The pattern speed of the nuclear disk of M31 using a variant of the Tremaine-Weinberg method

The twin peaks in the nucleus of M31 have been interpreted by Tremaine as a thick, eccentric disk of stars orbiting a massive dark object; the require d alignment of the apoapsides of the stellar orbits could be maintained by self-gravity, and the whole structure might be a discrete, nonlinear eigenm ode. The pattern speed of this mode could, in principle, be determined by t he Tremaine-Weinberg (TW) method, which requires measurements of the surfac e brightness and radial velocity along a strip parallel to the line of node s. However, spectroscopic observations along the line of nodes are not avai lable. We propose a variant of the TW method, which exploits a basic featur e of the eccentric disk model, to extract estimates of the pattern speed fr om Hubble Space Telescope spectroscopic data, taken along the line joining the two peaks. Within limitations imposed by the data, we estimate that the pattern rotates in a prograde manner and, for an assumed disk inclination of 77 degrees, the pattern speed \Omega(p)\ < 30 km s(-1) pc(-1), or the pe riod is more than 200,000 yr.