Search for Dormant Black Holes in Ellipsoidal Variables I. Revisiting the Expected Amplitudes of the Photometric Modulation

TL;DR

This paper updates the analytical model for ellipsoidal light-curve modulations caused by stellar distortion, providing more accurate amplitude predictions to aid in detecting binaries with compact objects.

Contribution

It presents revised amplitude calculations for ellipsoidal variables based on numerical simulations, improving the model's accuracy for identifying binaries with compact companions.

Findings

Updated amplitudes can differ by up to 30% from previous models.

The model enables estimation of mass ratios using harmonic amplitudes and stellar temperature.

High amplitudes indicate potential binaries with compact-object secondaries.

Abstract

Ellipsoidal variables present light-curve modulations caused by stellar distortion, induced by tidal interaction with their companions. An analytical approximated model of the ellipsoidal modulation is given as a discrete Fourier series by Morris and Naftilan 1993 (MN93). Based on numerical simulations using the PHOEBE code we present here updated amplitudes of the first three harmonics of the model. The expected amplitudes are given as a function of the mass ratio and inclination of the binary system and the fillout factor of the primary---the ratio between the stellar radius and that of its Roche lobe. The corrections can get up to 30% relative to the MN93 model for fillout factors close to unity. The updated model can be instrumental in searching for short-period binaries with compact-object secondaries in large data sets of photometric light curves. As shown in one OGLE light-curve example, the minimum mass ratio can be obtained by using only the amplitudes of the three harmonics and an estimation of the stellar temperature. High enough amplitudes can help to identify binaries with mass ratios larger than unity, some of which might have compact companions.