Rotation of the solar convection zone from helioseismology

Helioseismology has provided very detailed inferences about rotation of the solar interior. Within the convection zone the rotation rate roughly shares the latitudinal variation seen in the surface differential rotation. The transition to the nearly uniformly rotating radiative interior takes place in a narrow tachocline, which is likely important to the operation of the solar magnetic cycle.The convection-zone rotation displays zonal flows, regions of slightly more rapid and slow rotation, extending over much of the depth of the convection zone and converging towards the equator as the solar cycle progresses. In addition, there is some evidence for a quasi-periodic variation in rotation, with a period of around 1.3 yr, at the equator near the bottom of the convection zone.Comment: 12 pages, 8 figures. To appear in Proc. IAU Symposium 239: Convection in Astrophysics,eds F. Kupka, I. W. Roxburgh & K. L. Chan, Cambridge University Pres

Correcting stellar oscillation frequencies for near-surface effects

In helioseismology, there is a well-known offset between observed and computed oscillation frequencies. This offset is known to arise from improper modeling of the near-surface layers of the Sun, and a similar effect must occur for models of other stars. Such an effect impedes progress in asteroseismology, which involves comparing observed oscillation frequencies with those calculated from theoretical models. Here, we use data for the Sun to derive an empirical correction for the near-surface offset, which we then apply three other stars (alpha Cen A, alpha Cen B and beta Hyi). The method appears to give good results, in particular providing an accurate estimate of the mean density of each star.Comment: accepted for publication in ApJ Letter

Measurements of Stellar Properties through Asteroseismology: A Tool for Planet Transit Studies

Oscillations occur in stars of most masses and essentially all stages of evolution. Asteroseismology is the study of the frequencies and other properties of stellar oscillations, from which we can extract fundamental parameters such as density, mass, radius, age and rotation period. We present an overview of asteroseismic analysis methods, focusing on how this technique may be used as a tool to measure stellar properties relevant to planet transit studies. We also discuss details of the Kepler Asteroseismic Investigation -- the use of asteroseismology on the Kepler mission in order to measure basic stellar parameters. We estimate that applying asteroseismology to stars observed by Kepler will allow the determination of stellar mean densities to an accuracy of 1%, radii to 2-3%, masses to 5%, and ages to 5-10% of the main-sequence lifetime. For rotating stars, the angle of inclination can also be determined.Comment: To appear in the Proceedings of the 253rd IAU Symposium: "Transiting Planets", May 2008, Cambridge, M

Improvements to stellar structure models, based on a grid of 3D convection simulations. II. Calibrating the mixing-length formulation

We perform a calibration of the mixing length of convection in stellar structure models against realistic 3D radiation-coupled hydrodynamics (RHD) simulations of convection in stellar surface layers, determining the adiabat deep in convective stellar envelopes. The mixing-length parameter $\alpha$ is calibrated by matching averages of the 3D simulations to 1D stellar envelope models, ensuring identical atomic physics in the two cases. This is done for a previously published grid of solar-metallicity convection simulations, covering from 4200 K to 6900 K on the main sequence, and 4300-5000 K for giants with logg=2.2. Our calibration results in an $\alpha$ varying from 1.6 for the warmest dwarf, which is just cool enough to admit a convective envelope, and up to 2.05 for the coolest dwarfs in our grid. In between these is a triangular plateau of $\alpha$ ~ 1.76. The Sun is located on this plateau and has seen little change during its evolution so far. When stars ascend the giant branch, they largely do so along tracks of constant $\alpha$, with $\alpha$ decreasing with increasing mass.Comment: 22 pages, 15 figures, accepted for publication in MNRA

Improvements to Stellar Structure Models, Based on a Grid of 3D Convection Simulations. I. T(τ)T(\tau)-Relations

Relations between temperature, T, and optical depth, tau, are often used for describing the photospheric transition from optically thick to optically thin in stellar structure models. We show that this is well justified, but also that currently used T(tau) relations are often inconsistent with their implementation. As an outer boundary condition on the system of stellar structure equations, T(tau) relations have an undue effect on the overall structure of stars. In this age of precision asteroseismology, we need to re-assess both the method for computing and for implementing T(tau) relations, and the assumptions they rest on. We develop a formulation for proper and consistent evaluation of T(tau) relations from arbitrary 1D or 3D stellar atmospheres, and for their implementation in stellar structure and evolution models. We extract radiative T(tau) relations, as described by our new formulation, from 3D simulations of convection in deep stellar atmospheres of late-type stars from dwarfs to giants. These simulations employ realistic opacities and equation of state, and account for line-blanketing. For comparison, we also extract T(tau) relations from 1D MARCS model atmospheres using the same formulation. T(tau)-relations from our grid of 3D convection simulations display a larger range of behaviours with surface gravity, compared with those of conventional theoretical 1D hydrostatic atmosphere models. Based on this, we recommend no longer to use scaled solar T(tau) relations. Files with T(tau) relations for our grid of simulations are made available to the community, together with routines for interpolating in this irregular grid. We also provide matching tables of atmospheric opacity, for consistent implementation in stellar structure models.Comment: 18 pages, 7 figures, 2 tables. Accepted for publication in MNRAS, 201