Tilted Bianchi Type I Cosmological Models for Barotropic Perfect Fluid in General Relativity

In this paper, we have investigated that tilted Bianchi Type I cosmological models for stiff perfect fluid under a supplementary condition A = B ⁿ between metric potentials, is not possible. The tilted solution is also not possible when we assume A = t ^ℓ, B = t ^m , C = t ⁿ ; ℓ, m and n are constants for ε = p. Thus to preserve tilted nature of model, we assume p = γε, 0 ≤ γ ≤ 1 (barotropic equation of state) for the case A = t ^ℓ B = t ^m and C = t ⁿ . The physical and geometrical aspects of the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bianchi Type-1 vacuum models in modified theory of general relativity

In this paper, the problem of spatially homogeneous and an isotropic Bianchi type-1 space time with perfect fluid distribution is considered in Barber's second theory of gravitation. To obtain determinate solutions, we have assumed the equation of statep= γρ, 0 ≤ γ ≤ 1. It is observed that the general fluid distribution degenerates isotropic vacuum model whenγ = 1 and Λ < 0. Further it is observed that the vacuum model obtained in case of γ = 0, ρ = 0 andΛ = 0, reduces to well known Kasner model in Einstein's theory. Some physical and geometrical aspects of the models together with singularities in the models are also discussed This revised version was published online in July 2006 with corrections to the Cover Date.     

Plane symmetric cosmological models with perfect fluid and dark energy

We consider a self-consistent system of Plane symmetric cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein’s field equations are obtained as a quadrature. The cases of Zeldovich Universe, Dust Universe and Radiation Universe and models with power-law and exponential expansion have discussed in detail. For large t, the models tend to be isotropic.     

Homogeneous spheres with constant adriatic index

Compressible homogeneous spheres with constant adiabatic index γ were studied for their dynamical stability by Chandrasekhar and he found that for each value of u (≡ mass to size ratio), there is a value of γ = γ_c, such that for γ < γ_c, the configuration is dynamically unstable. On examining the properties of the Chandrasekhar's spheres (homogeneous spheres with constant γ) it is found that these spheres are non-isentropic, and the speed of sound within these spheres is finite. The authors find that (i) for the causality condition to be fulfilled throughout the configuration, the value of γ ≤ [2/(surface redshift)], (ii) for a given value of u, the binding coefficient, α_r = (M_r -M)/M, vanishes for some value of γ = γ_b and for all the values of γ < γ_b the configurations are unbound, and (iii) for u≤ (1/3), one can find configurations which are bound, dynamically stable, and the speed of sound is less than that of light throughout the configuration, whereas, for u >(1/3), the physically viable models of homogeneous density distribution are not possible. If the configuration is considered to be isentropic, then both γ and the speed of sound become infinite throughout the configuration. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bianchi type-I cosmological models for binary mixture of perfect fluid and dark energy

We consider a self consistent system of Bianchi Type-I cosmology and Binary Mixture of perfect fluid and dark energy. The perfect fluid is taken to be obeying equations of state p _PF =γρ _PF with γ∈[0,1]. The dark energy is considered to be obeying a quintessence-like equation of state where the dark energy obeys equation of state p _DE =ωρ _DE where ω∈[−1,0]. Exact solutions to the corresponding Einstein field equations are obtained. Some special cases are discussed and studied. Further more power law models and exponential models are investigated.     

Quasar correlation function and redshift space distortion from SDSS DR5 data

For z = 0.8–2.2 redshift interval, quasar pair correlation function parameters and β redshift space distortion parameter (connected to large-scale potential flows) values are estimated. We base them on the Main QSO Sample from SDSS Data Release 5. Standard correlation function form ξ(r) = (r ₀/r)^γ is used for comoving distances r = 2–50 Mpc between quasars. We fix the parameters of the cosmological model: Ω_Λ = 1 − Ω _M = 0.726 and H ₀ = 70.5 km/(s Mpc). We come to the best-fit parameter values of γ = 1.77 ± 0.20, r ₀ = 5.52 ± 0.95 Mpc/h for r in the range 2–30 Mpc, γ = 1.91 ± 0.11, r ₀ = 5.82 ± 0.61 Mpc for r in the range 2–50 Mpc. The mean β value is β = 0.43 ± 0.22.     

