Simulating Light Curves of Self-Lensing Binaries

Abstract

A fraction of stars in binary systems are known to be companion stars to compact objects: white dwarfs (WDs), neutron stars (NSs), or stellar mass black holes (BHs). When these systems are detached and edge-on to our line of sight, they are known as self-lensing binaries (SLBs). During the eclipses of a SLB, it is possible to see light curve bumps from gravitational lensing while observing the flux of the companion star.

So far, five WD SLBs with main sequence star companions have been detected, but none for SLBs with other compact objects. Recently, Gaia detected three non-lensing BH-MS binaries in their DR3, indicating that the first SLBs with BH or NS lenses may be detected in the near future with improved photometric precision.

To model what such systems might look like, I developed \texttt{SLBlensing}, a publicly available Python class that efficiently simulates light curve profiles of SLBs to leading order, implementing geometric lensing and occultation, limb and gravity darkening, Doppler boosting, ellipsoidal variation, and irradiation. This code is validated against previously calculated light curve profiles from observed systems KOI-3278 and three WD SLBs discovered by Kepler to reported survey precision ($\sim10^{-4}$ in relative flux), and then used to characterize lensing signatures for a broad range of stellar companions with compact object lenses. Lensing signatures for giant star companions are often overshadowed by Doppler boosting and ellipsoidal variation, while BH-MS binary pairs are found to produce the strongest lensing signals.

A Monte Carlo observability calculation for Gaia DR5, combining detectability and relative abundance of each binary type within 1000 pc, places upper limit estimates of $\lesssim578$, $\lesssim6$, and $\lesssim5$ detectable SLBs with WD, NS, and BH lenses, respectively. Despite NS lenses having the highest intrinsic photometric observability, NS binaries with companion stars are not abundant enough compared to WD systems to dominate future SLB detections at 1000 pc.

\texttt{SLBlensing} is publicly available at \url{https://github.com/lmanqiwang/SLBlensing}.