Robert D. Howe

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.

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.

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 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 p-mode frequencies and their dependence on solar-activity - recent results from the BISON network

We present here high-accuracy determinations of the frequencies of low-l solar p-modes and their solar-cycle dependence. The data were obtained using the Birmingham network of solar spectrometers (BISON). The precision of the measurements is discussed. Our previously published results of a significant frequency shift between solar minimum and solar maximum, apparently independent of l and similar to that found by other workers for intermediate-l modes, is confirmed and extended. This suggests that at most only a small fraction of the variation is due to the solar core. Sets of frequencies at high and low solar activity, and an average corrected for solar-activity effects, are presented. There is now evidence that the solar-activity dependence of the frequencies varies across the 5 minute spectrum.

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.

SOLAR SUBSURFACE FLUID DYNAMICS DESCRIPTORS DERIVED FROM GLOBAL OSCILLATION NETWORK GROUP AND MICHELSON DOPPLER IMAGER DATA

We analyze Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) observations obtained during Carrington rotation 1988 (2002 March 30-April 26) with a ring-diagram technique in order to measure the zonal and meridional flow components in the upper solar convection zone. We derive daily flow maps over a range of depths up to 16 Mm on a spatial grid of 75 in latitude and longitude covering ±60° in latitude and central meridian distance and combine them to make synoptic flow maps. We begin exploring the dynamics of the near-surface layers and the interaction between flows and magnetic flux by deriving fluid dynamics descriptors such as divergence and vorticity from these flow maps. Using these descriptors, we derive the vertical velocity component and the kinetic helicity density. For this particular Carrington rotation, we find that the vertical velocity component is anticorrelated with the unsigned magnetic flux. Strong downflows are more likely associated with locations of strong magnetic activity. The vertical vorticity is positive in the northern hemisphere and negative in the southern hemisphere. At locations of magnetic activity, we find an excess vorticity of the same sign as that introduced by differential rotation. The vertical gradient of the zonal flow is mainly negative except within 2 Mm of the surface at latitudes poleward of about 20°. The zonal-flow gradient appears to be related to the unsigned magnetic flux in the sense that locations of strong activity are also locations of large negative gradients. The vertical gradient of the meridional flow changes sign near about 7 Mm, marking a clear distinction between near-surface and deeper layers. GONG and MDI data show very similar results. Differences occur mainly at high latitudes, especially in the northern hemisphere, where MDI data show a counter cell in the meridional flow that is not present in the corresponding GONG data.

Localizing the Solar Cycle Frequency Shifts in Global p-Modes

The 6.5 yr span of observations from the Global Oscillation Network Group and the Michelson Doppler Imager aboard the Solar and Heliospheric Observatory allows a detailed study of the solar cycle-related frequency shifts at the level of central frequencies and a-coefficients from individual multiplets and even of individual modes within a multiplet. We analyze such data and show that the shifts at all levels of averaging are consistent with the hypothesis that the global p-mode frequency shifts are closely related to the surface magnetic field distribution. Furthermore, the evolution of the surface magnetic flux distribution can be reconstructed by an inversion technique operating on the shifts within individual (n, l) multiplets.

SOLAR CONVECTION-ZONE DYNAMICS, 1995-2004

The nine-year span of medium-degree helioseismic data from the Global Oscillation Network Group (GONG) and the Michelson Doppler Imager (MDI) allows us to study the evolving zonal flows in the solar convection zone over the rising phase, maximum, and early declining phase of solar cycle 23. Using two independent two-dimensional rotation inversion techniques, we investigate the depth profile of the flow pattern known as the torsional oscillation. The observations suggest that the flows penetrate deep within the convection zone—perhaps to its base—even at low latitudes, and that the phase of the pattern is approximately constant along lines of constant rotation rather than lines of constant latitude.

A NOTE ON THE TORSIONAL OSCILLATION AT SOLAR MINIMUM

We examine the evolution of the zonal flow pattern in the upper solar convection zone during the current extended solar minimum, and compare it with that during the previous minimum. The results suggest that a configuration matching that at the previous minimum was reached during 2008, but that the flow band corresponding to the new cycle has been moving more slowly toward the equator than was observed in the previous cycle, resulting in a gradual increase in the apparent length of the cycle during the 2007-2008 period. The current position of the lower-latitude fast-rotating belt corresponds to that seen around the onset of activity in the previous cycle.