Host galaxies of long gamma-ray bursts in the Millennium Simulation
  (abridged) In this work, we investigate the nature of the host galaxies of
long Gamma-Ray bursts (LGRBs) using a galaxy catalogue constructed from the
Millennium Simulation. We developed an LGRB synthetic model based on the
hypothesis that these events originate at the end of the life of massive stars
following the collapsar model, with the possibility of including a constraint
on the metallicity of the progenitor star. A complete observability pipeline
was designed to calculate a probability estimation for a galaxy to be
observationally identified as a host for LGRBs detected by present
observational facilities. This new tool allows us to build an observable host
galaxy catalogue which is required to reproduce the current stellar mass
distribution of observed hosts. This observability pipeline predicts that the
minimum mass for the progenitor stars should be ~75 solar masses in order to be
able to reproduce BATSE observations. Systems in our observable catalogue are
able to reproduce the observed properties of host galaxies, namely stellar
masses, colours, luminosity, star formation activity and metallicities as a
function of redshift. At z>2, our model predicts that the observable host
galaxies would be very similar to the global galaxy population. We found that
~88 per cent of the observable host galaxies with mean gas metallicity lower
than 0.6 solar have stellar masses in the range 10^8.5-10^10.3 solar masses in
excellent agreement with observations. Interestingly, in our model observable
host galaxies remain mainly within this mass range regardless of redshift,
since lower stellar mass systems would have a low probability of being observed
while more massive ones would be too metal-rich. Observable host galaxies are
predicted to preferentially inhabit dark matter haloes in the range
10^11-10^11.5 solar masses, with a weak dependence on redshift.
