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, LX. With a simple
bolometric correction to LX 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±0.18)log10{\lambda}Edd+(2.38± 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 (MBH≈106−107 Msol)
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.Comment: Accepted for publication in Ap