5. Application: UZ For
5.1. System geometry of UZ For
UZ For has been identified as a polar in 1988 (Berriman & Smith 1988; Beuermann et al. 1988; Osborne et al. 1988). Cyclotron radiation from a region with has been reported by Schwope et al. (1990) and Rousseau et al. (1996). The first mass estimates for the WD were rather high, and (Hameury et al. 1988; Beuermann et al. 1988), but Bailey & Cropper (1991) and Schwope et al. (1997) derived significantly smaller masses, and , respectively. We use reliable system parameters from Bailey & Cropper (1991), , , , . The optical light curve in Bailey (1995) shows two eclipse steps which are interpreted as the signature of hot spots near both magnetic poles of the WD, consecutively dissapearing behind the limb of the secondary star. From that light curve we measure the timing of the eclipse events with an accuracy of . The ingress of the spot on the lower hemisphere occurs at , its egress at . For the spot on the upper hemisphere, ingress is at and egress at .
To describe the spatial position of the dipole field line along which the matter is accreted, three angles are needed: The colatitude or tilt of the dipole axis , the longitude of the dipole axis , and the longitude of the stagnation region . Here, longitude is the angle between the secondary star and the respective point as seen from the centre of the white dwarf. With our choice of , and , we can reproduce the ingress and egress of the two hot spots as well as the dip at phase . A summary of the main system parameters used in this analysis is given in Table 3.
Having the correct geometry of the accretion stream is crucial for generating the correct reconstruction of the emission regions. As we have shown in Kube et al. (1999) especially the geometry of the dipole stream is sensitive to changes in , , and . For UZ For, the geometry of the dipole stream is relatively well constrained from the observed ingress and egress of both hot spots on the white dwarf (Bailey 1995). Fitting the UZ For light curves system geometries that differ within the estimated error range of less than five degrees does, however, not significantly affect our results. This situation is different if the errors in the geometry parameters are larger than only a few degrees.
5.2. Observational data
UZ For was observed with HST on June 11, 1992. A detailed description of the data is given by Stockman & Schmidt (1996). We summarize here only the relevant points.
Fast FOS/G160L spectroscopy with a time resolution of 1.6914 s was obtained, covering two entire eclipses in the phase interval . The two eclipses were observed starting at 05:05:33 UTC (`orbit 1') and 11:25:39 UTC (`orbit 2'). The spectra cover the range Å with a FWHM resolution of Å. The mid-exposure times of the individual spectra were converted into binary orbital phases using the ephemeris of Warren et al. (1995). The average trailed spectrum is shown in Fig. 9.
In order to obtain a light curve dominated by the accretion stream, we extracted the continuum subtracted C IV 1550 emission from the trailed spectrum. The resulting light curves are shown in Fig. 10 for both orbits separately. To reduce the noise to a bearable amount, the light curves were rebinned to resulting in a phase resolution of .
We note that the CIV light curve may be contaminated by emission from the heated side of the secondary star. HST/GHRS observations of AM Her, which resolve the broad component originating in the stream and the narrow component originating on the secondary, show that the contribution of the narrow component to the total flux of CIV is unlikely to be larger than % (G"ansicke et al. 1998). Furthermore, during the phase interval covered in the HST observations of UZ For, the irradiated hemisphere of the secondary is (almost) completely self-eclipsed, so that its CIV emission is minimized.
The light curves show small, but significant differences for the two orbits (Fig. 10). In orbit 1, the dip at is slightly deeper than in orbit 2. However, this very small feature has only a marginal effect on the results. The dip is well known from X-Ray and EUV observations (Warren et al. 1995) and has been observed to move in phase between and 0.92 on timescales of months (Sirk & Howell 1998). The ingress of the accretion stream into eclipse is much smoother in orbit 1 than in orbit 2, where an intermediate brightness level around with a flatter slope is seen. The CIV intensity maps resulting from our fits are shown in Fig. 11 for each observation interval separately. In Fig. 12, we show the relative intensity distributions of 10 fit runs for each orbit, proving that our algorithm finds the same result (except for noise) for each run. In Fig. 11, the resulting map from one arbitrary fit is shown.
The brightness maps for the two orbits show common features and differences. Common in both reconstructed maps are the bright regions (1) on the ballistic stream, (2) on the dipole stream above the orbital plane, and (3) on the dipole stream below the orbital plane. In orbit 1, there is an additional bright region on the northern dipole stream which appears as a mirror image of region 3. We denominate it 3b. The difference between both maps is found in the presence/absence of region 3b, and in the different sharpness of region 1, which is much brighter and more peaked in orbit 1 than in orbit 2.
Remarkable is that we do not find a bright region at the coupling region SR, where one would expect dissipative heating when the matter rams into the magnetic field and is decelerated. We will comment on this result in Sect. 6.2.
The sharp upper border of region 2 has to be discussed separately: As one can see from the data, the flux of the C IV 1550 emission ceases completely in the phase interval . Hence, all parts of the accretion stream which are not eclipsed during this phase interval can not emit light in C IV 1550. For the assumed geometry of UZ For, parts of the northern dipole stream remain visible throughout the eclipse. Thus, the sharp limitation of region 2 marks the border between those surface elements which are always visible and those which dissappear behind the secondary star. Uncertainties in the geometry could affect the location of the northern boundary of region 2, but should not change the general result, namely that there is emission above the orbital plane that accounts for a large part of the total stream emission in C IV 1550.
Region 3b has to be understood as an artifact: During orbit 1, the observed flux level at maximum emission line eclipse () does not drop to zero. Hence, our algorithm places intensity on the surface elements of the accretion stream which are still visible at that phase. Apparently, the evolution strategy tends to place these residual emission not uniformly on all the visible surface elements but on those closer to the WD, which leads to an intensity pattern that resembles the more intense region on the southern side of the dipole stream.
To underpin the fact that regions 1, 2, and 3 in our map are real features and not just regions which result by random fluctuations in the data, we test what happens to the reconstruction if the input light curve is changed. For the calculation which results in the map shown in Fig. 13, we generated a modified light curve from the data for orbit 1. For each phase step, we modified the flux, so that is the new value. is the local standard deviation as defined in Sect. 4.2, G are gaussian-distributed random values. Since the map from the light curve does not show significant differences from the map corresponding to the original data (Fig. 11), we conclude that the features 1, 2, and 3 are real.
© European Southern Observatory (ESO) 2000
Online publication: April 10, 2000