  The mass of the central black hole in the active galaxy NGC 4258 (M106) has
been measured to be $M=3.6\times10^7\Msun$ (Miyoshi et al. 1995). The Eddington
luminosity corresponding to this mass is $L_E=4.5\times10^{45}$ erg s$^{-1}$.
By contrast the X-ray luminosity of the nucleus of NGC 4258 between $2-10$ keV
is $(4\pm 1)\times10^{40}~{\rm erg\,s^{-1}}$ while the optical/UV luminosity is
less than $1.5\times10^{42} ~{\rm erg\,s^{-1}}$. The luminosity of NGC 4258 is
therefore extremely sub-Eddington, $L\sim10^{-5}L_E$ in X-rays and
$L\sim3\times10^{-4} L_E$ even if we take the maximum optical/UV luminosity.
Assuming the usual accretion efficiency of 0.1 would imply accretion rates
orders of magnitude lower than in Seyfert galaxies and quasars. We show that
the properties of the AGN in NGC 4258 can be explained by an accretion flow in
the form of a very hot, optically-thin plasma which advects most of the
viscously generated thermal energy into the central black hole and radiates
only a small fraction of the energy. In this case the accretion rate in
Eddington units could be as high as $\sim 0.16\alpha$, where $\alpha$ is the
standard viscosity parameter; and the size of the hot disk should be larger
than $\sim 10$ times the Schwarzschild radius. We compare the predictions of
this model with observations and discuss its application to other low
luminosity AGN.
