Clumps and streams in the local dark matter distribution

TL;DR

A simulation that resolves dark matter substructure even in the very inner regions of the Galactic halo is reported, finding hundreds of very concentrated dark matter clumps surviving near the solar circle, as well as numerous cold streams.

Abstract

In cold dark matter cosmological models, structures form and grow by merging of smaller units. Numerical simulations have shown that such merging is incomplete; the inner cores of halos survive and orbit as "subhalos" within their hosts. Here we report a simulation that resolves such substructure even in the very inner regions of the Galactic halo. We find hundreds of very concentrated dark matter clumps surviving near the solar circle, as well as numerous cold streams. The simulation reveals the fractal nature of dark matter clustering: Isolated halos and subhalos contain the same relative amount of substructure and both have cuspy inner density profiles. The inner mass and phase-space densities of subhalos match those of recently discovered faint, dark matter-dominated dwarf satellite galaxies and the overall amount of substructure can explain the anomalous flux ratios seen in strong gravitational lenses. Subhalos boost gamma-ray production from dark matter annihilation, by factors of 4-15, relative to smooth galactic models. Local cosmic ray production is also enhanced, typically by a factor 1.4, but by more than a factor of ten in one percent of locations lying sufficiently close to a large subhalo. These estimates assume that gravitational effects of baryons on dark matter substructure are small.

Figures (5)

• Figure 1: Projected dark matter density-square map of "Via Lactea II". An 800 kpc cube is shown. The insets focus on an inner 40 kpc cube, in local density (bottom), and in local phase space density calculated with EnBiD[2006MNRAS.373.1293S] (top). The Via Lactea II simulation has a mass resolution of 4,100 $M_\odot$ and a force resolution of 40 pc. It used over a million processor hours on the "Jaguar" Cray XT3 supercomputer at the Oak Ridge National Laboratory. A new method was employed to assign physical, adaptive time-steps2007MNRAS.376..273Z equal to 1/16 of the local dynamical timescale (but not shorter than 268,000 yr), which allows to resolve very high density regions. Initial conditions were generated with a modified, parallel version of GRAFIC2[2001ApJS..137....1B]. The high resolution region is embedded within a large periodic box (40 comoving Mpc) to account for the large scale tidal forces. The mass within 402 kpc (the radius enclosing 200 times the mean matter density) is $1.9\times 10^{12}\,M_\odot$.
• Figure 2: Density profiles of main halo and subhalos. Main panel: Profile of the Milky Way halo ( thick line) and of eight large subhalos ( thin lines). The lower panel gives the relative differences between the simulated main halo profile and a fitting formula with a core2004MNRAS.349.1039N$\rho(r) = \rho_s \exp \{ -2/\alpha \left[ (r/r_{s})^{\alpha} - 1 \right]$, with best fit parameters: $\alpha =0.170$, $r_s = 21.5\, {\rm kpc}$, $\rho_s=1.73 \times 10^{-3} \,{\rm M_\odot\,pc^{-3}}$ ( red curve) and one with a cusp2004MNRAS.353..624D$\rho(r) = \rho_s (r/r_{s})^{-\gamma} (r/r_{s} + 1)^ {-3+\gamma}$ with a best fit inner slope of $\gamma = 1.24$, $r_s = 28.1\, {\rm kpc}$, $\rho_s=3.50 \times 10^{-3} \,{\rm M_\odot\,pc^{-3}}$ ( blue curve). The vertical dotted line indicates the estimated convergence radius of 380 pc: simulated local densities are only lower limits inside of 380 pc and they should be correct to within 10% outside this region. The cuspy profile is a good fit to the inner halo, while the cored profile has a too shallow slope in the inner few kpc, causing it to overestimate densities around 4 kpc and to underestimate them at all radii smaller than 1 kpc. The simulated densities are higher than the best fit cored profile even at 80 pc, where they are certainly underestimated due to numerical limitations. We find the same behavior in the inner few kpc in all six snapshots we have analyzed so far between z=3 an z=0. The large residuals in the outer halos on the other hand are transient features, they are different in every snapshot. Inset: Rescaled host (thick line) and subhalo (thin lines) density profiles multiplied by radius square to reduce the vertical range of the figure.
• Figure 3: Subhalo and sub-subhalo abundances. Number of subhalos above $V_{\rm max}$ within $r_{200}=402$ kpc (thick solid lines) and within 100 and 50 kpc of the galactic center (thin solid lines). $V_{\rm max}$ is the peak height of the subhalo circular velocity $v_{circ} = \sqrt{GM(<r) / r}$ and serves as a simple proxy for the mass of a subhalo. The dotted line is $N(>V_{\rm max})=0.036\,(V_{\rm max} / V_{\rm max,host})^{-3}$, where $V_{\rm max,host} = 201 \,{\rm km\,s^{-1}}$ (at $r_{\rm Vmax,host}= 60$ kpc). It fits the subhalo abundance above $V_{\rm max} \simeq 3.5 \,{\rm km\,s^{-1}}$. The number of smaller subhalos is artificially reduced by numerical limitations. Inside $r_{200}$ this halo has 1.7 times more substructure than the first Via Lactea halo2007ApJ...667..859D, a factor well within the halo-to-halo scatter2005MNRAS.359.1537R. Inside 50 kpc the difference grows to 2.6, probably due to the improved mass and time resolution of Via Lactea II, which allows to resolve inner substructure better. The inset shows the sub-subhalo abundance within $r_{1000}$ (enclosing 1000 times the mean matter density) of the centers of eight (same ones as in Fig. 2) large subhalos (thin solid lines). $r_{1000}$ is well inside of the tidal radius for these systems. The thick solid line shows the subhalo abundace of the host halo inside of its $r_{1000} = 213$ kpc. The (sub-)subhalo $V_{\rm max}$ values are given in units of $V_{1000}=\sqrt{GM(<r_{1000}) / r_{1000} }$ of the corresponding host (sub-)halo. Lines stop at $V_{\rm max} = 2 \,{\rm km\,s^{-1}}$. The mean sub-substructure abundance is consistent with the scaled down version of main halo, and both the mean abundance and the scatter agree with results in2005MNRAS.359.1537R for distinct field halos.
• Figure 4: Abundance and concentrations of subhalos vs. distance from the galactic center. Top: The number density profile of subhalos (circles) is more extended than the dark matter density profile $\rho(r)$ (thick line). Their ratio turns out to be roughly proportional to the enclosed mass $M(<r)$, i.e. $\rho M(<r)$ (thin line) matches the subhalo number density quite well. Only subhalos larger than $V_{\rm max} = 3 \,{\rm km\,s^{-1}}$ are included here. Bottom: Subhalo concentrations (median and 68% range are shown) increase towards the center, where the stronger tidal force remove more of the outer, low density parts from the subhalos. To make sure their $c_{V}$ are resolved, only subhalos larger than $V_{\rm max} = 5 \,{\rm km\,s^{-1}}$ are used. The error bars indicate the statistical uncertainties in both panels.
• Figure 5: Subhalo abundance at different numerical resolutions, starting redshifts and cosmologies. Number of subhalos above $V_{\rm max} / V_{\rm max,host}$ within $r_{200}$ for the VL-II simulation and three lower resolution versions of the same halo.