An empirical calibration of star formation rate estimators

Abstract

The observational determination of the behaviour of the star formation rate (SFR) with look-back time or redshift has two main weaknesses: (i) the large uncertainty of the dust/extinction corrections, and (ii) that systematic errors may be introduced by the fact that the SFR is estimated using different methods at different redshifts. Most frequently, the luminosity of the H<it>α</it> emission line, that of the forbidden line [O <inf>ii</inf>] <it>λ</it>3727 and that of the far-ultraviolet continuum are used with low-, intermediate- and high-redshift galaxies, respectively. To assess the possible systematic differences among the different SFR estimators and the role of dust, we have compared SFR estimates using H<it>α</it>, [O <inf>ii</inf>] <it>λ</it>3727 Å, ultraviolet (UV) and far-infrared (FIR) luminosities [<it>SFR</it>(H<it>α</it>), <it>SFR</it>(O <inf>ii</inf>), <it>SFR</it>(UV) and <it>SFR</it>(FIR), respectively] of a sample comprising the 31 nearby star-forming galaxies that have high-quality photometric data in the UV, optical and FIR. We review the different ‘standard’ methods for the estimation of the SFR and find that while the standard method provides good agreement between <it>SFR</it>(H<it>α</it>) and <it>SFR</it>(FIR), both <it>SFR</it>(O <inf>ii</inf>) and <it>SFR</it>(UV) are systematically higher than <it>SFR</it>(FIR), irrespective of the extinction law. We show that the excess in the <it>SFR</it>(O <inf>ii</inf>) and <it>SFR</it>(UV) is mainly due to an overestimation of the extinction resulting from the effect of underlying stellar Balmer absorptions in the measured emission line fluxes. Taking this effect into consideration in the determination of the extinction brings the <it>SFR</it>(O <inf>ii</inf>) and <it>SFR</it>(UV) in line with the <it>SFR</it>(FIR), and simultaneously reduces the internal scatter of the SFR estimations. Based on these results, we have derived ‘unbiased’ SFR expressions for the <it>SFR</it>(UV), <it>SFR</it>(O <inf>ii</inf>) and <it>SFR</it>(H<it>α</it>). We have used these estimators to recompute the SFR history of the Universe using the results of published surveys. The main results are that the use of the unbiased SFR estimators brings into agreement the results of all surveys. Particularly important is the agreement achieved for the SFR derived from the FIR/millimetre and optical/UV surveys. The ‘unbiased’ star formation history of the Universe shows a steep rise in the SFR from <it>z</it>=0 to <it>z</it>=1 with <it>SFR</it>∝(1+<it>z</it>)4.5, followed by a decline for <it>z</it>>2 where <it>SFR</it>∝(1+<it>z</it>)-1.5. Galaxy formation models tend to have a much flatter slope from <it>z</it>=0 to <it>z</it>=1.