Dark Matter Halo

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Problem 1

Estimate the local density of the dark halo in the vicinity of the Earth, assuming that its density decreases as $\rho_g=C/r^2$.

Problem 2

Build the model of the spherically symmetric dark halo density corresponding to the observed galactic rotation curves.

Problem 3

In frames of the halo model considered in the previous problem determine the local dark matter density $\rho_0$ basing on the given rotation velocities of satellite galaxies at the outer border of the halo $v_\infty\equiv v(r\rightarrow\infty)$ and in some point $r_0$.

Problem 4

For the halo model considered in problem about halo model obtain the dependencies $\rho(r)$ and $v(r)$ in terms of $\rho_0$ and $v_\infty$. Plot the dependencies $\rho(r)$ and $v(r)$.

Problem 5

Many clusters are sources of X-ray radiation. It is emitted by the hot intergalactic gas filling the cluster volume. Assuming that the hot gas ($kT\approx10keV$) is in equilibrium in the cluster with linear size $R=2.5Mpc$ and core radius $r_c=0.25Mpc$, estimate the mass of the cluster.