Orbital inclination estimates for overcontact binaries using the derivatives of light curves

Abstract

The orbital inclination of an eclipsing binary is generally determined through light curve analysis. Binary parameters in the light curve analysis are typically constrained through the use of optimization and sampling techniques. We propose a new simple method, based on the derivatives of light curves, for estimating the orbital inclinations of overcontact systems. Our sample consists of 89670 synthetic light curves for overcontact binaries, covering a parameter space typical of overcontact systems. We classified the sample light curves on the basis of a recently proposed classification scheme: DP, SPp, SPb, SPf, and SPs types. For each type, we found that the orbital inclination is closely associated either with the time interval between local extrema in the derivatives of light curves or with the depth of the local minimum at phase 0.5 in the second derivative. Using regression analysis of the identified associations, we developed empirical formulae to estimate the orbital inclinations for each type of light curve. We also provide the associated uncertainties for the estimated inclinations. Application of the proposed method to real overcontact binary data demonstrated that our method can reasonably estimate both the inclinations and their uncertainties.