Stellar kinematics of the double nucleus of M31

We report observations of the double nucleus of M31 with the f/48 long-slit spectrograph of the Hubble Space Telescope Faint Object Camera. We obtain a total exposure of 19,000 s over seven orbits, with the 0".063-wide slit a long the line between the two brightness peaks (P.A. 42 degrees). Careful c orrection of the raw data for detector backgrounds and geometric distortion is essential. A spectrum of Jupiter obtained with the same instrument is u sed as a spectral template to extract rotation and velocity dispersion prof iles by cross-correlation. The rotation curve is resolved and reaches a max imum amplitude of similar to 250 km s(-1) roughly 0".3 to either side of a rotation center lying between peaks P1 and P2, 0".16 +/- 0".05 from the opt ically fainter P2. We find the velocity dispersion to be less than or simil ar to 250 km s(-1) everywhere except for a narrow "dispersion spike" center ed 0".06 +/- 0".03 on the anti-P1 side of P2, in which sigma peaks at 440 /- 70 km s(-1) At much lower confidence, we see local disturbances to the r otation curve at P1 and P2 and an elevation in sigma at P1. At very low sig nificance we detect a weak asymmetry in the line-of-sight velocity distribu tion opposite to the sense usually encountered. Convolving our V and sigma profiles to Canada-France-Hawaii Telescope resolution, we find good agreeme nt with the forthcoming results of Kormendy & Bender, although there is a 2 0% discrepancy in the dispersion that cannot be attributed to the dispersio n spike. Our results are not consistent with the location of the maximum di spersion found by Bacon et al. in 1994. Comparing with published models, we find that the more recent sinking star cluster model of Emsellem & Combes does not reproduce either the rotation curve or the dispersion profile. The eccentric-disk model proposed by Tremaine fares better and can be improved somewhat by adjusting the original parameters. However, detailed modeling will require dynamical models of significantly greater realism.