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Obscured star formation at z = 0.84 with HiZELS: the relationship between star formation rate and H-alpha or ultra-violet dust extinction

[Abridged] We compare H-alpha, ultraviolet (UV) and infrared (IR) indicators of star formation rate (SFR) for a sample of z = 0.84 galaxies from the High-z Emission Line Survey (HiZELS). Using multi-wavelength diagnostics, we estimate that 5 - 11 per cent of H-alpha emitters at this redshift are active galactic nuclei. We detect 35 per cent of the H-alpha emitters individually at 24 microns, and stack the star-forming emitters on deep 24-micron images in order to calculate the typical SFRs of our galaxies. These are compared to the observed H-alpha line fluxes in order to estimate the extinction at z = 0.84, and we find a significant increase in dust extinction for galaxies with higher SFRs. We demonstrate that the local relationship between SFR and extinction is suitable for our sample, and attribute the overall increase in dust extinction for z = 0.84 galaxies to an increase in the average SFR, rather than to a change in dust properties. We calculate the UV extinction, and find a similar dependence on SFR, but no evidence for a 2175 angstrom UV bump in the dust attenuation law. We calculate the conversion between the dust attenuation of nebular and stellar radiation, gamma, and show that gamma = 0.50 +/- 0.14. The extinction / SFR relationship is shown to be applicable to galaxies with a range of morphologies and bulge-to-disk ratios, to both merging and non-merging galaxies, and to galaxies within high- and low-density environments, implying that it is a fundamental property of star-forming regions. In order to allow future studies to correct for a SFR-dependent amount of dust extinction, we present an equation to predict the extinction of a galaxy, based solely upon its observed H-alpha luminosity, and use this to recalculate the H-alpha luminosity function and star formation rate density at z = 0.84.