3. Analysis and results
3.1. Average spectra
The high spectral resolution and signal-to-noise (S/N) of the GHRS data reveals a multitude of hitherto unexplored details in the UV emission of AM Her. Two average spectra are shown in Fig. 1. They contain the typical emission lines of a polar in a state of high accretion rate, i.e. strong emission of the high excitation lines N V and Si IV along with weaker emission of lower ionization species, such as Si II, III and C II, III. The N V and Si IV doublets are fully resolved, displaying substructure in the form of broad and narrow components. Interestingly, the intensity of the narrow emission of N V varies only little as a function of the orbital phase, while the narrow emission of Si IV vanishes during orbital maximum. The lower ionization species, C II, III and Si II, III, do not display narrow emission at all, except for Si III 1206.5 which shows a weak narrow emission in the faint phase spectrum.
Overlayed on the continuum and line emission from AM Her are numerous interstellar lines. The very low airglow during part of the HST orbit allows the unmistakable detection of interstellar absorption. No obvious photospheric metal absorption lines from the white dwarf are visible. Note also that the broad absorption is almost completely filled in with emission, reminiscent of the missing and absorption lines in the ORFEUS-I FUV spectra of AM Her (Raymond et al. 1995).
3.2. Interstellar absorption lines
During parts of the HST orbit when the satellite was in the earth shadow, the geocoronal emission is significantly reduced, clearly revealing interstellar absorption in the spectra of AM Her. Earth-shadowed intervals occurred at and (Fig. 2), which allow us to determine the absorption column density during orbital minimum and maximum, i.e. when looking either at the unheated backside of the white dwarf or looking along the accretion funnel feeding the main pole, respectively. Paerels et al. (1994) found a small orbital variation of the absorption column density from EXOSAT grating data, ranging from during the soft X-ray faint phase to during the soft X-ray bright phase. This increase of is intuitively explained by the higher mass flow rate onto the active pole.
We fitted a pure damping Lorentzian profile (Bohlin 1975) folded with an 0.6 Å FWHM Gaussian to the observed absorption line. The resulting neutral column density is for both phases, somewhat lower than the value derived from X-ray observations, (van Teeseling et al. 1994; Paerels 1994; Paper 1). There is no evidence for a phase-dependent variation of the neutral hydrogen column density. The higher column densities determined from X-ray data indicate the presence of material along the line of sight, presumably within the binary system, in which hydrogen is ionized to a high degree while the other elements are only partially ionized and still contribute to the soft X-ray absorption.
Assuming an average gas-to-dust ratio (Shull & van Steenberg 1985), our value of translates into a limit on the reddening of . Considering this very low absorption, we use throughout the following analysis the observed data without correction for reddening.
The GHRS spectra of AM Her contain several interstellar absorption lines from low ionization species in addition to , among which the strongest are N I 1200 (an unresolved triplet), Si II 1260.4 (blended with S II 1259.5), O I 1302.2, Si II 1304.4 and C II 1334.5. The equivalent widths measured from the average spectra are mÅ, comparable to those determined for a small sample of cataclysmic variables at pc (Mauche et al. 1988). The centroids of the interstellar lines can be used to check on the quality of the wavelength calibration of the GHRS spectra, which we found to be good to km s-1.
In Paper 1, we found weak evidence for absorption of Si II 1260.4,1265.0 in IUE low state spectra of AM Her, presumably originating in the photosphere of the white dwarf. We stress that all metal absorption lines in the GHRS spectrum are of interstellar nature. This is underlined by the fact that only the blue component of Si II 1260.4 is detected; the red component is caused by a transition from an excited level which is not populated in the interstellar medium.
