H. A. O. Hill

Finite Fourier transform definition of an edge on the solar disk

A new technique for locating the edge of the Sun is proposed. The technique uses a finite Fourier transform of the observed limb darkening function to achieve reduced sensitivity to atmospheric and instrumental effects and heightened sensitivity to the shape of the intrinsic limb darkening function. A theory is developed that predicts these sensitivities. In order to facilitate wider application, general relations are calculated. A testing program which complements the theory is also reported. The location of the edge is shown to be influenced only by solar phenomena down to the milli-arcsecond range. (AIP)

DETECTION OF INDIVIDUAL NORMAL MODES OF OSCILLATION OF THE SUN IN THE PERIOD RANGE FROM 2 HR TO 10 MIN IN SOLAR DIAMETER STUDIES

New observations of solar oscillations are reported. Power density spectra derived from these observations reveal narrow-b and oscillations that are spatially global, have spatial symmetry properties that are either symmetric or antisymmetric for reflection about the center of the solar disk and also about the solar equator, and have coherence times ≳ 41 days. Large-scale differential refraction effects have been reduced by a factor of 105 over that found in previous solar diameter studies by the design of the experiment; thus, these effects are eliminated as a possible source of the oscillations. A discussion is presented of this reduction as well as other features of the observing and analysis program. It is concluded that the probability is very high that individual normal modes of oscillation of the Sun have been detected in the period range from 2 hr to 10 min.

SCLERA: an Astrometric Telescope for Experimental Relativity

An f/100, 12.2-m focal length photoelectric telescope designed specifically for daytime astrometry of objects near the sun is now operative at its Tucson, Arizona, site. The design goal was to achieve accuracies of order 0.001 sec of arc in field position measurements of stars. To accomplish this, many features reducing systematic and random errors are employed, including Schupmann medial telescope optics, compensation for lateral color aberration, apodization for reduction of diffracted light, and use of an accurately measured solar diameter for calibrating the field.

Shearing interferometer as an interferometric filter for the reduction of scattered light.

The background radiation problem encountered in astronomical observations is reviewed, and it is observed that a considerable reduction of the background radiation can be achieved by using interferometric techniques. A longitudinal radial shearing interferometer is described which meets the requirements of this application. The formal development of its properties as well as the results of preliminary tests are presented. It is shown that for a small region of the telescope field, this interferometer can be expected to reduce the background radiation originating in the telescope by a factor of 50 to 500, to reduce the background radiation produced by Mie type scattering external to the telescope to a level below that produced by Rayleigh scattering, and to reduce the background radiation from Rayleigh scattering by a factor of two. These properties can be extended to broadband spectral operation and can be achieved without degrading the astrometric qualities of the telescope. The size of the interferometer is quite small making it easy to add to an existing telescope.

Rotational splitting of global solar oscillations and its relevance to tests of general relativity

The estimation of the suns internal angular velocity using rotational splitting of low-order, low-degree global oscillations in the limb-darkening function is reviewed. Observed spatial properties of the eigenfunctions confirm the multiplet classifications previously identified by the existence of Zeeman-like frequency patterns characteristic of rotational splitting. From the observed rotational splitting, a sidereal rotational frequency of ≥3.0 μ Hz is derived for the deep interior; this value is more than six times greater than the equatorial rotational frequency of the photosphere. Upper limits have also been estimated for the internal magnetic field by analyzing the splitting for departures from uniform spacing. The inferred angular velocity distribution, together with the estimated upper limit on the internal magnetic field, yield a gravitational quadrupole moment,J2 of (5.5±1.3)×10−6. When this result is combined with different published results from planetary radar observations, values of 0.987±0.006 and 0.991±0.006 are obtained for (2+2γ−β)/3, a combination of Eddington-Robertson PPN parameters which in general relativity takes the value of 1.

On the origin of oscillations in a solar diameter observed through the Earth's atmosphere: A terrestrial atmospheric or a solar phenomenon

Interpretations of current and past results from ground-based solar diameter measurements, as well as the planning of scientific programs for the 1980s, are strongly dependent on the perceived level of the degrading effects of the Earths atmosphere. One of the more effective approaches has been to design the observing program and the subsequent data analysis such that the solar diameter measurements themselves could provide an evaluation of atmospheric effects. Many important results have been obtained in studies of this type and these results are collected here to help in appraising the current situation. This evidence all points in one direction: the Earths atmosphere, while complicating the design of observational programs, is not the source of the oscillations observed in solar diameter measurements. Further, this same evidence indicates that the Earths atmosphere will not pose any serious limitations in ground-based solar diameter studies during the 1980s.

Observation of nonacoustic, 5 minute period, vertical traveling waves in the photosphere of the sun

Nonacoustic, radially propagating traveling waves have been observed in the solar photosphere. These traveling waves have a period of 278 +- 41 s. The vertical wavelength (approx.500 km) and phase velocity (approx.2 km s/sup -1/) of the waves are among their properties deduced from the data. It is also observed that the waves have outgoing phase part of the time and ingoing phase the remainder of the time. The traveling waves are interpreted to be gravity waves. Their role in the heating of the chromosphere is discussed.

Radiative damping of gravity waves in the solar atmosphere

The nonlocal character of the radiation field sianificantly modifies the radiative damping of perturbations in the solar photosphere. Gravity waves are not usually considered to exist in the solar photosphere because the radiative damping time, when based on the Newtonian approximation, is too short. However, this restriction does not apply to low order gravity waves. In fact, with the inclusion of nonlocal effects, the radiative damping for low order gravity waves becomes negative for some region in the photosphere and thus acts as a driving mechanism for gravity waves there.

Radiative transfer: Gaussian quadrature formulas for integrals with the weight functions exp(-|x−t|) and En(|x−t|)

Abstract One to six point Gaussian quadrature formulas have been computed for the roots and weight coefficients of the integrals, from zero to infinity, of the integrands f ( x ) exp(-| x − t |) and f ( x ) E n (| x − t |). These are then tabulated as functions of t . Analytic formulas are given explicitly for one and two point quadratures for any n . The asymptotic behavior of the roots and weight coefficients is discussed. Estimates of errors for the quadratures are also given.

Observations of Solar Pulsations

There have been several interesting developments during the last year with regard to global oscillations of the sun. However, because of the very full program of this Joint Discussion and the resulting tight schedule, only one point will be addressed here: the observational evidence for global oscillations of the sun with periods ≤ 1 hr and > 5 min. The most decisive test currently available for identifying global oscillations is their examination for coherence of phase over an extended period of time. This test discriminates against both nonsolar phenomena, such as effects caused by observing through the earth’s atmosphere, and solar phenomena which occur in the frequency range of interest but which are not global oscillations of the sun. The search for this coherence has been conducted using 2 sets of observations from SCLERA, the 1973 observations of Hill and Stebbins (1975) and the 1978 observations described by Caudell et al. (1979). The results of these examinations strongly support the interpretation of the reported oscillations as solar in origin and as global in character. The above observations consist of time chains of diameter measurements made at SCLERA. A list of references may be found in Hill and Stebbins (1975) and Hill (1978) which describe the telescope, the method for defining the solar diameter, the means of measuring the solar diameter, and the data reduction techniques used to produce the final Fourier transforms and associated power spectra of the diameter measurements.