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1 Introduction

IP Pegasi is a well-known deeply eclipsing dwarf nova with an orbital period of 3 $.\!\!^{\rm h}$79 (Lipovetskij & Stephanyan 1981; Wolf et al. 1993) and an outburst cycle of about 2.5 months. During high states, which last about 12 days, the system changes from V magnitude 14th during quiescence (out of eclipse) to 12 during outburst. Many times IP Peg was subject to detailed spectral investigations (Marsh & Horne 1990; Marsh 1988; Martin et al. 1989; Hessman 1989; Harlaftis et al. 1994; Wolf et al. 1998) and photometric researches (Wolf et al. 1993; Szkody & Mateo 1986; Wood & Crawford 1986; Wood et al. 1989; Bobinger et al. 1997). In the last years IP Peg deserved increasing interest as spiral shocks were detected in its accretion disk during outburst (Steeghs et al. 1997; Harlaftis et al. 1999).

The question on the existence of spiral shocks in the accretion disks has a long standing history. It is closely related to angular momentum transport mechanisms in accretion disks. At present there are two approaches to this problem: according to the first one, angular momentum is transported due to the presence of turbulent or magnetic viscosity in the disk (Shakura & Sunyaev 1973). On the other hand, hydrodynamical numerical calculations have shown that tidal forces of the secondary induce spiral shock waves in the accretion disk, which may provide an efficient transfer mechanism (Sawada et al. 1986; Matsuda et al. 1990). Self-similar solutions having spiral shocks, was constructed in a semi-analytic manner in two dimensions by Spruit (1987, see also Chakrabarti 1990). It should be noted that these two mechanisms are mutually exclusive, as shock waves in the presence of viscosity will be smeared out (Bunk et al. 1990; Chakrabarti 1990). Although Steeghs et al. (1997) found indications for spiral shocks in the hot accretion disks during an outburst, the problem on the spiral structure of the quiescent accretion disks still remains unsolved.

Most theorists do not support the hypothesis of the presence of spiral shocks in the accretion disks in quiescence due to the following arguments:

Since the disk expands during outburst (Smak 1984; Wolf et al. 1993), the outer parts of the expanded disk are subject to higher gravitational attraction of the secondary, leading to the formation of spiral arms. The tidal force is a very steep function of the distance to the secondary star, hence the spiral shocks rapidly become weak at smaller disk sizes.[*] Furthermore, the opening angle of the spirals is directly related to the temperature of the disk as it roughly propagates at sound speed. This effect was the principal reason to believe that spirals may not be present in accretion disks of cataclysmic variables, which are not hot enough. This is in principal the case in quiescent disks (Boffin 2001). Steeghs & Stehle found from their calculations (1999), using the grid of the 2D hydrodynamic accretion disk, that the spiral shocks in quiescent accretion disks are so tightly wound that they leave few fingerprints in the emission lines.

At the same time, the authors of the most comprehensive 3D simulations are in principle inclined to accept the presence of spiral shocks in the relatively cold disks. So, Makita et al. (2000) observed in their 3D calculations that spiral shocks are formed in an accretion disk for all specific heat ratios. In addition, they claim that in cool disks, when comparing 3D calculations with 2D ones, spiral arms are less tightly wound in the outer region of the disk. In connection with this, it is important to add that in 3D disks, there is a vertical resonance that can lie within the disk. This resonance causes a local thickening of the disk and generates waves that propagate radially. The first wavelength of this wave is longer than that of the usual 2D waves by a factor of about  (R/H)1/3 (Lubow 1981). The wavelength does increase with the level of non-linearity (Yuan & Cassen 1994). The non-linear effects can modify significantly the appearance of the spiral pattern: a longer wavelength produces a less tightly wound spiral pattern. Obviously the observations matches more closely a 3D disk, and the 2D approximation can poorly explain the observations. [Indeed, the two-dimensional disk simulations demonstrate that the spiral pattern resembles the observations only for unreally high temperatures (see, for example, Godon et al. 1998).] And at last, the calculations of Bisikalo et al. (1998a,1998b, see also Kuznetsov et al. 2001) only yield the one-armed spiral shock in the quiescent accretion disk. In the place where the second arm should form, the stream from L1 dominates and presumably prevents the formation of the second arm of the tidally induced spiral shock.

Thus, as stated above, the existence of the spiral shocks in the quiescent accretion disk has not been established convincingly. Their observational detection would be very important because spiral arms are indeed very efficient in transporting angular momentum into the outer part of the disk. If existing at all, spiral shocks would be much more difficult to detect than the strong shocks in the hot accretion disk during outburst. Nevertheless, first steps towards an observational confirmation have been started. So, studying the structure of the accretion disk of U Gem in quiescence we have detected sinusoidal variations ( $\sin 2\varphi$) of the double peak separations of the hydrogen emission lines and of their shape (Borisov & Neustroev 1999). These variations are the signature of an m=2 mode in the disk. This mode can be excited by the tidal forcing. We showed that such orbital behavior of the emission lines can be reproduced by means of a simple model of the accretion disk with two symmetrically located spiral shocks (Neustroev & Borisov 1998). Recently we have found, by means of Doppler tomography, new confirmation for spiral shocks in the quiescent accretion disk of U Gem (Neustroev et al. 2002). Further investigations in this area are strongly recommended.

The main goal of the present paper was the investigation of the accretion disk structure of IP Peg in order to locate the line emitting sites during quiescence. Special attention was payed to the search for evidences for a spiral structure of the accretion disk. Section 2 of this paper describes the observations and data reduction procedures, while Sect. 3 describes an average spectrum and emission lines variations. Section 4 presents the analysis of the optical spectra by means of Doppler tomography and Phase Modelling Technique. The results are discussed in Sect. 5 and summarized in Sect. 6.


  \begin{figure}
\par\includegraphics[width=7.6cm,clip]{h3680f1.eps}
\end{figure} Figure 1: The mean normalized spectra of IP Peg, based on first dataset.


  \begin{figure}
\par\mbox{\hspace*{5.5mm}\includegraphics[width=5.5cm,clip]{h3680...
...p]{h3680f2e.eps}\includegraphics[width=5.5cm,clip]{h3680f2f.eps} }\end{figure} Figure 2: The trailed spectra of the major emission lines. Top row: From left to right, the H$\beta $, H$\gamma $ and H$\delta $ lines from the first dataset are presented. Bottom row: From left to right, the H$\alpha $, H$\beta $ and H$\gamma $ lines from the second dataset are presented. Note, that we could only obtain 50% phase coverage of H$\alpha $ due to technical difficulties.


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