Some studies on the solar microwave bursts in relation to the slowly varying component

The occurrences of 5772 microwave bursts recorded by the Sagamore Hill and Manilla Solar Radio Observatories over the period January 1968 to July 1970, covering the maximum phase of the current solar cycle at frequencies 2695, 4995 and 8800 MHz and their energy excesses have been examined in relation to the S-component of solar radio emission. The average slowly varying component has been determined by the superposed epoch method commonly known as the Chree analysis. Similar treatment of the bursts, data, mentioned above has been made to examine any probable 27-day variation and the results obtained have been compared with that of the S-component. Further, spectra of the microwave bursts under the so-called spectral type - inverted U, particularly those having a peak at 4995 MHz, have also been examined and compared with the average spectrum of the S-component. Some of the important results obtained from the present analysis are: (1) the nature of variation of both the average number of occurrences and energy excesses of the microwave bursts follow in general the average 27-day variation of the S-component, (2) the number of occurrences and energy excesses of the microwave bursts are comparatively greater in the ascending phase of the 27-day cycle than those in the descending phase, (3) bursts at progressively higher frequencies originate at lower levels in the solar atmosphere than those of the associated S-component, and (4) the average spectrum of the microwave bursts of inverted U spectral type having a peak at 4995 MHz is quite identical in nature to that of the S-component.     

Exact solution of the problem of diffuse reflection and transmission by the method of Laplace transform and linear singular operators

The basic integro-differential equation is subjected to a one-sided finite Laplace transform to obtain linear integral equations of angular distribution of bounding faces. These linear integral equations have been transformed into linear singular integral equations which have been solved exactly to get the emergent distributions from the bounding faces by the theory of linear singular operators. Some solutions of linear singular integral equations have also been derived for future use in radiative transfer problems.     

Equilibrium structure of stars with radiation pressure in the presence of a magnetic field

Equilibrium configuration of the upper Main-Sequence stars, with significant radiation pressure and having an interior magnetic field (matching with an external dipole field) has been cosidered. The structural parameters have been calculated for low and high magnetic fields by using a first-order perturbation method and a modified perturbation technique respectively. With the increase of radiation pressure, the star is seen to become more centrally condensed.     

Green's function of one group transport equation for a finite slab of passive and multiplying media by Wiener-Hopf technique

We have applied the method of Wiener-Hopf technique to obtain the Green's functions of one-group transport equations (with anisotropic unit plane source and with isotroic unit plane source) for a finite slab of passive and multiplying media.     

Relative abundances of cosmic ray nuclei from neon to iron over Fort Churchill

The relative abundances of the nuclei from neon to iron in the energy interval 150–400 MeV/n have been estimated by using a balloon borne cellulose-nitrate plastic detector. The source abundances are obtained by extrapolating the near-earth abundances using leaky box model of cosmic ray propagation in the interstellar space. The results are compared with those of other investigators and a general agreement is obtained. However, a discrepancy arises especially in the case of Al which is not detected in the present investigation.     

The structure and oscillations of low-mass stars in the presence of a magnetic field

The equilibrium structure and oscillations of a partially degenerate standard model in the presence of a poloidal magnetic field have been studied. The magnetic field in the interior has been matched with an outside dipole field. The effect of magnetic field on the various structural parameters, e.g., mass, central condensation, moment of inertia, and oblateness has been computed for different values of the central degeneracy of the model. We have also studied the effect of magnetic field on radial oscillations of the configuration. A variational formulation is used to compute the changes in the frequency of radial mode of oscillation. It has been shown that the changes in frequency computed for various models using a two-parameter eigenfunction are in fair agreement with the values obtained by using the exact eigenfunction.     

Exact solution of a problem in radiative transfer by the laplace transform and the Wiener-Hopf technique when the incoming intensity at the surface is known

We consider the problem of determining the emergent intensity from the bounding face of a semi-infinite atmosphere having conservative scattering and the intensity at any optical depth by use of the Laplace transform in combination with the Wiener-Hopf technique when the incoming intensity at the bounding face of the atmosphere is known. The solution is exact.     

Some studies on solar microwave bursts in relation to the phases of the associated Hα-flares and their spectral nature

Occurrences of the flare-associated microwave bursts as well as their peak flux and energy excess spectra have been examined in relation to the pre- and post-maximum phases of the respective flares during the period 1969–72. Results obtained are: (i) about 76% of the flare-associated bursts occur in the pre-maximum phase and the remaining 24% occurs in the post-maximum phase irrespective of the flare classification, intensity-wise or area-wise; (ii) ‘impulsive’ and ‘gradual rise and fall’ bursts are relatively more important in the pre-maximum phase while ‘post burst increase’ bursts show comparatively higher occurrences in the post-maximum phase; (iii) peak flux and energy excess spectra of the concurrent microwave bursts in the pre-maximum phase of the flare are mostly of ‘inverted U’ and ‘increasing with frequency’ spectral types. Of these, ‘impulsive’ bursts are predominantly of the ‘inverted U’ and the ‘grf’ bursts are of the ‘increasing with frequency’ spectral type.     

Source mechanism of volcanic tremor: fluid-driven crack models and their application to the 1963 kilauea eruption

We propose a model for the mechanism of magma transport based on a fluid-filled tensile crack driven by the excess pressure of fluid. Such a transport mechanism can generate seismic waves by a succession of jerky crack extensions, if the fracture strength of rock varies in space, or if there is a difference between the dynamic and static values of the critical stress intensity factor. We also find that the opening and closing of a narrow channel connecting two fluid-filled cracks may be a source of seismic waves. Using the finite-difference method, we calculated the vibration of dry and fluid-filled cracks generated by: (1) a jerky extension at one end or at both ends and (2) a jerky opening of a narrow channel connecting two cracks. We then calculated the far-field and near-field radiation from these vibrating cracks. The spectra show peaked structures, but interestingly, most high-frequency peaks are only present in the near-field and cannot be transmitted to the far-field. The spectral features described above are often observed for volcanic tremors and in some cases for seismic signals associated with hydraulic fracturing experiments.We first consider as a model of volcanic tremor randomly occurring jerky crack extensions, and derive a formula relating the tremor amplitude to the excess pressure in the magma, the incremental area in each extension, and the frequency of extensions. These parameters are also constrained by other observations, such as the rate of magma flow.Our model was tested quantitatively against observations made in one of the best-described case histories of volcanic tremor: the October 5–6, 1963 Kilauea flank eruption. We found that a single, long crack extending from the summit to the eruptive site cannot explain the observations. The model of a steadily expanding crack ran into difficulties when quantitative comparisons were made with observations. The extension of crack area needed to explain the amplitude of volcanic tremor should accompany a large increase in tremor period which was not observed.Our second model is a chain of cracks connected by narrow channels which open and close. The length of each crack is around 1 km, the channel area connecting neighboring cracks is about 10³m², and the channel opens jerkily with the magmatic excess pressure of about 20 bars. The frequency of jerky opening of each channel is about once in 15 seconds. The channel is closed after each jerky opening, as soon as magma is moved through the channel.