The host galaxies of luminous type 2 AGN at $z \sim$0.3-0.4
  We study the morphological and structural properties of the host galaxies
associated with 57 optically-selected luminous type 2 AGN at $z\sim$0.3-0.4: 16
high-luminosity Seyfert 2 (HLSy2, 8.0$\le$log($L_{\rm [OIII]}/L_{\odot})<$8.3)
and 41 obscured quasars (QSO2, log($L_{\rm [OIII]}/L_{\odot})\ge$8.3). With
this work, the total number of QSO2 at $z<1$ with parametrized galaxies
increases from $\sim$35 to 76. Our analysis is based on HST WFPC2 and ACS
images that we fit with {\sc GALFIT}. HLSy2 and QSO2 show a wide diversity of
galaxy hosts. The main difference lies in the higher incidence of
highly-disturbed systems among QSO2. This is consistent with a scenario in
which galaxy interactions are the dominant mechanism triggering nuclear
activity at the highest AGN power. There is a strong dependence of galaxy
properties with AGN power (assuming $L_ {\rm [OIII]}$ is an adequate proxy).
The relative contribution of the spheroidal component to the total galaxy light
(B/T) increases with $L_ {\rm [OIII]}$. While systems dominated by the
spheoridal component spread across the total range of $L_ {\rm [OIII]}$, most
disk-dominated galaxies concentrate at log($L_{\rm [OIII]}/L_{\odot})<$8.6.
This is expected if more powerful AGN are powered by more massive black holes
which are hosted by more massive bulges or spheroids. The average galaxy sizes
($\langle r_{\rm e} \rangle$) are 5.0$\pm$1.5 kpc for HLSy2 and 3.9$\pm$0.6 kpc
for HLSy2 and QSO2 respectively. These are significantly smaller than those
found for QSO1 and narrow line radio galaxies at similar $z$. We put the
results of our work in context of related studies of AGN with quasar-like
luminosities.
