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Evolution of Star Formation in the UKIDSS Ultra Deep Survey Field - I. Luminosity Functions and Cosmic Star Formation Rate out to z=1.6

We present new results on the cosmic star formation history in the SXDS-UDS field out to z=1.6. We compile narrow-band data from the Subaru Telescope and the Visible and Infrared Survey Telescope for Astronomy (VISTA) in conjunction with broad-band data from the SXDS and UDS, to make a selection of 5725 emission-line galaxies in 12 redshift slices, spanning 10 Gyr of cosmic time. We determine photometric redshifts for the sample using 11-band photometry, and use a spectroscopically confirmed subset to fine tune the resultant redshift distribution. We use the maximum-likelihood technique to determine luminosity functions in each redshift slice and model the selection effects inherent in any narrow-band selection statistically, to obviate the retrospective corrections ordinarily required. The deep narrow-band data are sensitive to very low star formation rates (SFRs), and allow an accurate evaluation of the faint end slope of the Schechter function, alpha. We find that alpha is particularly sensitive to the assumed faintest broadband magnitude of a galaxy capable of hosting an emission line, and propose that this limit should be empirically motivated. For this analysis we base our threshold on the limiting observed equivalent widths of emission lines in the local Universe. We compute the characteristic SFR of galaxies in each redshift slice, and the integrated SFR density, rho_{SFR}. We find our results to be in good agreement with the literature and parametrize the evolution of the SFR density as rho_{SFR} proportional to (1 + z)^{4.58} confirming a steep decline in star formation activity since z = 1.6.