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Astron. Astrophys. 327, 173-182 (1997)

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4. Determination of system parameters

In this section, the masses [FORMULA] and [FORMULA], the radii [FORMULA] and [FORMULA], the inclination i, the distance a of the two stars, the distance f of the inner Lagrangian point [FORMULA] from the white dwarf, and the radius d of the disk in quiescence are calculated. First, the applied formulas are explained, then the parameters are calculated and discussed.

4.1. Functional context

The mass ratio [FORMULA] can be described by the radial velocities

[EQUATION]

For the calculation of the inclination i we applied the LFIT code (Wolf et al, 1995), keeping the q -value calculated above. This code decomposes eclipse light curves by fitting an N-component light curve model to the observational data. In this case, the model light curve is subdivided into 4 components: The white dwarf, assumed to be a spherical object with radius [FORMULA] ; the secondary depending on the mass ratio q and the inclination i, assuming Roche-geometry; the accretion disk, represented by the disk radius d and a radial intensity distribution; and last, the hot spot.

Furthermore, Kepler's third law combined with an empirical equation of Paczynski (1971)

[EQUATION]

yields a mass-radius relation of the secondary as a function of the orbital period P

[EQUATION]

with the gravitational constant G. The relative distance f of the inner Lagrangian point [FORMULA] from the white dwarf only depends on the mass ratio q (Warner, 1976; Plavec, 1964)

[EQUATION]

For the white dwarf, the mass-radius relation of Nauenberg (1972) is applied

[EQUATION]

4.2. Calculation of the parameters

The parameters and their corresponding errors are calculated by a Monte-Carlo simulation. For this, 10 000 Gauss-distributed starting-values of [FORMULA] and [FORMULA], and the orbital inclination i derived by the LFIT code are simulated. The error of the period is neglected. Assuming Roche geometry, the starting-values are taken and the following parameters are calculated together with their standard deviations:

- Mass ratio [FORMULA] - Inclination [FORMULA] - Distance f in units of a: [FORMULA] - Distance [FORMULA] - Mass [FORMULA] - Mass [FORMULA] - Radius [FORMULA] - Radius [FORMULA] - Relative mean radius of the disk in quiescence [FORMULA]

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© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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