3.3. The observed continuum flux variation
In order to study the orbital modulation of the continuum flux, we have selected three wavelength bands free of emission lines: 1150-1167 Å (Band 1), 1254-1286 Å (Band 2), and 1412-1427 Å (Band 3). The continuum light curves obtained from averaging the phase-resolved GHRS spectra in these three bands display a quasi-sinusoidal modulation with the amplitude increasing towards shorter wavelengths (Fig. 3). Maximum UV flux occurs at , which is consistent with previous IUE observations of AM Her, during both the high state and the low state (Paper 1). The phase of the UV flux maximum agrees with that of the maximum hard X-ray flux (e.g. Paerels et al. 1994; Paper 1) and EUV flux (Paerels et al. 1995), indicating that the UV excess radiation originates close to the main accreting pole.
In Paper 1, we ascribe the observed orbital modulation of the UV flux to the changing aspect of a rather large, moderately hot spot on the white dwarf. We fitted white dwarf model spectra to phase-resolved IUE observations, obtaining a flux-weighted mean temperature and a mean source radius from each spectrum. During the low state, the flux variation is accompanied by a variation of the absorption profile width, which allows a reliable determination of the white dwarf temperature, K, and a good estimate for the spot temperature, K, and the spot size, of the total white dwarf surface. However, during the high state, the broad geocoronal emission and the unresolved N V profile are significantly blended in the region of the IUE spectra. The derived spot temperature and size, K and , remained, therefore, somewhat uncertain. The main conclusion of Paper 1 was that the flux emitted by the UV spot roughly equals the sum of thermal bremsstrahlung and cyclotron radiation, indicating that irradiation by the hot plasma in the accretion column may cause the heating of the large UV spot.
In order to constrain the temperature distribution over the white dwarf surface, we have developed a 3D white dwarf model which allows the simulation of phase-resolved spectra and light curves. The white dwarf surface is defined by a fine grid of several thousand elements of roughly equal area. Each surface element is assigned an effective temperature, allowing to prescribe an arbitrary temperature distribution over the white dwarf surface. For each surface element, a synthetic white dwarf spectrum with a corresponding effective temperature is selected from a library of model spectra computed with the atmosphere code described in Paper 1. Simulated phase-resolved spectra are obtained by rotating the white dwarf model and by integrating the flux at each wavelength over the visible hemisphere at a given phase. The main characteristics of the model spectra are (a) pure hydrogen composition, (b) no magnetic field, (c) , and (d) no irradiation.
The strong magnetic field of the white dwarf in polars is expected to prevent spreading of the accreted metal-rich material perpendicular to the field lines until the gas pressure equals the magnetic pressure, a condition which occurs far below the photosphere. In fact, there is no compelling observational evidence for the presence of heavy elements in the photosphere of the white dwarf in AM Her (Paper 1), so assumption (a) therefore appears justified 1. As long as only the continuum is used for fitting purposes, the weak Zeeman splitting of for MG (S. Jordan, private communication) and the change of the absorption profile with will not significantly affect the results. The critical point is (d): we assume that the spectrum of a white dwarf heated by irradiation resembles that of a somewhat hotter but undisturbed white dwarf. In what follows, we describe a simple model which accounts for the main characteristics of the data.
For the sake of simplicity, we chose a circular spot with an opening angle . The spot has a temperature distribution decreasing linearly in angle from the central value at the spot centre until meeting the temperature of the underlying white dwarf at . The centre of the spot is offset from the rotational axis by an angle the colatitude. Note that does not necessarily equal the colatitude of the magnetic pole, commonly designated . The centre of the spot is offset in azimuth by an angle , measured from the line connecting the centres of the two stars.
We fitted simultaneously the observed light curves in Band 2 and 3 only. Because of uncertainties in the calibration of the absolute flux of the G140L spectra at the very short wavelengths (Sect. 2), Band 1 was not included in the fit. An evolution strategy algorithm (Rechenberg 1994) with 6 free parameters was used for the optimisation: the white dwarf temperature , the white dwarf radius , the maximum temperature of the spot , the opening angle of the spot , the colatitude , and the azimuth of the spot . Fixed parameters are the distance to AM Her, pc (Paper 1; Beuermann & Weichhold 1998), and the inclination of the system, (Davey & Smith 1996; Wickramasinghe et al. 1991).
