Frank Hill

The current state of solar modeling

Data from the Global Oscillation Network Group (GONG) project and other helioseismic experiments provide a test for models of stellar interiors and for the thermodynamic and radiative properties, on which the models depend, of matter under the extreme conditions found in the sun. Current models are in agreement with the helioseismic inferences, which suggests, for example, that the disagreement between the predicted and observed fluxes of neutrinos from the sun is not caused by errors in the models. However, the GONG data reveal subtle errors in the models, such as an excess in sound speed just beneath the convection zone. These discrepancies indicate effects that have so far not been correctly accounted for; for example, it is plausible that the sound-speed differences reflect weak mixing in stellar interiors, of potential importance to the overall evolution of stars and ultimately to estimates of the age of the galaxy based on stellar evolution calculations.

Evolving Submerged Meridional Circulation Cells within the Upper Convection Zone Revealed by Ring-Diagram Analysis

Using the local helioseismic technique of ring-diagram analysis applied to Michelson Doppler Imager (MDI) Dynamics Program data from the Solar and Heliospheric Observatory, we have discovered that the meridional flow within the upper convection zone can develop additional circulation cells whose boundaries wander in latitude and depth as the solar cycle progresses. We report on the large-scale meridional and zonal flows that we observe from 1996 to 2001. In particular, we discuss the appearance and evolution of a submerged meridional cell during the years 1998-2001, which arose in the northern hemisphere and disrupted the orderly poleward flow and symmetry about the equator that is typically observed. The meridional flows in the southern and northern hemispheres exhibit striking asymmetry during the past four years of the advancing solar cycle. Such asymmetry and additional circulation cells should have profound impact on the transport of angular momentum and magnetic field within the surface layers. These flows may have a significant role in the establishment and maintenance of the near-surface rotational shear layer.

The Global Oscillation Network Group (GONG) Project

Helioseismology requires nearly continuous observations of the oscillations of the solar surface for long periods of time in order to obtain precise measurements of the suns normal modes of oscillation. The GONG project acquires velocity images from a network of six identical instruments distributed around the world. The GONG network began full operation in October 1995. It has achieved a duty cycle of 89 percent and reduced the magnitude of spectral artifacts by a factor of 280 in power, compared with single-site observations. The instrumental noise is less than the observed solar background.

Differential rotation and dynamics of the solar interior

Splitting of the suns global oscillation frequencies by large-scale flows can be used to investigate how rotation varies with radius and latitude within the solar interior. The nearly uninterrupted observations by the Global Oscillation Network Group (GONG) yield oscillation power spectra with high duty cycles and high signal-to-noise ratios. Frequency splittings derived from GONG observations confirm that the variation of rotation rate with latitude seen at the surface carries through much of the convection zone, at the base of which is an adjustment layer leading to latitudinally independent rotation at greater depths. A distinctive shear layer just below the surface is discernible at low to mid-latitudes.

Rings and trumpets - three-dimensional power spectra of solar oscillations

When slices of characteristic trumpet surfaces visible in three-dimensional power spectra of the Doppler shifts observed on the solar surface are taken at constant temporal frequency, the cross sections form rings. Analysis of the shape and position of these rings provides information on the horizontal flow field and the thermodynamic structure below the photosphere. The relationship between the parameters of an elliptical approximation to the rings and the subphotospheric state is derived, and a numerical simulation is presented. A preliminary application to real data suggests the presence of a flow of 100 m/s directed from the equator toward the south pole. A comparison of the velocities inferred from a single ring obtained at different longitudes shows variations of 20-40 m/s, suggesting that large-scale convection is not azimuthally symmetric. 40 references.

The Seismic Structure of the Sun

Global Oscillation Network Group data reveal that the internal structure of the sun can be well represented by a calibrated standard model. However, immediately beneath the convection zone and at the edge of the energy-generating core, the sound-speed variation is somewhat smoother in the sun than it is in the model. This could be a consequence of chemical inhomogeneity that is too severe in the model, perhaps owing to inaccurate modeling of gravitational settling or to neglected macroscopic motion that may be present in the sun. Accurate knowledge of the suns structure enables inferences to be made about the physics that controls the sun; for example, through the opacity, the equation of state, or wave motion. Those inferences can then be used elsewhere in astrophysics.

The Solar Acoustic Spectrum and Eigenmode Parameters

The Global Oscillation Network Group (GONG) project estimates the frequencies, amplitudes, and linewidths of more than 250,000 acoustic resonances of the sun from data sets lasting 36 days. The frequency resolution of a single data set is 0.321 microhertz. For frequencies averaged over the azimuthal order m, the median formal error is 0.044 microhertz, and the associated median fractional error is 1.6 × 10−5. For a 3-year data set, the fractional error is expected to be 3 × 10−6. The GONG m-averaged frequency measurements differ from other helioseismic data sets by 0.03 to 0.08 microhertz. The differences arise from a combination of systematic errors, random errors, and possible changes in solar structure.

Solar Cycle Changes in GONG p-Mode Frequencies, 1995-1998

We have analyzed 27 3 month sets of Global Oscillaiton Network Group (GONG) data from the end of cycle 22 and the beginning of cycle 23 and here present evidence of significant shifts in the central frequencies and the even a-coefficients of the frequency splittings of the modes. The temporal behavior of the even a-coefficients is better reproduced by the corresponding coefficients of a Legendre polynomial decomposition of the surface magnetic field than by the total flux; i.e., the temporal variation is strongly correlated with the latitudinal distribution of the surface magnetic activity. These changes are consistent with available data from previous solar cycles. The even a-coefficients, which sense the asphericity of the solar structure, appear to show similar temporal evolution at all depths. The odd a-coefficients, which sense the internal differential rotation, show no significant variation with time or depth. In particular they show no significant correlation with either the magnetic flux or with the corresponding odd Legendre components of the flux. This suggests that the solar cycle related variation of the oscillation frequencies is not due to contamination of observed Doppler shifts by the surface magnetic fields.

GONG Observations of Solar Surface Flows

Doppler velocity observations obtained by the Global Oscillation Network Group (GONG) instruments directly measure the nearly steady flows in the solar photosphere. The suns differential rotation is accurately determined from single observations. The rotation profile with respect to latitude agrees well with previous measures, but it also shows a slight north-south asymmetry. Rotation profiles averaged over 27-day rotations of the sun reveal the torsional oscillation signal—weak, jetlike features, with amplitudes of 5 meters per second, that are associated with the sunspot latitude activity belts. A meridional circulation with a poleward flow of about 20 meters per second is also evident. Several characteristics of the surface flows suggest the presence of large convection cells.

A Comparison of Solar p-Mode Parameters from the Michelson Doppler Imager and the Global Oscillation Network Group: Splitting Coefficients and Rotation Inversions

Using contemporaneous helioseismic data from the Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) onboard SOHO, we compare frequency-splitting data and resulting inversions about the Suns internal rotation. Helioseismology has been very successful in making detailed and subtle inferences about the solar interior. But there are some significant differences between inversion results obtained from the MDI and GONG projects. It is important for making robust inferences about the solar interior that these differences are located and their causes eliminated. By applying the different analysis pipelines developed by the projects not only to their own data but also to the data from the other project, we conclude that the most significant differences arise not from the observations themselves but from the different frequency estimation analyses used by the projects. We find that the GONG pipeline results in substantially fewer fitted modes in certain regions. The most serious systematic differences in the results, with regard to rotation, appear to be an anomaly in the MDI odd-order splitting coefficients around a frequency of 3.5 mHz and an underestimation of the low-degree rotational splittings in the GONG algorithm.