New results from a large survey of H-alpha emission-line galaxies at z=0.84 using WFCAM/UKIRT and a custom narrow-band filter in the J band are presented as part of the HiZELS survey. Reaching an effective flux limit of 1e-16 erg/s/cm^2 in a comoving volume of 1.8e5 Mpc^3, this represents the largest and deepest survey of its kind ever done at z~1. There are 1517 potential line emitters detected across 1.4 sq.deg of the COSMOS and UKIDSS UDS fields, of which 743 are selected as H-alpha emitters. These are used to calculate the H-alpha luminosity function, which is well-fitted by a Schechter function with phi*=10^(-1.92+-0.10) Mpc^-3, L*=10^(42.26+-0.05)erg/s, and alpha=-1.65+-0.15. The integrated star formation rate density (SFRD) at z=0.845 is 0.15+-0.01 M_sun/yr/Mpc^3. The results robustly confirm a strong evolution of SFRD from the present day out to z~1 and then flattening to z~2, using a single star-formation indicator. Out to z~1, both the characteristic luminosity and space density of the H-alpha emitters increase significantly; at higher redshifts, L* continues to increase, but phi* decreases. The z=0.84 H-alpha emitters are mostly disk galaxies (82+-3%), while 28+-4% of the sample show signs of merger activity and contribute ~20% to the total SFRD. Irregulars and mergers dominate the H-alpha luminosity function above L*, while disks are dominant at fainter luminosities. These results demonstrate that it is the evolution of normal disk galaxies that drives the strong increase in the SFRD from the current epoch to z~1, although the continued strong evolution of L* beyond z=1 suggests an increasing importance of merger activity at higher redshifts.
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