Cosmic Ray Production Rates in Supernova Remnants

Supernova Remnants (SNRs) are the most likely sources of the galactic cosmic rays up to energies of about 10¹⁵ eV/nuc. The large scale shock waves of SNRs are almost ideal sites to accelerate particles up to these highly non-thermal energies by a first order Fermi mechanism which operates through scattering of the particles at magnetic irregularities. In order to get an estimate on the total amount of the explosion energy E _SNconverted into high energy particles the evolution of a SNR has to be followed up to the final merging with the interstellar medium. This can only be done by numerical simulations since the non-linear modifications of the shock wave due to particle acceleration as well as radiative cooling processes at later SNR stages have to be considered in such investigations. Based on a large sample of numerical evolution calculations performed for different ambient densities n _ext, SN explosion energies, magnetic fields etc. we discuss the final ‘yields’ of cosmic rays at the final SNR stage where the Mach number of the shock waves drops below 2. At these times the cosmic rays start to diffuse out of the remnant. In the range of external densities of10^-2 ≤ n _ext/[cm^-3] ≤ 30 we find a the total acceleration efficiency of about 0.15 E _SN with an increase up to 0.24 E _SN at maximum for an external density of n _ext = 10 cm^-3. Since for the larger ambient densities radiative cooling can reduce significantly the total thermal energy content of the remnant dissipation of Alfvén waves can provide an important heating mechanism for the gas at these later stages. From the collisions of the cosmic rays with the thermal plasma neutral pions are generated which decay subsequently into observable γ-rays above 100 MeV. Hence, we calculate these γ-ray luminosities of SNRs and compare them with current upper limits of ground based γ-raytelescopes. The development of dense shells due to cooling of the thermal plasma increases the γ-ray luminosities and e.g. an external density of n _ext = 10 cm^-3 with E _SN = 10⁵¹ erg can lead to a γ-ray flux above 10^-6 ph cm^-2 s^-1 for a remnant located at a distance of 1 kpc. This revised version was published online in July 2006 with corrections to the Cover Date.     

Closed form charged fluid with t = constant hypersurfaces as spheroids and hyperboloids

In the present article models of well behaved charged superdense stars with surface density 2×10¹⁴ gm/cm³ are constructed by considering a static spherically symmetric metric with t = const hypersurfaces as spheroids and hyperboloids. Maximum mass of the star is found to be 7.66300M _Θ with radius 19.35409 km for spheroids case while 1.51360M _Θ with radius 13.72109 km for hyperboloid case satisfying ultra-relativistic conditions. The solutions thus found satisfy all the reality and causality conditions. For brevity we don’t present a detailed analysis of the derived solutions in this paper.     

Radio-to-TeV γ-ray emission from PSR B1259–63

We discuss the implications of the recent X-ray and TeV γ-ray observations of the PSR B1259–63 system (a young rotation powered pulsar orbiting a Be star) for the theoretical models of interaction of pulsar and stellar winds. We show that previously considered models have problems to account for the observed behaviour of the system. We develop a model in which the broad band emission from the binary system is produced in result of collisions of GeV–TeV energy protons accelerated by the pulsar wind and interacting with the stellar disk. In this model the high energy γ-rays are produced in the decays of secondary neutral pions, while radio and X-ray emission are synchrotron and inverse Compton emission produced by low-energy (≤100 MeV) electrons from the decays of secondary charged π ^± mesons. This model can explain not only the observed energy spectra, but also the correlations between TeV, X-ray and radio emission components.      

The Process of Photon-Splitting and its Effect on Pulsar Emission:The Analytic Approach

Magnetic photon splitting γ → γγ, a quantum electrodynamic process that becomes important when magnetic field approaching the quantum critical value, B _c = 4.413 × 10¹³ G, may have important effects on pulsar radio emission. According to the standard model, the pulsar radio emission is produced by coherent curvature radiation of a large amounts of e ^± pairs, which are thought to be generated by the pair creation process γ + B → e ^±. However, if the magnetic field is strong enough, the photon splitting may dominate the pair creation process, then the amounts of e ^± pairs and the radio luminosity will be strongly suppressed and may be undetectable. Here we use the fitted analytical formula of the photon splitting attenuation coefficient to study the above process, and find that the photon splitting will strongly decrease the radio emission when B > 10¹³ G. We also note that the photon splitting can strongly but not totally suppress the creation of pairs due to the diminishing dependence of B in the attenuation coefficient. We find that the ratio of the probability of a photon being absorbed by photon splitting to that by pair creation is no more than about six. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cosmological Models with ‘Some’ Variable Constants

