parameter (Eq. 3) is defined by the luminosity ratio
and the giant radius in units of the separation of the components,
To determine these quantities we used published parameters and/or
made appropriate estimates. If applicable, we used spectral types
of the cool components in symbiotic binaries of
Mürset & Schmid (1999) and empirically determined dependencies
of effective temperature and linear radius upon the spectral type
given by van Belle et al. (1999). Table 4 summarizes the resulting
parameters. Their uncertainties represent mean square errors of
the mean value given by Eq. (3). A brief explanation to Table 4 is
given below for individual objects.
AXPer: Skopal (1994) determined . The luminosity of the giant, for the distance pc (Skopal 2000). The hot star luminosity, (Mürset et al. 1991) with the uncertainty resulting from that of d.
BFCyg: Parameters and (Skopal et al. 1997). The uncertainty of the luminosity ratio is 30%, which is relevant to its determination from the observed fluxes.
CICyg: Kenyon et al. (1991) estimated . Adopting their estimate of the total mass of the binary, , we get A = for = 855.25 days (Aller 1954), which yields . The spectral type (ST) of the red giant in CICyg, M5.5, corresponds to its effective temperature, K, which then yields . Finally, Mürset et al. (1991) determined (d/1.5kpc)2.
EGAnd: From the contact times of a minimum observed in continuum fluxes at 1320Å (Pereira 1996) we determined for the orbital period, = 482 days (Skopal 1997) and a circular orbit. As the minimum is caused by Rayleigh scattering of the hot star radiation on the neutral atoms of the cool giant wind, this is an upper limit. The luminosity ratio for the two stars, (Vogel et al. 1992). The uncertainty of this ratio is assumed to be of 30%.
AGDra: From the energy distribution in the spectrum during quiescence (Greiner et al. 1997) we estimated the observed fluxes and ergcm-2s-1, i.e. . Smith et al. (1996) estimated the surface gravity as (g in units of cms-2), which for the cool component mass of 1.5 (Mikolajewska et al. 1995), yields . This value is also consistent with that corresponding to the recent dependencies. For and = 550 days (Gális et al. 1999) we have and thus . We can also estimate the distance to AGDra pc from ( as for K3-4III giant) and .
V1329Cyg: The maximum width of the pre-outburst eclipses (Fig. 1 of Schild & Schmid 1997),
|V1329Cyg||3.1-1.2||<0.39||0.18 - 0.47|
|He2-467||60||0.05-0.03||0.07 - 0.2|
Here we investigate the suggested connection between the parameters
a and X (Sect. 4.2). STB derived the parameter X as
|Figure B.1: A correlation between the shape of the LC characterized by the parameter a (Sect. 3.2) and the extent of the symbiotic nebula given by the parameter X|
|Ref.: 1 - Fernández-Castro et al. (1988),
2 - Mikolajewska et al. (1995),
3 - Skopal et al. (in press), 4 - Vogel (1991): this value is needed to explain the nebular continuum.
In contrast, the value of 3-4 yr-1 suggested by effects of the Rayleigh scattering in the far UV continuum leads to X = 7.
In spite of these problems the present knowledge of the fundamental parameters of symbiotic binaries makes a correlation between a and X possible (Fig. 5). However, further investigation is needed to determine more accurate parameters, mainly the mass-loss rate via the wind from cool giants in binaries, to verify the relationship between the profile of the LC and the extent of the symbiotic nebula.
In this appendix we introduce a modification of the STB model
accounting for the additional ionizations due to the inflow of neutral
material into the ionized region through the ionization front due to
the orbital motion and the velocity of the giant wind.
|Figure C.1: The Hi/Hii boundary given by the STB model (dashed line) and its modification due to the orbital motion (solid line). Our model (Eq. C.1) was calculated for = 757 days, and the mass ratio q = 6. The binary rotates anti-clockwise|
At a boundary point, ,
the rate of particles,
crosses the area of the front,
dS = d
a small angle around the vector r pointing to
from the hot star and
is the velocity of atoms in the
direction of S (i.e. perpendicular to the boundary at the
Thus, within the Hii region, the rate of photons,
capable of ionizing hydrogen, has to balance a surplus of
in addition to the steady state situation;
the total hydrogenic recombination coefficient for case B.
from the hot star of the modified
ionization front is then given by the equilibrium condition