Exact solution of the equation of radiative transfer for semi-infinite plane-parallel isotropic scattering atmosphere with scattering albedo ω0 ≤ 1 by a method based on Laplace transform and Wiener-Hopf technique

By performing the one-sided Laplace transform on the scalar integro-differential equation for a semi-infinite plane-parallel isotropic scattering atmosphere with a scattering albedo ₀ 1, an integral equation for the emergent intensity has been derived. Application of the Wiener-Hopf technique to this integral equation will give the emergent intensity. The intensity at any optical depth for a positive scattering angle is also derived by inversion. The intensity at any optical depth for a negative scattering angle is also derived in terms of Cauchy's principal value using Plemelj's formulae.     

The wavelength dependence of granulation (0.38–2.4 μm)

Using 2 pinhole photometers the intensity of the undisturbed photosphere was recorded simultaneously in 6 and in 4 wavelength regions. The rms value of the intensity variation in each of the 10 wavelength regions decreases slightly with increasing value of the heliocentric angle; this result confirms recent observations by other authors and supports the critique of the results given by Edmonds (1964).We report the detection of a secondary maximum in the wavelength dependence of the intensity variation at 1.5 m.     

Intensity oscillation in Hα-fine structure

Using a new technique of directly measuring the intensity variation from the 16 mm time-lapse filtergram movies taken in the blue wing and in the line center of H, we found periodic intensity oscillations in the center of H-supergranulation network, in rosette centers and in plage granules. The oscillatory period of intensity in the network is of the order of 170 ± 44 seconds while in regions of stronger magnetic field, such as in plages and in rosettes, the period was found to be longer, on the order of 300 ± 50 seconds. It is suggested that observed intensity oscillation in the rosette center is related to the shooting out of dark mottles from rosettes. Oscillatory intensity fluctuations have been also observed in the sunspot umbra.     

Observations of the intensity of the penumbra of sunspots

Observations of the penumbral intensity of sunspots in 13 wavelength regions are presented. In 4 wavelength regions 54 sunspots are measured. In the other wavelength regions the number of sunspots considered ranges from 3–19.The penumbral intensity alters with position within the spot. This intensity variation is found to be comparable with the change in intensity from one spot to another. The penumbral intensity is found to be independent of spot size in the sample considered.The penumbra model of Kjeldseth Moe and Maltby (1969) with = 0.055 is supported by the measurements.     

Temporal properties of He I 1083 nm dark points

The intensity of a sample of large, high-contrast and isolated dark points has been observed with full-disk images in the light of Hei 1083 nm from the Chromospheric Helium line Intensity Photometer (CHIP) on Mauna Loa, Hawaii. Temporal variations in the intensity encompassing a broad range of time scales have been recorded. Long-term changes in the intensity, although highly variable, are characterized by e-folding times on the order of 5 h. Superposed on these variations are frequent intensity variations, which occur over time scales ranging from the typical observing cadence of 3 min, to tens of minutes. Microflares-involving intensity changes of at least 50% over periods of minutes are observed frequently. Rapid cadence ( min) observations reveal differences between rise and decay times and shorter-term variations in the intensity profiles of these microflares.     

On Novel Methods to Determine Areas of Sunspots from Photoheliograms

Two novel methods of measuring umbral and penumbral areas of sunspots and of complex sunspot groups are described. Both methods comprise the digitization of photoheliograms by a frame grabber and the computation of intensity histograms of selected areas of activity. The first method, called cumulative histogram method, in principle determines the intensity boundaries umbra–penumbra and penumbra–photosphere from the intersections of linear fits into the corresponding parts of the cumulative histograms of sunspots. The second method, called maximum gradient method, marks image pixels of a given intensity level ±2 units wide as a white isophote on a display. Interactive variation of this level makes it easy to visually select the contour line fitting the boundary penumbra–photosphere (or umbra–penumbra) best. At the same level usually the width of the contour line is smallest. In both cases the summation of the pixel numbers above the corresponding intensity levels yields the umbral and the total sunspot areas, respectively. Some limitations of the two methods are discussed.     

