There is evidence that some galaxy clusters may experience some bulk rotation. If this is true, how valid is it to use the Ideal Gas Law to estimate the mass (actually, it calculates the acceleration needed to create the pressure gradient - from which the mass is derived)? One of the conditions for an idea gas is that collisions with the 'container' are elastic. If the galaxy cluster is rotating, then gas plasma particles will pick up velocity as they travel outwards (due to the centripetal force) and not bounce back as far inward. This is clearly an inelastic collision.
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Unlike in a keplerian disk (for example), the rotational support in a cluster is definitely very small compared to the thermal pressure. Thus it is negligible in estimating the mass. In general, however, the radial velocity dispersion is an important component (as would be expected from virialization). Note that the assumptions are less related to the ideal gas law per se (any polytropic equation of state is fine) and more simply to the assumption of thermal equilibrium.
This is a nice presentation to look at, it includes both the basic theoretical elements of the calculation in addition to actual data which shows it in practice.
answered Oct 22, 2015 at 14:24
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$\begingroup$ In this document arxiv.org/abs/astro-ph/0702184 Hwang and Lee suggest the rotational velocity in some clusters could be significant, upwards of $1,200\space km\space s^{-1}$ in the Centaurus cluster. So speaking theoretically, what does this magnitude of rotation do for the suitability of the Ideal Gas Law for estimating mass? Again, it seems to me that the collisions against the 'wall' in a rotating system are inelastic, making the Ideal Gas Law unsuitable because a basic assumption is broken. $\endgroup$– user32023Commented Oct 22, 2015 at 16:12
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$\begingroup$ As I've already said, the ideal gas law per se, is not especially relevant. Additionally, there is no 'wall'. These are collisionless systems without any viscous, or noticeably dissipative interaction between galaxies. $\endgroup$ Commented Oct 22, 2015 at 19:07
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$\begingroup$ I appear to be missing something very basic so let's take this in small steps. If you don't use the Ideal Gas Law, how do you determine the mass of a galaxy cluster from the X-Ray Luminosity and Temperature data? $\endgroup$– user32023Commented Oct 22, 2015 at 19:51
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$\begingroup$ The slides I linked explain that pretty well. You just need to know the radial density, and temperature profiles (specifically their radial gradients). And you can calculate the total mass profile. $\endgroup$ Commented Oct 22, 2015 at 20:04
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$\begingroup$ Are you really just pointing to a bunch of sides without knowing that they derive from the Ideal Gas Law? Voting this one down. Please come back when you've studied the background material. $\endgroup$– user32023Commented Oct 22, 2015 at 20:06