The sizes, masses and specific star formation rates of massive galaxies at 1.3 < z < 1.5: strong evidence in favour of evolution via minor mergers

We report the results of a comprehensive study of the relationship between galaxy size, stellar mass and specific star formation rate (sSFR) at redshifts 1.3 < z < 1.5. Based on a mass-complete (M-* >= 6 x 10(10) M-circle dot), spectroscopic sample from the UK Infrared Deep Sky Survey (UKIDSS) Ultradeep Survey, with accurate stellar-mass measurements derived from spectrophotometric fitting, we find that at z similar or equal to 1.4 the location of massive galaxies on the size-mass plane is determined primarily by their sSFR. At this epoch, we find that massive galaxies which are passive (sSFR <= 0.1 Gyr(-1)) follow a tight size-mass relation, with half-light radii a factor of f(g) = 2.4 +/- 0.2 smaller than their local counterparts. Moreover, amongst the passive sub-sample we find no evidence that the off-set from the local size-mass relation is a function of stellar population age. In contrast, we find that massive star-forming galaxies at this epoch lie closer to the local late-type size-mass relation and are only a factor of f(g) = 1.6 +/- 0.2 smaller than observed locally. Based on a sub-sample with dynamical-mass estimates, which consists of both passive and star-forming objects, we also derive an independent estimate of f(g) = 2.3 +/- 0.3 for the typical growth in half-light radius between z similar or equal to 1.4 and the present day. Focusing on the passive sub-sample, we conclude that to produce the necessary evolution predominantly via major mergers would require an unfeasible number of merger events and overpopulate the high-mass end of the local stellar-mass function. In contrast, we find that a scenario in which mass accretion is dominated by minor mergers can comfortably produce the necessary evolution, whereby an increase in stellar mass of only a factor of similar or equal to 2, accompanied by size growth of a factor of similar or equal to 3.5, is required to reconcile the size-mass relation at z similar or equal to 1.4 with that observed locally. Finally, we note that a significant fraction (44 +/- 12 per cent) of the passive galaxies in our sample have a disc-like morphology, providing additional evidence that separate physical processes are responsible for the quenching of star formation and morphological transformation in massive galaxies.