Dark matter substructure and gamma-ray annihilation in the Milky Way halo

TL;DR

This work presents Via Lactea, the then-highest-resolution CDM simulation of a Milky Way–sized halo, resolving ~10^4 subhalos and revealing substantial inner substructure that previously appeared smooth. It demonstrates that the subhalo mass function follows $N(>M_{\rm sub})=0.0064\,(M_{\rm sub}/M_{\rm vir})^{-1}$ and that the annihilation signal scales roughly as $S_{i}\propto M_{\rm sub}$, yielding a total halo luminosity modestly above a smooth halo but with large potential boosts if small-scale substructure is fully resolved. The analysis highlights an inner missing satellites problem, where many dark inner subhalos are predicted versus the few observed dwarfs, and discusses how galaxy formation models might reconcile this. All-sky gamma-ray maps indicate that a small number of subhalos could be detectable against the diffuse background for instruments like GLAST/LAT, making indirect detection of dark matter a tangible target under favorable conditions. Overall, the results emphasize the critical role of resolution in predicting substructure and the indirect-detection prospects of dark matter in Milky Way–size halos.

Abstract

We present initial results from ``Via Lactea'', the highest resolution simulation to date of Galactic CDM substructure. It follows the formation of a Milky Way-size halo with Mvir=1.8x10^12 Msun in a WMAP 3-year cosmology, using 234 million particles. Over 10,000 subhalos can be identified at z=0: Their cumulative mass function is well-fit by N(>Msub)= 0.0064 (Msub/Mvir)^(-1) down to Msun=4x10^6 Msun. The total mass fraction in subhalos is 5.3%, while the fraction of surface mass density in substructure within a projected distance of 10 kpc from the halo center is 0.3%. Because of the significant contribution from the smallest resolved subhalos, these fractions have not converged yet. Sub-substructure is apparent in all the larger satellites, and a few dark matter lumps are resolved even in the solar vicinity. The number of dark satellites with peak circular velocities above 10 km/s (5 km/s) is 124 (812): of these, 5 (26) are found within 0.1 Rvir, a region that appeared practically smooth in previous simulations. The neutralino self-annihilation gamma-ray emission from dark matter clumps is approximately constant per subhalo mass decade. Therefore, while in our run the contribution of substructure to the gamma-ray luminosity of the Galactic halo amounts to only 40% of the total spherically-averaged smooth signal, we expect this fraction to grow significantly as resolution is increased further. An all-sky map of the expected annihilation gamma-ray flux reaching a fiducial observer at 8 kpc from the Galactic center shows that at the current resolution a small number of subhalos start to be bright enough to be visible against the background from the smooth density field surrounding the observer.

Figures (10)

• Figure 1: Top: logarithmic slope of the density profile of our Via Lactea run, as a function of radius. Densities were computed in 50 radial logarithmic bins, and the local slope was determined by a finite difference approximation using one neighboring bin on each side. The thin line shows the slope of the best-fit NFW profile with scale radius of $24.6$ kpc. The vertical dotted line indicates the estimated convergence radius: local densities (but not necessarily the logarithmic slopes) should be correct to within 10% outside of this radius. Bottom: the residuals in percent between the density profile and the best-fit NFW profile, as a function of radius.
• Figure 2: Projected dark matter density-squared map of our simulated Milky Way-size halo ("Via Lactea") at the present epoch. The image covers an area of 800 $\times$ 600 kpc, and the projection goes through a 600 kpc-deep cuboid containing a total of 110 million particles. The logarithmic color scale covers 20 decades in density-square.
• Figure 3: Projected dark matter density-square map of the four most massive subhalos within the simulated Milky Way host at the present epoch. Sub-substructure is clearly visible. Only dark matter particles within the tidal radius $r_t$ are used for the projections. Clockwise from top left: ($M_{\rm sub}, r_t, r_{V_{\rm max}})= (9.8\times10^9\,\,\rm M_\odot, 40.1\,{\rm kpc}, 7.6\,{\rm kpc}), (3.7\times10^9\,\,\rm M_\odot, 33.4\,{\rm kpc}, 4.0\,{\rm kpc}), (3.0\times10^9\,\,\rm M_\odot, 28.0\,{\rm kpc}, 4.9\,{\rm kpc})$, and ($2.4\times10^9\,\,\rm M_\odot, 14.7\,{\rm kpc}, 6.1\,{\rm kpc})$. The mean subhalo densities within the tidal radius (in units of the cosmic background dark matter density) are 1002, 654, 904, and 4950, respectively. These values are related to the local matter density of the host (72, 46, 59 and 397 in the same units), and correlate only weakly with the subhalo distance from the Galactic center (345, 374, 280 and 185 kpc).
• Figure 4: Examples of subhalo circular velocity profiles ( crosses). The fitting functions ( dashed lines) are combinations of an NFW subhalo ( dotted lines) and a linear contribution form a constant background density ( solid lines). Stated above each panel are the subhalos distance form the galaxy center, tidal radius, tidal mass and the local background density.
• Figure 5: Cumulative subhalo mass functions within $r_{\rm vir}$ ( upper curves) and $0.1\,r_{\rm vir}$ ( lower curves). Solid crosses: Via Lactea run. Dashed crosses: lower resolution run. Solid line: power-law fit, $N(>M_{\rm sub})=0.0064\times(M_{\rm sub}/M_{\rm halo})^{-1}$.