  We present a novel quantitative scheme of cluster classification based on the
morphological properties that are manifested in X-ray images. We use a
conventional radial surface brightness concentration parameter (c_{SB}) as
defined previously by others, and a new asymmetry parameter, which we define in
this paper. Our asymmetry parameter, which we refer to as photon asymmetry
($A_{phot}), was developed as a robust substructure statistic for cluster
observations with only a few thousand counts. To demonstrate that photon
asymmetry exhibits better stability than currently popular power ratios and
centroid shifts, we artificially degrade the X-ray image quality by: (a) adding
extra background counts, (b) eliminating a fraction of the counts, (c)
increasing the width of the smoothing kernel, and (d) simulating cluster
observations at higher redshift. The asymmetry statistic presented here has a
smaller statistical uncertainty than competing substructure parameters,
allowing for low levels of substructure to be measured with confidence.
A_{phot} is less sensitive to the total number of counts than competing
substructure statistics, making it an ideal candidate for quantifying
substructure in samples of distant clusters covering wide range of
observational S/N. Additionally, we show that the asymmetry-concentration
classification separates relaxed, cool core clusters from
morphologically-disturbed mergers, in agreement with by-eye classifications.
Our algorithms, freely available as Python scripts
(https://github.com/ndaniyar/aphot) are completely automatic and can be used to
rapidly classify galaxy cluster morphology for large numbers of clusters
without human intervention.
