Microlensing of Kepler Stars as a Method of Detecting Primordial Black Hole Dark Matter

If the dark matter consists of primordial black holes (PBHs), we show that gravitational lensing of stars being monitored by NASA’s Kepler search for extrasolar planets can cause significant numbers of detectable microlensing events. A search through the roughly 150 000 light curves would result in large numbers of detectable events for PBHs in the mass range $5\times {10}^{-10}{M}_{\odot }$ to ${10}^{-4}{M}_{\odot }$. Nondetection of these events would close almost 2 orders of magnitude of the mass window for PBH dark matter. The microlensing rate is higher than previously noticed due to a combination of the exceptional photometric precision of the Kepler mission and the increase in cross section due to the large angular sizes of the relatively nearby Kepler field stars. We also present a new formalism for calculating optical depth and microlensing rates in the presence of large finite-source effects.

Figure 1

Top panel: The expected number of events, $N_{\exp }$ (defined as 4 sequential measurements with flux 3-sigma above average) in 390 000 star-years of Kepler data. The thin horizontal line shows $N_{\exp }=3$, the limit for a 95% C.L. if no events are detected. Bottom panel: Potential 95% C.L. exclusion of PBH dark matter. The area above the thick line would be ruled out if no events were seen in 390 000 star-years. Also shown as a thin dashed line is the limit from combined MACHO/EROS LMC microlensing searches [12]. The thin horizontal line shows a halo consisting entirely of PBHs with local DM density $\rho =0.3\mathrm{GeV}{\mathrm{cm}}^{-3}$.