The best-fit model results in K, cm, K, , and . The opening angle converts into a fractional spot area . The fit proved to be robust in , , and . However, the opening angle can be traded for the central temperature of the spot within certain limits (see below), because the continuum slope of the white dwarf model spectra approaches a Rayleigh-Jeans distribution for temperatures K and becomes independent of the temperature.
The simulated light curves in Bands 2 and 3 from the best fit are shown in Fig. 3. For completeness, Fig. 3 also compares the synthetic light curve in Band 1 with the observed one, showing that the model fluxes are somewhat too high. As noted above, this may be due to remaining imperfections in the absolute flux calibration of the GHRS/G140L setup at the shortest wavelengths. The white dwarf temperature derived from the HST light curves is in good agreement with the upper limit of 20 000 K based on IUE low state spectra (Heise & Verbunt 1988; Paper 1). The same is true for the temperature and the size of the spot, even though these are less well constrained. Smaller spots result in a flattening of the synthetic light curve in the range , as the spot eventually disappears entirely behind the limb of the white dwarf. A fit with e.g. K and , corresponding to , still yields a satisfying result. However, it is formally not possible to exclude even smaller spots with higher temperatures. Yet, even though not statistically significant (see below), the observed light curve is better fitted with a spot large enough not to be totally self-eclipsed, as the roundness of the observed light curve in the range is better reproduced. The temperature maps of the white dwarf surface resulting from the best fit are shown in Fig. 4.
A sample of simulated phase-resolved spectra along with the GHRS observations is shown in Fig. 5, clearly revealing the major shortcoming of our approach: the model predicts a deep and broad absorption line of , but the GHRS observations show only a rather shallow absorption. The most likely cause of this disagreement will be discussed in Sect. 4.1.
On close inspection, the observed light curves show a weak depression at . With an inclination and a colatitude of the spot centre , the line of sight is almost parallel to the accretion funnel at , and part of the hot spot will be obscured by the magnetic coupled part of the accretion stream. The weak absorption dip in the observed light curves may be due to this shadowing effect.
There are a number of caveats concerning our model for the UV light curve:
(a) A proper statistical assessment of the goodness of the fit is difficult: The statistical error for each individual point (the standard deviation of the flux bins in the band divided by the square root of the number of bins) is very small. Hence, the scatter in the observed light curves (Fig. 3) has some underlying physical origin. This is not too surprising, as AM Her shows strong flickering on various timescales both at optical wavelengths (e.g. Panek 1980) and at X-rays (e.g. Szkody et al. 1980). We computed the mean scatter in the observed light curve by subtracting a light curve smoothed with a 30 point boxcar. Adopting the standard deviation of this mean scatter, which is in the different bands, as the mean error of the individual points, our best fit yields a reduced . Even though this is formally satisfying, a number of systematic uncertainties remain.
(b) We assume in our model that all the continuum flux originates from the heated and unheated surface of the white dwarf. This overestimates the white dwarf flux and, hence, its radius, as the illuminated accretion stream certainly contributes to the observed continuum flux. In Paper 1, we were able to quantify this continuum contribution thanks to the broad wavelength coverage of the IUE SWP and LWP cameras. The narrow wavelength band covered in the GHRS spectra does not allow a similar treatment, and we rely on the results from Paper 1, i.e. that the contribution of the accretion stream to the observed continuum is likely to be for Å. The light curves of the broad emission lines are shifted in phase with respect to the continuum flux (Sect. 3.7; Fig. 11), with maximum line flux occurring at . Therefore, the error introduced by neglecting the stream continuum contribution is largest during the faint phase, partially explaining the shallowness of the broad absorption at .
(c) The spot may not be circular. Modelling phase-resolved polarimetry, Wickramasinghe et al. (1991) find a cyclotron emitting region elongated by in magnetic latitude. However, unless the spot is significantly asymmetric, the ultraviolet light curves are not sensitive to the actual shape of the spot.
