Modeling Long-term Variability in Stellar-compact Object Binary Systems for Mass Determinations

Abstract

This work models the effects of gravitational lensing, Doppler boosting, and ellipsoidal variations on eccentric eclipsing binary-system light curves. This is accomplished using a Newtonian orbital-motion code that simulates the orbital velocities and separation of the binary components as a function of time. Improving on previous literature, we examine the effects of orbital eccentricity and period, as well as stellar limb darkening on the expected light curves. Whether lensing, Doppler boosting, or ellipsoidal variation is dominant in the light curves is a function of the separation between the binary components; thus, the combination of all three effects allows for a unique mass-determination method that greatly expands the parameter space for the discovery of compact objects. This suggests the exciting possibility of revealing a large population of nonaccreting compact objects in galactic binary systems. At the same time, the model can be used on systems exhibiting any subset of these effects. In a case study, we fit our model to optical data from the ellipsoidal variable binary system Cygnus X-1, and we compare our determinations with those previously found by different modeling techniques.