The stellar kinematics of galactic disks are key to constraining disk formation and evolution processes. In this paper, for the first time, we measure the stellar age-velocity dispersion correlation in the inner 20 kpc (∼3.5 disk scale lengths) of M31 and show that it is dramatically different from that in the Milky Way (MW). We use optical Hubble Space Telescope/Advanced Camera for Surveys photometry of 5800 individual stars from the Panchromatic Hubble Andromeda Treasury survey and Keck/DEIMOS radial velocity measurements of the same stars from the Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo survey. We show that the average line-of-sight dispersion is a steadily increasing function of age exterior to R = 10 kpc, increasing from for the main-sequence stars to 90 km s-1 for the red giant branch stars. This monotonic increase implies that a continuous or recurring process contributed to the evolution of the disk. Both the slope and normalization of the dispersion versus age relation are significantly larger than in the MW, allowing for the possibility that the disk of M31 has had a more violent history than the disk of the MW, more in line with Λ cold dark matter predictions. We also find evidence for an inhomogeneous distribution of stars from a second kinematical component in addition to the dominant disk component. One of the largest and hottest high-dispersion patches is present in all age bins and may be the signature of the end of the long bar.
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