Theoretical Models of the Angular Momentum Evolution of Solar‐Type Stars

Abstract

We examine the e †ects of di †erent assumptions about the initial conditions, angular momentum loss law, and angular momentum transport on the angular momentum evolution of 0.5È1.2 solar mass stars. We Ðrst perform a parameter variation study to test the sensitivity of the surface rotation rate as a function of mass and age to changes in the initial conditions and input physics. We then check to see if the distribution of initial conditions for a given physical scenario is consistent for open clusters of di †er-ent ages.The behavior of the rapid rotators is highly sensitive to the saturation threshold for angular momentum loss above which angular momentum loss scales linearly with the rotation rate. Very high (u crit ), values for suppress rapid rotation prior to the main sequence, and very low values permit rapid u crit rotation to survive for too long. For solid-body (SB) and di †erential rotation (DR) models, higher mass models rotate more rapidly than lower mass models for the same initial conditions and DR models u crit . di †er from SB models in both the direct e †ect of core-envelope decoupling and a change in the calibration of the angular momentum loss law needed to reproduce the solar rotation at the age of the Sun ; the e †ects of both are discussed. Slow rotation in young clusters can be achieved with modest disk lifetimes (3È10 Myr) for the DR models and longer disk lifetimes for the SB models (10 or more Myr). In addition, the slowly rotating DR models spin down during the early main sequence more than the slowly rotating SB models do.When compared with the cluster data, the observed mass dependence of the rapid rotator phenomenon can be reproduced only with a mass-dependent for both the SB and DR models. A scaling of u crit inversely proportional to the convective overturn timescale can reproduce the observed massu crit dependent spindown. The observed spindown of the slow rotators in the young open clusters is in better agreement with the DR than the SB models. We also discuss observational tests to distinguish di †erent classes of models using low-mass stars and rotation periods in open clusters.

Cataclysmic Variables: An Empirical Angular Momentum Loss Prescription from Open Cluster Data

“…This assumption was confirmed later by Basri (1987). There has been a dramatic increase in the amount and quality of rotation data available for low-mass stars in open clusters and the field, from the important early work of Stauffer & Hartmann (1987) to the present (see Stauffer et al 1997;Krishnamurthi et al 1997;Reid & Mahoney 2000 for reviews). However, many theoretical studies of CVs use angular momentum loss rates (e.g., Rappaport, Verbunt, & Joss 1983) that precede these data.…”

“…It has long been known that the observed saturation threshold for chromospheric and coronal activity indicators is mass-dependent (see Walter 1982;Noyes et al 1984;Patten & Simon 1996). Krishnamurthi et al (1997) found that a scaling of ! crit with the inverse Rossby number (the ratio of the rotation period to the convective overturn timescale) gave a reasonable fit to the observed timescale for spin-down as a function of mass from 0.6 to 1.2 M .…”

Stellar models simulating the disk-locking mechanism and the evolutionary history of the Orion Nebula cluster and NGC 2264

“…To mimic the effect of disk-locking on the pMS, their models were allowed to lock the rotation rate of a young star on the Hayashi track for a specified time. Their models begin at the deuterium 2 Several authors cited in this work used the Yale Rotating Stellar Evolution Code (YREC) to study angular momentum evolution, for instance, Pinsonneault et al (1989Pinsonneault et al ( , 1990, Guenther et al (1992), Chaboyer et al (1995a), Krishnamurthi et al (1997), Barnes et al (1999Barnes et al ( , 2001). …”

The Solar-Stellar Connection

“…Finally, once on the main sequence, there is a rapid initial drop in rotation rate, followed by a pause where surface rotation changes little; older stars then resume spinning down at the predicted asymptotic rate. This is evidence for core-envelope decoupling (MacGregor and Brenner 1991;Krishnamurthi et al 1997) on timescales of tens to hundreds of Myr (see Denissenkov et al 2010;Gallet and Bouvier 2013, for recent discussions). The observed pattern is therefore richer than a simple power-law relationship, requiring both more sophisticated theory and stronger empirical constraints.…”

“…These formula further assumes that the convective envelope transmits instantaneously the applied surface torque to the base of the convective envelope. Such models have been used to explore the relevant coupling time scale between the convective envelope and the radiative interior in solar-like stars over the course of their evolution (MacGregor and Brenner 1991; Keppens et al 1995;Krishnamurthi et al 1997;Allain 1998) and (for recent developments see Denissenkov et al 2010;Bouvier 2013;Gallet and Bouvier 2013;Oglethorpe and Garaud 2013;Zhang and Penev 2014). It is found that a time scale of tens to hundreds of Myr can explain the core-envelope coupling in young open cluster stars (see Figure 6).…”