T. L. Duvall

A subsurface flow of material from the Sun's equator to its poles

Gas on the Suns surface has been observed to flow away from the equator towards both poles. If the same flow persists to great depths, it could play an important dynamical role in the eleven-year sunspot cycle, by carrying the magnetic remnants of the sunspots to high latitudes. An even deeper counterflow, which would be required to maintain mass balance, could explain why new sunspots form at lower latitudes as the cycle progresses. These deep flows would also redistribute angular momentum within the Sun, and therefore help to maintain the faster rotation of the equator relative to the poles. Here we report the detection, using helioseismic tomography, of the longitude-averaged subsurface flow in the outer 4% of the Sun. We find that the subsurface flow is approximately constant in this depth range, and that the speed is similar to that seen on the surface. This demonstrates that the surface flow penetrates deeply, so that it is likely to be an important factor in solar dynamics.

Modeling of solar oscillation power spectra

To produce accurate estimates of the line-profile parameters of a model used to represent the spectral features in a solar oscillation power spectrum, it is necessary to (1) select the appropriate probability density function when deriving the maximum-likelihood function to be employed for the parameter estimation and (2) allow for the redistribution of spectral power caused by gaps in the data string. This paper describes a maximum-likelihood method for estimating the model parameters (based on the observed power spectrum statistics) that accounts for redistribution of spectral power caused by gaps in the data string, by convolving the model with the power spectrum of the observed window function. The accuracy and reliability of the method were tested using both artificial and authentic solar oscillation power spectrum data. A comparison of this method with various least-squares techniques is also presented.

Investigation of Mass Flows beneath a Sunspot by Time-Distance Helioseismology

A time-distance helioseismic technique is employed to analyze a set of high-resolution Dopplergram observations of a large sunspot by SOHO/MDI on 1998 June 18. A regularized, damped least-squares inversion is applied to the measurements of travel times to infer mass flows around the sunspot below the solar surface. Powerful converging and downward directed flows are detected at depths of 1.5-5 Mm, which may provide observational evidence for the downdrafts and vortex flows that were suggested by Parker for a cluster model of sunspots. Strong outflows extending more than 30 Mm are found below the downward and converging flows. It is suggested that the sunspot might be a relatively shallow phenomenon, with a depth of 5-6 Mm, as defined by its thermal and hydrodynamic properties. A strong mass flow across the sunspot is found at depths of 9-12 Mm, which may provide more evidence in support of the cluster model, as opposed to the monolithic sunspot model. We suggest that a new magnetic emergence that was found 5 hr after our analysis period is related to this mass flow.

Acoustic absorption by sunspots

The paper presents the initial results of a series of observations designed to probe the nature of sunspots by detecting their influence on high-degree p-mode oscillations in the surrounding photosphere. The analysis decomposes the observed oscillations into radially propagating waves described by Hankel functions in a cylindrical coordinate system centered on the sunspot. From measurements of the differences in power between waves traveling outward and inward, it is demonstrated that sunspots appear to absorb as much as 50 percent of the incoming acoustic waves. It is found that for all three sunspots observed, the amount of absorption increases linearly with horizontal wavenumber. The effect is present in p-mode oscillations with wavelengths both significantly larger and smaller than the diameter of the sunspot umbrae. Actual absorption of acoustic energy of the magnitude observed may produce measurable decreases in the power and lifetimes of high-degree p-mode oscillations during periods of high solar activity. 10 references.

