Earth-mass dark-matter haloes as the first structures in the early Universe

TL;DR

Supercomputer simulations of the concordance cosmological model, which assumes neutralino dark matter (at present the preferred candidate), are reported, and it is found that the first objects to form are numerous Earth-mass dark-matter haloes about as large as the Solar System.

Abstract

The Universe was nearly smooth and homogeneous before a redshift of z = 100, about 20 million years after the Big Bang. After this epoch, the tiny fluctuations imprinted upon the matter distribution during the initial expansion began to collapse because of gravity. The properties of these fluctuations depend on the unknown nature of dark matter, the determination of which is one of the biggest challenges in present-day science. Here we report supercomputer simulations of the concordance cosmological model, which assumes neutralino dark matter (at present the preferred candidate), and find that the first objects to form are numerous Earth-mass dark-matter haloes about as large as the Solar System. They are stable against gravitational disruption, even within the central regions of the Milky Way. We expect over 10^15 to survive within the Galactic halo, with one passing through the Solar System every few thousand years. The nearest structures should be among the brightest sources of gamma-rays (from particle-particle annihilation).

Figures (3)

• Figure 1: A zoom into one of the first objects to form in the universe. The colours show the density of dark matter at redshift 26. Brighter colours correspond to regions of higher concentrations of matter. The blue background image shows the small scale structure in the top cube (cube size = [3 comoving kpc]$^3$) which has a similar filamentary topology as the large scale structure in the CDM universe. The first red image zooms by a factor of one hundred into the average density high resolution region. This region was initially a cube of [60 comoving pc]$^3$ resolved with 64 million particles with a gravitational softening of $10^{-2}$ comoving parsecs and masses $1.2\times 10^{-10}M_\odot\equiv M_{moon}/300$. The final image shows a close up of one of the individual dark matter halos in this region, again zooming in by a factor of one hundred so that the box has a physical length of 0.024 parsecs. This tiny triaxial Earth mass halo has a cuspy density profile and is smooth, devoid of the substructure that is found within galactic and cluster mass dark matter halos. Even though the index of the power spectrum is very steep on these scales, $n\approx-3$, we find that halos can collapse before merging into a larger system, rather than the niave expectation that all scales are collapsing simultaneously thus erasing such structures.
• Figure 2: Radial density profiles of three typical minihalos at redshift 26. The radial distance is plotted in physical units and we show low concentration $\alpha\beta\gamma$-profiles for comparison. We use the mean dark matter profile infered from the highest resolution galaxy cluster simulations Diemand2004pro, i.e. $(\alpha\beta\gamma)=(1,3,1.2)$. The vertical dotted line indicates our force resolution and the arrows indicate the radii that is 200 times the background density. Across the entire range of halo masses from $10^{-6}$ to $10^1 M_\odot$, we find small concentration parameters $c < 3$. We do not observe a trend of concentration with mass, possibly because the halos all form at a similar epoch as expected when the power spectrum is so steep.
• Figure 3: The abundance of collapsed and virialised dark matter halos of a given mass. The same region was simulated twice using different types of intial fluctuations: (A) SUSY-CDM with a 100 GeV neutralino (stars) and (B) an additional model with no small scale cut-off to the power spectrum (open circles) as might be produced by an axion dark matter candidate. Densities are given in co-moving units, masses in $h^{-1} {\rm M_\odot} = 1.41 {\rm M_\odot}$, where $h=0.71$ is the normalized present day Hubble expansion rate. Model (B) has a steep mass function down to the resolution limit whereas run (A) has many fewer halos below a mass of about $5\times 10^{-6} h^{-1}{\rm M_\odot} = 3.5\times 10^{-6}h^{-1}{\rm M_\odot}$. (Our simulations do not probe the mass range from about $3 \times 10^{-4} h^{-1}{\rm M_\odot}$ to $2 \times 10^{-1} h^{-1}{\rm M_\odot}$.) The dashed-dotted line shows an extrapolation of the number density of galaxy halos (from Reed2003a) assuming $dn(M) / d \log M \propto M^{-1}$. The solid line is the function $dn(M) / d \log M = 2.8\times10^9(M/h^{-1}{\rm M_\odot})^{-1} \exp[-(M/M_{\rm cutoff})^{-2/3}] (h^{-1}Mpc)^{-3}$, with a cutoff mass $M_{\rm cutoff} =5.7\times10^{-6}h^{-1}{\rm M_\odot}$. The power spectrum cutoff is $P(k) \propto \exp[-(k/k_{fs}]^2)$, where $k_{fs}$ is the free streaming scale and assuming $k \propto M^{-1/3}$ motivates the exponent of $-2/3$ in our fitting function.