Using a mass-selected ( M _ { \star } \geq 10 ^ { 11 } M _ { \odot } ) sample of 198 galaxies at 0 \leq z \leq 3.0 with HST /NICMOS H _ { 160 } -band images from the COSMOS survey , we find evidence for the evolution of the pair fraction above z \sim 2 , an epoch in which massive galaxies are believed to undergo significant structural and mass evolution .
We observe that the pair fraction of massive galaxies is 0.15 \pm 0.08 at 1.7 \leq z \leq 3.0 , where galaxy pairs are defined as massive galaxies having a companion of flux ratio from 1:1 to 1:4 within a projected separation of 30 kpc .
This is slightly lower , but still consistent with the pair fraction measured previously in other studies , and the merger fraction predicted in halo-occupation modelling .
The redshift evolution of the pair fraction is described by a power law F ( z ) = ( 0.07 \pm 0.04 ) \times ( 1 + z ) ^ { 0.6 \pm 0.5 } .
The merger rate is consistent with no redshift evolution , however it is difficult to constrain due to the limited sample size and the high uncertainties in the merging timescale .
Based on the merger rate calculation , we estimate that a massive galaxy undergoes on average 1.1 \pm 0.5 major merger from z = 3 to 0 .
The observed merger fraction is sufficient to explain the number density evolution of massive galaxies , but insufficient to explain the size evolution .
This is a hint that mechanism ( s ) other than major merging may be required to increase the sizes of the massive , compact quiescent galaxies from z \sim 2 to 0 .