4 Discussion

$BVR_{\rm c}I\rm _c$ observations of dwarf novae allow to evaluate the optical spectral behaviour and, therefore, they can be used as a test to compare theoretical models of accretion disk emission. In particular they can be used to verify the often quoted theoretical flux distribution of a stationary (infinitely) large accretion disk whose surface elements radiate black body spectra ($F(\nu)\propto\nu^{1/3}$).

To study the behaviour of the optical continuum of dwarf novae during the decline from the outburst, we converted the $BVR_{\rm c}I\rm _c$magnitudes in fluxes using the conversion factors reported by Bessell (1979).

For DX And, we corrected our observations by the interstellar extinction adopting the value A_V = 0.6 reported by Drew et al. (1993), and using the interpolation formulae of Cardelli et al. (1989). For the other DNs here reported, the interstellar extinction values are not known and, then, the fluxes are not corrected by this effect.

The flux spectral distributions of DX And, from the maximum to the minimum, are shown in Fig. 10 in logarithmic scale. It is worthy to note that at the minimum the spectral distribution of DX And is dominated by the emission of the secondary star, while at the maximum the spectral distribution follows a power law ($F(\nu)\propto\nu^{\alpha}$). The value of the spectral slope observed at maximum ($\alpha=1.00\pm0.04$)is greater than the one predicted by the steady state accretion disk theory ($\alpha = 0.33$).

The differences in outburst amplitude as a function of wavelengths, the strong change in decay rates and the change in flux distribution with time (see Fig. 10) are all probably the expression of the same phenomenon, i.e. the the strong contribution of the secondary to the total light in quiescence.

For V660 Her we observed a descending trend comparatively coherent in the $BVR_{\rm c}I\rm _c$ bands and a spectral flux distribution which is well described by a power law. Although this variable showed rapid spectral changes all during the outburst decline (probably related to flickering), the mean spectral slope remained quite constant around a value of $\alpha$ = 0.8 $\pm$ 0.2. This substantial stability of the mean spectral index seems to indicate the dominance of the accretion disk emission, while the contribution from the secondary star to the total light of the system seems to be negligible. This is opposite to the behaviour of DX And where the emission of the secondary star becomes soon evident after the first phase of the decline.

The spectral flux distribution of AL Com is well described by a power law with a constant slope $\alpha$=1.1 $\pm$ 0.1. Szkody et al. (1996) observed AL Com with IUE at the date 1995/04/16 UT and they found an UV continuum having a spectral slope $\alpha$ = 1.0, a value which is similar to that derived by us in the optical. Howell et al. (1996) give the J, H, K magnitudes obtained on 1995/04/10 and 1995/04/20 UT. Converting these values in fluxes, we computed an IR spectral slope $\alpha$=1.4 $\pm$ 0.1 in both the dates. In Fig. 11, these IR fluxes are combined with our data to obtain the optical-infrared spectral flux distribution. To do this, our $BVR_{\rm c}I\rm _c$ magnitudes obtained on 1995/04/09-11 and 1995/04/21 UT, were scaled to the same date of the near-IR observations using the decline rates previously reported. For both the dates the total spectral slopes are similar: $\alpha$=1.20 $\pm$ 0.04 and $\alpha$=1.26 $\pm$ 0.04 respectively.

  

Figure 10: Spectral flux distribution of DX And during the 1994 outburst

  

Figure 11: $BVR_{\rm c}I_{\rm c}JHK$ spectral flux distribution of AL Com during the outburst

Only for V516 Cyg and V544 Her our data show that, at least during the maximum, there is a substantial agreement with the predicted emission from an accretion disk in stationary state. In fact we obtained $\alpha$ = 0.3 $\pm$ 0.1 for V516 Cyg, and $\alpha$ = 0.4 $\pm$ 0.1 for V544 Her. However these values are obtained without the correction from the interstellar extinction and, therefore, they must be considered lower limits to the real ones.

For DX And, V660 Her and AL Com, we have seen that it is not possible to approximate their emission during the outburst as the contribute of a disk whose surface elements radiate black body spectra. On the other hand, the value of $\alpha$ = 0.33 is true only for an infinitely large steady state disk. In the UV this value gives relatively reasonable fits (see., e.g., Verbunt 1987), but in the optical the emission is dominated by the outer parts of the disk, and the finite size of the disk may result in a stronger slope at these wavelengths.

Atmospheric emission disk models seem to fit the observed emission spectra better than the standard Planckian emission disk model (see, e.g., Wade 1984, 1988). However, the lack of such basic parameters as the mass of the white dwarf and the inclination of the system make a proper comparison of the optical observations and any emission disk models rather uncertain (see, e.g., La Dous 1989).