Measuring supermassive black holes with gas kinematics: the active S0 galaxy NGC 3998

Context. We present results from a kinematical study of the gas in the nucleus of the active S0 galaxy NGC 3998 obtained from archival HST/STIS long-slit spectra. Aims. We analyzed the emission lines profiles and derived the map of the gas velocity field. The observed velocity curves are consistent with gas in regular rotation around the galaxy's center. Methods. By modeling the surface brightness distribution and rotation curve of the Ha emission line we found that the observed kinematics of the circumnuclear gas can be accurately reproduced by adding to the stellar mass component a compact dark mass (black hole) of M-BH = 2.7(+2.4)(-2.0) x 10(8) M-circle dot (uncertainties at a 2 sigma level); the radius of its sphere of influence (R-sph similar to 0.16) is well resolved at the HST resolution. Results. The BH mass estimate in NGC 3998 is in good agreement with both the M-BH - M-bul (with an upward scatter by a factor of similar to 2) and M-BH - sigma correlations (with a downward scatter by a factor of similar to 3-7, depending on the form adopted for the dependence of M-BH on sigma). Conclusions. Although NGC 3998 cannot be considered as an outlier, its location with respect to the M-BH - sigma relation conforms with the trend suggesting the presence of a connection between the residuals from the M-BH - sigma correlation and the bulge effective radius. In fact, NGC 3998 has one of the smallest values of R-e among the galaxies with measured M-BH (0.85 kpc) and it shows a negative residual. This suggests that a combination of both s and Re is necessary to drive the correlations between MBH and other bulge properties, an indication for the presence of a black holes "fundamental plane".