ChronoFlow: A Data-Driven Model for Gyrochronology

TL;DR

ChronoFlow proposes a data-driven, probabilistic gyrochronology framework that jointly learns the rotational evolution of stars as a function of age and color from an expanded catalog of ~7.6k Gaia DR3 rotators across 30 open clusters. Built on a Bayesian setup and a conditional normalizing flow, ChronoFlow forward-models the distribution P(rot|color,age) while accounting for cluster membership, photometric uncertainty, and contamination. The study delivers cluster ages with ~0.06 dex statistical precision (≈15%) and individual stellar ages with ~0.7 dex precision, with a total systematic-plus-statistical uncertainty near 0.08 dex. ChronoFlow also demonstrates agreement with literature in overlapping regimes, extends age inferences to younger populations, and provides a flexible benchmark for informing spin-down physics and calibrating future gyrochronology models.

Abstract

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, the observed dispersion in rotation rates for similar coeval stars has historically been difficult to characterize. To properly understand this complexity, we have assembled the largest standardized data catalog of rotators in open clusters to date, consisting of $\approx$8,000 stars across 30 open clusters/associations spanning ages of 1.5 Myr to 4 Gyr. We have also developed ChronoFlow: a flexible data-driven model which accurately captures observed rotational dispersion. We show that ChronoFlow can be used to accurately forward model rotational evolution, and to infer both cluster and individual stellar ages. We recover cluster ages with a statistical uncertainty of 0.06 dex ($\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. These contribute an additional 0.06 dex of uncertainty in cluster age estimates, resulting in a total error budget of 0.08 dex. We apply ChronoFlow to estimate ages for M34, NGC 2516, NGC 6709, and the Theia 456 stellar stream. 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 is publicly available at https://github.com/philvanlane/chronoflow.

Figures (35)

• Figure 1: Distribution of the fractional difference ($d_f$) in $P_{rot}$ for stars having two measurements. The value we use as a quality cut (0.2) is illustrated by the dashed grey line. The value of 0.2 was chosen to exclude the tail of stars with very discrepant $P_{rot}$ measurements, while keeping the large majority of these stars.
• Figure 2: De-reddened color-rotation space for all stars in our final catalog, including the young subgroups of Taurus and Sco-Cen. Stars are color-coded according to the age of their cluster. Older stars appear to have generally converged onto slowly rotating sequences more than younger stars.
• Figure 3: Distribution of $(BP-RP)_0$ uncertainties, including propagation of parallax, dustmap, and conversion errors. There is a minimum value of 0.01415 indicated by the red dashed line; this is the DR3 systematic floor corresponding to errors of 0.01 in the BP and RP bands. This plot is truncated at 0.2 mag, but there is a thin tail that extends to 1.24 mag.
• Figure 4: Literature age estimates for our clusters, demonstrating the coverage in our catalog. The values from the four main catalogs are highlighted explicitly as red, green, pink, and orange points, and the average value is shown as a black diamond (with an error bar showing the standard deviation across the four catalogs). Other literature estimates are shown as translucent blue circles (see Figure \ref{['fig: M67_lit_ages']} as an example). We exclude the young subgroups of Taurus and Upper Scorpius/$\rho$ Ophiucus from this plot.
• Figure 5: A zoomed in view of M67 from Figure \ref{['fig: logA_lit_all']}. Age estimates from all sources are shown here in detail, and jittered vertically for ease of visualization.