Difference between revisions of "Dark Matter Halo"

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(Problem 3)
(Problem 3)
Line 63: Line 63:
 
\[
 
\[
 
v^2 (r) = 4\pi G\frac{1}{r}\int_0^r {r'^2 \rho \left( {r'}\right)dr'}  = 4\pi G\rho _0 \left( {r_c^2  + r_0^2 } \right)\left[
 
v^2 (r) = 4\pi G\frac{1}{r}\int_0^r {r'^2 \rho \left( {r'}\right)dr'}  = 4\pi G\rho _0 \left( {r_c^2  + r_0^2 } \right)\left[
{1 - \left( {\frac{{r_c }}{r}} \right)arctg\left( {\frac{r}{r_0 }}
+
{1 - \left( \frac{r_c}{r} \right)arctg\left( \frac{r}{r_0 }
 
\right)} \right],
 
\right)} \right],
 
\]
 
\]

Revision as of 10:04, 4 October 2012




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 \ref{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.