3 Results

3.1 Spectrum description and variability

The averaged spectrum for grating 13 is shown in the upper panel of Fig. 2. It reveals a steep blue continuum with hydrogen and helium absorption lines. Spectrophotometric magnitude determination of this spectrum yields V = 14.4 and V-R = 0.8. The continuum can be approximated by a function $F_{\lambda} \propto \lambda^{-\alpha}$, with $\alpha = 3.50 \pm 0.01$. This spectral energy distribution is bluer than the expected for an infinitely large steady state disc, i.e. $F_{\lambda}$ $\propto$ $\lambda^{-7/3}$ (Lynden-Bell 1969). It also differs from the observed UV spectra of most dwarf novae during outburst, viz.  $\alpha \approx 2$(Verbunt 1987). A careful examination of the spectrum reveals the presence of emission cores inside the H$\alpha$ and He I absorption lines (Fig. 2, two lower panels).

We measured equivalent widths between two points of the continuum separated by $\pm$2000 (1250) km s^-1 from the H$\alpha$ (He I 5875) rest wavelength. In the case of H$\beta$, in order to avoid the blending with He I 4920, we made the measurements between continuum points located at -3500 km s^-1 and +2500 km s^-1 from the rest wavelength. The averaged equivalent widths and their standard deviations were $1.6 \pm 0.3$, $5.2 \pm 0.5$ and $0.91 \pm 0.15$ Å, for H$\alpha$, H$\beta$ and He 5875 and they did not change during the two nights. The H$\delta$ and H$\gamma$ absorption lines seen in the grating 13 spectra had equivalent widths of 8 and 7 Å, respectively. They were measured as in H$\beta$ but with the upper limit wavelength of 3500 km s^-1. In the average grating 8 spectrum we also detected weak lines of He I 4474, He II 4686, He I 4920, He I 5016/5048 and He I 6678 (Fig. 2 middle and bottom panel). The He I 5016/5048 blend shows a central emission at 5027 Å, while He I 4920 and He I 5875 show emission cores at $\lambda$ 4922 and 5874 Å. He II 4686 also shows an emission core at $\lambda$ 4687 Å. The strength of the emission component, relative to their absorption component, is much stronger in the He II line than in the H and He I lines. The FWHM for the double peak H$\alpha$emission core seen in the averaged grating 8 spectrum is 580 km s^-1 and the peak separation 270 km s^-1.

Figure 2: Upper graph: flux-calibrated low resolution spectra of V 592 Her. Middle graph: higher resolution normalized spectrum around the H$\beta$ line. Lower graph: same as middle graph but around the H$\alpha$ line.

3.2 Radial velocities and the orbital period

We measured radial velocities for several features in the spectra. We applied the cross correlation technique to the absorption wings and emission lines separately yielding very noise velocity curves. After several trials, we realized that the least noisy radial velocities were obtained by measuring the position of the H$\alpha$ emission core interactively with the cursor in the splot IRAF routine. For that, we used the k key and also choose by eye the position where the intensity was maximum. Both methods yielded similar results. We searched for periodic variations in these velocities using both the Scargle and the AOV algorithm (Scargle 1982; Schwarzenberg-Czerny 1989) implemented in MIDAS. The results in Fig. 3 show possible periods at $P_{1} = 0.0633 \pm 0.0004$ days (91.2 min), $P_{2} =0.0594 \pm 0.0003$ days (85.5 min) and $P_{3} = 0.0561 \pm 0.0004$ days (80.8 min). The errors correspond to the HWHM of the peaks. In order to discriminate between the possible frequencies and to derive the true period, we applied the method described in Mennickent & Tappert (2001). In this method, sets of radial velocity curves are generated with the same noise characteristics and time distribution as the original dataset. These datasets were analyzed with the idea that, after many simulations, the true period emerges like the most recurrent period in the trial periodograms. We fitted the data with a sine function corresponding to the peak frequency (this was done for the three candidate frequencies). Then a Monte Carlo simulation was applied in such a way that a random value from an interval consisting of $\pm$3 times the sigma of the sine fit was added to each data point on the fit function. The Scargle algorithm was applied to the resulting data set and the highest peak was registered. The histogram for these values is shown in Fig. 4. The peak at 0.0594 days shows the narrowest and highest peak, while the other periods have a broader distribution. The total number of maxima is 327, 338 and 335 for periods P₁, P₂ and P₃ respectively. From the above we conclude that P₂ is slightly, but not conclusively favoured. However, there is another line of evidence favouring P₂. Duerbeck & Mennickent (1998) gave two possible orbital periods, based on the modern calibration of the Schoembs & Stolz relation, namely, P₁( ${\it SHP}_{1}$) = 0.06239 $\pm$ 0.00020 and P₂( ${\it SHP}_{2}$) = 0.05898 $\pm$0.00020 days. This seems to exclude P₃. In addition, the differences between observed and predicted periods are P₁ - P₁( ${\it SHP}_{1}$) = 0.0009 $\pm$ 0.0004 days and P₂ - P₂( ${\it SHP}_{2}$) = 0.0004 $\pm$ 0.0004 days. According to Mennickent et al.  (1999), these differences rarely exceed 0.00075 days, so P₂ is also favoured in this case. The near coincidence between the superhump and orbital period arises the question if the radial velocity is being modulated by rotation around the center of mass of the binary or, alternatively, by the superhump period. To our knowledge, there is no evidence for "superhump-modulated'' radial velocities in previously published work, so here and thereafter we will assume that the period found really reflects the binary orbital period.