(d) A second active region offset by has been detected in polarimetry (Wickramasinghe 1991) and may contribute to the UV continuum flux during the faint phase. This would result in an overestimate of .
(e) The temperature distribution undoubtedly deviates from a linear gradient in angle. An indication that this is the case comes from the observed EUV flux of AM Her. Choosing K, as derived by Paerels et al. (1996), it is not possible to reproduce the observed ultraviolet modulation without exceeding the measured EUV flux. Assuming a linear decrease of the temperature with angle gives an upper limit K, and a lower limit .
Fig. 6 shows the trailed spectra of the C III 1176 line and the N V 1239, 1243 and Si IV 1394, 1403 doublet lines constructed by combining the 341 individual AM Her spectra, extracting narrow regions around the line centres, and subtracting the continuum by means of a third-order polynomial fit. In the doublet lines, the zero point of the velocity scale was set at the central wavelength of the blue doublet peak. Both a narrow and a broad emission component are clearly visible in the trailed spectra of the two doublet lines, while the C III line appears to contain only a broad component.
The trailed spectrum of the C III line shows a broad, weak S-wave with a full-width of km s-1 and a maximum (edge-to-edge) amplitude of km s-1. The line intensity is strongest at orbital phases , and weakest at phases . Both of the doublet lines have trailed spectra displaying a broad S-wave component similar to the C III line, and a superimposed, narrow (full-width km s-1), low amplitude ( km s-1) S-wave component. As in the C III line, the doublet line intensities are strongest at , and weakest at . Other than the difference in blue and red component separation, the trailed spectra of the two doublet lines differ in one obvious respect: the narrow S-wave in the N V line is visible throughout the entire orbit at approximately equal strength (slightly weaker at ), but the narrow component of the Si IV line completely vanishes in the phase range 0.75-1.15.
In order to construct Doppler tomograms from the data, the spectra were resampled onto a uniform velocity scale, and averaged into orbital phase bins of width . This resulted in 3-4 spectra combined into each phase bin, thereby increasing the signal-to-noise while preserving a high phase resolution. The tomograms were calculated using the Fourier-filtered back projection technique (e.g., Marsh & Horne 1988; Horne 1991). Fig. 7 shows the tomograms of the C III line and the blue components of the N V (1239Å) and Si IV (1394Å) doublets. Tomograms for two other relatively strong emission lines in the UV spectrum of AM Her are not shown. The tomogram of the C II 1335 line, which lacks a narrow component, is qualitatively similar to that of the stronger C III line. The trailed spectrum of the Si III emission complex at Å (which also lacks a narrow component) is qualitatively similar to that of the C III line, and we would expect it to produce a correspondingly similar tomogram. However, the presence of two strong interstellar absorption features produced substantial artifacts in the Si III tomogram that prevent a direct comparison with the other lines.
The ring with a radius of km s-1 visible in the N V tomogram is an artifact produced when the flux in the red peak of the doublet (which is located at a velocity offset of km s-1 from the blue peak - see Fig. 6) is smeared out around the tomogram. A similar artifact is observed when the Si IV tomogram is plotted to larger velocities (the doublet separation in Si IV, km s-1, is larger than in N V). The red halves of the doublet lines, as should be expected, yield tomograms identical in structure (above the noise) to the blue halves (although the former are somewhat weaker in overall intensity than the latter, as expected from the relative strengths of the doublet peaks, which are also weaker on the red side).
The Si IV tomogram contains two main emission regions: (1) a roughly circular area of strong emission located near the velocity origin, and (2) a broad "fan" of less intense emission emanating from the velocity origin and extending (primarily) into the quadrant of the tomogram. These emission regions can be directly attributed to the narrow and broad emission line components, respectively. The general location of the strong emission region is suggestive of an origin on or near the secondary star (see the figure in Horne 1991 comparing velocity and position coordinates in a CV) - we will explore this possibility further in Sect. 4.3. We used contours plotted at intervals of 5% of the peak intensity in the tomogram (not shown) to locate the centre of the strong emission region, at km s-1 (with an uncertainty of km s-1 in each coordinate). This emission is asymmetrically distributed relative to both velocity axes. The 70% peak contour extends from to km s-1 and from to km s-1.
