R. S. Bogart

Helioseismic Studies of Differential Rotation in the Solar Envelope by the Solar Oscillations Investigation Using the Michelson Doppler Imager

The splitting of the frequencies of the global resonant acoustic modes of the Sun by large-scale flows and rotation permits study of the variation of angular velocity Ω with both radius and latitude within the turbulent convection zone and the deeper radiative interior. The nearly uninterrupted Doppler imaging observations, provided by the Solar Oscillations Investigation (SOI) using the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft positioned at the L1 Lagrangian point in continuous sunlight, yield oscillation power spectra with very high signal-to-noise ratios that allow frequency splittings to be determined with exceptional accuracy. This paper reports on joint helioseismic analyses of solar rotation in the convection zone and in the outer part of the radiative core. Inversions have been obtained for a medium-l mode set (involving modes of angular degree l extending to about 250) obtained from the first 144 day interval of SOI-MDI observations in 1996. Drawing inferences about the solar internal rotation from the splitting data is a subtle process. By applying more than one inversion technique to the data, we get some indication of what are the more robust and less robust features of our inversion solutions. Here we have used seven different inversion methods. To test the reliability and sensitivity of these methods, we have performed a set of controlled experiments utilizing artificial data. This gives us some confidence in the inferences we can draw from the real solar data. The inversions of SOI-MDI data have confirmed that the decrease of Ω with latitude seen at the surface extends with little radial variation through much of the convection zone, at the base of which is an adjustment layer, called the tachocline, leading to nearly uniform rotation deeper in the radiative interior. A prominent rotational shearing layer in which Ω increases just below the surface is discernible at low to mid latitudes. Using the new data, we have also been able to study the solar rotation closer to the poles than has been achieved in previous investigations. The data have revealed that the angular velocity is distinctly lower at high latitudes than the values previously extrapolated from measurements at lower latitudes based on surface Doppler observations and helioseismology. Furthermore, we have found some evidence near latitudes of 75° of a submerged polar jet which is rotating more rapidly than its immediate surroundings. Superposed on the relatively smooth latitudinal variation in Ω are alternating zonal bands of slightly faster and slower rotation, each extending some 10° to 15° in latitude. These relatively weak banded flows have been followed by inversion to a depth of about 5% of the solar radius and appear to coincide with the evolving pattern of torsional oscillations reported from earlier surface Doppler studies.

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.

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.

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 PHOTOSPHERIC CONVECTION SPECTRUM

Spectra of the cellular photospheric flows are determined from observations acquired by the MDI instrument on the SOHO spacecraft. Spherical harmonic spectra are obtained from the full-disk observations. Fourier spectra are obtained from the high-resolution observations. The p-mode oscillation signal and instrumental artifacts are reduced by temporal filtering of the Doppler data. The resulting spectra give power (kinetic energy) per wave number for effective spherical harmonic degrees from 1 to over 3000. Significant power is found at all wavenumbers, including the small wavenumbers representative of giant cells. The time evolution of the spectral coefficients indicates that these small wavenumber components rotate at the solar rotation rate and thus represent a component of the photospheric cellular flows. The spectra show distinct peaks representing granules and supergranules but no distinct features at wavenumbers representative of mesogranules or giant cells. The observed cellular patterns and spectra are well represented by a model that includes two distinct modes – granules and supergranules.

Systematic Center-to-limb Variation in Measured Helioseismic Travel Times and its Effect on Inferences of Solar Interior Meridional Flows

We report on a systematic center-to-limb variation in measured helioseismic travel times, which must be taken into account for an accurate determination of solar interior meridional flows. The systematic variation, found in time-distance helioseismology analysis using SDO/HMI and SDO/AIA observations, is different in both travel-time magnitude and variation trend for different observables. It is not clear what causes this systematic effect. Subtracting the longitude-dependent east-west travel times, obtained along the equatorial area, from the latitude-dependent north-south travel times, obtained along the central meridian area, gives remarkably similar results for different observables. We suggest this as an effective procedure for removing the systematic center-to-limb variation. The subsurface meridional flows obtained from inversion of the corrected travel times are approximately 10 m s{sup -1} slower than those obtained without removing the systematic effect. The detected center-to-limb variation may have important implications in the derivation of meridional flows in the deep interior and needs to be better understood.

Flows and Horizontal Displacements from Ring Diagrams

A new algorithm for analyzing ring diagrams from helioseismic data is presented. This method is applied to two months of Solar and Heliospheric Observatory/Michelson Doppler Imager data from 1996 May 24 through July 24 to study flows and to measure the ratio of the horizontal displacement to the vertical displacement for the oscillations. We find that (1) the rotation rate agrees well with that measured from global modes, extending the measurements closer to the surface; (2) there is a 20 m s-1 poleward meridional flow; (3) there are medium-scale velocity features persisting for several days; (4) the radial gradient of the near surface rotation rate decreases with latitude; and (5) meridional flow decreases with depth. The measured horizontal-to-vertical displacement ratio is in agreement with that expected from theoretical considerations.

Meridional Flows from Ring Diagram Analysis

In order to search for meridional circulation in the solar envelope, we have applied ring diagram analysis to a set of small regions over the surface. The helioseismic data consist of Solar Oscillation Investigation/Michelson Doppler Imager Dopplergrams taken over a time span of about 50 hr (~3000 images) on 1998 June 20-22. The regions studied cover 115° in latitude centered on the equator and 30° in longitude. We find poleward flows between r/ R=0.97 and the surface. There is no evidence in this depth range for the return path of these meridional flows. The temporal stability of these flows will be discussed after the analysis of a synoptic map obtained using the same technique.

Observables Processing for the Helioseismic and Magnetic Imager Instrument on the Solar Dynamics Observatory

NASA’s Solar Dynamics Observatory (SDO) spacecraft was launched 11 February 2010 with three instruments onboard, including the Helioseismic and Magnetic Imager (HMI). After commissioning, HMI began normal operations on 1 May 2010 and has subsequently observed the Sun’s entire visible disk almost continuously. HMI collects sequences of polarized filtergrams taken at a fixed cadence with two 4096×4096

SOLAR MERIDIONAL FLOW IN THE SHALLOW INTERIOR DURING THE RISING PHASE OF CYCLE 24

4096 \times 4096