## [1911.09417] First simulations of axion minicluster halos

 Authors: Benedikt Eggemeier, Javier Redondo, Klaus Dolag, Jens C. Niemeyer, Alejandro Vaquero Abstract: We study the gravitational collapse of axion dark matter fluctuations in the post-inflationary scenario, so-called axion miniclusters, with N-body simulations. Largely confirming theoretical expectations, overdensities begin to collapse in the radiation-dominated epoch and form an early distribution of miniclusters with masses up to $10^{-12}\,M_\odot$. After matter-radiation equality, ongoing mergers give rise to a steep power-law distribution of minicluster halo masses. The density profiles of well-resolved halos are NFW-like to good approximation. The fraction of axion DM in these bound structures is $\sim 0.75$ at redshift $z=100$. [PDF]  [PS]  [BibTex]  [Bookmark]

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### [1911.09417] First simulations of axion minicluster halos

This paper was commented on through Cosmo Comments. The following comments can also be viewed as annotations on the paper via Hypothesis.

This is a very interesting paper that simulates an era of QCD axion dark matter that hasn’t previously been simulated (at least at this resolution and depth). The era is the first gravitational growth of structures (“mini clusters” and their haloes) during radiation domination through until after matter-radiation equality (down to $z=99$).

During this time, very small distance scales become non-linear and have some potentially interesting effects. Firstly, the initial conditions aren’t the usual adiabatic ones, nor are they Gaussian, due to their relevance during the earlier evolution through the Peccei-Quinn symmetry breaking phase and the QCD phase transition. Secondly, the structures that form here form the background for potential growth of “axion stars”, which are already well studied.

The results and machinery developed are relevant for a range of reasons. e.g., determining what dark matter is, potential observational evidence of the QCD axion, studies of the evolution of the non-linear Schrödinger equation (i.e. the evolution of axion stars) and it is relevant to people who simulate cold dark matter because their expertise and tools would be immediately translatable for use here.

I have some questions:
1. The y-axis label of figure 4 is confusing to me. An uppercase "N" is used, indicating it is the actual number of halos of a given mass, rather than the number density per $\log(M)$, as in figure 2. But the description indicates it isn't the total number greater or smaller than a given mass (as in figure 3) – and the plot wouldn't make sense in this context anyway. Is it the total number of halos within a logarithmic mass bin that is plotted (normalised to total number of subhalos of any mass)? Or is it something else?
2. My personal, a priori, belief for the profiles in figure 5 is that the lines should be closer to NFW than power-law, which is what is claimed in the text. However, if I try not to give into confirmation bias, the evidence isn't overwhelming in the paper. The main issues are that no comparison fit was given to a power-law as an alternative and that the relative error for the fit to NFW gets as large as ~0.5 in the bottom panel. I would be interested in seeing an additional set of dashed lines in the lower panel showing the relative error to the best fit power-law profile. Of course, for the smallest mass bin this would actually give a better fit because the NFW scale radius is smaller than the smallest radius being fitted to and therefore the "NFW" fit is actually to an $r^{-3}$ power-law, but this is explained in the text already. It is the largest mass bin that would yield the interesting comparison between NFW and power-law.
3. Do the authors have any idea or speculation as to why the low- and medium-mass profiles are under-dense compared to NFW at larger r? Are these haloes simply not fully virialised yet for some reason? Or is there a lack of additional mass to accrete to these haloes in their outer regions?
4. Is there any expectation for what the value of $\alpha$ (the fit to the slope of the mini cluster halo mass function) should be. Or, is $\alpha=-0.7$ a pure empirical fit at this stage (to be explained later)?
5. It isn't ever mentioned (that I can see) how many haloes are in each mass bin for Table 1 and Figure 5. Also, in Figure 5 why only stack 20 profiles in each bin and not all of them?
6. In the appendices, I didn't fully understand why the velocities of the N-body particles needed to be set to zero and why this is OK physically. Surely, if the authors evolve the output of the early universe simulation forward with linear theory, they know the rate of change of the relevant quantities, which can then be used to define a velocity field alongside the density field? As they state in the text, setting the velocities to zero removes the initial logarithmic growth, but wouldn't including this growth be important? Or is it actually the correct physics to set these to zero because these modes aren't coming from adiabatic initial conditions? But if this is the correct physics, what is the use of the linear "evolution" step? Clarification would be really helpful (for me)!
The last sentence of S1 is: "The velocities of the particles are set to zero, which is compatible with the last smoothing procedure." I don't understand what this sentence means. It might be a clue as to what I'm missing for answering the last question.

[These comments were shared with us by a member of the cosmology community. They do not necessarily reflect the opinion of the Cosmo Comments team.]