ChronoFlow: A Data-Driven Model for Gyrochronology

Gyrochronology is a technique for constraining stellar ages using rotation periods, which change over a star's main sequence lifetime due to magnetic braking. This technique shows promise for main sequence FGKM stars, where other methods are imprecise. However, models have historically struggled to capture the observed rotational dispersion in stellar populations. To properly understand this complexity, we have assembled the largest standardized data catalog of rotators in open clusters to date, consisting of ~7,400 stars across 30 open clusters/associations spanning ages of 1.5 Myr to 4 Gyr. We have also developed ChronoFlow: a flexible data-driven model which accurately captures observed rotational dispersion. We show that ChronoFlow can be used to accurately forward model rotational evolution, and to infer both cluster and individual stellar ages. We recover cluster ages with a statistical uncertainty of 0.06 dex ($\approx$ 15%), and individual stellar ages with a statistical uncertainty of 0.7 dex. Additionally, we conducted robust systematic tests to analyze the impact of extinction models, cluster membership, and calibration ages on our model's performance. These contribute an additional $\approx$ 0.06 dex of uncertainty in cluster age estimates, resulting in a total error budget of 0.08 dex. We estimate ages for the NGC 6709 open cluster and the Theia 456 stellar stream, and calculate revised rotational ages for M34, NGC 2516, NGC 1750, and NGC 1647. Our results show that ChronoFlow can precisely estimate the ages of coeval stellar populations, and constrain ages for individual stars. Furthermore, its predictions may be used to inform physical spin down models. ChronoFlow will be publicly available at https://github.com/philvanlane/chronoflow.