Deep MMT Transit Survey of the Open Cluster M37 IV: Limit on the Fraction of Stars With Planets as Small as 0.3 R_J

We present the results of a deep (15 ~< r ~< 23), 20 night survey for transiting planets in the intermediate age open cluster M37 (NGC 2099) using the Megacam wide-field mosaic CCD camera on the 6.5m MMT. We do not detect any transiting planets among the ~1450 observed cluster members. We do, however, identify a ~ 1 R_J candidate planet transiting a ~ 0.8 Msun Galactic field star with a period of 0.77 days. The source is faint (V = 19.85 mag) and has an expected velocity semi-amplitude of K ~ 220 m/s (M/M_J). We conduct Monte Carlo transit injection and recovery simulations to calculate the 95% confidence upper limit on the fraction of cluster members and field stars with planets as a function of planetary radius and orbital period. Assuming a uniform logarithmic distribution in orbital period, we find that < 1.1%, < 2.7% and < 8.3% of cluster members have 1.0 R_J planets within Extremely Hot Jupiter (EHJ, 0.4 < T < 1.0 day), Very Hot Jupiter (VHJ, 1.0 < T < 3.0 days) and Hot Jupiter (HJ, 3.0 < T < 5.0 days) period ranges respectively. For 0.5 R_J planets the limits are < 3.2%, and < 21% for EHJ and VHJ period ranges, while for 0.35 R_J planets we can only place an upper limit of < 25% on the EHJ period range. For a sample of 7814 Galactic field stars, consisting primarily of FGKM dwarfs, we place 95% upper limits of < 0.3%, < 0.8% and < 2.7% on the fraction of stars with 1.0 R_J EHJ, VHJ and HJ assuming the candidate planet is not genuine. If the candidate is genuine, the frequency of ~ 1.0 R_J planets in the EHJ period range is 0.002% < f_EHJ < 0.5% with 95% confidence. We place limits of < 1.4%, < 8.8% and < 47% for 0.5 R_J planets, and a limit of < 16% on 0.3 R_J planets in the EHJ period range. This is the first transit survey to place limits on the fraction of stars with planets as small as Neptune.