Deborah A. Haber

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.

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.

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.

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.

Meridional Circulation Variability from Large‐Aperture Ring‐Diagram Analysis of Global Oscillation Network Group and Michelson Doppler Imager Data

Ring-diagram analysis, a local helioseismology technique, has proven to be very useful for studying solar subsurface velocity flows down to a depth of about 0.97 R☉. The depth range is determined by the modes used in this type of analysis, and thus depends on the size of the area analyzed. Extending the area allows us to detect lower spherical harmonic degree (l) modes which, at a constant frequency, penetrate deeper in the Sun. However, there is a compromise between the size of the area and the validity of the plane-wave approximation used by the technique. We present the results of applying the ring diagrams to 30° diameter areas over the solar surface in an attempt to reach deeper into the solar interior. Meridional flows for 25 consecutive Carrington rotations (1985-2009) are derived by applying this technique to Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) data. This covers a time span of almost 2 yr, starting at the beginning of 2002. The amplitude of the meridional flow shows a variation of the order of 5 m s-1 during this period. Our results indicate that the flows increase toward the interior of the Sun for the depth range studied. We find a 1 yr periodicity in the appearance of an equatorward meridional cell at high latitudes that coincides with maximum values of the solar inclination toward the Earth (B0 angle).

Comparison of Solar Subsurface Flows Assessed by Ring and Time‐Distance Analyses

The solar near-surface shear layer exhibits a rich medley of flows that are now being measured by a variety of local helioseismic techniques. We present comparisons of the horizontal flows obtained with two of these techniques, ring and time-distance analyses, applied to Michelson Doppler Imager (MDI) Dynamics Program data from the years 1998 and 1999. The ring analyses use the frequencies of both f and p modes in inversions to obtain flows within the near-surface shear layer as a function of depth. The f-mode time-distance analyses make velocity inferences just beneath the photosphere. After degrading the spatial resolution of the time-distance analyses to match the coarser resolution of the ring analyses, we find that the flows deduced with the two methods are remarkably similar, with common inflow and outflow sites as well as agreement in flow direction. The flows from ring and time-distance analyses are highly correlated with each other (correlation coefficients ~0.8); direct correspondence of features in the flows is largely realized in both the quiet-Sun and magnetic active regions.

Organized Subsurface Flows near Active Regions

Local helioseismic techniques, such as ring analysis and time-distance helioseismology, have already shown that large-scale flows near the surface converge towards major active regions. Ring analysis has further demonstrated that at greater depths some active regions exhibit strong outflows. A critique leveled at the ring-analysis results is that the Regularized Least Squares (RLS) inversion kernels on which they are based have negative sidelobes near the surface. Such sidelobes could result in a surface inflow being misidentified as a diverging outflow at depth. In this paper we show that the Optimally Located Averages (OLA) inversion technique, which produces kernels without significant sidelobes, generates flows markedly similar to the RLS results. Active regions are universally zones of convergence near the surface, while large complexes evince strong outflows deeper down.

Divergence and Vorticity of Solar Subsurface Flows Derived from Ring‐Diagram Analysis of MDI and GONG Data

We measure the relation between divergence and vorticity of subsurface horizontal flows as a function of unsigned surface magnetic flux. Observations from the Michelson Doppler Imager (MDI) Dynamics Program and Global Oscillation Network Group (GONG) have been analyzed with a standard ring-diagram technique to measure subsurface horizontal flows from the surface to a depth of about 16 Mm. We study residual horizontal flows after subtracting large-scale trends (low-order polynomial fits in latitude) from the measured velocities. On average, quiet regions are characterized by weakly divergent horizontal flows and small anticyclonic vorticity (clockwise in the northern hemisphere), while locations of high activity show convergent horizontal flows combined with cyclonic vorticity (counterclockwise in the northern hemisphere). Divergence and vorticity of horizontal flows are anticorrelated (correlated) in the northern (southern) hemisphere. This is especially noticeable at greater depth, where the relation between divergence and vorticity of horizontal flows is nearly linear. These trends show a slight reversal at the highest levels of magnetic flux; the vorticity amplitude decreases at the highest flux levels, while the divergence changes sign at depths greater than about 10 Mm. The product of divergence and vorticity of the horizontal flows, a proxy of the vertical contribution to the kinetic helicity density, is on average negative (positive) in the northern (southern) hemisphere. The helicity proxy values are greater at locations of high magnetic activity than at quiet locations.

Flares, Magnetic Fields, and Subsurface Vorticity: A Survey of GONG and MDI Data

We search for a relation between flows below active regions and flare events occurring in those active regions. For this purpose, we determine the subsurface flows from high-resolution Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) Dynamics Program data using the ring-diagram technique. We then calculate the vorticity of the flows associated with active regions and compare it with a proxy of the total X-ray flare intensity of these regions using data from the Geostationary Operation Environmental Satellite (GOES). We have analyzed 408 active regions with X-ray flare activity from GONG and 159 active regions from MDI data. Both data sets lead to similar results. The maximum unsigned zonal and meridional vorticity components of active regions are correlated with the total flare intensity; this behavior is most apparent at values greater than 3.2 × 10-5 W m-2. These vorticity components show a linear relation with the logarithm of the flare intensity that is dependent on the maximum unsigned magnetic flux; vorticity values are proportional to the product of total flare intensity and maximum unsigned magnetic flux for flux values greater than about 36 G. Active regions with strong flare intensity show a dipolar pattern in the zonal and meridional vorticity component that reverses at depths between ~2 and 5 Mm. A measure of this pattern shows the same kind of relation with total flare intensity as the vorticity components. The vertical vorticity component shows no clear relation to flare activity.

Activity-related Changes in Local Solar Acoustic Mode Parameters from Michelson Doppler Imager and Global Oscillations Network Group

We use the ring-diagram technique of local helioseismology to study the amplitude and line width of high-degree solar acoustic modes from 474 days of data from the Michelson Doppler Imager Dynamics program, covering the period 1996-2002. The 2002 data are compared with contemporaneous data from the Global Oscillations Network Group network. The results, once instrumental effects have been removed, show a strong dependence of the amplitude and lifetime of the modes on the local magnetic flux, with the amplitude and lifetime decreasing in the 5 minute band and a reversed trend at high frequencies. We relate these findings to results from global modes and from other approaches for analyzing high-degree local oscillations.