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4. The broad components and the mass-loss rate

The evolution of the hot component of the AG Peg system has been considered by Mürset et al. (1991), Kenyon et al. (1993), Vogel & Nussbaumer (1994) and Altamore & Cassatella (1997). Their analyses show that after the year 1978 the radius, the luminosity and the mass-loss rate of this star have been decreased at nearly constant temperature. We will examine if the variations of the line intensities, observed by us, are in line with the variations of these parameters. Only the broad components of the lines Htex2html_wrap_inline1418, Htex2html_wrap_inline1406 and HeII 4686 will be considered since only they appear in the wind of the hot companion (see Sect. 5) and depend solely on its parameters. The fluxes of these lines will be calculated and compared with the observed ones.

The mass-loss rate has been derived by Vogel & Nussbaumer (1994) and Altamore & Cassatella (1997) with the same methods using UV spectra obtained during approximately one and the same period of time. The first of these methods is based on the dependence of the equivalent width of the HeII 1640 line on the mass-loss rate of the Wolf-Rayet stars (Schmutz et al. 1989) and is related to the case when the line is optically thick. This dependence has been extrapolated to the atmosphere of the hot companion of AG Peg. The second method is based on the relation between the energy emitted in the HeII 1640 line and the mass-loss rate when the wind has spherical symmetry and a constant velocity. It is related to the case when the line is optically thin. The results obtained with the two methods are in good agreement.

In our study we will consider the hot wind in the nebular approach, i.e. we will follow the second of these methods and that is why the value of the mass-loss rate, derived in this case will be used. The arithmetical means of the data of Vogel & Nussbaumer (1994) and Altamore & Cassatella (1997) for the years 1986 and 1995 are 1.55 10-7 tex2html_wrap_inline1896yr-1 and 8.7510-8 tex2html_wrap_inline1896yr-1 respectively. The second of them was calculated using the value of Vogel & Nussbaumer for the year 1993, as their observations were up to this moment.

The line flux determined by recombinations is given by
where tex2html_wrap_inline1906 is the density of the ion treated; tex2html_wrap_inline1908, the electron density; tex2html_wrap_inline1910tex2html_wrap_inline1912, the effective recombination coefficient of this line and V, the emitting volume. If helium is ionized twice in this volume, the electron density will be tex2html_wrap_inline1916 and the density of the given ion tex2html_wrap_inline1918, where a(X) is the abundance by number of the element X relative to hydrogen. Then for the line flux we obtain
The abundance by number of He relative to H, tex2html_wrap_inline1924, is adopted to be 0.1 (Vogel 1993; Vogel & Nussbaumer 1994). The recombination coefficient tex2html_wrap_inline1926 corresponds to an electron temperature of tex2html_wrap_inline1928 K (Pottasch 1984). The distance to the system d is assumed to be 650 pc, which value is used mostly in the current analyses (Mürset et al. 1991; Vogel & Nussbaumer 1994; Mürset et al. 1995; Altamore & Cassatella 1997). The density in the hot wind is a function of the distance to the center and can be expressed via the continuity equation
where tex2html_wrap_inline1932 is the mass-loss rate; tex2html_wrap_inline1934, the wind velocity equal to 1000 kms-1 and tex2html_wrap_inline1938, the mean molecular weight in the hot wind, tex2html_wrap_inline1940 (Nussbaumer & Vogel 1987). Using Eqs. (2) and (3) we can calculate the line flux emitted by a nebula formed by a wind with spherical symmetry and a constant velocity.

We will consider that the temperature of the hot companion of the AG Peg system in both moments has been equal to 90000 K, which is approximately an average of the results of Mürset et al. (1991), Kenyon et al. (1993) and Altamore & Cassatella (1997). In this case the photon fluxes beyond the limits of the ground series of hydrogen and ionized helium (Nussbaumer & Vogel 1987) are fully sufficient for ionizing these elements in the hot wind to infinity.


Line 1986 1995

tex2html_wrap_inline1948 tex2html_wrap_inline1950 tex2html_wrap_inline1948 tex2html_wrap_inline1950
Htex2html_wrap_inline1956 (B) 2.86 2.43 1.12 1.61
Htex2html_wrap_inline1958 (B) 1.36 1.95 0.53 <0.70
HeII 4686 (B) 3.12 4.35 1.22 1.65

Table 5: The line fluxes of the broad components in units of 10-11 ergcm-2s-1


It is necessary for the calculation of the line fluxes to determine the region of integration. We treat the wind in the nebular approach (Vogel 1993; Vogel & Nussbaumer 1994) and that is why the inner radius is thought to be the radius of the star. We will use for its value the arithmetical means of Vogel & Nussbaumer (1994) and Altamore & Cassatella (1997), which are 0.11 tex2html_wrap_inline1962 and 0.09 tex2html_wrap_inline1962 in the two moments respectively. Let's consider the outer radius. The fact that the radial velocity of the broad components varies with the orbital phase (Tomov & Tomova 1992) means that their emitting volumes are gravitationaly connected with the star and are not probably extended to a great distance. The calculation of the line fluxes supports this conclusion since the gas at a distances greater than half of the binary separation was found to have no contribution. We will use for this reason an outer radius equal to 300 tex2html_wrap_inline1962.

The calculated fluxes are listed in Table 5 (click here) where they are compared with the observed ones. It is seen that their difference ranges up to about 45%. One of the reasons for this difference is the equivalent width error, which is due to the error of the local continuum. The equivalent width error of the broad components reaches 50%.

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