2. MEASURING AGN MASSES: DIRECT METHODS

Very general arguments suggest that quasar engines have masses M_BH ~ 10⁶ to 10⁹ M. Gravitational collapse is believed to liberate energy with an efficiency of 0.1; Lynden-Bell's arguments then imply that typical remnant masses are M_BH ~ 10⁸ M. Better estimates can be derived by asking what we need in order to power quasar luminosities, which range from 10⁴⁴ to 10⁴⁷ erg s^-1 or 10¹¹ to 10¹⁴ L. For = 0.1, the engine must consume 0.02 to 20 M yr^-1. How much waste mass accumulates depends on how long quasars live. This is poorly known. If they live long enough to make radio jets that are collimated over several Mpc, and if their lifetimes are conservatively estimated as the light travel time along the jets, then quasars last 10⁷ yr and reach masses M_BH 10⁵ to 10⁸ M. But the most rigorous lower limit on M_BH follows from the condition that the outward force of radiation pressure on accreting matter not overwhelm the inward gravitational attraction of the engine, a condition which, admittedly, strictly holds only if the accreting material and the radiation have spherical symmetry. This so-called Eddington limit requires that L L_E (4 G c m_p / _T) M_BH = 1.3 x 10³⁸ (M_BH / M) erg s^-1, or equivalently that M_BH 8 x 10⁵ (L / 10⁴⁴ erg s^-1) M. Here G is the gravitational constant, m_p is the mass of the proton, and _T is the Thompson cross section for electron scattering. We conclude that we are looking for BHs with masses M_BH ~ 10⁶ to 10⁹ M. Finding them has become one of the ``Holy Grails'' of astronomy because of the importance of confirming or disproving the AGN paradigm.

AGNs provide the impetus to look for BHs, but active galaxies are the most challenging hunting ground. Stellar dynamical searches first found central dark objects in inactive galaxies (see the next article), but they cannot be applied in very active galaxies, because the nonthermal nucleus outshines the star light. We can estimate masses using the kinematics of gas, but only if it is unperturbed by nongravitational forces. Fortunately, this complication can be ruled out a posteriori if we observe that the gas is in Keplerian rotation around the center, i.e., if its rotation velocity as a function of radius is V(r) r^-1/2. We can also stack the cards in our favor by targeting galaxies that are only weakly active and that appear to show gas disks in images taken through narrow bandpasses centered on prominent emission lines.