R. I. Bush

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.

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.

On the Constancy of the Solar Diameter. II.

The Michelson Doppler Imager instrument on board SOHO has operated for most of a solar cycle. Here we present a careful analysis of solar astrometric data obtained with it from above the Earths turbulent atmosphere. These data yield the most accurate direct constraint on possible solar radius variations on timescales from minutes to years and the first accurate determination of the solar radius obtained in the absence of atmospheric seeing.

Spectral Line Selection for HMI: A Comparison of Fe I 6173 Å and Ni I 6768 Å

We present a study of two spectral lines, Fe I 6173 Å and Ni I 6768 Å, that were candidates to be used in the Helioseismic and Magnetic Imager (HMI) for observing Doppler velocity and the vector magnetic field. The line profiles were studied using the Mt. Wilson Observatory, the Advanced Stokes Polarimeter and the Kitt Peak-McMath Pierce telescope and one-meter Fourier transform spectrometer atlas. Both Fe I and Ni I profiles have clean continua and no blends that threaten instrument performance. The Fe I line is 2% deeper, 15% narrower, and has a 6% smaller equivalent width than the Ni I line. The potential of each spectral line to recover pre-assigned solar conditions is tested using a least-squares minimization technique to fit Milne-Eddington models to tens of thousands of line profiles that have been sampled at five spectral positions across the line. Overall, the Fe I line has a better performance than the Ni I line for vector-magnetic-field retrieval. Specifically, the Fe I line is able to determine field strength, longitudinal and transverse flux four times more accurately than the Ni I line in active regions. Inclination and azimuthal angles can be recovered to ≈2° above 600 Mx cm−2 for Fe I and above 1000 Mx cm−2 for Ni I. Therefore, the Fe I line better determines the magnetic-field orientation in plage, whereas both lines provide good orientation determination in penumbrae and umbrae. We selected the Fe I spectral line for use in HMI due to its better performance for magnetic diagnostics while not sacrificing velocity information. The one exception to the better performance of the Fe I line arises when high field strengths combine with high velocities to move the spectral line beyond the effective sampling range. The higher geff of Fe I means that its useful range of velocity values in regions of strong magnetic field is smaller than Ni I.

MEASURING THE SOLAR RADIUS FROM SPACE DURING THE 2003 AND 2006 MERCURY TRANSITS

The Michelson Doppler Imager (MDI) aboard the Solar and Heliospheric Observatory observed the transits of Mercury on 2003 May 7 and 2006 November 8. Contact times between Mercury and the solar limb have been used since the seventeenth century to derive the Suns size but this is the first time that high-quality imagery from space, above the Earths atmosphere, has been available. Unlike other measurements, this technique is largely independent of optical distortion. The true solar radius is still a matter of debate in the literature as measured differences of several tenths of an arcsecond (i.e., about 500 km) are apparent. This is due mainly to systematic errors from different instruments and observers since the claimed uncertainties for a single instrument are typically an order of magnitude smaller. From the MDI transit data we find the solar radius to be 96012 ± 009 (696, 342 ± 65 km). This value is consistent between the transits and consistent between different MDI focus settings after accounting for systematic effects.

On the Constancy of the Solar Radius. III.

The Michelson Doppler Imager on board the Solar and Heliospheric Observatory satellite has operated for over a sunspot cycle. This instrument is now relatively well understood and provides a nearly continuous record of the solar radius in combination with previously developed algorithms. Because these data are obtained from above Earths atmosphere, they are uniquely sensitive to possible long-term changes of the Suns size. We report here on the first homogeneous, highly precise, and complete solar-cycle measurement of the Suns radius variability. Our results show that any intrinsic changes in the solar radius that are synchronous with the sunspot cycle must be smaller than 23 mas peak to peak. In addition, we find that the average solar radius must not be changing (on average) by more than 1.2 mas yr{sup -1}. If ground- and space-based measurements are both correct, the pervasive difference between the constancy of the solar radius seen from space and the apparent ground-based solar astrometric variability can only be accounted for by long-term changes in the terrestrial atmosphere.

Rossby waves on the Sun as revealed by solar 'hills'

It is a long-standing puzzle that the Suns photosphere—its visible surface—rotates differentially, with the equatorial regions rotating faster than the poles. It has been suggested that waves analogous to terrestrial Rossby waves, and known as r-mode oscillations, could explain the Suns differential rotation: Rossby waves are seen in the oceans as large-scale (hundreds of kilometres) variations of sea-surface height (5-cm-high waves), which propagate slowly either east or west (they could take tens of years to cross the Pacific Ocean). Calculations show that the solar r-mode oscillations have properties that should be strongly constrained by differential rotation. Here we report the detection of 100-m-high ‘hills’ in the photosphere, spaced uniformly over the Suns surface with a spacing of (8.7 ± 0.6) × 104 km. If convection under the photosphere is organized by the r-modes, the observed corrugated photosphere is a probable surface manifestation of these solar oscillations.

The Precise Solar Shape and Its Variability

Our Constant Sun The exact shape of the Sun provides information on its internal structure. Based on data obtained by the Helioseismic and Magnetic Imager aboard NASAs Solar Dynamics Observatory, Kuhn et al. (p. 1638, published online 16 August; see the Perspective by Gough) measured the solar shape during a 2-year period in which the Sun evolved from a minimum to a maximum of sunspot activity. Against expectations, the Suns oblate shape was found to be constant and not to vary with the 11-year solar cycle. Observations with NASA’s Solar Dynamics Observatory show that the shape of the Sun does not vary with the 11-year solar cycle. The precise shape of the Sun has not been convincingly determined, despite half a century of modern photoelectric observations. The expected deviation of the solar-limb shape from a perfect circle is very small, but such asphericity is sensitive to the Sun’s otherwise invisible interior conditions, as well as the solar atmosphere. We use evidence from a long-running experiment based in space to show that, when analyzed with sufficiently high spatial resolution, the Sun’s oblate shape is distinctly constant and almost completely unaffected by the solar-cycle variability seen on its surface. The solar oblateness is significantly lower than theoretical expectations by an amount that could be explained by a slower differential rotation in the outer few percent of the Sun.

A changing solar shape

The Suns shape is sensitive to the influence of gravity, rotation, and local turbulence and magnetic fields in its outer atmosphere. A careful measurement of this shape has long been sought to better understand the solar structure and its change during the 11 yr solar cycle. Numerous disparate measurements of the solar oblateness or the fractional difference between equatorial and polar radii have been difficult to interpret, in part because this quantity is much smaller than terrestrial atmospheric seeing and most instrumental noise sources. In 1997 the Michelson Doppler Imager (MDI) aboard the Solar and Heliospheric Observatory (SOHO) obtained a precise measurement of the oblateness from above the atmosphere by utilizing a spacecraft roll procedure to remove instrumental influences. In 2001 this technique was repeated, and we report here on the detection of a time-variable solar shape from these data. The changing oblateness we find from 1997 to 2001 is smaller than the apparent discrepancy between earlier ground-based observations, but is significantly larger than MDIs astrometric measurement uncertainty. The shape change appears to be anticorrelated with the observed helioseismic variability. This fact and our MDI measurements suggest that the outer solar atmosphere expands nonhomologously during the cycle. It is possible that solar cycle changes in the turbulent pressure in the outer atmosphere can account for both the optical limb change and the helioseismic acoustic global solar shape change.

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