J. T. Hoeksema

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.

Spatial structure of the solar wind and comparisons with solar data and models

Data obtained by instruments on the Ulysses spacecraft during its rapid sweep through >90° of solar latitude, crossing the solar equator in early 1995, were combined with data obtained near Earth by the Wind spacecraft to study the spatial structure of the solar wind and to compare to different models of the interplanetary magnetic field derived from solar observations. Several different source-surface models matched the double sinusoidal structure of the heliospheric current sheet (HCS) but with differences in latitude as great as 21°. The source-surface model that included an interplanetary current sheet gave poorer agreement with observed current-sheet crossings during this period than did the other source-surface models or an MHD model. The differences between the calculated and observed locations of the HCS were minimized when 22° of solar rotation was added to the constant-velocity travel time from the source surface to the spacecraft. The photospheric footpoints of the open field lines calculated from the models generally agreed with observations in the He 10,830 A line of the locations of coronal holes with the exceptions that (1) in some places, open field lines originated outside the coronal hole boundaries and (2) the models show apparently closed-field regions just inside some coronal hole boundaries. The patterns of mismatches between coronal hole boundaries and the envelopes of open field lines persisted over at least three solar rotations. The highest-speed wind came from the polar coronal holes, with the wind originating deeper within the hole being faster than the wind coming from near the hole boundary. Intermediate and slow streams originated in smaller coronal holes at low latitudes and from open field regions just outside coronal hole boundaries. Although the HCS threaded regions of low speed, low helium abundance, high ionization temperature, and a high ratio of magnesium to oxygen densities (a surplus of an element with low first-ionization potential), there was a great deal of variation in these parameters from one place to another along the HCS. The gradient of speed with latitude varied from 14 to 28 km s−1 deg−1.

The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: SHARPs – Space-Weather HMI Active Region Patches

A new data product from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) called Space-weather HMI Active Region Patches (SHARPs) is now available. SDO/HMI is the first space-based instrument to map the full-disk photospheric vector magnetic field with high cadence and continuity. The SHARP data series provide maps in patches that encompass automatically tracked magnetic concentrations for their entire lifetime; map quantities include the photospheric vector magnetic field and its uncertainty, along with Doppler velocity, continuum intensity, and line-of-sight magnetic field. Furthermore, keywords in the SHARP data series provide several parameters that concisely characterize the magnetic-field distribution and its deviation from a potential-field configuration. These indices may be useful for active-region event forecasting and for identifying regions of interest. The indices are calculated per patch and are available on a twelve-minute cadence. Quick-look data are available within approximately three hours of observation; definitive science products are produced approximately five weeks later. SHARP data are available at jsoc.stanford.edu and maps are available in either of two different coordinate systems. This article describes the SHARP data products and presents examples of SHARP data and parameters.

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.

Polar Plume Anatomy: Results of a Coordinated Observation

On 7 and 8 March 1996, the SOHO spacecraft and several other space- and ground-based observatories cooperated in the most comprehensive observation to date of solar polar plumes. Based on simultaneous data from five instruments, we describe the morphology of the plumes observed over the south pole of the Sun during the SOHO observing campaign. Individual plumes have been characterized from the photosphere to approximately 15 R⊙ yielding a coherent portrait of the features for more quantitative future studies. The observed plumes arise from small (∼ 2-5 arc sec diameter) quiescent, unipolar magnetic flux concentrations, on chromospheric network cell boundaries. They are denser and cooler than the surrounding coronal hole through which they extend, and are seen clearly in both Feix and Fexii emission lines, indicating an ionization temperature between 1.0–1.5 x 106 K. The plumes initially expand rapidly with altitude, to a diameter of 20–30 Mm about 30 Mm off the surface. Above 1.2 R⊙ plumes are observed in white light (as ‘coronal rays’) and extend to above 12 R⊙. They grow superradially throughout their observed height, increasing their subtended solid angle (relative to disk center) by a factor of ∼10 between 1.05 R⊙ and 4–5 R⊙ and by a total factor of 20–40 between 1.05 R⊙ and 12 R⊙. On spatial scales larger than 10 arc sec, plume structure in the lower corona (R < 1.3 R⊙) is observed to be steady-state for periods of at least 24 hours; however, on spatial scales smaller than 10 arc sec, plume XUV intensities vary by 10–20% (after background subtraction) on a time scale of a few minutes.

