5 Discussion

As already noted in Sect. 4.1, our Doppler maps show two bright emitting regions (Figs. 6 and 7, left column). Now we also point out that the part of the bright region which we have interpreted as bright spot, is located near the intersection of a ring-shaped structure and the upper arc of the tomograms. It indicates the nearly Keplerian velocities of the matter in the area of the bright spot.

The modelling of the Balmer line profiles has allowed us to find the dependence of the brightness of this spot on the orbital phase (Fig. 9). The derived brightness curves of the spot for both observing sets are very similar. One can see that the brightness considerably oscillates, and during a significant part of the period ( $\varphi \sim 0.2$ to 0.6) the spot is not visible. This happens when the spot is on the distant half of the accretion disk. On the contrary, the spot becomes brightest at the moment of inferior conjunction. It is important to note that even near to the moment of inferior conjunction the brightness of the spot varies. Probably, this is connected to an anisotropic radiation of the bright spot. In consequence of it we get an asymmetric change in radiation during one orbital revolution of the system. However, the anisotropy alone cannot explain the missing emission of the bright spot during the orbital phases when the spot has turned away from the observer's point of view. (In this case it is more correct to name "a bright spot'' as "an invisible hot spot''.) We think this fact can additionally be explained by a self-eclipse of the bright spot owing to the large inclination of the orbital plane of IP Peg and of its accretion disk. This scenario causes an eclipse of the bright spot by an outer edge of the accretion disk followed by a drop of observable spot brightness. Thus we suggest at least two mechanisms for explanation of the observable variations of the spot brightness: an anisotropic radiation of the bright spot and an eclipse of the bright spot by the outer edge of the accretion disk. We have no possibility to discuss in this paper, which of these mechanisms is more important. It will be the subject of the separate paper.

Figure 10: The dependence of the velocity of the outer edge of the accretion disk (top panel) and of the emissivity parameter $\alpha$ (bottom panel) on orbital phase, obtained on basis of modelling H$\beta$ emission line from the second dataset. Filled and open circles represent those values of parameters, which were found on spectra obtained in phases of minimum and maximum brightness of the spot respectively.

The second area of increased luminosity is located too far from the region of interaction between the stream and the disk particles. None of the theories do predict here the presence of a bright spot, which is connected with such an interaction. This area was interpreted recently by Wolf et al. (1998) as beginning of the formation of a spiral arm in the outer disk in context of the tidal force from the secondary.

The majority of the simulations predicts the presence of the spiral structure with two symmetrically located spiral shocks in the accretion disk. Exactly such a two-armed structure was detected by Steeghs et al. (1997) in the accretion disk of IP Peg during outburst. However, the second spiral arm in our tomograms is not visible. If it does exist, it is probably hidden in the intensive emission of the bright spot. If the contribution of the bright spot from the initial profiles of the emission lines (or from the resulting Doppler maps), could be removed, it may be possible to detect the second spiral arm.

For this we have constructed the new Doppler maps using only half of the spectra obtained in phases of minimum brightness of the spot ( $\varphi = 0.15$to 0.65) (Figs. 6 and 7, right column). Although the used profiles of the emission lines practically do not contain information about the bright spot, on the left side of the Doppler maps we can see an area of increased luminosity! However its location has changed. It was displaced downwards and has taken practically a symmetrical position concerning the second area of the increased luminosity. However, in contradiction to Steeghs et al. (1997), we cannot confidently assert that the form of both bright areas is spiral, first of all because of their low brightness. Indeed, the emissivity contrast between the proposed spirals and other parts of the disk is less than 1.3 for all emission lines. At the same time we consider that even the really spiral features in the tomograms can be caused by a different effect than the spiral shocks (see, for example, Smak 2001; Ogilvie 2001). Additional evidences for this are necessary.

Figure 11: Left: The distribution of  $\rho ^{2}T^{1/2}$ over the equatorial plane in 3D calculations of Kuznetsov et al. (2001) ($\rho$ is density, T is temperature). Arrows are the velocity vectors in observer's frame. The asterisk is the white dwarf. The white dotted line is the tidally induced spiral shock. A black dotted line is the shock wave along the edge of the stream ("hot line''). The main emission regions are marked by A, B, C, D. Right: Synthetic Doppler map for $I\sim \rho ^{2}T^{1/2}$. The secondary Roche lobe (a bold black line) and the white dwarf (an asterisk) are also shown. The white line with circles and black line with squares show gas dynamical trajectories in the velocity coordinates. The main emission regions are marked by A, B, C, D as above. Both figures are reproduced under the kind permission by O. A. Kuznetsov and D. V. Bisikalo.

