Specific merger mass accretion rate (in units of Gyr-1) as a function of the stellar mass ratio of mergers, x, for z = 2. The lines represent an sMMR fixed at 10% of the sSFR due to accreted stars (black solid line) and the total sMMR (including stars and gas) for various initial central galaxy stellar masses (indicated in the legend). We assumed sSFR = 3 Gyr-1. On the righthand ordinate, we indicate the sSMR/sSFR ratio to compare the stellar mass growth due to merging and to star formation. The black point indicates the merger rate determined for z ≈ 2–4 by Tasca et al. (2014) for an assumed merger time scale of 1 Gyr – the value indicated is likely a lower limit since the time scale may be shorter.
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