A method for quantifying the Gamma Ray Burst "bias". Application in the redshift range 0-1.1

Long Gamma Ray Bursts (LGRBs) are related to the final stages of evolution of massive stars. As such, they should follow the star formation rate (SFR) of galaxies. We can use them to probe for star-forming galaxies (SFGs) in the distant universe following this assumption. The relation between the rate of LGRBs in a given galaxy and its SFR (that we call the LGRB "bias") may be complex, as we have indications that the LGRB hosts are not perfect analogues to the general population of SFGs. In this work, we try to quantify the dependence of the LGRB bias on physical parameters of their host galaxy such as the SFR or the stellar mass. We propose an empirical method based on the comparison of stellar mass functions (and SFR distributions) of LGRB hosts and of SFGs in order to find how the bias depends on the stellar mass or the SFR. By applying this method to a sample of LGRB hosts at redshifts lower than 1.1, where the properties of SFGs are well established, and where the properties of LGRB host galaxies can be deduced from observations (for stellar masses larger than 10**9.25 Msun and SFR larger than 1.8 Msun / yr), we find that the LGRB bias depends on both the stellar mass and SFR. We find that the bias decreases with the SFR, i.e. we see no preference for highly SFGs, once taken into account the larger number of massive stars in galaxies with larger SFR. We do not find any trend with the specific star formation rate (SSFR) but the dynamical range in SSFR in our study is narrow. Although through an indirect method, we relate these trends to a possible decrease of the LGRBs rate / SFR ratio with the metallicity. The method we propose suggests trends that may be useful to constrain models of LGRB progenitors, showing a clear decrease of the LGRB bias with the metallicity. This is promising for the future as the number of LGRB hosts studied will increase.