The radial velocities of the H$\alpha$ emission core, folded with the P₂ period, are shown in Fig. 4. The ephemeris for the red to blue passing is:

T₀ = 2 451 054.4969(12) + 0.0594(3) E. (1)

The figure also shows the best sine fit, with amplitude $179 \pm 11$ km s^-1 and zero point $-192 \pm 15$ km s^-1. We obtained $161 \pm 39$ km s^-1and $217 \pm 22$ km s^-1for the amplitudes of first and second night, respectively, and $-165 \pm 28$ km s^-1 and $-195 \pm 17$ km s^-1 for the corresponding zero points, so we do not find evidence for a $\gamma$ shift like those observed in other dwarf novae during outburst (e.g. in VY Aqr, Augusteijn 1994 derived a shift of 155 km s^-1, in TU Men Stolz & Schoembs 1984 derived a full amplitude of $\sim$560 km s^-1, in Z Cha Hoeny et al. 1988 derived $\sim$160 km s^-1 and in TY PsA, Warner et al.  1989 derived $\sim$600 km s^-1). Variations in the system velocity have been explained with the "precessing eccentric disc'' model of Whitehurst (1998) for superhumps. In this model $\gamma$ is expected to change with the precession period of the disc, which is equal to the beat period between the superhump and the orbital period. For V 592 Her the expected precession period of the disc is $\sim$5 or $\sim$7 days. Therefore, the non-detection of a significant $\gamma$ shift during two consecutive nights in V 592 Her could be the result of our very short baseline.

The application of the "double Gaussian'' convolution mask algorithm (Schneider & Young 1980; Shafter 1983) to the radial velocities of the inverted H$\beta$ absorption profile resulted in a large half-amplitude radial velocity near the line center (about $110 \pm 30$ km s^-1 between 250 and 1200 km s^-1, probably reflecting contamination by unseen emission) and a lower half-amplitude of $46 \pm 25$ km s^-1 in the line wings (between 1200-2500 km s^-1 from the line center, probably indicating different gas dynamics for the emission and absorption disc regions). The application of period searching algorithms to these datasets yields results which seem to exclude P₃ but are not conclusive regarding the other two possible periods. It is generally known for dwarf novae (see, e.g. Warner 1995) that, especially during outburst, the radial velocity half-amplitude does not reflect the white dwarf motion, likely due to the presence of complex gas flow patterns in the accretion disk which are still not well understood. For this reason we do not intend here to constraint the stellar masses using the binary mass function based on the radial velocity half amplitude.

Figure 3: Scargle (top) and AOV (bottom) periodograms of the H$\alpha$radial velocity data. Possible frequencies are labeled.

Figure 4: Histogram of the maximum-peak frequency.

Figure 5: The H$\alpha$ radial velocities folded with the orbital period. Data of the first and the second night are indicated by squares and circles, respectively. The best sine fit is also shown.