2D stellar population and gas kinematics of the inner kiloparsec of the post-starburst quasar SDSS J0330-0532

We have used optical Integral Field Spectroscopy in order to map the star formation history of the inner kiloparsec of the Post-Starburst Quasar (PSQ) J0330--0532 and to map its gas and stellar kinematics as well as the gas excitation. PSQs are hypothesized to represent a stage in the evolution of galaxies in which the star formation has been recently quenched due to the feedback of the nuclear activity, as suggested by the presence of the post-starburst population at the nucleus. We have found that the old stellar population (age $\ge$ 2.5 Gyr) dominates the flux at 5100 \AA\ in the inner 0.26 kpc, while both the post-starburst (100 Myr $\le$ age $<$ 2.5 Gyr) and starburst (age $<$ 100 Myr) components dominate the flux in a circumnuclear ring at $\approx$0.5 kpc from the nucleus. With our spatially resolved study we do not have found any post-starburst stellar population in the inner 0.26\,kpc. On the other hand, we do see the signature of AGN feedback in this region, which does not reach the circumnuclear ring where the post-starburst population is observed. We thus do not support the quenching scenario for the J0330-0532. In addition, we have concluded that the strong signature of the post-starburst population in larger aperture spectra (e.g. from Sloan Digital Sky Survey) is partially due to the combination of the young and old age components. Based on the M$_{\rm BH}-\sigma_{\rm star}$ relationship and the stellar kinematics we have estimated a mass for the supermassive black hole of 1.48 $\pm$ 0.66 $\times$10$^7$ M$_\odot$.