ng-Huai Li

YREC: The Yale Rotating Stellar Evolution Code

Abstract The stellar evolution code YREC is outlined with emphasis on its applications to helio- and asteroseismology. The procedure for calculating calibrated solar and stellar models is described. Other features of the code such as a non-local treatment of convective core overshoot, and the implementation of a parametrized description of turbulence in stellar models, are considered in some detail. The code has been extensively used for other astrophysical applications, some of which are briefly mentioned at the end of the paper.

Three-dimensional convection simulations of the outer layers of the Sun using realistic physics

This paper describes a series of 3D simulations of shallow inefficient convection in the outer layers of the Sun. The computational domain is a closed box containing the convection-radiation transition layer, located at the top of the solar convection zone. The most salient features of the simulations are that: i)The position of the lower boundary can have a major effect on the characteristics of solar surface convection (thermal structure, kinetic energy and turbulent pressure). ii)The width of the box has only a minor effect on the thermal structure, but a more significant effect on the dynamics (rms velocities). iii)Between the surface and a depth of 1 Mm, even though the density and pressure increase by an order of magnitude, the vertical correlation length of vertical velocity is always close to 600 km. iv) In this region the vertical velocity cannot be scaled by the pressure or the density scale height. This casts doubt on the applicability of the mixing length theory, not only in the superadiabatic layer, but also in the adjacent underlying layers. v) The final statistically steady state is not strictly dependent on the initial atmospheric stratification.

INCLUSION OF TURBULENCE IN SOLAR MODELING

The general consensus is that in order to reproduce the observed solar p-mode oscillation frequencies, turbulence should be included in solar models. However, until now there has not been any well-tested efficient method to incorporate turbulence into solar modeling. We present here two methods to include turbulence in solar modeling within the framework of the mixing length theory, using the turbulent velocity obtained from numerical simulations of the highly superadiabatic layer (SAL) of the Sun at three stages of its evolution. The first approach is to include the turbulent pressure alone, and the second is to include both the turbulent pressure and the turbulent kinetic energy. The latter is achieved by introducing two variables: the turbulent kinetic energy per unit mass and the effective ratio of specific heats owing to the turbulent perturbation. These are treated as additions to the standard thermodynamic coordinates (e.g., pressure and temperature). We investigate the effects of both treatments of turbulence on the structure variables, the adiabatic sound speed, the structure of the highly superadiabatic layer, and the p-mode frequencies. We find that the second method reproduces the SAL structure obtained in three-dimensional simulations and produces a p-mode frequency correction an order of magnitude better than the first method.

Global Parameter and Helioseismic Tests of Solar Variability Models

We construct models of the structure and evolution of the Sun which include variable magnetic fields and turbulence. The magnetic effects are (1) magnetic pressure, (2) magnetic energy, and (3) magnetic modulation to turbulence. The effects of turbulence are (1) turbulent pressure, (2) turbulent kinetic energy, and (3) turbulent inhibition of the radiative energy loss of a convective eddy, and (4) turbulent generation of magnetic fields. Using these ingredients we construct five types of solar variability models (including the standard solar model) with magnetic effects. These models are in part based on three-dimensional numerical simulations of the superadiabatic layers near the surface of the Sun. The models are tested with several sets of observational data, namely, the changes of (1) the total solar irradiance, (2) the photospheric temperature, (3) radius, (4) the position of the convection zone base, and (5) low- and medium-degree solar oscillation frequencies. We find that turbulence plays a major role in solar variability, and only a model that includes a magnetically modulated turbulent mechanism can agree with all the current available observational data. We find that because of the somewhat poor quality of all observations (other than the helioseismological ones), we need all data sets in order to restrict the range of models.

The nonhomologous nature of solar diameter variations

We show in this Letter that the changes of the solar diameter in response to variations of large-scale magnetic fields and turbulence are not homologous. For the best current model, the variation at the photospheric level is over 1000 times larger than the variation at a depth of 5 Mm, which is about the level at which f-mode solar oscillations determine diameter variations. This model is supported by observations that indicate larger diameter changes for high-degree f-modes than for low-degree f-modes, since the energy of the former is concentrated at shallower layers than the latter.

