Probability Friends-of-Friends (PFOF) Group Finder: Performance Study
  and Observational Data Applications on Photometric Surveys
  (Abridged) In tandem with observational datasets, we utilize realistic mock
catalogs, based on a semi-analytic galaxy formation model, constructed
specifically for Pan-STARRS1 Medium Deep Surveys in order to assess the
performance of the Probability Friends-of-Friends (PFOF, Liu et al.) group
finder, and aim to develop a grouping optimization method applicable to surveys
like Pan-STARRS1. Producing mock PFOF group catalogs under a variety of
photometric redshift accuracies ({\sigma}{\Delta}z/(1+zs)), we find that
catalog purities and completenesses from ``good' {\sigma}{\Delta}z/(1+zs)) ~
0.01) to ``poor' {\sigma}{\Delta}z/(1+zs)) ~ 0.07) photo-zs gradually degrade
respectively from 77% and 70% to 52% and 47%. To avoid model dependency of the
mock for use on observational data we apply a ``subset optimization' approach,
using spectroscopic-redshift group data from the target field to train the
group finder for application to that field, as an alternative method for the
grouping optimization. We demonstrate this approach using these
spectroscopically identified groups as the training set, i.e. zCOSMOS groups
for PFOF searches within PS1 Medium Deep Field04 (PS1MD04) and DEEP2 EGS groups
for searches in PS1MD07. We ultimately apply PFOF to four datasets spanning the
photo-z uncertainty range from 0.01 to 0.06 in order to quantify the dependence
of group recovery performance on photo-z accuracy. We find purities and
completenesses calculated from observational datasets broadly agree with their
mock analogues. Further tests of the PFOF algorithm are performed via matches
to X-ray clusters identified within the PS1MD04 and COSMOS footprints. Across
over a decade in group mass, we find PFOF groups match ~85% of X-ray clusters
in COSMOS and PS1MD04, but at a lower statistical significance in the latter.
