A Search for Transiting Planets in the Globular Cluster M4 with K2: Candidates and Occurrence Limits

We perform a search for transiting planets in the NASA K2 observations of the globular cluster (GC) M4. This search is sensitive to larger orbital periods (P ≲ 35 days, compared to the previous best of P ≲ 16 days), and at the shortest periods, smaller planet radii (R _p ⪆ 0.3 R _J, compared to the previous best of R _p ⪆ 0.8 R _J) than any previous search for GC planets. Seven planet candidates are presented. An analysis of the systematic noise in our data shows that most, if not all, of these candidates are likely false alarms. We calculate planet occurrence rates assuming our highest significance candidate is a planet and occurrence rate upper limits assuming no detections. We calculate 3σ occurrence rate upper limits of 6.1% for 0.71-2 R _J planets with 1-36 days periods and 16% for 0.36-0.71 R _J planets with 1-10 days periods. The occurrence rates from Kepler, TESS, and radial velocity studies of field stars are consistent with both a nondetection of a planet and detection of a single hot Jupiter in our data. Comparing to previous studies of GCs, we are unable to place a more stringent constraint than Gilliland et al. for the radius-period range they were sensitive to, but do place tighter constraints than both Weldrake et al. and Nascimbeni et al. for the large-radius regimes to which they were sensitive.