MEASUREMENTS OF SOLAR IRRADIANCE AND EFFECTIVE TEMPERATURE AS A PROBE OF SOLAR INTERIOR MAGNETIC FIELDS

We argue that a variety of solar data suggest that the activity-cycle timescale variability of the total irradiance is produced by structural adjustments of the solar interior. Assuming these adjustments are induced by variations of internal magnetic fields, we use measurements of the total irradiance and effective temperature over the period from 1978 to 1992 to infer the magnitude and location of the magnetic field. Using an updated stellar evolution model, which includes magnetic fields, we find that the observations can be explained by fields with peak values ranging from 120 to 2.3 kG, located in the convection zone between 0.959 and 0.997 R., respectively. The corresponding maximal radius changes are 17 km when the magnetic field is located at 0.959 R. and 3 km when it is located at 0.997 R.. At these depths, the W-parameter (defined by Delta lnR/Delta lnL, where R and L are the radius and luminosity) ranges from 0.02 to 0.006. All these predictions are consistent with helioseismology and recent measurements carried out by the Michelson Doppler Imager experiment on the Solar and Heliospheric Observatory.

Space- and ground-based pulsation data of η bootis explained with stellar models including turbulence

The space telescope MOSTis now providing us with extremely accurate low-frequency p-mode oscillation data for the starBoo. We demonstrate in this paper that these data, when combined with ground-based measurements ofthehigh-frequencyp-modespectrum,canbereproducedwithstellarmodelsthatincludetheeffectsofturbulence in their outer layers.Withoutturbulence, thel ¼ 0modes ofour models deviatefromeithertheground-basedorthe space data by about 1.5-4 � Hz. This discrepancy can be completely removed by including turbulence in the models, and we can exactly match 12 out of 13 MOST frequencies that we identified as l ¼ 0 modes, in addition to 13 out of 21 ground-based frequencies within their observational 2 � tolerances. The better agreement between model frequencies and observed frequencies depends for the most part on the turbulent kinetic energy that was taken from a three-dimensional convection simulation for the Sun.

Two-dimensional Stellar Evolution Code Including Arbitrary Magnetic Fields. I. Mathematical Techniques and Test Cases

A high-precision two-dimensional stellar evolution code has been developed for studying solar variability due to structural changes produced by varying internal magnetic fields of arbitrary configurations. Specifically, we are interested in modeling the effects of a dynamo-type field on the detailed internal structure and on the global parameters of the Sun. The high precision is required to model both very small solar changes (of the order of 10-4) and short timescales (of the order of 1 yr). It is accomplished by using the mass coordinate to replace the radial coordinate, by using fixed and adjustable time steps, a realistic stellar atmosphere, and element diffusion, and by adjusting the grid points. We have also built into the code the potential to subsequently include rotation and turbulence. The current code has been tested for several cases, including its ability to reproduce the one-dimensional results.

Solar Models with Revised Abundance

We present new solar models in which we use the latest low abundances and further include the effects of rotation, magnetic fields, and extra-mixing processes. We assume that the extra-element mixing can be treated as a diffusion process, with the diffusion coefficient depending mainly on the solar internal configuration of rotation and magnetic fields. We find that such models can well reproduce the observed solar rotation profile in the radiative region. Furthermore, the proposed models can match the seismic constraints better than the standard solar models, also when these include the latest abundances, but neglect the effects of rotation and magnetic fields.

Seismological Analysis of the Stars γ Serpentis and ι Leonis: Stellar Parameters and Evolution

In order to assess the information that will be available from targets of the Microvariability and Oscillations of Stars (MOST) satellite, we explore the possible evolutionary status and perform preliminary seismological analysis of two targets: the stars gamma Ser and iota Leo, which show solar-like oscillations. Taking into account the astrometric observational constraints on the stars, we find that gamma Ser is in the main-sequence phase of evolution, while iota Leo has two distinct solutions that match well with observations: main-sequence models and post-main-sequence models. The evolutionary tracks cover the following ranges of mass and initial metallicity: gamma Ser, 1.15-1.20 M-circle dot and Z = 0.0135 +/- 0.003; iota Leo, 1.62-1.70 M-circle dot and Z = 0.024 +/- 0.002 (for values of the Galactic helium enrichment ratio Delta Y/Delta Z in the range 0 - 2). By combining stellar models with observational constraints, we determine age ranges of 3.2 +/- 0.6 Gyr for gamma Ser and 1.7 +/- 0.2 Gyr for iota Leo. The results show that the masses and ages of the stars are very sensitive to metallicity and evolutionary phase. Furthermore, we find that models with overshooting from a convective core predict a larger age for a given mass. Finally, we discuss future prospects for constraining stellar models with the help of asteroseismic observations.