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.
