Minimal Energy and Gravitation

Quantum theory in Robertson – Walker spacetime suggests the existence of a minimal energy ε of the order of 10⁻⁴⁵ erg. Reasonable forms for ε give the expansion factor R=R(t)(t= the cosmic time) with no need of gravitational field equations.Einstein's theory should be modified in gravitational fields of strength less than ε c/ħ ∼ 10⁻⁸ cm/s² where c is the speed of light and ħ is the reduced Planck constant. The cosmological term λ is expected to decrease as the universe expands.In the Appendix, ε is derived from a big bang – big crunch Newtonian cosmology.     

Rhombic Cell Analysis. Ⅱ. Application to the IRAS／PSCz Catalogue

Rhombic cell analysis as outlined in the first paper of the present seriesis applied to samples of varying depths and liming luminosities of the IRAS/PSCzCatalogue. Numerical indices are introduced to summarize essential information.Because of the discrete nature of the analysis and of the space distribution of galax-ies, the indices for a given sample must be regarded as each having an irreduciblescatter. Despite the scatter, the mean indices show remarkable variations acrossthe samples. The underlying factor for the variations is shown to be the limitingluminosity rather than the sampling depth. As samples of more and more luminousgalaxies are considered over a range of some 2.5 magnitudes (a factor of some 75in space density), the morphology of the filled and empty regions defined by thegalaxies degrades steadily towards insignificance, and the degrading is faster for thefilled than the empty region.     

Amplification of primordial magnetic fields by anisotropic gravitational collapse

If a magnetic field is frozen into a plasma that undergoes spherical compression, then the magnetic field B varies with the plasma density ρ according to   B ∝ρ^2/3  . In the gravitational collapse of cosmological density perturbations, however, quasi-spherical evolution is very unlikely. In anisotropic collapses the magnetic field can be a much steeper function of gas density than in the isotropic case. We investigate the distribution of amplifications in realistic gravitational collapses from Gaussian initial fluctuations using the Zel'dovich approximation. Representing our results using a relation of the form   B ∝ρ^α  , we show that the median value of α can be much larger than the value  α= 2/3  resulting from spherical collapse, even if there is no initial correlation between magnetic field and principal collapse directions. These analytic arguments go some way towards understanding the results of numerical simulations.     

Interpreting the transmission windows of distant quasars

We propose the apparent shrinking criterion (ASC) to interpret the spatial extent, R _w, of transmitted flux windows in the absorption spectra of high- z quasars. The ASC can discriminate between the two regimes in which R _w corresponds either to the physical size,   R _{H  ii}   , of the quasar H  ii region or to the distance,   R ^max_w  , at which the transmitted flux drops to  =0.1  and a Gunn–Peterson (GP) trough appears. In the first case [H  ii region (HR) regime], one can determine the intergalactic medium mean H  i fraction,   x _H I  ; in the second [proximity region (PR) regime], the value of R _w allows one to measure the local photoionization rate and the local enhancement of the photoionization rate,  Γ_G  , due to nearby/intervening galaxies. The ASC has been tested against radiative transfer+smoothed particle hydrodynamics numerical simulations, and applied to a sample of 15 high-   z ( z > 5.8  ) quasar spectra. All sample quasars are found to be in the PR regime; hence, their observed spectral properties (inner flux profile, extent of transmission window) cannot reliably constrain the value of   x _{H  i}   . Four sample quasars show evidence for a local enhancement (up to 50 per cent) in the local photoionization rate possibly produced by a galaxy overdensity. We discuss the possible interpretations and uncertainties of this result.     

Variable 21-cm absorption at z=0.3127

We report multi-epoch Giant Metrewave Radio Telescope (GMRT) H  i observations of the z  = 0.3127 damped absorber towards the quasar PKS 1127−145, which reveal variability in both the absorption profile and the flux of the background source, over a time-scale of a few days.
The observed variations cannot be explained by simple interstellar scintillation (ISS) models where there are only one or two scintillating components and all of the ISS occurs in the Galaxy. More complicated models, where either there are more scintillating components or some of the ISS occurs in the interstellar medium of the z =0.3127 absorber, may be acceptable. However, the variability can probably be best explained in models incorporating motion (on sub-VLBI scales) of a component of the background continuum source, with or without some ISS.
All models producing the variable 21-cm absorption profile require small-scale variations in the 21-cm optical depth of the absorber. The length-scale for the opacity variations is ∼0.1 pc in pure superluminal motion models, and ∼10 pc in pure ISS models. Models involving subluminal motion, combined with scintillation of the moving component, require opacity variations on far smaller scales of ∼ 10–100 au .