The use of millimeter-interferometer data for the study of chromospheric structure and dynamics is tested using 85 GHz observations with the 10-element Berkeley-Illinois-Maryland Array (BIMA). Interferometer data have the advantage over single-dish data that they allow both high spatial resolution and dense temporal sampling simultaneously. However, snapshot imaging of the quiet solar atmosphere with a small number of dishes is challenging. We demonstrate that techniques are available to carry out this task successfully using maximum entropy deconvolution from a default image constructed from the entire observation: one of our results is that the solar chromosphere at millimeter wavelengths exhibits features that are long-lasting and the map of the entire observation is significant provided that atmospheric phase errors do not prevent deconvolution. We compare observations of quiet Sun, active region and coronal hole targets. The interferometer is not sensitive to the disk emission and the positivity constraint of the maximum entropy algorithm used forces the zero level in the images to be at the temperature of the coolest feature in each field. The brightest features in the images are typically 1000–1500 K above the zero level, with a snapshot noise level of order 100 K. We use extensive tests to determine whether oscillation power can be recovered from sequences of snapshot images and show that individual sources can be down to quite weak levels at locations in the image where significant flux is present; oscillation power located in cool regions of the image is not well recovered due to the deconvolution method used and may be redistributed to brighter regions of the millimeter image. We then investigate whether the data do show oscillation power using uninterrupted 30-min scans of the target regions. Intensity oscillations with significant power in the frequency range 1.5–8.0 mHz are found in the quiet-Sun and active region targets. For the quiet-Sun region we compare the oscillation properties of network boundaries and cell interiors (internetwork) in the spatially-resolved time series. In agreement with investigations at other wavelengths, in the millimeter data the power in the network tends to be at periods of 5 min and longer while power in the internetwork is present also at shorter (3-min) periods.

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High-resolution millimeter-interferometer observations of the solar chromosphere

The authors have previously discussed an improved method for obtaining the absolute solar brightness temperature using the new Moon as a calibration source. New measurements of the Sun-to-new Moon ratio at three frequencies near 36 GHz (λ = 8 mm) and also at two frequencies near 93 GHz (λ = 3 mm) are reported. The slopes of the solar brightness temperature spectrum based on these ratios are then discussed. The absolute solar brightness spectrum derived from all current available measurements is also presented and discussed.

The solar brightness temperature at millimeter wavelengths

Observations of the Sun were made at 3 mm wavelength during the total eclipse of 1976 October 23. Analysis of the record obtained near third contact indicates that the Sun at this wavelength is slightly limb-brightened, and that the solar radius is 1.007 times the photospheric radius.

Solar brightness distribution at 3mm wavelength from observations of the eclipse of 1976 October 23

We report observations of the solar radio radius at wavelengths between 1.2 and 11 cm performed with the Bonn 100 m-telescope. In combination with former measurements of the centre-to-limb variation of the solar brightness these observations are discussed in terms of atmospheric models. We consider the solar disk to be covered by arches at low latitudes, while at the poles coronal holes are located. The temperature dependence on height is taken from EUV-line intensities, hydrostatic equilibrium is adopted, spicules are assumed to be responsible for the relatively low brightening. The interpretation of our measurements demands certain values of the brightness temperature of spicules as a function of wavelength within a modest interval.

The radius of the Sun at centimeter waves and the brightness distribution across the disk

The Sun emits radiation at several wavelengths of the electromagnetic spectrum. In the optical band, the solar radius is 695 700 km, and this defines the photosphere, which is the visible surface of the Sun. However, as the altitude increases, the electromagnetic radiation is produced at other frequencies, causing the solar radius to change as a function of wavelength. These measurements enable a better understanding of the solar atmosphere, and the radius dependence on the solar cycle is a good indicator of the changes that occur in the atmospheric structure. We measure the solar radius at the subterahertz frequencies of 0.212 and 0.405 THz, which is the altitude at which these emissions are primarily generated, and also analyze the radius variation over the 11-year solar activity cycle. For this, we used radio maps of the solar disk for the period between 1999 and 2017, reconstructed from daily scans made by the Solar Submillimeter-wave Telescope (SST), installed at El Leoncito Astronomical Complex (CASLEO) in the Argentinean Andes. Our measurements yield radii of $966.5'' \pm2.8''$
 for 0.2 THz and $966.5'' \pm2.7''$
 for 0.4 THz. This implies a height of $5.0 \pm2.0 \times10^{6}$
 m above the photosphere. Furthermore, we also observed a strong anticorrelation between the radius variation and the solar activity at both frequencies.

