# Do galaxies have a halo of neutrinos and cosmic microwave background?

If virial arguments as in "How can dark matter collapse without collisions or radiation?" allow concluding that dark matter could collapse to galactic halos purely gravitationally, then is this true of other "collisionless gases" such as cosmic background of neutrinos or photons (microwave background) from the big bang?

If so, how much denser is the neutrino or photon background expected to be in our neighborhood compared to the voids between galaxy clusters?

The answer is "sort-of" for both neutrinos (which have a small rest mass) and the cosmic microwave background photons which don't.

Both are affected by gravity, such that their trajectories can be altered.

The C$\nu$B neutrinos have a temperature of 2K and current kinetic energies of a tenth of an meV or so. The neutrino rest masses are not pinned down yet - at least one has a rest mass energy of >0.04 meV, whilst the total mass for all three flavours is likely to be <0.3 meV. Thus the neutrinos are not highly relativistic and there will be a tail of (relatively) slow-moving neutrinos that could be trapped by galaxies or, more likely, galaxy clusters.

The neutrino velocities will be of order $\sqrt{kT/m_{\nu}} \sim 0.1c$ if they had a Maxwell-Boltzmann distribution. However, a more detailed treatment, using the appropriate Fermi-Dirac distribution in the expanding universe shows that the mean velocities of neutrinos are (e.g. Lesgourges & Pastor 2012) $$\langle v \rangle \simeq 160 (1+z) \left(\frac{{\rm eV}}{m_{\nu}}\right)\ {\rm km/s}.$$ So for neutrino masses of $\sim 0.1$ meV you would expect that a small fraction could be trapped (e.g. see section 2.2 of Yanagisawa 2014) in the halos of galaxies and in massive clusters, because their escape velocities are of order hundreds to a few thousands of km/s.

Even for neutrino masses as low as 0.15 meV, numerical simulations suggest a modest (up to a factor of two) increase in neutrino density within our galaxy compared to the average value (obviously this is critically dependent on the actual neutrino masses) and perhaps overdensities in massive nearby clusters (like Virgo) of as much as a factor of 5 (Ringwald & Wong 2004).

The photons of the CMB travel at the speed of light and therefore cannot be gravitationally captured. However, the photons are lensed by foreground massive galaxy clusters, mainly at redshifts of 2-3. This causes fluctuations in the CMB (quite separate from the cosmological ripples from the epoch of recombination) on a number of angular scales. It should be very important at very small angular scales (less than arcminutes - and currently very difficult to measure), but does causes coherent deflections of the CMB from the surface of last scattering on angular scales of 1-5 degrees (e.g. Lewis & Challinor 2006 ) that have been clearly detected by Planck and other ground-based instruments.