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 offset 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 stellar-dynamical models. We present spectroscopy of the nucleus of M31 obtained with the Canada-France-Hawaii Telescope and Subarcsecond Imaging Spectrograph. Spectra at the Ca 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 velocity distributions (LOSVDs). All spectra confirm the steep rotation and velocity dispersion gradients that imply that M31 contains a 3.3 x 107 M. central 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 maximum velocity dispersion is 287 +/- 9 km s(-1). The dispersion peak is displaced by 0".20 +/- 0".03 from the velocity center in the direction opposite to P1, confirming a result by Bacon and coworkers. The higher surface brightness 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 nucleus 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 is 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 subtraction and 0".10 +/- 0".01 after bulge subtraction. (2) The model predicts a minimum sigma similar or equal to 135 km s(-1) at Pi. We observe sigma = 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 made 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 is 60 km s(-1) higher on the P2 side than on the P1 side. At sigma(*) = 0".27, we observe an asymmetry of 54 + 4 km (-1) after bulge subtraction. We regard this as confirmation of the model's essential idea that stellar orbits are eccentric and coherently aligned. (4) The model predicts that P1 and P2 should have the same stellar population. We confirm this: P1 is more similar 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 that 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 alignment and have phase-mixed around the galaxy's center. The dispersion peak coincides with a cluster of ultraviolet-bright stars seen in Hubble Space Telescope images. We propose that the BH is in this cluster. 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 dynamically 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 center 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 the 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 COM also confirms the mass of the BH, largely independent of dynamical models. 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 measurements of M/L-V. This result and the COM argument greatly strengthen the detection of a central dark object in M31.