The mathematical properties of gravitational lens equations are examined in the frame work of gravitational micro-lensing effects. The caustics of the gravitational lens may be defined in terms of "cusp" and "folding" in general. In some cases for overfocussing, however, the critical curves (caustics) have no cusp and no folding. If the observer is in the overfocussed region, he may not see any lensed image.
We construct a simple photometric evolution model of galaxies based on the evolutionary population synthesis. In our models an exponentially decreasing SFR with a power law IMF is used to compute the UBV colors of galaxies from ellipticals to late type spirals. It is shown that the integrated colors of galaxies with different Hubble type can be explained by one parameter, SFR.
The evolution of the Galaxy is examined by the halo-disk model, using the time-dependent bimodal IMF and contraints such as cumulative metallicity distribution, differential metallicity distribution and PDMF of main sequence stars. The time scale of the Galactic halo formation is about 3Gyr during which the most of halo stars and metal abundance are formed and ∼ 95 of the initial halo mass falls to the disk. The G-dwarf problem could be explained by the time-dependent bimodal IMF which is suppressed for low mass stars at the early phase (t < 1Gyr) of the disk evolution. However, the importance of this problem is much weakened by the Pagel's differential metallicity distribution which leads to less initial metal enrichment and many long-lived metal-poor stars with Z < 1 / 3 Z ⊙ The observational distribution of abundance ratios of C, N, O elements with respect to [Fe/H] could be reproduced by the halo-disk model, including the contribution of iron product by SNIs of intermediate mass stars. The initial enrichment of elements in the disk could be explained by the halo-disk model, resulting in the slight decrease and then the increase in the slopes of the [N/Fe]- and [C/Fe]-distributions with increasing [Fe/H] in the range of [Fe/H] < -1.
Infrared emission maps are constructed at 12.5, 25, 60, and 100 μ m for dark globules B5, B34, B133, B134, B361, L134 and L1523 by using Infrared Astronomical Satellite data base. These clouds are selected on the basis of their appearance in Palomar print as dark obscuring objects with angular sizes in the range of 3 to 30 arcminutes. The short wavelength(12.5 and 25 μ m ) maps show the embedded infrared sources. We found many such sources only in B5, B361 and B34 regions, Diffuse component at 12.5 and 25 μ m , possibly arising from the stochastically heated very small dust grains(a < 0.01 μ m ) by interstellar radiation field, is found in B361 and L1523 regions. Such emission is characterized by the limb brightening, and it is confirmed in L1523 and in B361. Infrared emissions at the long wavelengths(60 and 100 μ m ) are due to colder dusts with temperature less than 20 K. The distribution of color index determined by the ratio 60 to 100 μ m intensities shows monotonic decrease of dust temperature toward the center. The black body temperature determined from these ratios is found to lie between 16 and 23 K. Such temperature is possible for small(i.e., a ≲ 0.01 μ m ) graphite grains if the grains are mainly heated by interstellar radiation field. Thus IRAS 100 and 60 μ m emissions are arising mainly from small grains in the colud. The distribution of such dust grains implied from the emissivity distributions at 100 and 60 μ m resembles that of isothermal sphere. This contrasts to earlier findings of much steeper distribution of dusts contributing visible extinction. These dust grains are mainly larger ones(i.e., a ≃ 0.1 μ m ). Therefore we conclude that the average grain size increase, toward the cloud center.
With the 14 m radio telescope at DRAO and the 4 m at Nagoya University, we have made detailed maps of 12 C O and 13 C O emissions from two Barnard objects B133 and B134 in the J = 1 → O rotational transition lines. Usual LTE analyses of the CO observations led us to determine the distribution of column densities over an entire area encompassing both globules. Total gas masses estimated from the column density map are 90 M ⊙ and 20 M ⊙ for B133 and B134, respectively. The radial velocity of B133 is red shifted with respect to B134 by 0.8 k m s − 1 , which is too lagre to bind the two clouds as a binary system. We have shown that the usual stability analysis based on the simplified version of virial theorem with the second time-derivative of the moment of inertia term ¨ I being ignored could mislead us in determining whether a given cloud eventually collapses or not. The lull version of the scalar virial theorem with the ¨ I term is shown to be useful in following up the time-dependent variations of the cloud size R and its streaming velocity ˙ R as functions of time. Results of our stability analysis suggest that B133 will eventually collapse in ( 2 ∼ 4 ) × 10 6 years.
In the presence of synchrotron losses, diffusion of an ensembel of relativistic particles in an intraculster medium is investigated. The diffusion coefficient in the medium is found to be constrained by 28.8 ± 0.4 ≤ L o g D ≤ 30.5 ± 0.4 c m 2 s − 1 with the energy dependency of D 0 ε μ of μ = 0.4 ± 0.2 as the previous observations suggested. As an important implication of the result, the brightest head-tail radio source NGC 4869, whose radio tail structure is indicative for its orbit within the cluster core, is considered to be the major contributor of particles for the formation of the Coma radio halo.
With a modern microdensitometer and POSS glass copies, we have performed an automated star counting in two colors, blue and red, over the region containing Bok globule B361. Distribution of the measured extinction values over the projected angular distance from the cloud center was approximated by a power-law, and the resulting power-law indices for the blue and red are shown to be distinctly different from each other. The difference in the power-law index indicates that the mean dust size increases towards the cloud center. Possible physical causes for such size variation are briefly discussed.
Here I report the confirmation of a long-term modulation of a period of 92 + 21 − 13 years with the "time-delay correlation" method on the sunspot data compiled over the last a total of 289 years. This periodicity better specifies the cycle which falls pretty well within Gleissberg cycle, and clearly contrasts with the 55 year grand cycle which Yoshimura (1979) claimed. It is argued that the period-amplitude diagram method. which Yoshimura used, ana lysed peak amplitudes only so that a large number of data were disregarded, and thus was more susceptible to a bias. The planetary tidal force on Sun as for the possible cause to the solar activity was investigated and its possibility was ruled out in view of no period correlation between them.