Statistical Fitting of Evolution Models to Rotation Rates of Sun-Like Stars

Abstract

We apply for the first time a two-dimensional fitting statistic, ${\tau }^2$, to rotational evolution models (REMs) of stars (0.1 to 1.3 $M_{\odot }$) on the period-mass plane. The ${\tau }^2$ statistic simultaneously considers all cluster rotation data to return a goodness of fit, allowing for data-driven improvement of REMs. We construct data sets for Upper Sco, the Pleiades and Praesepe, to which we tune our REMs. We use consistently determined stellar masses (calculated by matching $K_{\text{s}}$ magnitudes to isochrones) and literature rotation periods. As a first demonstration of the ${\tau }^2$ statistic, we find the best-fitting gyrochronology age for Praesepe, which is in good agreement with the literature. We then systematically vary three parameters which determine the dependence of our stellar wind torque law on Rossby number in the saturated and unsaturated regimes, and the location of the transition between the two. By minimising ${\tau }^2$, we find best-fit values for each parameter. These values vary slightly between clusters, mass determinations and initial conditions, highlighting the precision of ${\tau }^2$ and its potential for constraining REMs, gyrochronology, and understanding of stellar physics. Our resulting REMs, which implement the best-possible fitting form of a broken power-law torque, are statistically improved on previous REMs using similar formulations, but still do not simultaneously describe the observed rotation distributions of the lowest masses, which have both slow and fast rotators by the Praesepe age, and the shape of the converged sequence for higher masses. Further complexity in the REMs is thus required to accurately describe the data.

18 pages, 10 figures. Accepted for publication in ApJ

References in corpus (27)

• Gaia Data Release 1. Summary of the astrometric, photometric, and survey properties
• The K2 Mission: Characterization and Early results
• New evolutionary models for pre-main sequence and main sequence low-mass stars down to the hydrogen-burning limit
• The Stellar Populations of Praesepe and Coma Berenices
• The Mass-Dependence of Angular Momentum Evolution in Sun-Like Stars
• A spin-down clock for cool stars from observations of a 2.5-billion-year-old cluster
• Improved angular momentum evolution model for solar-like stars II. Exploring the mass dependence
• Lithium depletion and the rotational history of exoplanet host stars
• The Factory and The Beehive II. Activity and Rotation in Praesepe and the Hyades
• The Age and Age Spread of the Praesepe and Hyades Clusters: a Consistent, ~800 Myr Picture from Rotating Stellar Models
• The Monitor project: Rotation of low-mass stars in the open cluster NGC 2516
• Near and Mid-IR Photometry of the Pleiades, and a New List of Substellar Candidate Members
• A maximum likelihood method for fitting colour-magnitude diagrams
• The effect of rotation on the abundances of the chemical elements of the A-type stars in the Praesepe cluster
• Powerful Winds from Low-Mass Stars: V374 Peg
• The Seven Sisters DANCe. I. Empirical isochrones, Luminosity and Mass Functions of the Pleiades cluster
• The Metastable Dynamo Model of Stellar Rotational Evolution
• The Gaia-ESO Survey: Lithium depletion in the Gamma Velorum cluster and inflated radii in low-mass pre-main-sequence stars
• The Impact of Metallicity on the Evolution of Rotation and Magnetic Activity of Sun-Like Stars
• The Effect of Binarity on Stellar Rotation - Beyond the Reach of Tides
• The Effect of Combined Magnetic Geometries on Thermally Driven Winds I: Interaction of Dipolar and Quadrupolar Fields
• Pre-main-sequence isochrones -- III. The Cluster Collaboration isochrone server
• Stellar rotational periods in the planet hosting open cluster Praesepe
• Stellar population astrophysics (SPA) with the TNG. Revisiting the metallicity of Praesepe (M44)
• The first rotation periods in Praesepe
• M Dwarf rotation from the $K2$ young clusters to the field. I. A Mass-Rotation Correlation at 10 Myr
• New BVIc Photometry of Low-mass Pleiades Stars: Exploring the Effects of Rotation on Broadband Colors

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