| Abstract
| - Aims. Long gamma-ray bursts (LGRBs) are associated with massive stars and are therefore linked to star formation. However, the conditions needed for the progenitor stars to produce LGRBs can affect the relation between the LGRB rate and star formation. By using the power of a complete LGRB sample, our long-term aim is to understand whether such a bias exists and, if it does, what its origin is. Methods. To reach our goal we use the Swift/BAT6 complete sample of LGRBs. In this first paper, we build the spectral energy distribution (SED) of the 14 z< 1 host galaxies of the BAT6 LGRB sample and determine their stellar masses ( M⋆) from SED fitting. To investigate the presence of a bias in the LGRB-star formation relation we compare the stellar mass distribution of the LGRB host galaxies (i) with star-forming galaxies observed in deep surveys (UltraVISTA) within the same redshift limit; (ii) with semi-analytical models of the z< 1 star-forming galaxy population; and (iii) with dedicated numerical simulations of LGRB hosts having different metallicity thresholds for the progenitor star environment. Results. We find that at z< 1 , LGRBs tend to avoid massive galaxies and are very powerful for selecting a population of faint low-mass star-forming galaxies, partly below the completeness limits of galaxy surveys. The stellar mass distribution of the hosts is not consistent with that of the UltraVISTA star-forming galaxies weighted by their star formation rate (SFR). This implies that, at least at z< 1 , LGRBs are not unbiased tracers of star formation. To make the two distributions consistent, a much steeper faint end of the mass function would be required or a very shallow SFR-mass relation for the low-mass galaxy population. The comparison with the GRB host galaxy simulations indicates that, to reproduce the stellar mass distribution, a metallicity threshold of the order of Zth = 0.3−0.5 Z⊙ is necessary to form a LGRB. Models without a metallicity threshold or with an extreme threshold of Zth = 0.1 Z⊙ are excluded at z< 1 . Under a very basic assumption, we estimate that the LGRB rate can directly trace the SFR starting from z ~ 4 and above. Conclusions. GRB hosts at z< 1 have lower luminosities and stellar masses than expected if LGRBs were unbiased star formation tracers. The use of the Swift/BAT6 complete sample keeps this result from being affected by possible biases that could have influenced past results based on incomplete samples. The preference for low metallicities ( Z ≲ 0.5 Z⊙) inferred by the comparison with the simulations can be a consequence of the particular conditions needed for the progenitor star to produce a GRB.
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