Transport and mixing in the radiation zones of rotating stars: I-Hydrodynamical processes

The purpose of this paper is to improve the modelization of the rotational mixing which occurs in stellar radiation zones, through the combined action of the thermally driven meridional circulation and of the turbulence generated by the shear of differential rotation. The turbulence is assumed to be anisotropic, due to the stratification, with stronger transport in the horizontal directions than in the vertical. The main difference with the former treatments by Zahn (1992) and Maeder & Zahn (1998) is that we expand here the departures from spherical symmetry to higher order, and include explicitly the differential rotation in latitude, to first order. This allows us to treat simultaneously the bulk of a radiation zone and its tachocline(s). Moreover, we take fully into account the non-stationarity of the problem, which will enable us to tackle the rapid phases of evolution. The system of partial differential equations, which govern the transport of angular momentum, heat and chemical elements, is written in a form which makes it ready to implement in a stellar evolution code. Here the effect of a magnetic field is deliberately ignored; it will be included in forthcoming papers.Comment: 16 pages, no figures, accepted for publication in A&

Dynamical Tide in Solar-Type Binaries

Circularization of late-type main-sequence binaries is usually attributed to turbulent convection, while that of early-type binaries is explained by resonant excitation of g modes. We show that the latter mechanism operates in solar-type stars also and is at least as effective as convection, despite inefficient damping of g modes in the radiative core. The maximum period at which this mechanism can circularize a binary composed of solar-type stars in 10 Gyr is as low as 3 days, if the modes are damped by radiative diffusion only and g-mode resonances are fixed; or as high as 6 days, if one allows for evolution of the resonances and for nonlinear damping near inner turning points. Even the larger theoretical period falls short of the observed transition period by a factor two.Comment: 17 pages, 2 postscript figures, uses aaspp4.sty. Submitted to Ap

Influence of the Tachocline on Solar Evolution

Recently helioseismic observations have revealed the presence of a shear layer at the base of the convective zone related to the transition from differential rotation in the convection zone to almost uniform rotation in the radiative interior, the tachocline. At present, this layer extends only over a few percent of the solar radius and no definitive explanations have been given for this thiness. Following Spiegel and Zahn (1992, Astron. Astrophys.), who invoke anisotropic turbulence to stop the spread of the tachocline deeper in the radiative zone as the Sun evolves, we give some justifications for their hypothesis by taking into account recent results on rotating shear instability (Richard and Zahn 1999, Astron. Astrophys.). We study the impact of the macroscopic motions present in this layer on the Sun's structure and evolution by introducing a macroscopic diffusivity $D_T$ in updated solar models. We find that a time dependent treatment of the tachocline significantly improves the agreement between computed and observed surface chemical species, such as the $^7$Li and modify the internal structure of the Sun (Brun, Turck-Chi\`eze and Zahn, 1999, in Astrophys. J.).Comment: to appear in Annals of the New York Academy of Sciences, vol 898. Postscript file, 9 pages and 5 figures New Email Address for A. S. Brun: [email protected]

A Robust Measure of Tidal Circularization in Coeval Binary Populations: The solar-type spectroscopic Binary Population in The Open Cluster M35

We present a new homogeneous sample of 32 spectroscopic binary orbits in the young (~ 150 Myr) main-sequence open cluster M35. The distribution of orbital eccentricity vs. orbital period (e-log(P)) displays a distinct transition from eccentric to circular orbits at an orbital period of ~ 10 days. The transition is due to tidal circularization of the closest binaries. The population of binary orbits in M35 provide a significantly improved constraint on the rate of tidal circularization at an age of 150 Myr. We propose a new and more robust diagnostic of the degree of tidal circularization in a binary population based on a functional fit to the e-log(P) distribution. We call this new measure the tidal circularization period. The tidal circularization period of a binary population represents the orbital period at which a binary orbit with the most frequent initial orbital eccentricity circularizes (defined as e = 0.01) at the age of the population. We determine the tidal circularizationperiod for M35 as well as for 7 additional binary populations spanning ages from the pre main-sequence (~ 3 Myr) to late main-sequence (~ 10 Gyr), and use Monte Carlo error analysis to determine the uncertainties on the derived circularization periods. We conclude that current theories of tidal circularization cannot account for the distribution of tidal circularization periods with population age.Comment: 37 pages, 9 figures, to be published in The Astrophysical Journal, February 200

The New Transiting Planet OGLE-TR-56b: Orbit and Atmosphere

Motivated by the identification of the very close-in extrasolar giant planet OGLE-TR-56b, we explore the implications of its existence on problems of tidal dissipation, planet migration, and atmospheric stability. The small orbit of OGLE-TR-56b makes the planet an interesting test particle case for tidal dissipation in stellar convection zones. We show that it favors prescriptions of suppressed convective eddy viscosity. Precise timing of the transits of OGLE-TR-56b might place interesting constraints on stellar convection theory, if orbital period change is detected in the near future.Comment: 12 pages, 1 figure, submitted to ApJ

Dissipation Efficiency in Turbulent Convective Zones in Low Mass Stars

We extend the analysis of Penev et al. (2007) to calculate effective viscosities for the surface convective zones of three main sequence stars of 0.775Msun, 0.85Msun and the present day Sun. In addition we also pay careful attention to all normalization factors and assumptions in order to derive actual numerical prescriptions for the effective viscosity as a function of the period and direction of the external shear. Our results are applicable for periods that are too long to correspond to eddies that fall within the inertial subrange of Kolmogorov scaling, but no larger than the convective turnover time, when the assumptions of the calculation break down. We find linear scaling of effective viscosity with period and magnitudes at least three times larger than the Zahn (1966, 1989) prescription.Comment: 13 pages, 3 figures Effective viscosity scaling changed by a factor of ~100. More details provided for the numerical model