Sabatino Sofia

Evolutionary models of the rotating sun

This paper reviews current work on the evolution of a differentially rotating solar model. Although we discuss global features of the evolution with rotation in general terms, the specific models described are those computed with the new Yale Rotating Evolution Code (YREC). YREC uses the Kippenhahn and Thomas (1970, KT) formalism as implemented by Endal and Sofia (1976), although the numerical formulation of our code is totally new. Particular calculations that we describe include the effects of different initial total angular momentum, the consequences of varying the properties and magnitude of angular momentum losses by wind torquing, and the consequences of specific composition and angular momentum redistribution mechanisms. This paper is a progress report which points out the complexity of the problem, and the need for a broad-based observational program to solve it. Because the final solution is not yet in hand, we outline the steps that, in our estimation, need to be undertaken in order to make progress.

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

We examine the effects of different assumptions about the initial conditions, angular momentum loss law, and angular momentum transport on the angular momentum evolution of 0.5-1.2 solar mass stars. We first 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 different ages. The behavior of the rapid rotators is highly sensitive to the saturation threshold for angular momentum loss (ωcrit), above which angular momentum loss scales linearly with the rotation rate. Very high values for ωcrit suppress rapid rotation prior to the main sequence, and very low values permit rapid rotation to survive for too long. For solid-body (SB) and differential rotation (DR) models, higher mass models rotate more rapidly than lower mass models for the same initial conditions and ωcrit. DR models differ from SB models in both the direct effect 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 effects of both are discussed. Slow rotation in young clusters can be achieved with modest disk lifetimes (3-10 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 ωcrit for both the SB and DR models. A scaling of ωcrit inversely proportional to the convective overturn timescale can reproduce the observed mass-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 different classes of models using low-mass stars and rotation periods in open clusters.

The QUEST RR Lyrae Survey: Confirmation of the Clump at 50 Kiloparsecs and Other Overdensities in the Outer Halo

We have measured the periods and light curves of 148 RR Lyrae variables from V = 13.5 to 19.7 from the first 100 deg2 of the Quasar Equatorial Survey Team RR Lyrae survey. Approximately 55% of these stars belong to the clump of stars detected earlier by the Sloan Digital Sky Survey. According to our measurements, this feature has ~10 times the background density of halo stars, spans at least 375 by 35 in α and δ (≥30 by ≥3 kpc), lies ~50 kpc from the Sun, and has a depth along the line of sight of ~5 kpc (1 σ). These properties are consistent with the recent models that suggest that it is a tidal stream from the Sagittarius dwarf spheroidal galaxy. The mean period of the type ab variables, 0.58 days, is also consistent. In addition, we have found two smaller overdensities in the halo, one of which may be related to the globular cluster Pal 5.

Turbulent compressible convection in a deep atmosphere. IV. Results of three-dimensional computations

The behavior of turbulent convection in deep atmospheres is studied by numerically solving the three-dimensional Navier Stokes equations. It is found that the mean vertical velocity is an important link between the buoyancy work and the heat flux. In regions with efficient convection, the total flux is composed of the enthalpy flux and the flux of kinetic energy. The characteristics of these components of the total flux are examined. It is shown that the production of kinetic energy depends on the local variables and the flux. However, the dissipation of kinetic energy is nonlocal. A substantial amount of kinetic energy is carried away from the location of production to be dissipated in lower regions. 8 references.

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.

Solar activity forecast for solar cycle 23

In this paper, we predict the next cycles activity and improve the timing of solar cycle predictions. Dynamobased solar activity prediction techniques rely upon two properties inherent in the solar cycle: that solar magnetism oscillates between poloidal and toroidal components; and that there is a degree of “magnetic persistence” in dynamos, which in the case of the Sun, results in the dependence of many magnetic related quantities (activity related quantities) upon the amount of magnetism embedded below the Suns surface. Using the SODA (SOlar Dynamo Amplitude) index as a measure of magnetic persistence, we predict that solar cycle #23 will reach a mean smoothed F10.7 peak of 182±30 solar flux units (sfu) and a mean sunspot number Rz of 138±30. This is particularly intriguing because the “folklore” is that odd cycles are larger than the preceding even cycle. Additionally, by tracking the equatorward march of solar activity, the timing of the cycle can be better estimated. From this, we estimate that the next solar maximum will occur near May, 2000 ±9 months.

Solar irradiance modulation by active regions during 1980

The solar irradiance modulation due to active regions during 1980 has been investigated in detail. Specifically, we estimate the uncertainties caused by ground-based data used as input in the modeling effort, and by our currently incomplete knowledge of the proper parameters that describe the angular variation of sunspot and facular contrasts. We conclude that the most significant uncertainties are due to errors in area measurements and, possibly, varying spot and facular brightness. A ‘standard model’ for later use is derived by a best-fit technique of the currently available ACRIM irradiance data and the predictions of our models with appropriately varied parameters. Finally, we compute the expected irradiance for the entire year of 1980.

Solar Constant: Constraints on Possible Variations Derived from Solar Diameter Measurements

Climatically significant variation of the solar constant (the energy output of the sun) implies measurable change in the solar radius. The available data limit variations of the solar radius between 1850 and 1937 to about 0.25 arc second; modeling of the sun indicates that the solar constant did not vary by more than 0.3 percent during that time.

Dynamo-based scheme for forecasting the magnitude of solar activity cycles

In this paper we present a general framework for forecasting the smoothed maximum level of solar activity in a given cycle, based on a simple understanding of the solar dynamo. This type of forecasting requires knowledge of the Suns polar magnetic field strength at the preceeding activity minimum. Because direct measurements of this quantity are difficult to obtain, we evaluate the quality of a number of proxy indicators already used by other authors which are physically related to the Suns polar field. We subject these indicators to a rigorous statistical analysis, and specify in detail the analysis technique for each indicator in order to simplify and systematize reanalysis for future use. We find that several of these proxies are in fact poorly correlated or uncorrelated with solar activity, and thus are of little value for predicting activity maxima.We also present a scheme in which the predictions of the individual proxies are combined via an appropriately weighted mean to produce a compound prediction. We then apply the scheme to the current cycle 22, and estimate a maximum smoothed International sunspot number of 171 ± 26, which can be expressed alternatively as a smoothed 2800 MHz radio flux (F10.7) of 211 ± 23 × (10−22 Wm−2Hz−1), or as a smoothed sunspot area of 2660 ± 430 millionths of a solar disk. Once the actual maximum for cycle 22 has been established, we will have both additional statistics for all the proxy indicators, and a clearer indication of how accurately the present scheme can predict solar activity levels.

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.