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. 
J.D. Hartman, B.S. Gaudi, M.J. Holman, B.A. McLeod, K.Z. Stanek, J.A.   Barranco, M.H. Pinsonneault, S. Meibom, J.S. Kalirai