How Good a Clock is Rotation? The Stellar Rotation-Mass-Age Relationship for Old Field Stars

TL;DR

This paper models stellar rotation evolution to evaluate the accuracy of rotation-based age estimates for old stars, highlighting key uncertainties and comparing this method's potential with other age-dating techniques.

Contribution

It introduces a new rotation-mass-age model based on open cluster data and quantifies fundamental uncertainties affecting rotation-based stellar age estimates.

Findings

Latitudinal differential rotation limits age precision to ~2 Gyr.

Initial rotation rate variability causes significant age ambiguity, especially in young and low-mass stars.

Current data permit systematic errors of about 30% in rotation-based ages.

Abstract

The rotation-mass-age relationship offers a promising avenue for measuring the ages of field stars, assuming the attendant uncertainties to this technique can be well characterized. We model stellar angular momentum evolution starting with a rotation distribution from open cluster M37. Our predicted rotation-mass-age relationship shows significant zero-point offsets compared to an alternative angular momentum loss law and published gyrochronology relations. Systematic errors at the 30 percent level are permitted by current data, highlighting the need for empirical guidance. We identify two fundamental sources of uncertainty that limit the precision of rotation-based ages and quantify their impact. Stars are born with a range of rotation rates, which leads to an age range at fixed rotation period. We find that the inherent ambiguity from the initial conditions is important for all young stars, and remains large for old stars below 0.6 solar masses. Latitudinal surface differential rotation also introduces a minimum uncertainty into rotation period measurements and, by extension, rotation-based ages. Both models and the data from binary star systems 61 Cyg and alpha Cen demonstrate that latitudinal differential rotation is the limiting factor for rotation-based age precision among old field stars, inducing uncertainties at the ~2 Gyr level. We also examine the relationship between variability amplitude, rotation period, and age. Existing ground-based surveys can detect field populations with ages as old as 1-2 Gyr, while space missions can detect stars as old as the Galactic disk. In comparison with other techniques for measuring the ages of lower main sequence stars, including geometric parallax and asteroseismology, rotation-based ages have the potential to be the most precise chronometer for 0.6-1.0 solar mass stars.