4. Structure of Dark Matter halos Obviously, we cannot observe the ...

6-4-10see http://www.strw.leidenuniv.nl/˜ franx/college/galaxies10 10-c04-15
In our own Milky Way, the number of satellites appears
much smaller than predicted by the models:
The solution for this problem is not clear. Are we missing
a lot of satellites ? Or do we underestimate their
mass ? Or is the dark matter model wrong ?
Problem sets
1) Derive the enclosed mass M(< r) for the NFW
profile ρ(r) = ρs/[(r/rs)(1 + r/r2) 2 ]. Use r/(1 + r) 2
= 1/(r + 1) − 1/(1 + r) 2
2) Derive the circular velocity as a function of radius
6-4-10see http://www.strw.leidenuniv.nl/˜ franx/college/galaxies10 10-c04-16
for the NFW profile
3) Approximate the rotation curve of UGC 4325 by a
straight line, through (0 arcsec, 0 km/s) and (60 arcsec,
110 km/s). What is the best fitting NFW model ?
This would be the model for which
χ 2 = � (Vobs − Vmodel) 2 dr is minimized.
What is the average rms residual ? [(Vobs − Vmodel)] ?
4) We can see from the figure from Springel et al. that
about 30-40 % of the mass of a halo is in subhalos.
This appears quite different from the situation in clusters,
where the light is dominated by the ensemble of
regular cluster galaxies, and NOT by the brightest cluster
galaxy. Can you think of an explanation ?