An Analytic Model for Stellar Metallicity Gradient Residuals in Cold, Phase-Mixed Galactic Disks
Abstract
The distribution of stellar metallicities over phase space in galactic disks is sculpted by both star formation and secular orbital transport processes. As a result, chemo-dynamical models that infer radial heating and migration histories from observations typically rely on sophisticated numerical modeling of stellar distribution functions, star formation histories, and various dynamical perturbations. Here, we develop a complementary minimal analytic model for constraining radial migration, using stellar metallicity residuals relative to overarching galactic metallicity gradients. Incorporating residuals imprinted during formation and produced dynamically, and assuming a cold, phase-mixed stellar disk, we derive a closed-form expression for the resulting residual distribution. Applying our model to observed [Fe/H] residuals for stars in the Galactic thin disk, we find the root-mean-square amplitude of radial migration for stars of age τ to be ⟨ (δRg)2 ⟩1/2 ≈ (2.79 ± 0.07) kpc × [τ/(6 Gyr)]1/2, consistent with results derived from more complex numerical frameworks. Our results clarify the physical origins of covariances and degeneracies common across chemo-dynamical transport models, and demonstrate that metallicity residuals provide a flexible, interpretable probe of radial migration in galactic disks.
Related
- Age dependence of the radial metallicity gradient in the Galactic disc with LAMOST and Gaia
- Power spectrum of longitudinal-velocity residuals in the Galactic disk from Gaia DR3 red-giant-branch stars
- Cepheid Metallicity in the Leavitt Law (C-MetaLL) survey: X First spectroscopic characterization of Galactic Type II Cepheids and calibration of the Period-Wesenheit-Metallicity relations
- Constraints on the Metallicity-dependent Explodability of Massive Stars from Galactic Chemical Evolution: Toward Alleviating the Red Supergiant Problem
- Enabling Metallicity Measurements of M-dwarf Microlensing Lenses out to the Galactic Bulge
BibTeX
@misc{modak2026analytic,
title = {{An Analytic Model for Stellar Metallicity Gradient Residuals in Cold, Phase-Mixed Galactic Disks}},
author = {Shaunak Modak and Zoe Hackshaw and Keith Hawkins},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.14850},
eprint = {2606.14850},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.14850},
}
RIS
TY - UNPB
TI - An Analytic Model for Stellar Metallicity Gradient Residuals in Cold, Phase-Mixed Galactic Disks
AU - Shaunak Modak
AU - Zoe Hackshaw
AU - Keith Hawkins
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2606.14850
UR - https://arxiv.org/abs/2606.14850
AB - The distribution of stellar metallicities over phase space in galactic disks is sculpted by both star formation and secular orbital transport processes. As a result, chemo-dynamical models that infer radial heating and migration histories from observations typically rely on sophisticated numerical modeling of stellar distribution functions, star formation histories, and various dynamical perturbations. Here, we develop a complementary minimal analytic model for constraining radial migration, using stellar metallicity residuals relative to overarching galactic metallicity gradients. Incorporating residuals imprinted during formation and produced dynamically, and assuming a cold, phase-mixed stellar disk, we derive a closed-form expression for the resulting residual distribution. Applying our model to observed [Fe/H] residuals for stars in the Galactic thin disk, we find the root-mean-square amplitude of radial migration for stars of age τ to be ⟨ (δR_g)^2 ⟩^1/2 ≈ (2.79 ± 0.07) kpc × [τ/(6 Gyr)]^1/2, consistent with results derived from more complex numerical frameworks. Our results clarify the physical origins of covariances and degeneracies common across chemo-dynamical transport models, and demonstrate that metallicity residuals provide a flexible, interpretable probe of radial migration in galactic disks.
ER -