Is the Accretion Flow in NGC 4258 Advection-dominated?

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.