) is principally a straightforward application of model atmosphere theory, (b) includes many uncertainties with respect to the geometry of the accretion region. The model developed by Wickramasinghe et al. (1991) to explain polarimetric observations could be used as a first estimate of the size and shape of the cyclotron emitting region.

Finally, we note that the situation during the low state is somewhat different: our IUE data (Paper 1) show an almost 100% modulated [FORMULA] absorption line during both the bright and faint phase. These data can be very well fitted with model spectra of an undisturbed white dwarf of 24 000 K and 20 000 K, respectively. The heated side of the white dwarf, hence, appears as an undisturbed but hotter white dwarf; the depth of the [FORMULA] absorption prohibits ascribing the flux modulation observed during the low state to a heated component as described above (Fig. 12a-d). An HST observation of AM Her during a low state is necessary order to confirm these IUE results at a higher orbital phase resolution and a better S/N.

4.2. Binary parameters

Various estimates for the mass of the white dwarf in AM Her have been published so far, an incomplete list includes [FORMULA] (Young & Schneider 1981), [FORMULA] (Wu et al. 1995), [FORMULA] (Mukai & Charles 1987), [FORMULA] (Mouchet 1993), and, the latest value, [FORMULA] (Cropper et al. 1998). Accepting the distance to be [FORMULA] pc (Paper 1; Beuermann & Weichhold 1998), the UV observations constrain the white dwarf mass. From our fit to the GHRS light curve, we obtain [FORMULA] cm, which corresponds to [FORMULA], (carbon core model; Hamada & Salpeter 1961). This can be considered a lower limit of [FORMULA], as we assumed that all the continuum light comes from the (heated) white dwarf; any contribution from the accretion stream will decrease the white dwarf radius and increase its mass. On the other hand, the flux of the IUE low state data require [FORMULA] cm, or [FORMULA]. A mass as high as 1.22 [FORMULA], or [FORMULA] cm, would reduce the distance to the system to [FORMULA] pc in order to produce the observed UV flux. A distance that low can be excluded both from the spectrum of the secondary star (Paper 1; Beuermann & Weichhold 1998) and from the parallax (Dahn et al. 1982). We conclude that the mass of the white dwarf in AM Her is [FORMULA], unless the distance differs largely from [FORMULA] pc.

The mass of the secondary star has been estimated by Southwell et al. (1995) to be [FORMULA], a result confirmed by Beuermann & Weichhold (1998). Thus, the range for the mass ratio [FORMULA] is 0.38 to 0.74.

4.3. The origin of the narrow emission lines

The narrow component seen in the emission lines of a number of AM Her systems is commonly attributed to emission from the side of the secondary star facing the white dwarf (e.g. Liebert & Stockman 1985). This region is heated by irradiation from the white dwarf and/or the hot spot(s) on the white dwarf surface at the impact point(s) of the magnetically-controlled accretion flow. The surface of the secondary star, which is defined by the geometry of its Roche lobe for a given mass ratio and orbital period, is preserved in the mapping from spatial coordinates to the velocity coordinates of a Doppler tomogram. The secondary star's Roche lobe is symmetric about the [FORMULA] axis in a tomogram, with its centre offset from [FORMULA] by an amount equal to the radial velocity semi-amplitude of the secondary star, [FORMULA]. The asymmetry relative to the [FORMULA] axis of the strong emission regions in the Si IV and N V tomograms of AM Her (Sect. 3.6) can be understood as due to non-uniform heating of the secondary star's face (Smith 1995). The accretion stream shades the leading side of the secondary star from irradiation by the white dwarf/hot spot(s). This results in less heating on the [FORMULA] side of the [FORMULA] axis, and, therefore, stronger emission on the [FORMULA] side of the [FORMULA] axis. This shielding effect is observed also in other AM Her stars, e.g. in HU Aqr (Schwope et al. 1997).

Closer inspection of the tomograms of N V and Si IV reveals, however, some difficulties in ascribing the entire narrow emission to the irradiated face of the secondary star. Fig. 14 shows blow-ups of the tomograms of N V and Si IV from Fig. 7. The Si IV emission falls completely within the secondary Roche lobe for reasonable parameters, [FORMULA] and [FORMULA] km s-1. However, the N V emission requires extreme values as [FORMULA] and [FORMULA] km s-1. As discussed in Sect. 4.2, the mass ratio is rather unlikely to be larger than 0.75. A number of radial velocity measurements have been obtained from the Na I [FORMULA] 8183, 8195 doublet, the most reliable measurement yields [FORMULA] km s-1 (Southwell et al. 1995). As discussed by Southwell et al., this value is an upper limit to the real K-velocity of the secondary, as the irradiated face of the secondary contributes less to the Na I absorption. After some corrections, they give as a best estimate [FORMULA] km s-1. Considering these limits on q and [FORMULA], our N V tomogram indicates narrow emission originating from material of low velocity dispersion inside the Roche lobe of the white dwarf, close to the [FORMULA] point.