Detection of Equatorward Meridional Flow and Evidence of Double-Cell Meridional Circulation inside the Sun

Meridional flow in the solar interior plays an important role in redistributing angular momentum and transporting magnetic flux inside the Sun. Although it has long been recognized that the meridional flow is predominantly poleward at the Suns surface and in its shallow interior, the location of the equatorward return flow and the meridional flow profile in the deeper interior remain unclear. Using the first 2 yr of continuous helioseismology observations from the Solar Dynamics Observatory/Helioseismic Magnetic Imager, we analyze travel times of acoustic waves that propagate through different depths of the solar interior carrying information about the solar interior dynamics. After removing a systematic center-to-limb effect in the helioseismic measurements and performing inversions for flow speed, we find that the poleward meridional flow of a speed of 15 m s–1 extends in depth from the photosphere to about 0.91 R ☉. An equatorward flow of a speed of 10 m s–1 is found between 0.82 and 0.91 R ☉ in the middle of the convection zone. Our analysis also shows evidence of that the meridional flow turns poleward again below 0.82 R ☉, indicating an existence of a second meridional circulation cell below the shallower one. This double-cell meridional circulation profile with an equatorward flow shallower than previously thought suggests a rethinking of how magnetic field is generated and redistributed inside the Sun.

The absorption of high-degree p-mode oscillations in and around sunspots

The paper presents a technique for directly measuring the effect of local regions on solar p-mode oscillations. It was used to detect and measure p-mode absorption in and around several sunspots. Sunspots are found to absorb an energy flux of the order of about 10 to the 7th ergs/ sq cm s, which is about 0.0001 of the sunspot energy deficit. Thus, p-modes have only a negligible effect on the total sunspot energetics. However, the effect of active regions in dissipating high-degree p-mode energy appears to be very significant. 24 references.

STRUCTURE AND ROTATION OF THE SOLAR INTERIOR: INITIAL RESULTS FROM THE MDI MEDIUM-L PROGRAM

The medium-l program of the Michelson Doppler Imager instrument on board SOHO provides continuous observations of oscillation modes of angular degree, l, from 0 to ∼ 300. The data for the program are partly processed on board because only about 3% of MDI observations can be transmitted continuously to the ground. The on-board data processing, the main component of which is Gaussian-weighted binning, has been optimized to reduce the negative influence of spatial aliasing of the high-degree oscillation modes. The data processing is completed in a data analysis pipeline at the SOI Stanford Support Center to determine the mean multiplet frequencies and splitting coefficients.

The NASA/NSO spectromagnetograph

The NASA/NSO Spectromagnetograph is a new focal plane instrument for the National Solar Observatory/Kitt Peak Vacuum Telescope which features real-time digital analysis of long-slit spectra formed on a two-dimensional CCD detector. The instrument is placed at an exit port of a Littrow spectrograph and uses an existing modulator of circular polarization. The new instrument replaces the 512-channel Diode Array Magnetograph first used in 1973. Commercial video processing boards are used to digitize the spectral images at video rates and to separate, accumulate, and buffer the spectra in the two polarization states. An attached processor removes fixed-pattern bias and gain from the spectra in cadence with spatial scanning of the image across the entrance slit. The data control computer performs position and width analysis of the line profiles as they are acquired and records line-of-sight magnetic field, Doppler shift, and other computed parameters. The observer controls the instrument through windowed processes on a data control console using a keyboard and mouse. Early observations made with the spectromagnetograph are presented and plans for future development are discussed.

Asymmetries of solar oscillation line profiles

Asymmetries of the power spectral line profiles of solar global p-modes are detected in full-disk intensity observations of the Ca II K Fraunhofer line. The asymmetry is a strong function of temporal frequency being strongest at the lowest frequencies observed and vanishing near the peak of the power distribution. The variation with spherical harmonic degree is small. The asymmetry is interpreted in terms of a model in which the solar oscillation cavity is compared to a Fabry-Perot interferometer with the source slightly outside the cavity. A phase difference between an outward direct wave and a corresponding inward wave that passes through the cavity gives rise to the asymmetry. The asymmetry is different in velocity and intensity observations. Neglecting the asymmetry when modeling the power spectrum can lead to systematic errors in the measurement of mode frequencies of as much as 10 exp -4 of the mode frequency. The present observations and interpretation locate the source of the oscillations to be approximately 60 km beneath the photosphere, the shallowest position suggested to date.

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.