The mass of the central black hole in the giant elliptical galaxy M84 has previously been measured by two groups using the same observations of emission-line gas with the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope, giving strongly discrepant results: Bower et al. (1998) found M_BH = (1.5^{+1.1}_{-0.6}) x 10^9 M_sun, while Maciejewski & Binney (2001) estimated M_BH = 4 x 10^8 M_sun. In order to resolve this discrepancy, we have performed new measurements of the gas kinematics in M84 from the same archival data, and carried out comprehensive gas-dynamical modeling for the emission-line disk within ~70 pc from the nucleus. In comparison with the two previous studies of M84, our analysis includes a more complete treatment of the propagation of emission-line profiles through the telescope and STIS optics, as well as inclusion of the effects of an intrinsic velocity dispersion in the emission-line disk. We find that an intrinsic velocity dispersion is needed in order to match the observed line widths, and we calculate gas-dynamical models both with and without a correction for asymmetric drift. Including the effect of asymmetric drift improves the model fit to the observed velocity field. Our best-fitting model with asymmetric drift gives M_BH = (8.5^{+0.9}_{-0.8}) x 10^8 M_sun (68% confidence). This is a factor of ~2 smaller than the mass often adopted in studies of the M_BH - sigma and M_BH - L relationships. Our result provides a firmer basis for the inclusion of M84 in the correlations between black hole mass and host galaxy properties.
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