Finite-lens Effect on Self-lensing in Detached White Dwarfs-main Sequence Binary Systems

Abstract

In edge-on and detached binary systems, including a white dwarf (WD) and a main-sequence (MS) star system (or WDMS), when the source star is passing behind the compact companion its light is bent and magnified. Meanwhile, some part of its image's area is obscured by the WD's disk. These two effects occur simultaneously, and the observer receives the stellar light magnified and partially obscured due to the finite lens size. We study these effects in different WDMS binary systems numerically using inverse ray-shooting and analytically using approximate relations close to reality. For WDMS systems with long orbital periods ≳300 days and M _WD ≳ 0.2M _☉ (where M _WD is the mass of the WD), lensing effects dominate the occultations due to finite-lens effects, and for massive WDs with masses higher than solar mass, no occultation happens. The occultations dominate self-lensing signals in systems with low-mass WDs (M _WD ≲ 0.2M _☉) in close orbits with short orbital periods T ≲ 50 days. The occultation and self-lensing cancel each other out when the WD's radius equals times the Einstein radius, regardless of the source radius, which offers a decreasing relation between the orbital period and WD mass. We evaluate the errors in the maximum deviation in the self-lensing/occultation normalized flux, which is done by using its known analytical relation, and conclude that these errors could be up to 0.002, 0.08, and 0.03 when the orbital period is T = 30, 100, and 300 days, respectively. The size of stellar companions in WDMS systems has a twofold manner, decreasing the depth of self-lensing/occultation signals but enlarging their width.