Inside the Stagnation Radius of the Nearest Billion-Solar-Mass Black Hole

We used the NSF Jansky Very Large Array at a frequency $\nu =$ 22\,GHz to study the nearest billion-solar-mass black hole, in the early-type galaxy NGC\,3115 at a distance of 9.7\,Mpc. We localize a faint continuum nucleus, with flux density $S_{\rm 22\,GHz} = 48.2\pm6.4\,\mu$Jy, to a FWHM diameter $d_{\rm 22\,GHz} <$ 59\,mas (2.8\,pc). We find no evidence for adjacent emission within a stagnation region of radius $R_{\rm sta} \sim$ 360\,mas (17\,pc) identified in a recent hydrodynamic simulation tailored to NGC\,3115. Within that region, the simulated gas flow developed into an advection-dominated accretion flow (ADAF). The nucleus' luminosity density $L_{\rm 22\,GHz} = 5.4 \times 10^{17}\,\rm W\,Hz^{-1}$ is about 60 times that of Sagittarius\,A$^\star$. The nucleus' spectral index $\alpha_{\rm 10\,GHz}^{\rm 22\,GHz} = -1.85\pm0.18$ ($S_\nu \propto \nu^\alpha$) indicates optically-thin synchrotron emission. The spectral energy distribution of the nucleus peaks near $\nu_{\rm peak} =$ 9\,GHz. Modeling this radio peak as an ADAF implies a black hole mass $M_{\rm ADAF} = (1.2\pm0.2) \times 10^9\,M_\odot$, consistent with previous estimates of $(1-2) \times 10^9\,M_\odot$ from stellar or hot-gas dynamics. Also, the Eddington-scaled accretion rate for NGC\,3115, $\dot{M}_{\rm ADAF}/\dot{M}_{\rm Edd} = 1.2^{+1.0}_{-0.6} \times 10^{-8}$, is about 4-8 times lower than recent estimates for Sagittarius\,A$^\star$.