The fan-shaped emission component in the Si IV tomogram is most likely produced by the accretion stream of AM Her. The initial ballistic trajectory of the stream would produce emission at velocities starting at the point on the axis, and extending roughly parallel to the axis for some length before curving into the quadrant (e.g., see Horne 1991 and Fig. 15), thus accounting for the weak emission above the axis in the quadrant (and, presumably, some continuing contribution along the outer edge of the fan). The remaining weak emission is produced by the range of observed radial velocities of the stream material once it is being channelled along the magnetic field lines (e.g., Schwope et al. 1995). As expected for a strongly magnetic CV like AM Her, there is no ring of emission indicative of a disc in the tomogram. There is also no apparent enhancement to the Si IV emission anywhere along the axis, where a contribution from the white dwarf would be located.
The N V tomogram of AM Her is similar in appearance to the Si IV tomogram. Again, a strong, compact emission region is present on the axis, and a weaker fan of emission extends to larger negative velocities. However, the fan emission is weaker overall than in the Si IV tomogram, and has its strongest part along the trajectory most consistent with the initial, ballistic accretion stream. It is not clear if this difference in the fan emission intensity distribution implies an actual difference in the physical distribution of N V and Si IV emission regions in AM Her, or if it is simply an artifact in the tomogram caused by contamination from the broad emission component of the red half of the more closely spaced N V doublet.
On closer inspection, we also found the strong emission region in the N V tomogram to be somewhat different from that in the Si IV tomogram. Specifically, the centre of this region (determined by plotting the 5% intensity contours as for Si IV) is located at km s-1. This implies a smaller orbital velocity around the centre-of-mass and a higher degree of asymmetry relative to rotation around the axis than for the strong emission region in the Si IV tomogram (see Sect. 4.3). The 70% contour level extends from to km s-1 and, despite the increased offset of the emission centre, from to km s-1 (i.e., the same extent as the 70% contour in the Si IV tomogram).
The C III tomogram contains only a broad, fan-shaped emission component very similar in extent to that in the Si IV tomogram. The strong, compact emission region on the axis is absent from this tomogram, corresponding to the lack of a narrow component in the C III emission lines (see Fig. 6).
In order to measure radial velocity and line flux curves for the UV emission lines in AM Her, we binned the HST spectra into 24 orbital phase bins of width (a 25th bin is empty because a section of the CV's orbit was not observed by HST). We then fit single or multiple Gaussians (plus a linear function for continuum subtraction) to the line profiles. The number of Gaussians used for a given line depended on the complexity of the line profile. For the C II, Si III, and C III lines, a single Gaussian was used. For the Si IV doublet, a total of 6 Gaussians were used, 3 for each half of the doublet. These 3 Gaussians, in turn, were used to fit the narrow and broad line components seen in the tomographic results (see Sect. 3.6), as well as a weak, high velocity component revealed as a residual component during an initial attempt to fit the Si IV doublet profiles with 2 times 2 Gaussians. The separations of each of the 3 blue-red pairs of Gaussians was fixed to the separation of the Si IV doublet and their centres were allowed to vary in tandem only. In addition, the FWHM of the Gaussians in each of the 3 blue-red pairs were required to be equal to each other, under the assumption that both halves of each of the 3 doublet components should form in the same region and, hence, display the same intrinsic velocity broadening in their profiles. To provide an additional constraint in fitting this complicated line profile, the amplitudes of each blue-red Gaussian pair were required to be related in the ratio blue:red = 1.0:0.8 (Reader et al. 1980). We attempted a similar approach with the N V doublet, but the more variable continuum and more severe blending of the doublet halves prevented us from obtaining a reliable 6-Gaussian fit. We were only able to fit 2 Gaussians of fixed FWHM and separation to the narrow components in the N V doublet in order to obtain a radial velocity curve of the narrow component.
