3 Analysis

Gänsicke et al. (1997) analysed an IUE spectrum of EKTrA obtained during the late decline from a superoutburst with a composite accretion disk plus white dwarf model. They found that a white dwarf with $\mbox{$T_{\rm eff}$ }\approx16\,000$-$20\,000$ contributes $\sim$25% to the ultraviolet flux. Considering that the first HST observation of EKTrA was obtained a long time after its last outburst, and that the ultraviolet flux corresponds quite well to the flux level of the white dwarf predicted by Gänsicke et al., we modelled the observed ultraviolet spectrum with a set of white dwarf model spectra, and neglect the possible continuum contribution of the accretion disk. The likely contribution of the disk is discussed below.

3.1 White dwarf effective temperature and surface gravity

We have computed a grid of solar abundance model spectra covering $\mbox{$T_{\rm eff}$ }=16\,000$-$20\,000$ K in 200 K steps and $\log g=7.25$-8.50 in 0.25 steps for the analysis of the photospheric white dwarf emission. This spectral library was generated with the codes TLUSTY195 and SYNSPEC45 (Hubeny 1988; Hubeny & Lanz 1995). We fitted the model spectra to the STIS data, allowing for Gaussian emission of He II, C II,III, N V, and Si II,III (see Table 1), and we excluded from the fit a 20 Å broad region centered on the geocoronal ${\rm Ly\alpha}$ emission. In order to achieve a physically meaningful fit, we had to constrain the components of the Si II$\lambda$1260,65 doublet to have the same FWHM, and the components of Si II$\lambda$1527,33 to have the same FWHM and flux.

It is, in principle, possible to derive from such a fit both the effective temperature and the surface gravity of the white dwarf, as both parameters determine the detailed shape of the photospheric ${\rm Ly\alpha}$ absorption profile. Unfortunately, in our observation of EKTrA the ${\rm Ly\alpha}$ profile is strongly contaminated by various emission lines. In addition, the pressure-sensitive H₂⁺ transition at 1400 Å, which is formed in a white dwarf photosphere with  K, is totally covered up by emission of Si IV$\lambda$1394,1403. The best-fit parameters $(\mbox{$T_{\rm eff}$ },\log g)$ are approximately linearly correlated, $\mbox{$T_{\rm eff}$ }\approx2360\times\log g-95$with insignificant variations in $\chi^2$. As a result, it is not possible to derive an estimate for the surface gravity, and, hence, for the mass of the white dwarf. For the range of possible white dwarf masses, 0.3-1.4 $M_{\odot}$, the fit to the STIS data constrains the white dwarf temperature to $\mbox{$T_{\rm eff}$ }\approx17\,500$-$23\,400$ K, which confirms the results obtained by Gänsicke et al. (1997). The scaling factor of the model spectrum provides an estimate of the distance to EKTrA which depends, however, on the assumed white dwarf mass. For a typical 0.6 $M_{\odot}$ white dwarf, d=200 pc, for the extreme limits $\mbox{$M_{\rm wd}$ }=0.3$ (1.4) $M_{\odot}$, d=300 (34) pc. Considering that Gänsicke et al. (1997) derived a lower limit on the distance of $\sim$180 pc from the non-detection of the donor star - in agreement with the 200 pc estimated by Warner (1987) from the disk brightness - a massive white dwarf ( ) can probably be excluded.

Figure 5: Two regions of the STIS spectrum which contain narrow metal absorption lines (see Table 1). The STIS data and the model spectra are sampled in 0.3 Å steps, which resolves well the observed photospheric absorption lines. Plotted as thick lines is a ( $\mbox{$T_{\rm eff}$ }=18\,800$ K, $\log g=8.0$, abundances = 0.5$\times$solar) white dwarf model, broadened for rotational velocities of 100, 300, 500  $\rm km\,s^{-1}$ (from top to bottom). Note the narrow interstellar absorption features at Si II$\lambda$1260, O I$\lambda$1302, Si II$\lambda$1304, C II $\lambda \lambda$1334,35, and Si II$\lambda$1527.