Solar Radius at Subterahertz Frequencies and Its Relation to Solar Activity

The 7 March, 1970 total solar eclipse was observed at wavelengths of 3.2 and 8.3 mm; the object being to use the knife edge of the Moon as it passed across the Sun to improve angular resolution on the Sun. This in turn would provide a radial brightness distribution of the Sun with an angular resolution of a few seconds of arc. Excellent eclipse curves were obtained at 3 mm; however, some external interference marred the 8 mm record near totality. The 8 mm brightness distribution is subject to some uncertainty, but tends to show limb brightening. The 3 mm brightness distribution shows a well defined complex limb brightening within about 1 arc min of the optical limb. The maximum brightening is approximately 30% above the average disc temperature.

Observations of the 7 March, 1970 total solar eclipse at wavelengths of 3.2 and 8.3 mm

The radio radius of the Sun is determined from an analysis of the radio contact times of the 7 March, 1970 and 10 July, 1972 solar eclipses from λ = 3 mm to λ = 31 cm. Agreement with other eclipse measurements is good. A best fit curve through the several points gives the radio radius to within approximately ±0.01 of the photosheric radius below λ∼-5 cm.

The radio radius of the Sun at millimeter and centimeter wavelengths

The radial brightness distribution of the Sun at 3.2 mm is recalculated for the 7 March, 1970 total solar eclipse by an improved method. The results from the first contact of the 30 June, 1973 total eclipse are also analyzed. Limb brightening is apparent for the 1970 eclipse when all four contacts are averaged. The 1973 eclipse indicates strong limb brightening, although the detailed shape differs from the 1970 eclipse.

The Radial Brightness Distribution of the Sun at 3. 2 mm as Determined from the June 30, 1973 Total Solar Eclipse and a Reanalysis of the March 7, 1970 Total Solar Eclipse

THE brightness temperature of the quiet Sun has been measured over almost the complete radio spectrum. It ranges from approximately 6,000 K at millimetre wavelengths to over 106 K at metre wavelengths. Various compilations of the disk temperatures1–3 had at centimetre and millimetre wavelengths from 10 to 100 GHz (λ=3 cm to 3 mm) (Fig. 1). A monotonically decreasing brightness temperature presented by Shimabukuro and Stacey1 from a model by van de Hulst4 is also shown in Fig. 1. Zheleznyakov5 has pointed out that the apparent dip in the observed disk temperatures near 50 GHz and at the apparent peak near 70 GHz, if real, would indicate an effective temperature inversion in the solar chromosphere from 3,000 to 3,300 km above the photosphere. Reber3, however, measured the slope of the brightness against frequency curve at 50 GHz and found that the disk temperature is, in fact, decreasing with increasing frequency in nearly perfect agreement with the van de Hulst4 model. Reber's method does not depend on an absolute measurement of the brightness temperature but rather on a relative measurement between two closely spaced frequencies, with a single instrument, thereby giving the slope with more accuracy than can be obtained by comparing a number of independent, absolute measurements.

The solar spectrum at 8 mm

A computer program to convolve numerically any azimuthally symmetric, solar radial brightness distribution with standard antenna patterns of small half power beamwidths has been used to find a solar brightness distribution which is a good fit to the eclipse curve obtained during the 7 March 1970 partial solar eclipse with the NRAO 36-ft antenna at 3.5 mm. This brightness distribution is compared with the brightness distribution at 3.2 mm determined by the Pennsylvania State University Radio Astronomy Observatory group during the same eclipse but observed from Mexico where totality occurred. The two brightness distributions are very similar in shape, showing a double peak near the limb, but differing slightly in the positions of the peaks.

Paul N. Swanson

Papers

Observations of the 7 March, 1970 total solar eclipse at wavelengths of 3.2 and 8.3 mm

The radio radius of the Sun at millimeter and centimeter wavelengths

The Radial Brightness Distribution of the Sun at 3. 2 mm as Determined from the June 30, 1973 Total Solar Eclipse and a Reanalysis of the March 7, 1970 Total Solar Eclipse

The solar spectrum at 8 mm

FURTHER EVIDENCE FOR A COMPLEX LIMB STRUCTURE IN THE SOLAR RADIAL BRIGHTNESS DISTRIBUTION AT mm WAVELENGTHS