Abstract: In the standard model of cosmology (ΛCDM) the first stars, star clusters, and galaxies are expected to have formed in short bursts of star formation in low-mass dark matter halos at high redshifts (
). Up to this point, attempts to predict the properties and abundances of these luminous objects have made use of numerically expensive cosmological simulations. On top of being numerically expensive, these simulations often lack the required sub-parsec resolution needed to resolve the formation of compact star clusters and/or neglect possibly dominant stellar feedback processes. Motivated by this, I introduce Anaxagoras, as far as I know the most detailed analytical ab initio model of starbursts in low-mass halos to date. The model incorporates sub-models for gas cooling (including a new determination of the H2-cooling threshold in minihalos), central gas accretion and disk formation (using a new selfsimilarsolution), stellar feedback from radiation pressure (direct stellar radiation, Lyman-
scattering in H I, and multiple scattering of IR photons by dust), stellar winds, expanding HII regions, and (crudely) supernovae. The resulting star formation efficiency is used to predict the fraction of stars that remain gravitationally bound in a cluster following gas expulsion, andwhat fraction escape the central region of the halo, yet remain bound by the dark matter halo. I apply Anaxagoras to study star formation at 
in satellite halos of the Milky Way using a halo merger tree code, as well as Population III (Pop III) star formation in minihalos. For the Milky Way setup, hundreds of galaxies are predicted to form with luminosities (
), half-mass radii (
), mass-to-light ratios (
), and ages (
) in good agreement with the observed local population of Ultra-Faint Dwarfs. This shows that ΛCDM is able to explain the properties ofthe faintest dwarf galaxies without fine-tuning. Furthermore, at least ~ 40 compact (initial half-mass radii 
), old (
) globular cluster (GC) candidates with initial stellar masses 
are predicted to form at the center of low-mass halos, and could survive to the present-day and explain at least a fraction of the observed metal-poor GCs. Their properties are consistent with recent candidates for GCs residing in dark matter halos. Thus, Anaxagoras lends support to the viability of the scenario of GC formation in minihalos. Finally, the formation of Population III (Pop III) stars in minihalos is studied, with the conclusion that if Pop III stars are not overly massive (
) between ~ 1 − 30 stars could form per minihalo at 
, with the number increasing to ~ 10 − 500 stars per minihalo at 
as Lyman-Werner feedback delay star formation until halos reach larger masses. In the case where Pop III stars are more massive (
) most minihalos form just a single star. Due to self-shielding of H2 in minihalos, I find that the cosmological Lyman-Werner background is insufficient to produce Pop III galaxies in atomic-cooling halos, with the implication that the number of massive Pop III galaxies/star clusters in the early Universe has been greatly overestimated in the literature that ignores self-shielding.
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