Spurious Radial Migration from Relativistic Effects in the Milky-Way Disk

TL;DR

Relativistic effects like gravitational redshift and transverse Doppler shift cause apparent radial migration in the Milky-Way disk, which must be corrected in future stellar motion studies.

Contribution

This paper identifies and quantifies the impact of relativistic effects on observed stellar radial velocities in the Milky-Way disk.

Findings

Relativistic effects induce a spectroscopic shift of about -0.024 km/s/kpc at the solar radius.

These effects can cause apparent stellar migration comparable to the galaxy's size over cosmic timescales.

Correction for these effects is essential for accurate measurements of true stellar radial migration.

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 $[-2.4x10^{-2}/(r/8kpc)] km/s/kpc. 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.