A model fit with ( $\mbox{$T_{\rm eff}$ }=18\,800$ K, $\log g=8.0$), corresponding to a white dwarf mass of $\sim$0.6 $M_{\odot}$, is shown in Fig. 4. The observed flux exceeds the model flux by $\sim$10-15% at the red end of the STIS spectrum (  Å). In the optical, the model shown in Fig. 4 has V=17.4, which is well below the quasi-simultaneous optical magnitude of our CTIO photometry (Sect. 2.2). The optical flux excess over the white dwarf contribution has been modelled by Gänsicke et al. (1997) with emission from an optically thin accretion disk, providing a quite good fit to the Balmer emission lines. It is very likely that the flux excess at ultraviolet wavelengths is related to the same source. Indeed, the flux contribution of an optically thin accretion disk is dominated in the near-ultraviolet by bound-free opacity and its emission increases towards longer wavelengths, reaching a maximum at the Balmer jump. In view of the short available wavelength range where the disk noticeably contributes ($\sim$100 Å), we refrained from a quantitative analysis of the disk contribution. Nevertheless, as a conservative estimate, the contribution of the accretion disk to the continuum flux at wavelengths shorter than 1550 Å is certainly much lower than 10%.

3.2 Photospheric abundances and rotation rate

A number of narrow photospheric absorption lines are observed that clearly have an origin in the white dwarf photosphere (Table 1). Unfortunately most of these absorption lines are contaminated by optically thin radiation from the accretion disk. For instance, the STIS spectrum reveals weak emission of Si II $\lambda \lambda$1527,33. Consequently, even though no obvious Si II $\lambda \lambda$1260,65 emission is observed, we can not assume that the photospheric absorption lines of this Si II resonance doublet are uncontaminated. It is therefore clear that a quantitative analysis of the photospheric absorption lines will be prone to systematic uncertainties.

We computed a small grid of model spectra for ( $\mbox{$T_{\rm eff}$ }=18\,800$ K, $\log g=8.0$) covering white dwarf rotation rates of 100-500  $\rm km\,s^{-1}$ in steps of 100  $\rm km\,s^{-1}$ and abundances of 1.0, 0.5, and 0.1times the solar values. These spectra were fitted to the strongest Si II and C I lines observed in the STIS spectrum of EKTrA, again allowing for Gaussian emission lines of Si II (Table 1). No emission lines were added for the C I features, as C I was - to our knowledge - never observed in emission in the ultraviolet spectra of CVs. The quality of the fits varies somewhat depending on the considered lines, but generally indicates $v\sin i=200\pm100$  $\rm km\,s^{-1}$, and sub-solar abundances. The best-fit rotation rate does not significantly depend on the assumed abundances. Figure 5 shows the fits for $0.50\times$solar abundances and for 100, 300, and 500  $\rm km\,s^{-1}$.

The very narrow cores observed in Si II$\lambda$1260 and Si II$\lambda$1527 are of interstellar nature. Note that the 1265 Å and 1533 Å members of these two doublets do not show such narrow cores: they are transitions from excited levels, which are not populated in the interstellar medium. Additional strong interstellar features found in the STIS spectrum are O I$\lambda$1302, Si II$\lambda$1304, and C II $\lambda \lambda$1334,35. All these interstellar lines are clearly visibly also in the unbinned data. Their measured positions agree within $\pm10$  $\rm km\,s^{-1}$ with their rest wavelengths, which nicely demonstrates the quality of the absolute wavelength calibration. The positions of the photospheric white dwarf lines constrains the systemic velocity of EKTrA to   $\rm km\,s^{-1}$.

