On the mass-metallicity relation, velocity dispersion and gravitational
  well depth of GRB host galaxies
  We analyze a sample of 16 absorption systems intrinsic to long duration GRB
host galaxies at $z \gtrsim 2$ for which the metallicities are known. We
compare the relation between the metallicity and cold gas velocity width for
this sample to that of the QSO-DLAs, and find complete agreement. We then
compare the redshift evolution of the mass-metallicity relation of our sample
to that of QSO-DLAs and find that also GRB hosts favour a late onset of this
evolution, around a redshift of $\approx 2.6$. We compute predicted stellar
masses for the GRB host galaxies using the prescription determined from QSO-DLA
samples and compare the measured stellar masses for the four hosts where
stellar masses have been determined from SED fits. We find excellent agreement
and conclude that, on basis of all available data and tests, long duration
GRB-DLA hosts and intervening QSO-DLAs are consistent with being drawn from the
same underlying population. GRB host galaxies and QSO-DLAs are found to have
different impact parameter distributions and we briefly discuss how this may
affect statistical samples. The impact parameter distribution has two effects.
First any metallicity gradient will shift the measured metallicity away from
the metallicity in the centre of the galaxy, second the path of the sightline
through different parts of the potential well of the dark matter halo will
cause different velocity fields to be sampled. We report evidence suggesting
that this second effect may have been detected.
