An evolutionary missing link? A modest-mass early-type galaxy hosting an
  over-sized nuclear black hole
  SAGE1C\,J053634.78$-$722658.5 is a galaxy at redshift $z=0.14$, discovered
behind the Large Magellanic Cloud in the {\it Spitzer} Space Telescope
"Surveying the Agents of Galaxy Evolution" Spectroscopy survey (SAGE-Spec). It
has very strong silicate emission at 10 $\mu$m but negligible far-IR and UV
emission. This makes it a candidate for a bare AGN source in the IR, perhaps
seen pole-on, without significant IR emission from the host galaxy. In this
paper we present optical spectra taken with the Southern African Large
Telescope (SALT) to investigate the nature of the underlying host galaxy and
its AGN. We find broad H$\alpha$ emission characteristic of an AGN, plus
absorption lines associated with a mature stellar population ($>9$ Gyr), and
refine its redshift determination to $z=0.1428\pm0.0001$. There is no evidence
for any emission lines associated with star formation. This remarkable object
exemplifies the need for separating the emission from any AGN from that of the
host galaxy when employing infrared diagnostic diagrams. We estimate the black
hole mass, $M_{\rm BH}=3.5\pm0.8\times10^8$ M$_\odot$, host galaxy mass,
$M_{\rm stars}=2.5^{2.5}_{1.2}\times10^{10}$ M$_\odot$, and accretion
luminosity, $L_{\rm bol}({\rm AGN})=5.3\pm0.4\times10^{45}$ erg s$^{-1}$
($\approx12$ per cent of the Eddington luminosity) and find the AGN to be more
prominent than expected for a host galaxy of this modest size. The old age is
in tension with the downsizing paradigm in which this galaxy would recently
have transformed from a star-forming disc galaxy into an early-type, passively
evolving galaxy.