SOLAR MAGNETIC FIELD REVERSALS AND THE ROLE OF DYNAMO FAMILIES

The variable magnetic field of the solar photosphere exhibits periodic reversals as a result of dynamo activity occurring within the solar interior. We decompose the surface field as observed by both the Wilcox Solar Observatory and the Michelson Doppler Imager into its harmonic constituents, and present the time evolution of the mode coefficients for the past three sunspot cycles. The interplay between the various modes is then interpreted from the perspective of general dynamo theory, where the coupling between the primary and secondary families of modes is found to correlate with large-scale polarity reversals for many examples of cyclic dynamos. Mean-field dynamos based on the solar parameter regime are then used to explore how such couplings may result in the various long-term trends in the surface magnetic field observed to occur in the solar case.

Observational Upper Limits to Low-Degree Solar g-Modes

Observations made by the Michelson Doppler Imager (MDI) and Variability of solar IRradiance and Gravity Oscillations (VIRGO) on the Solar and Heliospheric Observatory (SOHO) and by the ground-based Birmingham Solar Oscillations Network (BiSON) and Global Oscillations Network Group (GONG) have been used in a concerted effort to search for solar gravity oscillations. All spectra are dominated by solar noise in the frequency region from 100 to 1000 μHz, where g-modes are expected to be found. Several methods have been used in an effort to extract any g-mode signal present. These include (1) the correlation of data—both full-disk and imaged (with different spatial-mask properties)—collected over different time intervals from the same instrument, (2) the correlation of near-contemporaneous data from different instruments, and (3) the extraction—through the application of complex filtering techniques—of the coherent part of data collected at different heights in the solar atmosphere. The detection limit is set by the loss of coherence caused by the temporal evolution and the motion (e.g., rotation) of superficial structures. Although we cannot identify any g-mode signature, we have nevertheless set a firm upper limit to the amplitudes of the modes: at 200 μHz, they are below 10 mm s-1 in velocity, and below 0.5 parts per million in intensity. The velocity limit corresponds very approximately to a peak-to-peak vertical displacement of δR/R☉ = 2.3 × 10-8 at the solar surface. These levels which are much lower than prior claims, are consistent with theoretical predictions.

The relationship between large‐scale solar magnetic field evolution and coronal mass ejections

The idea that coronal mass ejections (CMEs) originate from the evolution of the large-scale solar field and in particular arise from regions of freshly opening coronal flux is reexamined using a new approach. Potential field models constructed from Wilcox Solar Observatory magnetograms are applied to study both the rate of “opening” of coronal fields with time and the locations of observed CMEs compared to the inferred newly open field regions on the Sun. Case studies are drawn from SMM coronagraph data, Yohkoh soft X ray images, and counterstreaming electron events observed on the ICE spacecraft. The results suggest that the large-scale field evolution paradigm of CMEs deserves further attention and has potential for applications to “space weather” forecasting.

Rotation of the Coronal Magnetic Field

The coronal magnetic field rotates differently than the photosphere. The field configuration of the corona can be calculated from the observed photosphpere field using a potential field model. Correlation of the field patterns at different latitudes with a lag near one solar rotation shows much less differential rotation than observed in the photospheric field; however, the peak is very broad and determines the rotation rate rather poorly. Consideration of longer lags reveals a more complex rotational structure and indicates different rotation rates in the Northern and Southern Hemispheres. Spectral analysis of the equatorial dipole component of the coronal field reveals an organization into just a few discrete rotation frequencies which are apparently present simultaneously. Spectral analysis of the field at different latitudes shows that the frequencies are present simultaneously. Spectra analysis of the field at different latitudes shows that the frequencies are present simultaneously, but in different hemispheres, and that the Southern Hemisphere fields rotate more slowly than those in the north in solar cycle 21. 32 references.

How Should One Optimize Nonlinear Force-Free Coronal Magnetic Field Extrapolations from SDO/HMI Vector Magnetograms?

The Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) provides photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semianalytic and numeric equilibria and applied to vector magnetograms from Hinode and ground-based observations. Recently we implemented a new version which takes into account measurement errors in photospheric vector magnetograms. Photospheric field measurements are often affected by measurement errors and finite nonmagnetic forces inconsistent for use as a boundary for a force-free field in the corona. To deal with these uncertainties, we developed two improvements: i) preprocessing of the surface measurements to make them compatible with a force-free field, and ii) new code which keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which must be optimized for use with data from SDO/HMI. In this work we describe the corresponding analysis method and evaluate the force-free equilibria by how well force-freeness and solenoidal conditions are fulfilled, by the angle between magnetic field and electric current, and by comparing projections of magnetic field lines with coronal images from the Atmospheric Imaging Assembly (SDO/AIA). We also compute the available free magnetic energy and discuss the potential influence of control parameters.