2. The photometric data analysis
For our investigation we used the photoelectric observational material, obtained in the period JD 2 446 700 2 449 200 after the time of activity of AG Dra in 1985-86, since this material actually is the best sample of photometric U data, taken during quiescent state of the system. These data were obtained during four orbital cycles (Fig. 1) in the framework of the international campaign for symbiotic stars launched by Hric & Skopal (1989), and are presented in the papers of Hric et al. (1993) and Hric et al. (1994). For our calculations we used the U magnitudes of and giving the mean value of the light at the times of the orbital maximum and minimum on JD 2 447 700 and JD 2 448 000. They were selected because the data set is complete around these times and can be used for a reasonable estimate of the maximum and minimum fluxes. The magnitudes were converted into continuum fluxes without correcting for the emission lines included in the wavelength region of the U photometric system as we were not provided with spectral data during the time of these photometric observations.
The fluxes were corrected for the energy distribution of AG Dra in the U spectral region. The continuum of this star on the long wavelengths-side of the Balmer jump is considerably weaker, which leads to a reduction of the flux at 3650 Å. The corrections were made by means of the spectrum in Fig. 3 of Mikolajewska et al. (1995). It turned out that the observed U flux is 20% smaller than the real flux at 3650 Å. This amount was added to the observed flux.
Finally the fluxes were corrected for the interstellar reddening. We used the value (Mikolajewska et al. 1995; Greiner et al. 1997; Gonzalez-Riestra et al. 1999) and the extinction law by Seaton (1979). So the U magnitudes used by us led to dereddened continuum fluxes of 0.257 10-12 erg cm-2 s- 1 Å-1 and 0.122 10-12 erg cm- 2 s-1 Å-1 for the considered times of the orbital maximum and minimum, respectively. In this case the flux difference of 0.135 10-12 erg cm- 2 s-1 Å-1 corresponds to the amplitude of the light variations.
For realizing our calculations we must determine the ionized portion of the nebula. Fig. 1 shows that the U-light curve of AG Dra is well covered by observation near the orbital maxima. In the figure the cycle-to-cycle variations are clearly seen. Friedjung et al. (1998) came to the conclusion that the variation of the maximum flux is caused by changes of the cool giant mass-loss rate. The variation of the maximum flux is determined by variation of the number of recombinating H+ ions in the nebula. If the hot companion does not ionize the whole nebula, but only part of it, when changing the mass-loss rate of the giant, the volume of the ionized region will change too, because the hot companion having a constant photon flux in the Lyman continuum is able to ionize always the same amount of gas. To observe different numbers of recombinating H+ ions in the different orbital maxima will be possible when the hot companion has an excess of luminosity providing them the possibility to ionize always the whole nebula (excepting its portion occulted by the cool star) on changing the mass-loss rate of the giant. That is why we will perform our calculations supposing that the circumbinary nebula of AG Dra is a region of ionized hydrogen.
The next step of our consideration is to estimate the contribution of the stellar components of the system. The flux of the hot companion was determined supposing that it radiates as a blackbody and using the ratio of the fluxes at 1340 Å and 3650 Å of a blackbody with the same temperature and the observed flux at wavelength 1340 Å. Gonzalez-Riestra et al. (1999) have obtained a mean value of the dereddened quiescent flux at this wavelength of about 0.28 10-12 erg cm- 2 s-1 Å-1 and Zanstra temperature of the companion of 110 000 K. On the basis of these data we derived an U-band flux of 10-12 erg cm- 2 s-1 Å-1.
Let us consider the contribution of the cool component. The dereddened optical spectrum of AG Dra was fitted with that of a K giant and continuum emission with electron temperature K (Mikolajewska et al. 1995). We obtained the flux of this component supposing that it has the same continuum energy distribution like Boo and the rest of the observed U flux is a nebular emission. We calculated the 3650 Å 5500 Å flux ratio of Boo and scaled it to the dereddened visual flux of AG Dra. Using the flux of AG Dra in its orbital minimum, when the nebular emission can be supposed to be negligible, we obtained for the flux of its cool component 10-12 erg cm- 2 s-1 Å-1.
After subtraction of the fluxes of the two stellar components from the observed flux at the orbital maximum the nebular continuum turned out to be 10-12 erg cm- 2 s-1 Å-1. The contribution of the nebula near orbital minimum is 0.040 10-12 erg cm- 2 s-1 Å-1, close to that of the red giant.
The shape of the U light curve indicates that the region emitting a flux, equal to the orbital amplitude is not partially occulted at the time of the orbital maximum only. This means that it is located most probably around the hemisphere of the giant facing the hot companion. The density of this small region is probably much higher than the mean density of the unocculted part of the nebula, since the radiation of the whole occulted part of 0.135 10-12 erg cm- 2 s-1 Å-1 is by a factor of about 3 greater than the radiation of the unocculted part. One cause for the appearance of this small high density region was suggested by Galis et al. (1999), who assumed that the strong radiation pressure from the hot component tends to stop the matter of the giant's wind approaching the hot component and photoionization creates an ionized region with a higher density and emissivity.
© European Southern Observatory (ESO) 2000
Online publication: January 29, 2001