It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere, the logarithmic cusp slope γ of the tracers must be given exactly by γ = 2β where β is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster...

We have reexamined the similarity solution for a self-gravitating isothermal gas sphere and examined implication to star formation in a turbulent cloud. When parameters are adequately chosen, the similarity solution expresses an accreting isothermal gas sphere bounded by a spherical shock wave. The mass and radius of the sphere increases in proportion to the time, while the central density decr...

The postcollapse structure of objects which form by gravitational condensation out of the expanding cosmological background universe is a key element in the theory of galaxy formation. Towards this end, we have reconsidered the outcome of the nonlinear growth of a uniform, spherical density perturbation in an unperturbed background universe – the cosmological “top-hat” problem. We adopt the usu...

We observed the quadruple gravitationally lensed image of MG J0414+0534 on 23 November 1997 with a global VLBI array at 8. 4 GHz. We report wide-field imaging results of its four components at submilliarcsec-ond resolution , displaying complex core-like and jet-like extended structures. A simple model combining a singular isothermal ellipsoid to represent the main lens galaxy , external shear ,...

The concentration dependency of the isothermal compressibility of the Na-Cs liquid alloy at T=373K is calculated by the variational method with hard-sphere reference system. The local Animalu-Heine model pseudopotential and Toigo-Woodruff exchange-correlation function are used for the calculation. Very good agreement with experimental data is achieved.

Gravitational lensing by rotating extended deflectors is discussed. Due to spin, corrections on image positions, caustics and critical curves can be significant. In order to obtain realistic quantitative estimates, the lens is modeled as a singular isothermal sphere. Gravito-magnetic time delays of ∼ 0.2 days between different images of background sources can occur.

The gravitational lensing properties of cosmological halos depend upon the mass distribution within each halo. The description of halos as nonsingular, truncated isothermal spheres, a particular solution of the isothermal Lane-Emden equation (suitably modified for Λ 6= 0), has proved to be a useful approximation for the halos which form from realistic initial conditions in a CDM universe. We de...

The capture rates of stars and dark particles onto supermassive black holes depend strongly on the spatial and kinematical distribution of the stellar and dark matter at the centre of bulges and elliptical galaxies. We here explore the possibility that all ellipticals/bulges have initially isothermal cusps (ρ ∝ r). If the orbits can be adequately randomized a significant fraction of the total m...