Abstract

ABSTRACT Dekel & Birnboim proposed that the mass-scale that separates late-type and early-type galaxies is linked to the critical halo mass $M_{\rm vir}^{\rm crit}$ for the propagation of a stable shock and showed that they could reproduce the observed bimodality scale for plausible values of the metallicity of the accreted gas Zaccr and the shock radius rs. Here, we take their analysis one step further and present a new semianalytic model that computes rs from first principles. This advancement allows us to compute $M_{\rm vir}^{\rm crit}$ individually for each halo. Separating cold-mode and hot-mode accretion has little effect on the final galaxy masses if feedback does not preferentially couple to the hot gas. We also present an improved model for stellar feedback where ${\sim }70{{\ \rm per\ cent}}$ of the wind mass is in a cold galactic fountain with a shorter reaccretion time-scale at high masses. The latter is the key mechanism that allows us to reproduce the low-mass end of the mass function of galaxies over the entire redshift range 0 < z < 2.5. Cooling must be mitigated to avoid overpredicting the number density of galaxies with stellar mass $M_{\rm stars}\gt 10^{11}\, {\rm M}_\odot$ but is important to form intermediate-mass galaxies. At $M_{\rm vir}\gt 3\times 10^{11}\, {\rm M}_\odot$, cold accretion is more important at high z, where gas is accreted from smaller solid angles, but this is not true at lower masses because high-z filaments have lower metallicities. Our predictions are consistent with the observed metallicity evolution of the intergalactic medium at 0 < z < 5.

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