3. The mass-loss rate
Besides the U photometric data, for our calculations the mass-loss rate of the giant is needed as well. The mass-loss rate of the cool components of the symbiotic stars is not an observed quantity and is difficult to determine. This quantity for AG Dra was estimated by Mikolajewska et al. (1995) using the radio flux at 4.9 GHz from Seaquist & Taylor (1990) and adopting a wind velocity of 30 km s-1. This estimate, however, depends on their assumed system distance of 2.5 kpc, and cannot, therefore, be used for our purposes.
Van Winckel et al. (1993) suggested that the H emission profile of the symbiotic stars affected by self-absorption can be an indicator for the mass-loss rate of their cool components, whose atmospheres are ionized by a hot source. They created a classification system of the symbiotic stars, based on their H profiles. Later this idea was quantitatively considered by Schwank et al. (1997). They calculated a variety of models of an expanding atmosphere of a cool giant of S-type symbiotic system. The atmosphere of the giant is irradiated and ionized from the outside by the hot stellar component. Schwank et al. also calculated the H emission profile at phase when this component is in front of the giant, taking into account the optical depth of the atmosphere and supposing that the line is mainly due to recombination. The profile includes an absorption which moves from the center of the line to its short wavelength-side depending on the velocity of the absorbing particles. When the mass-loss rate of the giant increases, the ionized portion decreases and the transition zone between the ionized and the neutral volumes shifts outwards approaching the hot component. An outward shift of this zone in a region with higher velocity gradient leads to an increase of the difference between the velocity of the absorbing particles and that of the underlying recombination region, and, consequently, to a blue shift of the absorption. So the position of the absorption can be an indicator of the mass-loss rate.
Taking into account the relation between the H profile of the symbiotic stars and the mass-loss rate of their cool components we decided to search another star having Balmer emission characteristics close to that of AG Dra and a known mass-loss rate of its cool component.
A good comparison object seems to be AG Peg whose cool component loses mass at a rate of 1-2 10-7 yr-1 (Vogel & Nussbaumer 1994; Mürset et al. 1995; Proga et al. 1998). Let us compare the Balmer emission spectrum of the two systems. The characteristics and the orbital variations of the H profile of AG Peg were studied by Boyarchuk et al. (1987), and those of AG Dra during its quiescent state - by Tomova & Tomov (1999). H profiles of these stars can be also found in other works (e.g. Ivison et al. 1994; Viotti et al. 1998). In both symbiotic systems the intensity of H emission varies with the orbital phase as a result of both changes of the optical depth and of the giant's occultation. The maximum intensity is around the phase of the light maximum, when the hot component is closer to the observer. The orbital variations of the profile of this line in the two systems are also similar, being due also to optical depth changes. At the phases of the maximal intensity it is single-peaked with a blue shifted absorption producing a small shoulder or a general asymmetry only.
The profiles of the two stars are shown in Fig. 2. They are different from the theoretical profiles of Schwank et al. (1997), as the absorption is far away from the center of the line. This is due to the peculiar structure of the circumbinary nebulae of these stars. We used the H profile of AG Peg observed on 30 June 1986 before the photometric maximum, instead of that of 29 July 1991 which is nearer to the maximum but after it (Ivison et al. 1994). These data indicate that the H line reaches its maximum intensity probably a somewhat earlier than the light maximum, being more intense on 30 June 1986. The wings of the two lines in Fig. 2 are symmetric. As for comparison, we have divided the profiles of the two stars, as illustrated in the lower panel of the figure.
Let us now compare some other characteristics of the two systems in the light of the theoretical treatment of Schwank et al. (1997). These authors have shown that the H profile affected by the optical depth depends on the luminosity of the hot stellar component, the separation, the mass-loss rate of the cool giant and the velocity law of its wind. The AG Peg system (Boyarchuk 1966; Kenyon et al. 1993) as well as the AG Dra system (Mikolajewska et al. 1995; Greiner et al. 1997) have high luminosity hot companion, whose ionizing radiation probably reaches the innermost layers of the giant's wind where its density is the highest and where the bulk of the energy of the line is emitted. Then it will not be necessary to compare the companion's luminosities and the separations but only the velocity laws and the mass-loss rates. The velocity laws are different, but since the energy is emitted mostly from the layers near the giant's surface, the velocities and their gradients in these layers are low having probably close values. On the other hand there is similarity of the profiles morphology and according to the treatment of Schwank et al. (1997) the mass-loss rates must be probably close as well. Supposing that the mass-loss rate of the giant of AG Peg is 12 10-7 yr-1, for its counterpart in the AG Dra system we adopt 2.02.5 10-7 yr-1. As it will be shown in the next section, the mass-loss rates smaller than the lower limit lead to stellar radii below 28 . So small values are probably not plausible, as the cool component of the AG Dra system is supposed not to be a normal giant, but K-type bright giant (Huang et al. 1994; Mikolajewska et al. 1995; Smith et al. 1996).
© European Southern Observatory (ESO) 2000
Online publication: January 29, 2001