Galactic star formation and accretion histories from matching galaxies to dark matter haloes

We present a new statistical method to determine the relationship between the stellar masses of galaxies and the masses of their host dark matter haloes over the entire cosmic history from z ∼ 4 to the present. This multi-epoch abundance matching (MEAM) model self-consistently takes into account that satellite galaxies first become satellites at times earlier than they are observed. We employ a redshift-dependent parameterization of the stellar-to-halo mass relation to populate haloes and subhaloes in the Millennium simulations with galaxies, requiring that the observed stellar mass functions at several redshifts be reproduced simultaneously. We show that physically meaningful growth of massive galaxies is consistent with these data only if observational mass errors are taken into account. Using merger trees extracted from the dark matter simulations in combination with MEAM, we predict the averageassembly histories of galaxies, separating into star formation within the galaxies (in-situ) and accretion of stars (ex-situ). Our main results are: The peak star formation efficiency decreases with redshift from 23 per cent at z = 0 to 9 per cent at z = 4 while the