Using Magnetic Activity and Galactic Dynamics to Constrain the Ages of M Dwarfs

TL;DR

This work addresses how to age-date field M dwarfs by linking magnetic activity, traced by Hα, to stellar age through Galactic height as a statistical proxy. It leverages the SDSS DR5 spectroscopic sample to quantify how active fractions and activity strength vary with spectral type and height, and employs a 1‑D thin-disk dynamical model to translate these trends into spectral-type–dependent activity lifetimes and an empirical age–activity relation. The authors derive a parametric age-activity relation for M2–M7 dwarfs, showing a marked increase in activity lifetimes across the fully convective transition and providing fit coefficients that describe how activity decays with age. These results offer a statistical framework to estimate ages for large M-dwarf samples and provide calibration opportunities with white-dwarf binaries and deep cluster studies, advancing both Galactic archaeology and dynamo theory in low-mass stars.

Abstract

We present a study of the dynamics and magnetic activity of M dwarfs using the largest spectroscopic sample of low-mass stars ever assembled. The age at which strong surface magnetic activity (as traced by H-alpha) ceases in M dwarfs has been inferred to have a strong dependence on mass (spectral type, surface temperature) and explains previous results showing a large increase in the fraction of active stars at later spectral types. Using spectral observations of more than 40000 M dwarfs from the Sloan Digital Sky Survey, we show that the fraction of active stars decreases as a function of vertical distance from the Galactic plane (a statistical proxy for age), and that the magnitude of this decrease changes significantly for different M spectral types. Adopting a simple dynamical model for thin disk vertical heating, we assign an age for the activity decline at each spectral type, and thus determine the activity lifetimes for M dwarfs. In addition, we derive a statistical age-activity relation for each spectral type using the dynamical model, the vertical distance from the Plane and the H-alpha emission line luminosity of each star (the latter of which also decreases with vertical height above the Galactic plane).

Figures (5)

• Figure 1: Fraction of active stars as a function of spectral type (reproduced from West et al. 2004). Numbers above each point represent the number of stars used to compute the fraction.
• Figure 2: The fraction of active M7 stars as a function of vertical distance from the Galactic plane (reproduced from West et al. 2006). There is a significant decrease in the active fraction as a function of Galactic height, which can be used as a proxy for age. Younger stars near the Plane are almost all active, whereas older stars, further from the Plane have ceased being active.
• Figure 3: Median log($L_{\rm{H}\alpha}$/$L_{\rm{bol}}$) as a function of vertical distance from the Plane (reproduced from W08). The narrow error bars represent the spread of the values and the wide error bars indicate the uncertainty of the median relation in each bin. The decrease as a function of height is a statistically significant over most of the spectral types.
• Figure 4: The H$\alpha$ activity lifetimes of M dwarfs as determined by comparing the SDSS DR5 spectroscopic data to 1D dynamical simulations (stars; reproduced from W08). The Hawley et al. (2000) activity lifetime relation is overplotted for comparison. As predicted, the Hawley relation provides a lower limit to the ages. W08 found that there is a significant increase in activity lifetimes between spectral types M3 and M5, possibly indicating a physical change in the production of magnetic fields as full convection sets in.
• Figure 5: Median log($L_{\rm{H}\alpha}$/$L_{\rm{bol}}$) as a function of age (as derived from the median age of the same bins in the W08 dynamical models). The error bars represent the spread in the distributions. The best-fit function is overplotted for each spectral type (dashed).