[FIGURE] Fig. 14. The central regions of the N V (left) and Si IV (right) tomograms of AM Her, from Fig. 7. Top: Superimposed on the tomograms are the secondary star Roche lobes for mass ratios of [FORMULA] (innermost Roche lobe), 0.50, 0.75, 1.00 (outermost Roche lobe), assuming [FORMULA] km s-1 for all values of q. The corresponding centres of mass of the white dwarf are marked on the [FORMULA] axis at [FORMULA] km s-1, respectively. Bottom: Secondary star Roche lobes for a constant mass ratio of [FORMULA] with [FORMULA] (smallest Roche lobe), 150, 200 (largest Roche lobe) km s-1. The corresponding centres of mass of the white dwarf are marked on the [FORMULA] axis at [FORMULA] km s-1, respectively.

We can even exclude that significant parts of the narrow N V emission originate on the secondary. The Si IV narrow emission disappears at [FORMULA] (Fig. 6; Fig. 11), which is due to the self-eclipse of the [FORMULA] region on the secondary, where heating by irradiation from the white dwarf is strongest, and where, hence, emission is expected to be strongest. From Fig. 6, it is apparent that the N V narrow emission intensity does not show a significant orbital modulation. A consistent origin of N V on the secondary would require the emission region to be located further away from [FORMULA] than the Si IV emission region, hence at larger radial velocities. However, the N V narrow emission has a lower radial velocity than the Si IV narrow emission (Table 2).

We conclude that the GHRS spectra clearly demonstrate the presence of highly ionized low-velocity-dispersion material which co-rotates with the binary and is located between [FORMULA] and the centre of mass. A tempting possibility is that this material is kept in place in a magnetic slingshot prominence emanating from the secondary star. Evidence for such prominences have been found before in the dwarf novae IP Peg and SS Cyg (Steeghs et al. 1996). We will explore the physical properties of the material hold in the prominence in a future paper.

4.4. On the broad emission lines

A consistent interpretation of the broad emission lines encounters some difficulties. The radial velocity curves (Fig. 10) clearly indicate an origin in the accretion stream, with maximum redshift at [FORMULA], i.e. when looking parallel to the stream, and maximum blueshift at [FORMULA], i.e. when looking anti-parallel to the stream. The Doppler tomograms (Fig. 15) show that most emission is centred around the ballistic part of the accretion stream if reasonable values are chosen for the mass ratio, e.g. [FORMULA] and [FORMULA] km s-1.

[FIGURE] Fig. 15. Detail of the emission regions in the Si IV tomogram of AM Her from Fig. 7. The left panel shows the ballistic trajectories of the accretion stream (i.e., in the absence of a white dwarf magnetic field) for the cases discussed in the caption to Fig. 14, for [FORMULA] km s-1 and [FORMULA] (a ) 0.25, (b ) 0.50, (c ) 0.75, (d ) 1.00. The right panel shows the ballistic trajectories of the accretion stream for a constant mass ratio of [FORMULA] with (starting from the innermost curve) [FORMULA] km s-1.

The single-humped light curves of the broad emission lines with maximum flux at [FORMULA] and minimum flux at [FORMULA] (Fig. 11) are not quantitatively understood. On one hand, if the accretion stream were optically thick, one would naively expect a double-humped light curve: the projected area of the stream is minimal at phases [FORMULA] and maximal during phases [FORMULA]. This behaviour is observed e.g. in HU Aqr (Schwope et al. 1997) and QQ Vul (Gänsicke 1997). On the other hand, if the stream were optically thin, one would expect no variation of the line fluxes around the binary orbit. Optical depth effects, self-eclipse and irradiation of the stream may be responsible for the observed variation of the broad line fluxes.

An interesting result of the GHRS observations is the detection of a high-velocity component in the emission of Si IV. The low flux of this component, however, prevents a location of its origin in the Doppler tomograms, as already noted in Sect. 3.6. The similar phasing of the radial velocity curves of the broad and the high velocity component (Fig. 8) indicates that both components originate in regions of the accretion stream not too far apart, with the source of the high-velocity emission probably being located closer to the white dwarf.

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© European Southern Observatory (ESO) 1998

Online publication: September 17, 1998