Self-Lensing Signals in Binary Systems Containing White Dwarfs with Neutron star or Stellar-mass Black hole Companions

Light curves from binary systems containing white dwarfs with neutron star or stellar-mass black hole companions (WD+NS and WD+BH) with edge-on orbital planes potentially show self-lensing/eclipsing signals. Here, we evaluate the properties and detectability of these signals in the NASA's Transiting Exoplanet Survey Satellite (TESS), and the Nancy Grace Roman Space Telescope (Roman) observations. WD+NS systems with orbital periods $T\lesssim25~$days mostly have considerable finite-source sizes with the normalized source radii $\rho_{\star}\gtrsim1$. WD+BH systems with $T\gtrsim3$ days have $\rho_{\star}\lesssim1$, and $\rho_{\star}\sim0.01$ for BHs with a few tens solar-mass. Our analytical calculations show the probabilities of occurring self-lensing signals in WD+NS and WD+BH systems are $\sim10^{-3},~10^{-2}$, and maximize for systems with low-mass WDs revolving massive NSs/BHs. We simulate their light curves and generate synthetic data for them by applying the observing protocols of these two satellites. We assume self-lensing signals are detectable if (i) $1\leq T\leq T_{\rm{obs}}$ (where $T_{\rm{obs}}=62~\rm{and}~27.4$ days are the Roman and TESS continuous observing windows), (ii) $\rm{SNR}\ge3,~6$, their signals are (iii) deeper than twice the photometric error, and (iv) covered by at least one datum. Systems with detectable self-lensing signals in the TESS and Roman observations on average have small inclination angles $i\lesssim0.2^{\circ}$, with the orbital periods $\sim6,~19~$days, and their signals last $\sim[6,~30]~\rm{minutes}$. The TESS and Roman efficiencies for detecting these signals are $\sim2-6\times10^{-4}$ and $\sim2-12\times10^{-10}$. Although detecting these self-lensing signals by Roman is impossible, the TESS telescope potentially manifests at least one self-lensing signal due to these binary systems, if $8\%,~\rm{and}~3\%$ of WDs have NS and BH companions.