The benchmark black hole in NGC 4258: dynamical models from high-resolution two-dimensional stellar kinematics

NGC 4258 is the galaxy with the most accurate (maser-based) determination for the mass of the supermassive black hole (SMBH) in its nucleus. In this work we present a two-dimensional mapping of the stellar kinematics in the inner 3.0 x 3.0 arcsec = 100 x 100 pc of NGC 4258 using adaptative-optics observations obtained with the Near-Infrared Integral Field Spectrograph of the GEMINI North telescope at a 0.11 arcsec (4 pc) angular resolution. The observations resolve the radius of influence of the SMBH, revealing an abrupt increase in the stellar velocity dispersion within 10 pc from the nucleus, consistent with the presence of a SMBH there. Assuming that the galaxy nucleus is in a steady state and that the velocity dispersion ellipsoid is aligned with a cylindrical coordinate system, we constructed a Jeans anisotropic dynamical model to fit the observed kinematics distribution. Our dynamical model assumes that the galaxy has axial symmetry and is constructed using the multi-gaussian expansion method to parametrize the observed surface brightness distribution. The Jeans dynamical model has three free parameters: the mass of the central SMBH, the mass-luminosity ratio of the galaxy and the anisotropy of the velocity distribution. We test two types of models: one with constant velocity anisotropy, and another with variable anisotropy. The model that best reproduces the observed kinematics was obtained considering that the galaxy has radially varying anisotropy, being the best-fitting parameters with 3$sigma$ significance $M_bullet=4.8^{+0.8}_{-0.9}times 10^7,{rm M_odot}$ and $Gamma_k = 4.1^{+0.4}_{-0.5}$. This value for the mass of the SMBH is just 25 per cent larger than that of the maser determination and 50 per cent larger that a previous stellar dynamical determination obtained via Schwarzschild models.