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Astron. Astrophys. 348, 364-370 (1999)

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5. Discussion

In the above section we have showed how the theoretical linewidth/K vs. mass ratio relation fails to reproduce the observations of SU UMa stars. To explain this new finding we critically examine the basic assumptions yielding Eq. 4.

The disk radius was assumed a constant fraction of the primary's Roche lobe and the linewidth a good tracer of the disk velocity at a fixed radius. The first assumption conflicts with the observations but not in a critical way. In fact, a smooth exponential-type decay of the disk radius after outburst has been observed in U Gem (Smak 1984), Z Cha (O'Donoghue 1986), IP Peg (Wolf et al. 1993) and WZ Sge (Neustroev 1998). Simulations by Ichikawa & Osaki (1992) also show this phenomenon. However, in all the above cases the disk radius varies by just 10% during most the outburst cycle; the larger changes occur only near outburst. As most data of Table 2 was obtained in quiescence, the cyclic variability of disc radius should be a second-order effect. The second assumption, that the linewidth is a good tracer of the disk velocity at a fixed radius, fails if a significant non rotational contribution broadens the line. For example, the Stark effect could be efficient in some optically thick regions of the disk (Lin et al. 1988). This effect could be especially important in high inclination systems with prominent (eventually optically thick) hot spots. However, residuals of Eq. 4 are not inclination dependent, e.g. the eclipsing binaries WZ Sge, HT Cas and Z Cha do not show any especial trend. Therefore, we do not think that the above effects explain the SU UMa star deviations.

However, these could be explained if a large fraction of the inner disk is removed by some agent. In this cases the FWHM indicates the disk velocity at a larger (fractional) radius than in a non truncated disk. To estimate the effect of a central hole on the FWHM we generated synthetic profiles for several values of [FORMULA] ([FORMULA]). The range of [FORMULA] was chosen accordingly to recent spectroscopic studies suggesting the existence of central holes in the disk of long supercycle SU UMa stars (Mennickent & Arenas 1998). The extreme value ([FORMULA] = 0.3) corresponds to WZ Sge during 1991 whereas [FORMULA] = 0.03 is representative of non truncated disks. Our results, shown in Fig. 5, indicate that the larger the central hole, the larger the FWHM. The largest effect, for [FORMULA] = 0.3, implies a decrease of R by a factor 0.7. In order to compare with Fig. 2 we assume a constant outer disk radius. This is basically consistent with the lower cyclic variability shown by the peak separation when compared to the FWHM (above section). We find that this effect is enough to explain the large deviations observed in some SU UMa stars. Moreover, the deviations associated to EG Cnc and WZ Sge are so large, that a truncation radius [FORMULA] 60% of the outer radius is required to explain the observations at certain epochs.

[FIGURE] Fig. 5. Emission line profiles calculated with synthetic Smak's (1981) model. The integrated flux is normalized to the unity and the velocity to the half peak separation. The disk line emissivity was assumed proportional to [FORMULA] and the normalized instrumental resolution 0.2 (see Smak 1981 for details about the model). The profiles are labeled according to the ratio between the inner and outer disk radius. The projection of the solid circles onto the velocity axis indicates the half FWHM of each profile. We find that a hole in the inner disk decreases FWHM and therefore R. This might explain the deviations observed in Fig. 2.

The above picture is not valid if the assumption of a Keplerian disk is violated. In this case, K doesn't represent the white dwarf binary motion and Eq. 4 fails by two reasons: a bad interpretation of K and the wrong use of the Kepler third law for the disk. In this case Fig. 3 should indicate departures of Keplerian motions in the disks of SU UMa stars, specially in those of the post-period-minimum candidates EG Cnc and WZ Sge. In contrast, nearly Keplerian disks are observed in dwarf novae above the period gap. As the nature of K is unknown in non-Keplerian disks, we cannot decide between sub-Keplerian or super-Keplerian motions from the sign of the residuals of Eq. 4. Instead, Fig. 3 suggests a transition from a Keplerian to non-Keplerian stage when the mass accretion rate in the disk goes to an extremely low or high value. This view could be supported by the non-consistent system parameters occasionally found in the dynamical solutions of some SU UMa stars, e.g. HS Vir (Mennickent et al. 1999).

In the above paragraphs we have outlied two distinct scenarios compatible with the observations: removed inner disks and non-Keplerian disks. We favor the inner disk depletion hypothesis based on theoretical and observational evidence: it provides a natural explanation for the long recurrence time of WZ Sge (Lasota et al. 1995, on the observational side see Mennickent & Arenas 1998) and for the delay between optical and UV radiation at rise to outburst observed in some dwarf novae (Mineshige et al. 1998). In addition, promissory mechanisms to remove the inner disk have been proposed: the influence of a magnetosphere (Livio & Pringle 1992) or the effect of mass flow via a vertically extended hot corona above the cool disk (also referred as "coronal evaporation", Meyer & Meyer-Hofmeister 1994, Liu et al. 1997, Mineshige et al. 1998). The coronal-evaporation model has been used to model the evolution of the accretion disk of WZ Sge during quiescence (Meyer-Hofmeister et al. 1998). In this model, cyclic variations in the inner and outer disk radius are found; the results with the "standard parameters" (their Fig. 2) show a maximum [FORMULA] 0.26 around supercycle phase [FORMULA] = 0.08 whereas [FORMULA] 0.08 is observed during most of the outburst cycle. The published spectroscopic data of WZ Sge are not enough to check this prediction, although Fig. 2 suggests maximum disk's depletion around supercycle phase 0.3.

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© European Southern Observatory (ESO) 1999

Online publication: July 26, 1999