How does neutrino free streaming length affect the growth of structures in the universe?

Question

I cannot quite wrap my head around the exact mechanism by which neutrinos affect cosmic structure growth. Their effect as dark matter is clear to me but I don't understand how their longer free streaming length sets them apart from other particles. Here is my understanding:

Neutrinos have a longer free streaming length and can therefore carry away energy from forming structures over long distances and thus wash out those structures.

What this means to me is that these structures become more distributed and less clustered. But a larger mass leads to a longer FSL (why?) which, in turn, should lead to even less clustering. But it does not. At least not according to these figures from my lecture notes:

The figure shows that a larger mass leads to more clustering. At least that is how I interpret it.

Where exactly is the mistake in my thinking? Am I completely missing the point of this illustration?

Answer 1

But a larger mass leads to a longer FSL (why?)

This is incorrect. A larger neutrino mass leads to a smaller free-streaming length. Neutrinos decouple at a known temperature $\sim 1~\text{MeV}$ and hence a known momentum $p$ that are independent of the neutrino mass $m$. As the universe expands, (peculiar) momenta drop as $p\propto 1/a$, where $a$ is the scale factor. The particles eventually become nonrelativistic when $p$ drops below $m$. Particles of higher mass $m$ become nonrelativistic and begin to lose velocity earlier, so they traverse shorter distances.

But it is true nonetheless that neutrinos of greater mass lead to a greater suppression of structure. This is because even with eV-scale masses, neutrinos still have a long enough free-streaming length to suppress initial density variations at the scales of galaxies and sufficient residual thermal motion that they can stream out of dwarf galaxies. But meanwhile, increasing the neutrino mass increases their energy density and hence the degree to which they contribute to structure.

More quantitatively, there are about 336 neutrinos per cubic centimeter throughout the universe. This number follows from the thermal history of the universe. If the neutrinos are massless, then they have a negligible energy density today (under $10^{-5}$ the critical density). On the other hand, if the masses of the three neutrinos sum to $1.9~\text{eV}$, then their total mass density is about 4% of the critical density, or about 1/7 of the matter (1/6 of the dark matter). The reason small-scale structure is suppressed in this scenario is that a significant fraction of the matter cannot contribute to it.

Answer 2

I typed "neutrino free streaming simulation" on Google Imagens and I found your post, but I also found the link to the American Physics Society (APS) and where the image of your post may have been taken from. The figure used in the APS post, in its turn, is a courtesy given by the authors of the paper arXiv 1006.0689 (see Fig. 5). The main point (and the source of confusion) is that in your figure the labels are switched. It seems to me that even in the figure's caption of the APS post the information isn't totally accurate with respect to the paper: a cosmological model with massless neutrino isn't the same thing that a neutrinoless universe.

So, following the original source arXiv 1006.0689 we have that: the left panel of your post actually is a simulation with massive neutrinos ($M_\nu\equiv\Sigma m_\nu=1.9$ eV) while the right panel of your post is a simulation without neutrinos (not massless neutrino). In the middle panel of Fig. 5 of the paper arXiv 1006.0689 the authors have the intermediate case with $M_\nu=0.95$ eV.