Solar cycle variation of sunspot intensity

Broad band pinhole photometer intensity observations of 15 large sunspots covering the spectral region 0.387–2.35 m are presented. The data are based on measurements on approximately 500 days during the period June, 1967 to December, 1979.We have found real and significant intensity differences between large sunspots. These differences may be explained by a systematic variation in the umbral temperature throughout the solar cycle. A connection between umbra intensity and heliographic latitude is discussed.No center-limb variation in the umbra/photosphere intensity ratio is detected. We have searched for possible connections between umbra intensity and a number of other sunspot parameters, like the spot size, without detecting any significant correlation. We conclude that the umbra/photosphere intensity ratio seems to be a unique function of epoch for large sunspots.     

Exact solution of the transport equation for radiative transfer with scattering albedo ωO < 1 using the Laplace transform and the Wiener-Hopf technique and an expression ofH-function

We have considered the transport equation for radiative transfer to a problem in semi-infinite non-conservative atmosphere with no incident radiation and scattering albedo ₀ < 1. Usint the Laplace transform and the Wiener-Hopf technique, we have determined the emergent intensity and the intensity at any optical depth. We have obtained theH-function of Dasgupta (1977) by equating the emergent intensity with the intensity at zero optical depth.     

Holes in the Hα Eruptive Prominence Structure

The eruptive prominence observed on 27 May 1999 in H at Ondejov Observatory is analyzed using image-processing techniques. To understand the physical processes behind the prominence eruption, heated structures inside the cold H prominence material are sought. Two local minima of intensity (holes), the first above and the second below the erupting H prominence, have been found in the processed H images. A comparison of H images with the SOHO/EIT and Yohkoh/SXT images showed: (a) the cold H prominence is visible as a dark feature in the EIT images, (b) the upper local minimum of intensity in the H image corresponds to a hot structure seen in EIT, (c) the lower minimum corresponds to a hot loop observed by SXT. The physical significance of the H intensity minima and their relation to the hot structures observed by EIT and SXT is discussed. The time sequence of observed processes is in favor of the prominence eruption model with the destabilization of the loop spanning the prominence. For comparison with other events the velocities of selected parts of the eruptive prominence are determined.     

Cosmological molecular hydrogen and the distortion of the relict radiation spectrum

The distortions of the relict radiation spectrum in the region of the wavelength <120 are considered. These distortions are due to the emission of photons under the formation of molecular hydrogen in the expanding universe in the cosmological epoch 40z200. It is shown that the real intensity of the relict radiation in the region of the wavelength under consideration must significantly exceed Planck's intensity, with a radiation temperature amounting to 2.8 K.     

The spectrum of the inner corona observed during the total solar eclipse of 30 May 1965

A series of spectrograms of the inner solar corona were obtained at the total solar eclipse of 30 May 1965 using a fast spectrograph with a circular slit that recorded the spectrum from 3000 to 9000 at all position angles around the limb simultaneously. In this paper absolute intensity is given as a function of position angle for the stronger lines and the continuum. In the coronal enhancement or condensation centered at heliocentric position angle 293°, absolute intensity is given for 34 forbidden emission lines and the continuum.     

Precise wideband photometry of photospheric faculae with an emphasis on the disk center

The center-to-limb variation of the excess intensity in faculae was obtained for 266 active regions with an accuracy of 10^–3. For this observation full-disk images were obtained with a rotating one-dimensional diode array whose rotation axis was set at the disk center, at the wavelength of 5450 Å with a bandpass of 400 Å. From the center-to-limb variation of excess intensity of active regions the excess effective temperature was found to be 6.4 K on the average where the mean longitudinal magnetic field is 65 G as measured by 5233 Å line. In other words the ratio of the excess radiative flux to the total flux was 0.44% on the average for the present measurements of low spatial resolution of 20.The average excess intensity for 60 active regions near the disk center was found to be 4 × 10^–4 of the quiet Sun intensity. This very low excess brightness averaged over the whole active region, in contrast to the reported high excess brightness of facular points (diameter 0.2) of 0.4, leads to a hypothesis that the background in between facular points in the active region is darker than the true quiet photosphere by 1%. It is further surmised that the inferred darkness of intra facular points is due to partial compensation for excess total irradiance of facular points. This interpretation is also consistent with previous observations of the contrast of facular points near the limb.     

