The knowledge of the history of star formation at cosmic scales is fundamental to the understanding of the formation and evolution of galaxies. Madau and collaborators combined the results from the ultraviolet surveys of Lilly et al. (1996) with the information from the Hubble Deep Field to give an estimate of the star formation history from z = 0 to z = 4. Subsequent studies have indicated the crucial role played by dust in the estimates of SFR. Large correction factors were suggested for z > 1-2 by several authors (Meurer et al. 1997, Meurer, Heckman and Calzetti 1999, Steidel et al. 1999, Dickinson 1998). But even these large dust extinction corrections do not seem to be enough to bring the optical/UV SFR estimates in line with the mm/sub-mm ones (Hughes et al. 1998; Rowan-Robinson et al. 1997 (RR97); Chapman et al. 2001).
On top of the uncertainties associated with the extinction correction, most of the SFR estimates have been performed using expressions derived from spectra constructed using population synthesis methods, an approach that requires four rather uncertain ingredients: 1) an initial mass function (IMF); 2) a stellar evolutionary model grid giving the luminosity and effective temperature as a function of time; 3) a stellar atmospheres grid that assigns a spectrum to each star for a given luminosity and effective temperature, and 4) a star formation history. The fact that the redshift evolution of the SFR is constructed using different estimators at different redshift ranges is a potential source of systematic effects with redshift that can distort the shape of the evolutionary curve. In practice the H luminosity is used to estimate the SFR for galaxies with redshifts up to 0.4; the [OII] 3727Å line , for those with 0.4 > z > 1.0 and the UV continuum luminosity for galaxies with z > 2.0. In addition, dust extinction corrections are not treated uniformly over the whole redshift range.
It is therefore important to ensure that there are no systematic differences between the different estimators and corrections that can distort the results.
This paper has two main aspects, in the first 5 sections we review the "standard" methods for the estimation of the SFR and test the consistency of the different SFR estimators by applying them to a sample of well studied nearby star forming galaxies and comparing the results. In the absence of systematic differences among them, all should give the same SFR for each one of the galaxies in the sample. We then use the results of the nearby sample to construct a set of "unbiased" SFR estimators and apply them to published surveys.