Angular Momentum Transport in Solar-Type Stars: Testing the Timescale for Core-Envelope Coupling

Abstract

We critically examine the constraints on internal angular momentum transport which can be inferred from the spin down of open cluster stars. The rotation distribution inferred from rotation velocities and periods are consistent for larger and more recent samples, but smaller samples of rotation periods appear biased relative to v sin i studies. We therefore focus on whether the rotation period distributions observed in star forming regions can be evolved into the observed ones in the Pleiades, NGC 2516, M 34, M 35, M 37, and M 50 with plausible assumptions about star-disk coupling and angular momentum loss from magnetized solar-like winds. Solid body models are consistent with the data for low mass fully convective stars but highly inconsistent for higher mass stars where the surface convection zone can decouple for angular momentum purposes from the radiative interior. The Tayler-Spruit magnetic angular momentum transport mechanism, commonly employed in models of high mass stars, predicts solid-body rotation on extremely short timescales and is therefore unlikely to operate in solar-type pre-MS and MS stars at the predicted rate. Models with core-envelope decoupling can explain the spin down of 1.0 and 0.8 solar mass slow rotators with characteristic coupling timescales of 55 ± 25 Myr and 175 ± 25 Myr respectively. The upper envelope of the rotation distribution is more strongly coupled than the lower envelope of the rotation distribution, in accord with theoretical predictions that the angular momentum transport timescale should be shorter for more rapidly rotating stars. Constraints imposed by the solar rotation curve are also discussed. We argue that neither hydrodynamic mechanisms nor our revised and less efficient prescription for the Tayler-Spruit dynamo can reproduce both spin down and the internal solar rotation profile by themselves. It is likely that a successful model of angular momentum evolution will involve more than one mechanism. Further observational studies, especially of clusters younger than 100 Myr, will provide important additional constraints on the internal rotation of stars and could firmly rule out or confirm the operation of major classes of theoretical mechanisms.

Improved angular momentum evolution model for solar-like stars

“…Using a diffusive approach, Eggenberger et al (2012b) showed that an enhanced "anomalous" viscosity of ν = 3 × 10 4 cm 2 s −1 is required to account for the rotational splitting of the red giant KIC 8366239, whose rotational profile is much shallower than diffusive models would predict. Using the conversion we derived above from Denissenkov et al (2010), this translates into a coupling timescale of 78 Myr, i.e. not very different than the one we derived from our PMS-MS models.…”

“…These new observational results provide extremely useful guidance for the modelling of angular momentum evolution of low-mass stars (M * < 1.2 M ) from 1 Myr to 10 Gyr (e.g. Irwin et al 2007;Bouvier 2008;Denissenkov et al 2010;Spada et al 2011;Reiners & Mohanty 2012;Gallet & Bouvier 2013) and offer a unique insight into the physical processes that dictate rotational evolution. To account for the observations, parametric models have to incorporate at least three major processes: the star-disk interaction during the early pre-main sequence (PMS; Matt & Pudritz 2005b;Zanni & Ferreira 2009Ferreira et al 2000;Matt et al 2010), the loss of angular momentum through powerful stellar winds on the early main sequence (MS; Weber & Davis 1967;Kawaler 1988;Matt & Pudritz 2005a;Vidotto et al 2011Vidotto et al , 2014bZanni & Ferreira 2011;Cranmer & Saar 2011;Matt et al 2012a,b;Reiners & Mohanty 2012;Réville et al 2015), and the redistribution of angular momentum in the stellar interior at all phases of evolution (MacGregor & Brenner 1991;Allain 1998;Palacios et al 2003Palacios et al , 2006Charbonnel & Lagarde 2010;Lagarde et al 2011Lagarde et al , 2012Charbonnel et al 2013).…”

“…Krishnamurthi et al 1997), internal magnetic fields (see e.g. Denissenkov & Pinsonneault 2007;Denissenkov et al 2010;Spada et al 2010;Eggenberger et al 2012a), and internal gravity waves (see , 2003Charbonnel et al 2013). …”

“…Denissenkov et al (2010) converted this viscosity to a characteristic timescale that can be compared to the core-envelope coupling timescales used here. This conversion can be expressed as τ c−e = 6.3 × 10 20 ν −1.208 , with ν in cm 2 s −1 .…”

Effects of rotation and magnetic fields on the lithium abundance and asteroseismic properties of exoplanet-host stars

“…The first important observational fact in this context is that the rotational periods of young solar-type stars suggest that slow rotators develop a high degree of differential rotation between the radiative core and the convective envelope, while solid-body rotation is favoured for fast rotators (see e.g. Irwin et al 2007;Bouvier 2008;Denissenkov et al 2010). The rotation of the star on the ZAMS basically depends on its initial velocity and on the disc lifetime during the pre-main sequence.…”