Solving light curves of WR+O binaries by Tikhonov’s regularization method

Abstract

Eclipsing Wolf–Rayet (WR)+O binaries are natural laboratories allowing one to study WR winds by analysing their light curves. We present a method of analysis based on solving the most general form of integral equations describing a light curve of a WR+O binary – Fredholm’s equations of the first kind. The unknown functions are the brightness and opacity distributions across the disc of the WR component. The equations represent an ill-posed problem. To get a stable solution, one needs to impose some a priori constraints on the unknown functions. We review various physically justified sets of constraints and, using artificially simulated light curves with known solutions, show how these constraints and the so-called Tikhonov’s regularization algorithm work to retrieve the functions of interest. The influence of errors in the input light curve on the solution is discussed. We use the method to solve the light curve of V444 Cyg (WN5+O6) and show preliminary results. Potential applications of the algorithm are much wider than just solving this particular problem. The computer code is open to scientific community.