Stellar velocity dispersion and black hole mass in the blazar Markarian 501

The recently discovered correlation between black hole mass and stellar velocity dispersion provides a new method to determine the masses of black holes in active galaxies. We have obtained optical spectra of Mrk 501, a nearby gamma-ray blazar with emission extending to TeV energies. The stellar velocity dispersion of the host galaxy, measured from the calcium triplet lines in a 2" x 3."7 aperture, is 372 +/- 18 km s(-1). If Mrk 501 follows the M-BH-sigma(double dagger) correlation defined for local galaxies, then its central black hole has a mass of (0.9-3.4) x 10(9) M.. This is significantly larger than some previous estimates for the central mass in Mrk 501 that were based on models for its nonthermal emission. The host galaxy luminosity implies a black hole of similar to6 x 10(8) M., but this is not in severe conflict with the mass derived from sigma(*) because the M-BH-L-bulge correlation has a large intrinsic scatter. Using the emission-line luminosity to estimate the bolometric luminosity of the central engine, we find that Mrk 501 radiates at an extremely sub-Eddington level of L/L-Edd approximate to 10(-4). Further applications of the M-BH-sigma(*) relation to radio-loud active galactic nuclei may be useful for interpreting unified models and understanding the relationship between radio galaxies and BL Lac objects.