The Size of the Emitting Region in the Magnetic Eclipsing Cataclysmic Variable Stars

TL;DR

This paper introduces a refined method for estimating the size of the emitting region near compact stars in eclipsing binary systems, correcting overestimations caused by previous spherical models and applying it to a specific polar system.

Contribution

It compares different geometric approximations of the Roche lobe projection to improve size estimates of emitting regions in eclipsing binaries.

Findings

Spherical models overestimate the radius by 4-6%.

Elliptical approximations provide more accurate size estimates.

Application to CSS 081231:071126+440405 demonstrates method effectiveness.

Abstract

We discuss a method for determination of the size of the emitting region close to the compact star in a binary system with eclipses by a secondary, which fills its Roche lobe. The often used approach is to model the Roche lobe by a sphere with the "effective radius" corresponding to the volume of the Roche lobe. This approach leads to a 4-6% overestimate of the radius, if taking into account the angular dimensions of the Roche lobe seen form the compact star. Andronov (1992) had shown that the projection of the Roche lobe onto the celestial sphere is close to an ellipse and had tabulated these dimensions as a function of the mass ratio. Also he published the coefficients of the approximation similar to that of the Eggleton (1983) for the "sphere corresponding to the same volume". We compare results obtained for the "circle+circle", "ellipse+circle" and "ellipse+point" approximations of the projections of the red dwarf and a white dwarf, respectively. Results are applied to the recently discovered eclipsing polar CSS 081231:071126+440405.