A Number Estimate of Detectable Detached Black Hole-star Binaries using a Photometric Telescope

Detached and wide-orbit black hole-star binaries (BHSBs) can generate three types of periodic photometric signals: Ellipsoidal Variation, Doppler beaming and Self-Lensing (SL), providing a proxy to discover these black holes. We estimate the relative amplitude of the three signals for such systems and the detectability for black holes of a photometric telescope like Kepler in several steps. We estimate the searchable star number by assuming every star has a black hole companion, and apply the occurrence of BHSBs in field stars to estimate the detectable black hole signals. We consider three types of Initial Mass Function (IMF) model with different high end exponential slopes. "When spot and white noise are both considered, there is about one detectable signal for SL and less than one event is expected for beaming and Ellipsoidal Variation signal in Kepler Input Catalog stars with the standard IMF model" "Due to contamination by stellar spots and white noise, one may expect one detectable signal for SL and less than one detectable signal for both beaming and Ellipsoidal Variation in Kepler Input Catalog stars with the standard IMF model." On the other hand, if we assume that only white noise affects the detection efficiency of the BHSBs, we expect about 10 Ellipsoidal Variation signals and 17 beaming signals to be detectable while the number of SL signals remains unchanged.