Additional evidences for a spiral structure of the accretion disk of IP Peg arise from the dependence of the velocity of the outer edge of the disk on orbital phase. Earlier, studying the structure of the accretion disk of U Gem, we have detected a sinusoidal variation of the parameters of the disk (and especially the velocities V of its outer edge) of the form $\sin 2\varphi$. We interpreted this by the presence of a spiral structure (Neustroev & Borisov 1998) in the disk of U Gem. We have tried to detect similar effects in IP Peg. In Fig. 10 (top panel) the dependence of the velocity of the accretion disk on orbital phase is shown. One can see, that the amplitude of variation of V in this case is even higher than for U Gem. However, the most significant variations of velocity occur at the moment of maximum brightness of the spot. In this case we cannot unequivocally eliminate the probable influence of the bright spot on the double peak separation of the emission lines. Therefore in Fig. 10 we have selected those values of velocity V, which were found from spectra obtained in phases of minimum brightness of the spot. Such a spot distorts the line profile only marginally, therefore the velocity V is determined confidently.

Although the dependence of the velocity V on orbital phase, obtained from the first dataset, does not allow us confidently to reveal any regularity in modification of the velocity V, the second dataset confidently indicates the deviation from the Keplerian velocity field in the accretion disk of IP Peg (Fig. 10). It is important to note that other parameters of the disk also vary as $\sin 3\varphi$ simultaneously with V. Moreover, the explicit anti-correlation between a change of V and $\alpha$ is observed, the correlation coefficient being more than 0.96 with a confidence probability of 99%. Variations of the peak separation of the hydrogen lines of the form $\sin 3\varphi$ is the signature of an m=3 mode in the disk. This mode can be excited, also as in U Gem, by the tidal forcing (whose main component is the m=2 mode) and the detected variations can also be explained by the presence of spiral shocks in the accretion disk.

The presence of the compact zone of energy release in the area of interaction of the stream and the accretion disk and the spiral shocks in the disk of IP Peg in quiescence does not contradict the most accurate modern 3D gasdynamical models (Bisikalo et al. 1998a, 1998b; Makita et al. 2000). Let us consider the results of these investigations in more detail in application to IP Peg. Kuznetsov et al. (2001) presented synthetic Doppler maps of gaseous flows in this system based on the results of their 3D gasdynamical simulations. They concluded that there are four elements of the flow structure which contribute to the total system luminosity: the "hot line'' (region A in Fig. 11), the most luminous part of the stream where the density is still large enough and the temperature already increases due to dissipation (region B), the dense region near the apastron of the disk (region C), and the dense post-shock region attached to the spiral shock (region D). The income of each element obviously can vary depending on the peculiarities of the considered binary system. The comparison of the observational tomograms from Figs. 6 and 7 and with synthetic ones from Fig. 11 reveals that the dominating elements in the accretion disk of IP Peg are the "hot line'', the dense zone near the disk's apastron (region C) and the post-shock zone attached to the arm of a spiral shock (region B). Signatures of a spiral shock in the region D are not detected.

Thus we believe that our observations as a whole confirm the spiral structure of the quiescent accretion disk of IP Peg. At the same time we point out that the determined structure of the accretion disk of IP Peg satisfies modern 3D simulations, which predict a considerably more complicated structure of the accretion disk than found by earlier calculations. Note that Marsh & Horne (1990) and Harlaftis et al. (1994) have also obtained the tomograms of IP Peg which are very similar to ours, indicating that the detected spiral structure of the IP Peg's accretion disk is long-lived structure.

In conclusion we would like to discuss possible reasons for the detected variability of the wings of the emission lines. The results of 3D numerical simulations of Bisikalo et al. (2001a, 2001b) have shown that if spiral shocks are present in the accretion disk then any disturbance of the disk would result in the appearance of a blob, the later moving through the disk with variable velocity but with constant period of revolution. Generally the period of the blob revolution depends on the value of viscosity, and for typical accretion disks with $\alpha \sim 0.01{-}0.1$ the period should be in the range of $0.10{-}0.20P_{\rm orb}$. This dense formation lives long enough and retains its main characteristics for a time of the order of tens orbital periods. Furthermore, every new disturbance of the disk structure will transform into a blob.

If such a blob exists, it should distort the profiles of the spectral lines with the period of the blob's revolution. From Figs. 3 and 4 in Bisikalo et al. (2001b) it can be seen, that the distance from the blob to the white dwarf is about 0.1 of the binary separation. Hence maximum radial velocity of the line component which forms in the blob should be close to $\pm$1200 km s^-1. Consequently, best areas of the spectral line for detecting of the blob should be the line wings. Thus, the detected variability of the wings of the emission lines with the period of 0 $.\!\!^{\rm h}$61 ($\sim$0.15 $P_{\rm orb}$) can be really explained by a blob. Furthermore, there is additional evidence for the presence of spiral shocks in the accretion disk of IP Peg, as the existence of the blob is maintained by the spiral shocks.