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 (1) adding extra background counts, (2) eliminating a fraction of the counts, (3) increasing the width of the smoothing kernel, and (4) 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 a wide range of observational signal-to-noise ratios. 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://urldefense.proofpoint.com/v1/url?u=https://github.com/ndaniyar/aphot&k=diZKtJPqj4jWksRIF 4bjkw%3D%3D%0A&r=UpUi4hY04iGuRFIqvI40bIbHeCQwTKuVYBJxwGoVKtk%3D%0A&m=VXh1 NEiIklADomwhySY7T5Bw1FDJ05vSQKEOGhQmkKU%3D%0A&s=31f1aa6b3f5096ed40f648a4bf9c eca0cb2eb99b082e251d807a3ec8d1872316), are completely automatic and can be used to rapidly classify galaxy cluster morphology for large numbers of clusters without human intervention.
