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I found this: http://adsabs.harvard.edu/abs/1992A&A...259L..31B document that describes how the X-Ray emissions from galaxy clusters are used to calculate the mass of the cluster. I'm unable to follow the steps to calculating the gas mass.
Specifically, in section (2) there is a formula for the surface brightness profile that appears to be pretty standard:
The authors then go on to calculate the central electron density:
Specifically, in section (2) there is a formula for the surface brightness profile that appears to be pretty standard:
[itex]S(r) = S_0(1+({\frac{r}{a}})^2)^{(0.5-3\beta)}[/itex]
The authors then go on to calculate the central electron density:
[itex]n_0 = 2.89 \times 10^{-3} h_{50}^{1/2} cm^{-3}[/itex]
I can't make the connection from the central electron density to a function that provides the mass at a given radius, r. The authors conclude the hot gas mass is
[itex]5.1 \times 10^{14} h_{50}^{\frac{-5}{2}} M⊙[/itex]
but I don't see how they get from A to B.
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