Daily observations of Doppler line shifts made with very low spatial resolution (3′) with the Stanford magnetograph have been used to study the equatorial rotation rate, limb effect on the disk, and the mean meridonial circulation. The equatorial rotation rate was found to be approximately constant over the interval May 1976–January 1977 and to have the value 2.82 μrad s−1 (1.96 km s−1). This average compares favorably with the results of Howard (1977) of 2.83 μrad s−1 for the same time period. The RMS deviation of the daily measurements about the mean value was 1% of the rate (20 m s−1), much smaller than the fluctuations reported by Howard and Harvey (1970) of several per cent. These 1% fluctuations are uncorrelated from day-to-day and may be due to instrumental problems. The limb effect on the disk was studied in equatorial scans (after suppressing solar rotation). A redshift at the center of the disk relative to a position 0.60R⊙ from the center of 30 m s−1 was found for the line Fe i λ5250 A. Central meridian scans were used (after correcting for the limb effect defined in the equatorial scans) to search for the component of mean meridonial circulation symmetric across the equator. A signal is found consistent with a polewards flow of 20 m s−1 approximately constant over the latitude range 10–50°. Models of the solar differential rotation driven by an axisymmetric meridonial circulation and an anisotropic eddy viscosity (Kippenhahn, 1963; Cocke, 1967; Kohler, 1970) predict an equatorwards flow at the surface. However, giant cell convection models (Gilman, 1972, 1976, 1977) predict a mean polewards flow (at the surface). The poleward-directed meridonial flow is created as a by-product of the giant cell convection and tends to limit the differential rotation. The observation of a poleward-directed meridonial circulation lends strong support to the giant cell models over the anisotropic eddy viscosity models.

Large-scale solar velocity fields

Asymmetries and wavelengths of solar spectral lines and the solar rotation determined from Fourier-transform spectra

In this paper we describe a filter which utilizes magneto-optical effects for velocity fields measurements. The working principle of the instrument is described and its transmission profiles are given. Velocitygrams are shown of the five minutes oscillations (FMO) and the results compared with the expected (theoretical) signal from the instrument. We found a Vrms of 400 m s−1 for the FMO.

The Magneto-Optical Filter. II. Velocity Field Measurements

Possible sources of systematic error in solar Doppler rotational velocities are examined. Scattered light is shown to affect the Mount Wilson solar rotation results, but this effect is not enough to bring the spectroscopic results in coincidence with the sunspot rotation. Interference fringes at the spectrograph focus at Mount Wilson have in two intervals affected the rotation results. It has been possible to correlate this error with temperature and thus correct for it. A misalignment between the entrance and exit slits is a possible source of error, but for the Mount Wilson slit configuration the amplitude of this effect is negligibly small. Rapid scanning of the solar image also produces no measurable effect.

Solar rotation measurements at Mount Wilson. II - Systematic instrumental effects and the absolute rotation rate

Transmission curves and theoretical calculi of the magneto-optical filter, designed and built by the authors, are shown together with some observed transmission spectra. At present the filter has a total halfwidth of ≈80mA; and the maximum transmission is 25%. From the analysis of the theoretical curves and from the observed spectra, we deduced the possibility of making up a filter with a very narrow passband (less than 30mA) and a very high transmission (up to nearly 100% apart from losses arising from the glass cell, lenses and polarizers).

The magneto-optical filter

An explanation of the solar limb shift

Model stars whose convection zones had been prepared in accordance with the standard mixing-length theory were used as a basis for the computation of unstable convective modes. It was found that no superposition of statistically independent, nonviscous, adiabatic, convective modes can reproduce the radial dependence of the convective flux of the model. This implies that the representation of a stellar convection zone as a superposition of unstable adiabatic linear modes is inconsistent with the mixing-length theory, and that conclusions based upon such a representation should be regarded with caution. It is also shown that if the linear scale of convective motions is greater than (or of the same order as) the pressure scale height, then the fractional deviation of the pressure from equilibrium will generally not be negligible, as assumed in the mixing-length theory, but will be at least of the same order as the fractional deviation of the density from equilibrium.

Michael H. Hart

Papers

An explanation of the solar limb shift

Linear convective modes and the energy transport in stellar convection zones