PHANGS-HST: New Methods for Star Cluster Identification in Nearby
  Galaxies
  We present an innovative and widely applicable approach for the detection and
classification of stellar clusters, developed for the PHANGS-HST Treasury
Program, an $NUV$-to-$I$ band imaging campaign of 38 spiral galaxies. Our
pipeline first generates a unified master source list for stars and candidate
clusters, to enable a self-consistent inventory of all star formation products.
To distinguish cluster candidates from stars, we introduce the Multiple
Concentration Index (MCI) parameter, and measure inner and outer MCIs to probe
morphology in more detail than with a single, standard concentration index
(CI). We improve upon cluster candidate selection, jointly basing our criteria
on expectations for MCI derived from synthetic cluster populations and existing
cluster catalogues, yielding model and semi-empirical selection regions
(respectively). Selection purity (confirmed clusters versus candidates,
assessed via human-based classification) is high (up to 70$\%$) for moderately
luminous sources in the semi-empirical selection region, and somewhat lower
overall (outside the region or fainter). The number of candidates rises steeply
with decreasing luminosity, but pipeline-integrated Machine Learning (ML)
classification prevents this from being problematic. We quantify the
performance of our PHANGS-HST methods in comparison to LEGUS for a sample of
four galaxies in common to both surveys, finding overall agreement with
$50-75\%$ of human verified star clusters appearing in both catalogues, but
also subtle differences attributable to specific choices adopted by each
project. The PHANGS-HST ML-classified Class 1 or 2 catalogues reach $\sim1$
magnitude fainter, $\sim2\times$ lower stellar mass, and are $2{-}5\times$
larger in number, than attained in the human classified samples.