3.3 Short-term variability

Both the ultraviolet flux (Fig. 2) and the optical flux (Fig. 3) show short-term fluctuations on time scales much shorter than the orbital period of 90.5 min (15.9  ${\rm d}^{-1}$). We have computed Lomb-Scargle periodograms for the all three wavelength ranges, and find significant power at $32~{\rm d}^{-1}$, $67~{\rm d}^{-1}$, $93~{\rm d}^{-1}$ in the ultraviolet and at $45~{\rm d}^{-1}$ and $65~{\rm d}^{-1}$ in the optical/IR. The white dwarf rotation rate derived above, $v\sin i\approx200$  $\rm km\,s^{-1}$, implies a spin period of a few minutes, depending somewhat on the white dwarf radius and the inclination of the system ($\sim$60$^{\circ}$, Mennickent & Arenas 1998). The detected periods are much longer, and most likely represent the preferred quasiperiodic time scale for flickering during the observations. The fact that the V and the I band light curves are practically identical both in shape and in amplitude is somewhat surprising, as this suggests a flat spectrum for the flickering.

In order to identify the spectral origin of the ultraviolet flickering we constructed light curves from the STIS photon event file for the strongest emission line, C IV$\lambda$1550 (using the range 1530-1565 Å), and for an adjacent emission line-free region (using the range 1414-1530 Å). The (continuum-subtracted) C IV light curve shows a similar variation as the total light curve (Fig. 2), but with a much larger amplitude. For comparison, the standard deviation from the mean count rate is $\sigma\approx30$% in the C IV light curve vs. $\sigma\approx9$% in the total light curve. The variation in the continuum count rate extracted from the line-free region is $\sigma\approx6$%, which is comparable to the errors due to photon statistics. This confirms the assumption that the continuum is mainly made up of photospheric emission from the white dwarf. Considering that $\sim$25% of the total ultraviolet flux observed with STIS is contained in the various emission lines, we conclude that the flickering is primarily associated with an optically thin region, possibly some kind of corona above a cold accretion disk. For a discussion of the possible excitation mechanisms causing the line emission, see Mauche et al. (1997). Assuming a distance of 180 pc, the luminosity of the ultraviolet line emission is $\sim$ $6.6\times10^{30}$  $\rm erg\;s^{-1}$, about $\sim$20% of the sum of the optical disk luminosity and the X-ray luminosity (Gänsicke et al. 1997). Including the ultraviolet disk emission in the energy balance of the system does, therefore, not noticeably change the conclusion of Gänsicke et al. (1997) that the accretion rate in EKTrA is a factor $\sim$5 lower than in the prototypical SUUMa dwarf nova VWHyi.

It is interesting to compare the short-term ultraviolet variability of EKTrA with that of a long-period dwarf nova. Hoard et al. (1997) analysed fast HST/FOS spectroscopy of IPPeg and found a strong contribution of the continuum to the ultraviolet flickering. This indicates that for the higher accretion rates prevailing above the period gap the disk/corona is a significant source of ultraviolet continuum emission. Indeed, in IPPeg the white dwarf emission is not detected in the ultraviolet. Hoard et al. (1997) could also show that in IPPeg the flickering in the continuum, medium-excitation, and high-excitation lines is uncorrelated, suggesting a rather complex multi-component spectrum from a structured emission region.

 

 

Table 2: White dwarf rotation rates measured from Doppler-broadened absorption lines, and effective temperatures measured in deep quiescence.

System	Type	$P_{\rm orb}$	$v\sin i$	$\mbox{$T_{\rm eff}$ }$	Ref.
		[min]	[ $\rm km\,s^{-1}$]	[K]
WZSge	DN/WZ	81.6	1200	14900	1
EKTrA	DN/SU	90.5	200	18800	2
VWHyi	DN/SU	106.9	400	19000	3,4
UGem	DN/UG	254.7	$\le100$	32000	5,6
RXAnd	DN/UG	302.2	150	35000	7
(1) Cheng et al. (1997); (2) this paper; (3) Sion et al. (1995); (4) Gänsicke & Beuermann (1996); (5) Sion et al. (1994); (6) Long et al. (1995); (7) Sion et al. (2001).