Simulation of the temporal variations of the galactic cosmic-ray intensity at neutron monitor energies

We show that the temporal variations of the integrated galactic cosmic-ray intensity at neutron monitor energies (approximately above 3 GeV) can be reproduced applying a semi-empirical 1-D diffusion-convection model for the cosmic-ray transport in interplanetary space. We divide the interplanetary region into `magnetic shells' and find the relative reduction that each shell causes to the cosmic-ray intensity. Then the cosmic-ray intensity at the Earth is reproduced by the successive influence of all shells between the Earth and the heliospheric termination shock. We find that the position of the termination shock does not significantly affect the cosmic-ray intensity although there are some differences between the results for a constant and a variable termination shock radius. We also reproduce the cosmic-ray intensity applying the analytical solution of the force-field approximation (Perko, 1987) and find that the results cannot fit the observed data. Our results are compared with the Climax (geomagnetic cut-off 3 GV) and Huancayo (geomagnetic cut-off 13 GV) neutron monitor measurements for almost two solar cycles (1976–1996).     

Exact solution of the equation of transfer with planetary phase function

We have considered the transport equation for radiative transfer to a problem in semi-infinite atmosphere with no incident radiation and scattering according to planetary phase function w(1 + xcos ). Using Laplace transform and the Wiener-Hopf technique, we have determined the emergent intensity and the intensity at any optical depth. The emergent intensity is in agreement with that of Chandrasekhar (1960).     

Coronal He+ λ304 radiation

The intensity of the He⁺ 304 coronal line relative to the H⁰ 1216 line, including the dominant contribution due to resonance scattering, is presented. All physical processes important in the corona are included. It is found that He⁺ 304 is a major contributor to the XUV corona, and that the sensitivity of the He⁺ 304/H⁰ 1216 intensity ratio to coronal temperature is very weak, supporting the belief that this ratio is a good indicator of the coronal helium abundance.     

Oscillations in the Coronal Green-Line Intensity Observed at Lominický Štít and Norikura Nearly Simultaneously.

We studied intensity oscillations of the coronal green line ([Fexiv] 530.3 nm) observed with two coronagraphs at Lomnický tít and Norikura nearly simultaneously. In the spectroscopic data obtained at Norikura, we have detected and confirmed the earlier detection of 5-minute oscillations in photoelectric photometer observations made at Lomnický tít. Quasi-periodic structures in the green-line intensity with a tangential speed up to 400 km s^–1 have been detected for the first time. We briefly discuss the implications of these oscillations on the coronal heating mechanisms.     

Chromospheric oscillations observed in the line C ii λ1336 with OSO-8

Satellite observations of velocity and intensity oscillations were made of the upper chromospheric line C ii 1336. The dominant period of oscillation is 300 s, with little evidence of the power peak in the range 150–200 s which has been observed in other chromospheric lines. Peak-to-peak amplitudes are 2 km s^–1 and 8% in velocity and intensity, respectively. Tentative evidence for 900-s periodicity is presented. Relative phase measurements show that maximum intensity for the 300-s oscillation leads maximum blueshift by approximately 145 s. Comparison of line and background (scattered light) intensity variation shows upward wave propagation, with time delays between the 1800 continuum and C ii 1336 variation of 27 s and 70 s for different cases.     

Spectral analyses of solar photospheric fluctuations

Residual intensity fluctuation measurements within the wings of the 5183.6 Mgi b₁ line, obtained from two, high-resolution, high-dispersion, Sacramento Peak Observatory spectrograms, have been subtracted from intensity fluctuations in the adjacent continuum in order to isolate fluctuations associated exclusively with line formation. The useable spectral range for studying these lineformation fluctuations is restricted to wavelengths between 1040 and 7170 km because the subtraction increases the relative importance of noise and large-scale photographic variations across the spectrograms could not be completely removed. Power and cross-power (coherence and phase) spectra proved to be valuable diagnostic tools in isolating line-formation fluctuations.Over this spectral range, the line-formation fluctuations are characterized by flat power spectra as compared to those for continuum fluctuations, appreciable fluctuation rms relative to that for continuum fluctuations, and the necessity to multiply the wing fluctuations by a factor 0.95 _min 1.00 to most effectively isolate these fluctuations (Figures 3 and 4). That continuum fluctuations are modified in shape but otherwise not drastically changed in the line wings explains the flat spectrum. The relative rms's vary from 0.34 in the inner wing to 0.22 in the outer. The range of possible values for _min results from uncertainties in the photographic density-residual intensity calibration.     

On the interpretation of some peculiarities observed in zeeman-split line contours in sunspots

Measurements of the H line intensity in a large active prominence indicate that , the fraction of length in the line of sight which contains emitting material, is less or equal to 0.1.