Detailed Abundances of Planet-Hosting Open Clusters. The Praesepe
  (Beehive) Cluster
  It is not yet fully understood how planet formation affects the properties of
host stars, in or out of a cluster; however, abundance trends can help us
understand these processes. We present a detailed chemical abundance analysis
of six stars in Praesepe, a planet-hosting open cluster. Pr0201 is known to
host a close-in (period of 4.4 days) giant planet (mass of 0.54$\rm
M_{\rm{J}}$), while the other five cluster members in our sample (Pr0133,
Pr0081, Pr0208, Pr0051, and Pr0076) have no detected planets according to RV
measurements. Using high-resolution, high signal-to-noise echelle spectra
obtained with Keck/HIRES and a novel approach to equivalent width measurements
(XSpect-EW), we derived abundances of up to 20 elements spanning a range of
condensation temperatures (Tc). We find a mean cluster metallicity of [Fe/H] =
+0.21$\pm$0.02 dex, in agreement with most previous determinations. We find
most of our elements show a [X/Fe] scatter of $\sim$0.02-0.03 dex and conclude
that our stellar sample is chemically homogeneous. The Tc slope for the cluster
mean abundances is consistent with zero and none of the stars in our sample
exhibit individually a statistically significant Tc slope. Using a planet
engulfment model, we find that the planet-host, Pr0201, shows no evidence of
significant enrichment in its refractory elements when compared to the cluster
mean that would be consistent with a planetary accretion scenario.
