Finite-Lens Effect on Self-Lensing in detached White Dwarfs-Main Sequence Binary Systems

In an edge-on and detached binary system, including a white dwarf (WD) and a main-sequence star (WDMS), when the source star is passing behind the compact companion its light is bent and magnified. Meanwhile, some part of its images' 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 (IRS) and analytically using approximate relations close to reality. For WDMS systems with long orbital periods $\gtrsim 300$ days and $M_{\rm{WD}}\gtrsim 0.2 M_{\sun}$ ($M_{\rm{WD}}$ is the mass of 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($M_{\rm WD}\lesssim 0.2 M_{\sun}$) in close orbits with short orbital periods $T\lesssim 50$ days. The occultation and self-lensing cancel each other out when the WD's radius equals $\sqrt{2}$ times the Einstein radius, regardless of the source radius, which offers a decreasing relation between the orbital periods and WDs' mass. We evaluate the errors in maximum deviations in self-lensing/occultation normalized flux which are made by using its known analytical relation and conclude that these errors could be up to $0.002,~0.08,~0.03$ when the orbital period is $T=30,~100,~300$ days, respectively. The size of stellar companions in WDMSs has a twofold manner as it decreases the depth of self-lensing/occultation signals but enlarges their width.