D. O. Gough

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.

The current state of solar modeling

Data from the Global Oscillation Network Group (GONG) project and other helioseismic experiments provide a test for models of stellar interiors and for the thermodynamic and radiative properties, on which the models depend, of matter under the extreme conditions found in the sun. Current models are in agreement with the helioseismic inferences, which suggests, for example, that the disagreement between the predicted and observed fluxes of neutrinos from the sun is not caused by errors in the models. However, the GONG data reveal subtle errors in the models, such as an excess in sound speed just beneath the convection zone. These discrepancies indicate effects that have so far not been correctly accounted for; for example, it is plausible that the sound-speed differences reflect weak mixing in stellar interiors, of potential importance to the overall evolution of stars and ultimately to estimates of the age of the galaxy based on stellar evolution calculations.

Solar Interior Structure and Luminosity Variations

The assumptions of standard solar evolution theory are mentioned briefly, and the principle conclusions drawn from them are described. The result is a rationalization of the present luminosity and radius of the Sun. Because there is some uncertainty about the interior composition of the Sun, a range of models is apparently acceptable.To decide which model is the most accurate, other more sensitive comparisons with observations must be made. Recent measurements of frequencies of dynamical oscillations are particularly valuable in this respect. The most accurate observations are of the five-minute oscillations, which suggest that the solar composition is not atypical of other stars of the same age as the Sun.The theory predicts that the solar luminosity has risen steadily from about 70% of its current value during the last 4.7 x 109yr. Superposed on this there might have been variations on shorter timescales. Variations lasting about 107yr and occurring at intervals of 108yr have been suggested as being the cause of terrestrial ice ages. Moreover, there may be other variations, associated with instabilities arising from the coupling between the convection zone and the radiative interior, that occur on a timescale of 105yr and which also have climatic consequences. These issues are quite uncertain.We do know that the Sun varies magnetically with a period of about 22 yr, and that this oscillation is modulated irregularly on a timescale of centuries. This appears to be a phenomenon associated with the convection zone and its immediate neighbourhood, though control from a more deeply-seated mechanism is not out of the question. There is a small luminosity variation associated with this cycle, and the way by which this might come about is discussed in terms of certain theories of the solar dynamo.Finally, there must be small surface flux variations associated with the dynamical oscillations mentioned above. Though the total luminosity variations are extremely small, the flux in any specific direction, and in particular that of the earth, may be measurable.

Inevitability of a magnetic field in the Sun's radiative interior

The gas in the convective outer layers of the Sun rotates faster at the equator than in the polar regions, yet deeper inside (in the radiative zone) the gas rotates almost uniformly. There is a thin transition layer between these zones, called the tachocline. This structure has been measured seismologically, but no purely fluid-dynamical mechanism can explain its existence. Here we argue that a self-consistent model requires a large-scale magnetic field in the Suns interior, as well as consideration of the Coriolis effects in the convection zone and in the tachocline. Turbulent stresses in the convection zone induce (through Coriolis effects) a meridional circulation, causing the gas from the convection zone to burrow downwards, thereby generating the horizontal and vertical shear that characterizes the tachocline. The interior magnetic field stops the burrowing, and confines the shear, as demanded by the observed structure of the tachocline. We outline a dynamical theory of the flow, from which we estimate a field strength of about 10−4 tesla just beneath the tachocline. An important test of this picture, after numerical refinement, will be quantitative consistency between the predicted and observed interior angular velocities.

Inferring the sun's internal angular velocity from observed p-mode frequency splittings

The suns internal solar velocity Omega is studied as a function of latitude and radius using the solar oscillation data of Brown and Morrow (1987). An attempt is made to separate robust inferences about the sun from artifacts of the analysis. It is found that a latitudinal variation of Omega similar to that observed at the solar surface exists throughout the suns convection zone and that the variation of Omega with latitude persists to some extent even beneath the convection zone. 44 refs.

The depth of the solar convection zone

The transition of the temperature gradient between being subadiabatic and adiabatic at the base of the solar convection zone gives rise to a clear signature in the sound speed. Helioseismic measurements of the sound speed therefore permit a determination of the location of the base of the convection zone. Two techniques were tested by applying them to artifical data, obtained by adding simulated noise to frequencies computed from two different solar models. The determinations appear to be relatively insensitive to uncertainties of the physics of the solar interior. From an analysis of observed frequencies of solar oscillation it is concluded that the depth of the solar convection zone is (0.287 + or - 0.003) solar radii.

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 Seismic Structure of the Sun

Global Oscillation Network Group data reveal that the internal structure of the sun can be well represented by a calibrated standard model. However, immediately beneath the convection zone and at the edge of the energy-generating core, the sound-speed variation is somewhat smoother in the sun than it is in the model. This could be a consequence of chemical inhomogeneity that is too severe in the model, perhaps owing to inaccurate modeling of gravitational settling or to neglected macroscopic motion that may be present in the sun. Accurate knowledge of the suns structure enables inferences to be made about the physics that controls the sun; for example, through the opacity, the equation of state, or wave motion. Those inferences can then be used elsewhere in astrophysics.

Global Oscillations at Low Frequency from the SOHO mission (GOLF)

The GOLF experiment on the SOHO mission aims to study the internal structure of the sun by measuring the spectrum of global oscillations in the frequency range 10−7 to 10−2 Hz. Bothp andg mode oscillations will be investigated, with the emphasis on the low order long period waves which penetrate the solar core. The instrument employs an extension to space of the proven ground-based technique for measuring the mean line-of-sight velocity of the viewed solar surface. By avoiding the atmospheric disturbances experienced from the ground, and choosing a non-eclipsing orbit, GOLF aims to improve the instrumental sensitivity limit by an order of magnitude to 1 mm s−1 over 20 days for frequencies higher than 2.10−4 Hz. A sodium vapour resonance cell is used in a longitudinal magnetic field to sample the two wings of the solar absorption line. The addition of a small modulating field component enables the slope of the wings to be measured. This provides not only an internal calibration of the instrument sensitivity, but also offers a further possibility to recognise, and correct for, the solar background signal produced by the effects of solar magnetically active regions. The use of an additional rotating polariser enables measurement of the mean solar line-of-sight magnetic field, as a secondary objective.

Virgo: Experiment for Helioseismology and Solar Irradiance Monitoring

The scientific objective of the VIRGO experiment (Variability of solar IRradiance and Gravity Oscillations) is to determine the characteristics of pressure and internal gravity oscillations by observing irradiance and radiance variations, to measure the solar total and spectral irradiance and to quantify their variability over periods of days to the duration of the mission. With these data helioseismological methods can be used to probe the solar interior. Certain characteristics of convection and its interaction with magnetic fields, related to, for example, activity, will be studied from the results of the irradiance monitoring and from the comparison of amplitudes and phases of the oscillations as manifest in brightness from VIRGO, in velocity from GOLF, and in both velocity and continuum intensity from SOI/MDI. The VIRGO experiment contains two different active-cavity radiometers for monitoring the solar ‘constant‘, two three-channel sunphotometers (SPM) for the measurement of the spectral irradiance at 402, 500 and 862 nm, and a low-resolution imager (LOI) with 12 pixels, for the measurement of the radiance distribution over the solar disk at 500 nm. In this paper the scientific objectives of VIRGO are presented, the instruments and the data acquisition and control system are described in detail, and their measured performance is given.