The supermassive black hole coincident with the luminous transient
  ASASSN-15lh
  The progenitors of astronomical transients are linked to a specific stellar
population and galactic environment, and observing their host galaxies hence
constrains the physical nature of the transient itself. Here, we use imaging
from the Hubble Space Telescope, and spatially-resolved, medium resolution
spectroscopy from the Very Large Telescope obtained with X-Shooter and MUSE to
study the host of the very luminous transient ASASSN-15lh. The dominant stellar
population at the transient site is old (around 1 to 2 Gyr), without signs of
recent star-formation. We also detect emission from ionized gas, originating
from three different, time-invariable, narrow components of
collisionally-excited metal and Balmer lines. The ratios of emission lines in
the Baldwin-Phillips-Terlevich diagnostic diagram indicate that the ionization
source is a weak Active Galactic Nucleus with a black hole mass of $M_\bullet =
5_{-3}^{+8}\cdot10^{8} M_\odot$, derived through the $M_\bullet$-$\sigma$
relation. The narrow line components show spatial and velocity offsets on
scales of 1 kpc and 500 km/s, respectively; these offsets are best explained by
gas kinematics in the narrow-line region. The location of the central
component, which we argue is also the position of the supermassive black hole,
aligns with that of the transient within an uncertainty of 170 pc. Using this
positional coincidence as well as other similarities with the hosts of Tidal
Disruption Events, we strengthen the argument that the transient emission
observed as ASASSN-15lh is related to the disruption of a star around a
supermassive black hole, most probably spinning with a Kerr parameter
$a_\bullet\gtrsim0.5$.
