A consistent measure of the merger histories of massive galaxies using close-pair statistics I: Major mergers at $z < 3.5$

We use a large sample of $\sim 350,000$ galaxies constructed by combining the UKIDSS UDS, VIDEO/CFHT-LS, UltraVISTA/COSMOS and GAMA survey regions to probe the major merging histories of massive galaxies ($>10^{10}\ \mathrm{M}_\odot$) at $0.005 < z < 3.5$. We use a method adapted from that presented in Lopez-Sanjuan et al. (2014) using the full photometric redshift probability distributions, to measure pair $\textit{fractions}$ of flux-limited, stellar mass selected galaxy samples using close-pair statistics. The pair fraction is found to weakly evolve as $\propto (1+z)^{0.8}$ with no dependence on stellar mass. We subsequently derive major merger $\textit{rates}$ for galaxies at $> 10^{10}\ \mathrm{M}_\odot$ and at a constant number density of $n > 10^{-4}$ Mpc$^{-3}$, and find rates a factor of 2-3 smaller than previous works, although this depends strongly on the assumed merger timescale and likelihood of a close-pair merging. Galaxies undergo approximately 0.5 major mergers at $z < 3.5$, accruing an additional 1-4 $\times 10^{10}\ \mathrm{M}_\odot$ in the process. Major merger accretion rate densities of $\sim 2 \times 10^{-4}$ $\mathrm{M}_\odot$ yr$^{-1}$ Mpc$^{-3}$ are found for number density selected samples, indicating that direct progenitors of local massive ($>10^{11}\mathrm{M}_\odot$) galaxies have experienced a steady supply of stellar mass via major mergers throughout their evolution. While pair fractions are found to agree with those predicted by the Henriques et al. (2014) semi-analytic model, the Illustris hydrodynamical simulation fails to quantitatively reproduce derived merger rates. Furthermore, we find major mergers become a comparable source of stellar mass growth compared to star-formation at $z < 1$, but is 10-100 times smaller than the SFR density at higher redshifts.