5 Discussion

The periods of statistically significant QPOs observed in MV Lyr vary about 50 min. Accepting system parameters $M_{\rm wd}=0.7\,M_{\hbox{$\odot$}}$, $M_{2}=0.3\,M_{\hbox{$\odot$}}$(Skillman et al. 1995) and $P_{\rm orb}=0.1336^{\rm d}$(Schneider et al. 1981) we found that at distances $r=0.8-0.9\,R_{\rm RL}$($R_{\rm RL}$ is Roche lobe radius of white dwarf) the Keplerian periods are $P_{\rm K}=43-54$ min. Therefore, if MV Lyr accretion disc extends to $0.8-0.9\,R_{\rm RL}$, its outer edge can be responsible for the observed QPOs.

Borisov (1992) suggested that "50 min" QPOs may be connected to the inhomogeneity motions at the disc outer edge induced by the gas stream from the red companion. We tried to apply the model of the trapped oscillations developed by Yamasaki et al. (1995) and originally directed to explain observed QPOs in dwarf novae during the outburst. According to the thermal instability scenario, during the outburst the accretion disc consists of two parts with different physical conditions: a hot inner region where the hydrogen is fully ionized and an outer cool region in which the hydrogen is neutral. Between these two parts there appears a narrow transition zone where the hydrogen is partially ionized. Yamasaki et al. (1995) have shown by a linear analysis that there are modes of growing oscillations which are trapped just inside the transition zone and their period is approximately equal to the local Keplerian period. Since resulting brightness variations are sum of oscillations with close periods, large amplitude QPOs can be expected.

  

Figure 6: Radial distribution of effective temperature in MV Lyr accretion disc (solid curves). The dotted curves point at $T_{\rm eff,max}$and $T_{\rm eff,min}$ at which the disc changes its structure. The dashed-dotted lines limit the zone in which radial oscillations can be trapped

In active state VY Scl type novalikes contain hot accretion discs and typically exhibit relatively steady high mass transfer rate $\sim 10^{\rm -8} \,M_{\hbox{$\odot$}}\,{\rm yr}^{-1}$. We assumed that in some of these systems the outer disc edge might be cool enough to allow recombination of the hydrogen and thus might play the part of the transition zone necessary for excitation of trapped oscillations. Further, the accretion rate that could cause partial recombination of the hydrogen in the outer part of MV Lyr accretion disc was estimated. According to Herter et al. (1979) the radial distribution of the disc effective temperature is

$$T_{\rm eff}(x) = T_{0}\,x^{-3/4}\,\left(1-x^{-1/2}\right)^{1/4} \hspace{0.5cm}\mbox{K},$$ (5)

where $x=r/R_{\rm wd}$, $R_{\rm wd}$ is white dwarf radius calculated according to Eggleton (1983) and

$$T_{0} = 4.1\ 10^{4}\,\dot{M}^{1/4}_{16}\,M^{1/4}_{1}\,R^{-3/4}_{1,9} \hspace{0.5cm}\mbox{K},$$ (6)

$\dot{M}_{16}$ is mass transfer rate in units $10^{16} \,\mbox{g}\, {\rm s}^{-1}$, $M_{1}=M_{\rm wd}/M_{\hbox{$\odot$}}$ and R_1,9 is white dwarf radius in units 10⁹ cm. $T_{\rm eff,max}$and $T_{\rm eff,min}$at which accretion disc changes its structure were evaluated according to Cannizzo (1993). The results are shown in Fig. 6. It is seen that if the mass transfer rate is $\sim\dot{M}=10^{-8.4}\,M_{\hbox{$\odot$}}\,{\rm yr}^{-1}$the hydrogen in the outer disc parts ($r\gt.8\,R_{\rm RL}$) will be partially ionized and consequently one can expect generation of QPOs with periods of 43-54 min, such as observed in MV Lyr.

In two of the runs (Jul. 05, 1992 and Jul. 20, 1993) periods longer than expected were detected. The length of these runs, however, is small and they cover 2-2.5 cycles of "50 min" QPOs only. In this case period determination may be strongly affected by flickering, gaps in the runs and varying length and shape of the individual cycles. To understand the behaviour of the QPOs better, regular, long photometric observations are needed.

Acknowledgements

This work was partially supported by NFSR under projects No. 346/93 and No. 715/97.