Spurious Radial Migration from Relativistic Effects in the Milky Way Disk

Abstract

Abstract The gradient of the gravitational redshift in the potential of the Milky Way induces an apparent spurious radial migration. I show that this effect is simply related to the local acceleration, which was measured recently by Gaia eDR3, implying a spectroscopic shift of −2.4 × 10−2(r/8 kpc)−1 km s−1 kpc−1. The transverse Doppler effect yields a comparable contribution. The spurious radial velocity from both relativistic effects amounts to crossing a major portion of the Milky Way disk during the age of the universe, and must be corrected for in any future measurement of the actual radial migration of stars.