The centres of the Gaussians for the individual line components were converted to velocity offsets from the corresponding line centres. In the case of the doublet lines, we present here only the results of the fits to the blue halves of the doublets. Fig. 8 shows the radial velocity curves of the 3 components of the blue half of the Si IV doublet, which are very similar to those obtained for the 3 components in the He II 4686 line of the polar HU Aqr (Schwope et al. 1997). The best least squares fit of the sinusoidal function
to the broad and high velocity components are shown in the figure. The parameters of the fits (i.e., the systemic velocity, , radial velocity semi-amplitude, K, and phase offset, , which is defined as the lag between the observed red-to-blue crossing of the emission line velocity and the expected phase of the superior conjunction of the white dwarf) are listed in Table 2, along with their uncertainties determined from a Monte Carlo simulation. The implications of the results for the narrow component velocity curves will be discussed in Sect. 4.3. Although the velocity curve of the broad component is fit quite well by a sine wave, the large parameter uncertainties and substantial of the high velocity component attest to the non-sinusoidal nature of its behaviour as a function of orbital phase. The weak, high velocity component detected in the Si IV line does not make a noticeable contribution to the tomogram of that line, even when the tomogram is plotted to larger velocities than shown in Fig. 7. There are two main reasons for this: first, the high velocity component is weak compared to the narrow and broad line components, and its apparent relative brightness in the tomogram will be further decreased by being smeared out around the high velocity perimeter of the tomogram. Second, the contamination from the red half of the Si IV doublet, which occurs at a velocity offset approximately equal to the maximum range of variability of the high velocity component, will overpower and mask whatever contribution from the high velocity component that might be contained in the tomogram.
Table 2. Velocity curve parameters for the narrow (NC), broad (BC) and high velocity (HVC) emission line components
Fig. 9 shows the velocity curves of the narrow components of the blue halves of both the Si IV and N V doublets, along with their best fit sine waves (see Table 2 for parameter values and uncertainties). There are no velocity points for the narrow component of Si IV in the orbital phase interval -0.1 since the narrow component vanishes during these phases (see Fig. 6), probably due to obscuration by the secondary star (Sect. 4.3). As suggested already by the tomograms, the implied radial velocity semi-amplitude of the narrow component of N V is substantially smaller than that of Si IV. The phase offsets of relative to superior conjunction of the white dwarf for both lines imply that the source of the narrow emission component is either on the secondary star or follows the motion of the secondary star around the binary's centre of mass.
Fig. 10 shows the velocity curves from the broad component of Si IV and the single Gaussian fits to C II, Si III, and C III; the fit parameters are listed in Table 2. All four curves have phase offsets of , but display a range of velocity semi-amplitudes: Si IV has the smallest K, the two carbon lines have larger, approximately equal K values, and Si III has the largest K.
Fig. 11 shows the flux curves determined from the Gaussian fits for the narrow component of Si IV (note that this is the flux of the blue half of the doublet only), and for the Si III, C II, and C III lines. A flux curve for the broad component of Si IV is also shown in the figure; however, this is actually the sum of the fluxes of the broad and the high velocity components of this line (again, the blue half of the doublet only). The fluxes determined individually for these components from the Gaussian fits suffered some confusion at orbital phases when the components' radial velocity curves crossed each other (see Fig. 8). Flux curves for N V are not available because of the difficulty in distinguishing the blended components of its line profile using the multi-Gaussian fitting approach (as mentioned above). The behaviour of the Si IV broad component and the non-doublet line flux curves is similar in all four of the lines, with a minimum at -0.0 and a maximum at -0.6. The flux curve of the narrow component of Si IV has a maximum at , and vanishes in the phase range .
© European Southern Observatory (ESO) 1998
Online publication: September 17, 1998