A growth-rate indicator for Compton-thick active galactic nuclei
  Due to their heavily obscured central engines, the growth rate of
Compton-thick (CT) active galactic nuclei (AGN) is difficult to measure. A
statistically significant correlation between the Eddington ratio,
{\lambda}$_{Edd}$, and the X-ray power-law index, {\Gamma}, observed in
unobscured AGN offers an estimate of their growth rate from X-ray spectroscopy
(albeit with large scatter). However, since X-rays undergo reprocessing by
Compton scattering and photoelectric absorption when the line-of-sight to the
central engine is heavily obscured, the recovery of the intrinsic {\Gamma} is
challenging. Here we study a sample of local, predominantly Compton-thick
megamaser AGN, where the black hole mass, and thus Eddington luminosity, are
well known. We compile results on X-ray spectral fitting of these sources with
sensitive high-energy (E> 10 keV) NuSTAR data, where X-ray torus models which
take into account the reprocessing effects have been used to recover the
intrinsic {\Gamma} values and X-ray luminosities, L$_X$. With a simple
bolometric correction to L$_X$ to calculate {\lambda}$_{Edd}$, we find a
statistically significant correlation between {\Gamma} and {\lambda}$_{Edd}$ (p
= 0.007). A linear fit to the data yields {\Gamma} =
(0.41$\pm$0.18)log$_{10}${\lambda}$_{Edd}$+(2.38$\pm$ 0.20), which is
statistically consistent with results for unobscured AGN. This result implies
that torus modeling successfully recovers the intrinsic AGN parameters. Since
the megamasers have low-mass black holes (M$_{BH}\approx10^6-10^7$ M$_{sol}$)
and are highly inclined, our results extend the {\Gamma}-{\lambda}$_{Edd}$
relationship to lower masses and argue against strong orientation effects in
the corona, in support of AGN unification. Finally this result supports the use
of {\Gamma} as a growth-rate indicator for accreting black holes, even for
Compton-thick AGN.
