Calculate Mass of X-Ray Gas in Galaxy Cluster

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I need a function for the total gas mass as a function of radius. The results must match with the value of 5.1 e13 M⊙ found in the latest research on the Coma Cluster found in this document: [login to view URL]

The full URL for the document is http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1989ApJ...337...21H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf
If you can go from Section (2) where they talk about the surface brightness profile to the calculated mass of 5.1 e14 M⊙ and show me the formula for M(<r) for the gas component of the galaxy cluster, you'll have solved the problem.

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