Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 66 / 4 / a / ii

Table of contents
- Solution ii

Solution

The hot intracluster gas emits X-rays, which constrain its temperature and density profile. If its pressure is predominantly thermal and it is in hydrostatic equilibrium,

\frac{d P}{d r} = - ρ_{g} \frac{GM ( < r )}{r ^{2}}, P = \frac{ρ _{g} k _{B} T}{μ m _{p}} .

Eliminating the pressure gives

M (< r) = - \frac{k _{B} T ( r ) r}{G μ m _{p}} (\frac{d lo g ρ _{g}}{d lo g r} + \frac{d lo g T}{d lo g r}) .

Here

μ m_{p}

is the mean mass per gas particle. A gas at the observed cluster temperatures would not remain confined without a deep gravitational potential; the inferred total mass exceeds the gas and stellar mass together. Nonthermal pressure, mergers, gas clumping and temperature-profile errors can bias this estimate, but do not turn X-ray luminosity itself into a direct measurement of total mass.

 Ancestors (11)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version