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

Abstract

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 required align- ment of the apoapsides of the stellar orbits could be maintained by self–gravity, and the whole structure might be a discrete, nonlinear eigenmode. The pattern speed of this mode could, in principle, be determined by the Tremaine–Weinberg (TW) method, which requires measurements of the surface brightness, and ra- dial velocity along a strip parallel to the line of nodes. However, spectroscopic observations along the line of nodes are not available. We propose a variant of the TW method, which exploits a basic feature of the eccentric disk model, to extract estimates of the pattern speed from 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◦ , the pattern speed |Ωp| < 30 kms−1 pc−1, or period more than 200, 000 years.