Are the host galaxies of long gamma-ray bursts more compact than star-forming galaxies of the field?

Context. Long gamma-ray bursts (GRBs) offer a promising tool for tracing the cosmic history of star formation, especially at high redshift, where conventional methods are known to suffer from intrinsic biases. Previous studies of GRB host galaxies at low redshift showed that high surface density of stellar mass and high surface density of star formation rate (SFR) can potentially enhance the GRB production. Evaluating the effect of such stellar densities at high redshift is therefore crucial to fully control the ability of long GRBs for probing the activity of star formation in the distant Universe. Aims. We assess how the size, stellar mass, and star formation rate surface densities of distant galaxies affect the probability of their hosting a long GRB, using a sample of GRB hosts at z>1 and a control sample of star-forming sources from the field. Methods. We gathered a sample of 45 GRB host galaxies at 1 2, however, GRB hosts appear to have sizes and stellar mass surface densities more consistent with those characterizing the field galaxies. This may reveal an evolution with redshift of the bias between GRB hosts and the overall population of star-forming sources, although we cannot exclude that our result at z > 2 is also affected by the prevalence of dark GRBs in our selection. Conclusions. In addition to a possible trend toward a low-metallicity environment, other environmental properties such as stellar density appear to play a role in the formation of long GRBs, at least up to z similar to 2. This might suggest that GRBs require special environments to enhance their production.