The Aquarius Project: the subhalos of galactic halos

TL;DR

The Aquarius Project advances CDM theory testing on galactic scales by delivering the largest Milky Way–sized halo simulation with rigorous convergence validation and a six-halo ensemble to quantify halo-to-halo scatter. Using ultra-high-resolution zoom-in runs with GADGET-3, the study reveals a near-universal subhalo mass function with slope around $n\approx -1.9$, and finds that the mass fraction in substructure remains modest (e.g., ${\lesssim}3\%$ within 100 kpc) even when extrapolating to Earth-mass scales. Subhalos are typically more concentrated than field halos, and their inner density profiles are well described by Einasto fits with no evidence for a fixed Moore-like cusp; substructure inside subhalos is generally suppressed relative to self-similar expectations due to tidal stripping and lack of replenishment. The results challenge some prior claims (notably from Via Lactea) and have implications for indirect dark matter searches and Milky Way satellite modeling, while establishing a robust framework for future comparisons with baryonic physics and annihilation signals.

Abstract

We have performed the largest ever particle simulation of a Milky Way-sized dark matter halo, and present the most comprehensive convergence study for an individual dark matter halo carried out thus far. We have also simulated a sample of 6 ultra-highly resolved Milky-way sized halos, allowing us to estimate the halo-to-halo scatter in substructure statistics. In our largest simulation, we resolve nearly 300,000 gravitationally bound subhalos within the virialized region of the halo. Simulations of the same object differing in mass resolution by factors up to 1800 accurately reproduce the largest subhalos with the same mass, maximum circular velocity and position, and yield good convergence for the abundance and internal properties of dark matter substructures. We detect up to four generations of subhalos within subhalos, but contrary to recent claims, we find less substructure in subhalos than in the main halo when regions of equal mean overdensity are compared. The overall substructure mass fraction is much lower in subhalos than in the main halo. Extrapolating the main halo's subhalo mass spectrum down to an Earth mass, we predict the mass fraction in substructure to be well below 3% within 100 kpc, and to be below 0.1% within the Solar Circle. The inner density profiles of subhalos show no sign of converging to a fixed asymptotic slope and are well fit by gently curving profiles of Einasto form. The mean concentrations of isolated halos are accurately described by the fitting formula of Neto et al. down to maximum circular velocities of 1.5 km/s, an extrapolation over some 5 orders of magnitude in mass. However, at equal maximum circular velocity, subhalos are more concentrated than field halos, with a characteristic density that is typically ~2.6 times larger and increases towards the halo centre.

Figures (29)

• Figure 1: Measured power spectrum (dimensionless variance $\Delta^2(k)\sim k^3P(k)$ per natural log interval) in our highest resolution 'zoom' initial conditions, Aq-A-1, linearly extrapolated to the values expected at $z=0$. The lower red points show the power spectrum measured in our homogeneously sampled parent simulation, shifted down by one dex for clarity. The upper red circles show our measurement for the zoom initial conditions for the whole box, while cyan and magenta circles show measurements from smaller boxes centred within the high-resolution region. The solid black lines show the linear theory input spectrum. The vertical dashed line on the right marks the Nyquist frequency of the high-resolution region, while the left vertical line is the joining point between the long wavelength modes from the parent simulation and the high frequency modes added to the high resolution cube.
• Figure 2: The top left panel shows the projected dark matter density at $z=0$ in a slice of thickness $13.7\,{\rm Mpc}$ through the full box ($137\,{\rm Mpc}$ on a side) of our $900^3$ parent simulation, centred on the 'Aq-A' halo that was selected for resimulation. The other five panels show this halo resimulated at different numerical resolutions. In these panels, all particles within a cubic box of side-length $2.5\times r_{50}$ centred on the halo are shown. The image brightness is proportional to the logarithm of the squared dark matter density $S(x,y)$ projected along the line-of-sight, and the colour hue encodes the local velocity dispersion weighted by the squared density along the line-of-sight. We use a two-dimensional colour table (as shown on the left) to show both of these quantities simultaneously. The colour hue information is orthogonal to the brightness information; when converted to black and white, only the density information remains, with a one-dimensional grey-scale colour map as shown on the left. The circles mark $r_{50}$.
• Figure 3: Projected dark matter density in our six different high-resolution halos at $z=0$, at the '2' resolution level. In each panel, all particles within a cubic box of side length $2.5\times r_{50}$ centred on the halo are shown, and the circles mark the radius $r_{50}$. The image brightness is proportional to the logarithm of the squared dark matter density, and the colour hue encodes the local particle velocity dispersion, with the same colour map as in Figure \ref{['FigDMDist']}.
• Figure 4: Spherically averaged density profile of the Aq-A halo at $z=0$, at different numerical resolutions. Each of the profiles is plotted as a thick line for radii that are expected to be converged according to the resolution criteria of Power2003. These work very well for our simulation set. We continue the measurements as thin solid lines down to $2\,\epsilon$, where $\epsilon$ is the Plummer-equivalent gravitational softening length in the notation of Springel2001a. The dotted vertical lines mark the scale $2.8\,\epsilon$, beyond which the gravitational force law is Newtonian. The mass resolution changes by a factor of $1835$ from the lowest to the highest resolution simulation in this series. Excellent convergence is achieved over the entire radial range where it is expected.
• Figure 5: Local logarithmic slope of the density profiles as a function of radius for the Aq-A halo simulated at different numerical resolution. Only the radial region that should be converged according to the criteria of Power2003 is shown. Note that the large fluctuations in the outer parts are caused by substructures but nevertheless reproduce well between simulations. In this regime, we expect significant halo-to-halo scatter.