The Mass Growth and Stellar Ages of Galaxies: Observations versus Simulations

Using observed stellar mass functions out to $z=5$, we measure the main progenitor stellar mass growth of descendant galaxies with masses of $\log M_{\ast }\mathrm{/}{M}_{\odot }=11.5,11.0,10.5,10.0$ at $z\sim 0.1$ using an evolving cumulative number density selection. From these mass growth histories, we are able to measure the time at which half the total stellar mass of the descendant galaxy was assembled, $t_a$, which, in order of decreasing mass corresponds to redshifts of $z_a=1.28,0.92,0.60$ and $0.51$. We compare this to the median light-weighted stellar age $t_{\ast }$ ($z_{\ast }=2.08,1.49,0.82$ and $0.37$) of a sample of low redshift SDSS galaxies (from the literature) and find the timescales are consistent with more massive galaxies forming a higher fraction of their stars ex-situ compared to lower mass descendants. We find that both $t_{\ast }$ and $t_a$ strongly correlate with mass which is in contrast to what is found in the EAGLE hydrodynamical simulation which shows a flat relationship between $t_a$ and $M_{\ast }$. However, the semi-analytic model of \citet{henriques2015} is consistent with the observations in both $t_a$ and $t_{\ast }$ with $M_{\ast }$, showing the most recent semi-analytic models are better able to decouple the evolution of the baryons from the dark matter in lower-mass galaxies.