Determination of Characteristics of Eclipsing Binaries with Spots: Phenomenological vs Physical Models

TL;DR

This paper compares phenomenological and physical models for analyzing eclipsing binary stars, proposing a combined minimization algorithm and evaluating simplified models for specific binary systems.

Contribution

It introduces a combined minimization algorithm based on the Hessian matrix and assesses simplified models for detached Algol-type systems.

Findings

The combined algorithm improves parameter estimation efficiency.

Simplified models are suitable for detached Algol-type systems.

Comparison of modeling approaches highlights their respective advantages.

Abstract

We discuss methods for modeling eclipsing binary stars using the "physical", "simplified" and "phenomenological" models. There are few realizations of the "physical" Wilson-Devinney (1971) code and its improvements, e.g. Binary Maker, Phoebe. A parameter search using the Monte-Carlo method was realized by Zola et al. (2010), which is efficient in expense of too many evaluations of the test function. We compare existing algorithms of minimization of multi-parametric functions and propose to use a "combined" algorithm, depending on if the Hessian matrix is positively determined. To study methods, a simply fast-computed function resembling the "complete" test function for the physical model. Also we adopt a simplified model of an eclipsing binary at a circular orbit assuming spherical components with an uniform brightness distribution. This model resembles more advanced models in a sense of correlated parameter estimates due to a similar topology of the test function. Such a model may be applied to detached Algol-type systems, where the tidal distortion of components is negligible.