The double nucleus and central black hole of M31

New spectroscopy of M31 supports Tremaine's model in which both nuclei are parts of a single eccentric disk of stars orbiting the black hole (BH). The kinematics and Hubble Space Telescope photometry are used to measure the o ffset of the BH from the center of mass. This confirms that the BH mass is similar to 3 x 10(7) M. by a technique that is nearly independent of stella r-dynamical models. We present spectroscopy of the nucleus of M31 obtained with the Canada-Fran ce-Hawaii Telescope and Subarcsecond Imaging Spectrograph. Spectra at the C a infrared triplet lines (seeing sigma(*) = 0".27) are used to measure the stellar kinematics, and spectra at the Mg I b lines (sigma(*) = 0".31) are to measure metallicities. We also measure nonparametric line-of-sight veloc ity distributions (LOSVDs). All spectra confirm the steep rotation and velo city dispersion gradients that imply that M31 contains a 3.3 x 107 M. centr al dark object. At sigma(*) = 0".27, the maximum bulge-subtracted rotation velocity of the nucleus is 233 +/- 4 km s(-1) on the P2 side, and the maxim um velocity dispersion is 287 +/- 9 km s(-1). The dispersion peak is displa ced by 0".20 +/- 0".03 from the velocity center in the direction opposite t o P1, confirming a result by Bacon and coworkers. The higher surface bright ness nucleus, P1, is colder than the bulge, with sigma similar or equal to 100 km s(-1) at r similar or equal to 1". Cold light from P1 contributes at the velocity center; this explains part of the sigma(r) asymmetry. The nuc leus is cold at r greater than or similar to 1" on both sides of the center . Our results are used to test Tremaine's model in which the double nucleus i s a single eccentric disk of stars orbiting the BH. (1) The model predicts that the velocity center of the nucleus is displaced by 0".2 from P2 toward P1. Our observations show a displacement of 0".08 +/- 0".01 before bulge s ubtraction and 0".10 +/- 0".01 after bulge subtraction. (2) The model predi cts a minimum sigma similar or equal to 135 km s(-1) at Pi. We observe sigm a = 123 +/- 2 km s(-1): Observations (1) and (2) may be reconciled with the model if its parameters are tweaked so that the orbital eccentricity is ma de larger and the orientation of the orbits is made to point more nearly at us. (3) The model rotation curve is asymmetric; at perfect resolution, V i s 60 km s(-1) higher on the P2 side than on the P1 side. At sigma(*) = 0".2 7, we observe an asymmetry of 54 + 4 km (-1) after bulge subtraction. We re gard this as confirmation of the model's essential idea that stellar orbits are eccentric and coherently aligned. (4) The model predicts that P1 and P 2 should have the same stellar population. We confirm this: P1 is more simi lar to P2 than it is to the bulge or to a globular cluster or to M32. This makes it unlikely that P1 consists of accreted stars. (5) Our observation t hat there is cold light on both sides of the center implies, if the nucleus is an eccentric disk, that some stars have escaped from the P1-P2 alignmen t and have phase-mixed around the galaxy's center. The dispersion peak coincides with a cluster of ultraviolet-bright stars se en in Hubble Space Telescope images. We propose that the BH is in this clus ter. Its center is displaced by 0".068 +/- 0".010 from the bulge center. If we put a 3.3 x 10(7) M. dark object in the UV cluster and adopt the dynami cally determined mass-to-light ratio of the stars, then the center of mass (COM) of the bulge, nucleus, and dark object coincides with the bulge cente r to within 0".017 +/- 0".016. The COM also agrees with the velocity center of the bulge and outer nucleus. Therefore, the asymmetry of the stars in t he double nucleus supports our suggestion that the BH is in the UV cluster. If the stars have a normal mass-to-light ratio, then the location of the C OM also confirms the mass of the BH, largely independent of dynamical model s. Tremaine's model implies that any dark cluster alternative to a BH is less than 0".13 +/- 0".03 = 0.49 pc in radius. The observed mass-to-light ratio is M/L-V similar or equal to 300 in a cylinder of radius r = 0".13 and M/L- V 2200 in a sphere of radius r = 0".13. This is much larger than previous m easurements of M/L-V. This result and the COM argument greatly strengthen t he detection of a central dark object in M31.