We infer the UV luminosities of Local Group galaxies at early cosmic times ($z sim 2$ and $z sim 7$) by combining stellar population synthesis modeling with star formation histories derived from deep color-magnitude diagrams constructed from Hubble S
pace Telescope (HST) observations. Our analysis provides a basis for understanding high-$z$ galaxies - including those that may be unobservable even with the James Webb Space Telescope (JWST) - in the context of familiar, well-studied objects in the very low-$z$ Universe. We find that, at the epoch of reionization, all Local Group dwarfs were less luminous than the faintest galaxies detectable in deep HST observations of blank fields. We predict that JWST will observe $z sim 7$ progenitors of galaxies similar to the Large Magellanic Cloud today; however, the HST Frontier Fields initiative may already be observing such galaxies, highlighting the power of gravitational lensing. Consensus reionization models require an extrapolation of the observed blank-field luminosity function at $z approx 7$ by at least two orders of magnitude in order to maintain reionization. This scenario requires the progenitors of the Fornax and Sagittarius dwarf spheroidal galaxies to be contributors to the ionizing background at $z sim 7$. Combined with numerical simulations, our results argue for a break in the UV luminosity function from a faint-end slope of $alpha sim -2$ at $M_{rm UV} < -13$ to $alpha sim -1.2$ at lower luminosities. Applied to photometric samples at lower redshifts, our analysis suggests that HST observations in lensing fields at $z sim 2$ are capable of probing galaxies with luminosities comparable to the expected progenitor of Fornax.
Reionizing the Universe with galaxies appears to require significant star formation in low-mass halos at early times, while local dwarf galaxy counts tell us that star formation has been minimal in small halos around us today. Using simple models and
the ELVIS simulation suite, we show that reionization scenarios requiring appreciable star formation in halos with $M_{rm vir} approx 10^{8},M_{odot}$ at $z=8$ are in serious tension with galaxy counts in the Local Group. This tension originates from the seemingly inescapable conclusion that 30 - 60 halos with $M_{rm vir} > 10^{8},M_{odot}$ at $z=8$ will survive to be distinct bound satellites of the Milky Way at $z = 0$. Reionization models requiring star formation in such halos will produce dozens of bound galaxies in the Milky Ways virial volume today (and 100 - 200 throughout the Local Group), each with $gtrsim 10^{5},M_{odot}$ of old stars ($gtrsim 13$ Gyr). This exceeds the stellar mass function of classical Milky Way satellites today, even without allowing for the (significant) post-reionization star formation observed in these galaxies. One possible implication of these findings is that star formation became sharply inefficient in halos smaller than $sim 10^9 ,M_{odot}$ at early times, implying that the high-$z$ luminosity function must break at magnitudes brighter than is often assumed (at ${rm M_{UV}} approx -14$). Our results suggest that JWST (and possibly even HST with the Frontier Fields) may realistically detect the faintest galaxies that drive reionization. It remains to be seen how these results can be reconciled with the most sophisticated simulations of early galaxy formation at present, which predict substantial star formation in $M_{rm vir} sim 10^8 , M_{odot}$ halos during the epoch of reionization.
We combine our Hubble Space Telescope measurement of the proper motion of the Leo I dwarf spheroidal galaxy (presented in a companion paper) with the highest resolution numerical simulations of Galaxy-size dark matter halos in existence to constrain
the mass of the Milky Ways dark matter halo (M_MW). Despite Leo Is large Galacto-centric space velocity (200 km/s) and distance (261 kpc), we show that it is extremely unlikely to be unbound if Galactic satellites are associated with dark matter substructure, as 99.9% of subhalos in the simulations are bound to their host. The observed position and velocity of Leo I strongly disfavor a low mass Milky Way: if we assume that Leo I is the least bound of the Milky Ways classical satellites, then we find that M_MW > 10^{12} M_sun at 95% confidence for a variety of Bayesian priors on M_MW. In lower mass halos, it is vanishingly rare to find subhalos at 261 kpc moving as fast as Leo I. Should an additional classical satellite be found to be less bound than Leo I, this lower limit on M_MW would increase by 30%. Imposing a mass weighted LCDM prior, we find a median Milky Way virial mass of M_MW=1.6 x 10^{12} M_sun, with a 90% confidence interval of [1.0-2.4] x 10^{12} M_sun. We also confirm a strong correlation between subhalo infall time and orbital energy in the simulations and show that proper motions can aid significantly in interpreting the infall times and orbital histories of satellites.
We present the Millennium-II Simulation (MS-II), a very large N-body simulation of dark matter evolution in the concordance LCDM cosmology. The MS-II assumes the same cosmological parameters and uses the same particle number and output data structure
as the original Millennium Simulation (MS), but was carried out in a periodic cube one-fifth the size (100 Mpc/h) with 5 times better spatial resolution (a Plummer equivalent softening of 1.0 kpc/h) and with 125 times better mass resolution (a particle mass of 6.9 times 10^6 Msun/h). By comparing results at MS and MS-II resolution, we demonstrate excellent convergence in dark matter statistics such as the halo mass function, the subhalo abundance distribution, the mass dependence of halo formation times, the linear and nonlinear autocorrelations and power spectra, and halo assembly bias. Together, the two simulations provide precise results for such statistics over an unprecedented range of scales, from halos similar to those hosting Local Group dwarf spheroidal galaxies to halos corresponding to the richest galaxy clusters. The Milky Way halos of the Aquarius Project were selected from a lower resolution version of the MS-II and were then resimulated at much higher resolution. As a result, they are present in the MS-II along with thousands of other similar mass halos. A comparison of their assembly histories in the MS-II and in resimulations of 1000 times better resolution shows detailed agreement over a factor of 100 in mass growth. We publicly release halo catalogs and assembly trees for the MS-II in the same format within the same archive as those already released for the MS.