Various models are considered with metric type flat FRW i.e. with k = 0 whose energy-momentum tensor is described by a perfect fluid whose generic equation of state is p = ωρ and taking into account the conservation principle div(T _i ^j ) = 0, but considering some of the‘constants’ as variable. A set of solutions through dimensional analysis is trivially found. The numeric calculations carried out show that the results obtained are not discordant with those presently observed for cosmological parameters together with the electromagnetic and quantum quantities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Gamma-ray emission expected from Kepler’s SNR

Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants (SNRs) is used to investigate the properties of Kepler’s SNR and, in particular, to predict the γ-eay spectrum expected from this SNR. Observations of the nonthermal radio and X-ray emission spectra as well as theoretical constraints for the total supernova (SN) explosion energy E _sn are used to constrain the astronomical and particle acceleration parameters of the system. Under the assumption that Kepler’s SN is a type Ia SN we determine for any given explosion energy E _sn and source distance d the mass density of the ambient interstellar medium (ISM) from a fit to the observed SNR size and expansion speed. This makes it possible to make predictions for the expected γ-eay flux. Exploring the expected distance range we find that for a typical explosion energy E _sn=10⁵¹ erg the expected energy flux of TeV γ-rays varies from 2×10⁻¹¹ to 10⁻¹³ erg/(cm² s) when the distance changes from d=3.4 kpc to 7 kpc. In all cases the γ-eay emission is dominated by π ⁰-decay γ-rays due to nuclear CRs. Therefore Kepler’s SNR represents a very promising target for instruments like H.E.S.S., CANGAROO and GLAST. A non-detection of γ-rays would mean that the actual source distance is larger than 7 kpc.     

Gamma-ray burst investigation via polarimetry and spectroscopy (GRIPS)

The primary scientific goal of the GRIPS mission is to revolutionize our understanding of the early universe using γ-ray bursts. We propose a new generation gamma-ray observatory capable of unprecedented spectroscopy over a wide range of γ-ray energies (200 keV–50 MeV) and of polarimetry (200–1000 keV). The γ-ray sensitivity to nuclear absorption features enables the measurement of column densities as high as 10²⁸cm^− 2. Secondary goals achievable by this mission include direct measurements of all types of supernova interiors through γ-rays from radioactive decays, nuclear astrophysics with massive stars and novae, and studies of particle acceleration near compact stars, interstellar shocks, and clusters of galaxies. See for the authors’ affiliations.     

Extremization of mass of charged superdense star models describe by Durgapal type space-time metric

In the present article, we have obtained a class of charged superdense star models, starting with a static spherically symmetric metric in curvature coordinates by considering Durgapal (J. Phys. A 15:2637, 1982) type metric i.e. g ₄₄=B(1+Cr ²) ⁿ , where n being any positive integer. It is observed that the maximum mass of the charged fluid models is monotonically increasing with the increasing values of n≤4. For n≥4, the maximum mass of the charged fluid models is throughout monotonically decreasing and over all maximum mass is attained at n=4. The present metric tends to another metric which describes the charged analogue of Kuchowicz neutral solution as n→∞. Consequently the lower limit of maximum mass of the charged fluid models could be determined and found to be 5.1165 solar mass with corresponding radius 18.0743 Km. While the upper limit of maximum mass of the model of this category is already known to be 5.7001 solar mass with corresponding radius 17.1003 Km for n=4. The solutions so obtained are well behaved.     

Ammonia in the atmospheres of Jupiter and Saturn: Absorption coefficients

Spectral values (with 1 nm spectral resolution) of the product of γk _ν and γ′k _ν (where k _ν is the monochromatic coefficient of ammonia absorption and γ and γ′ are the relative (with respect to 0.85/0.15 hydrogen-helium mixture and methane, respectively)) concentrations of ammonia for the absorption bands at λλ = 552, 604, 645, 787, and 932 nm in thermal conditions of Jupiter’s and Saturn’s atmospheres are determined ().     

The physics of E × B-drifting jets

E × B-drifting jets have been generally ignored for the past 25 years even though they may well describe all the astrophysical jet sources, both on galactic and stellar scales. Here we present closed-form solutions for their joint field-and-particle distribution, argue that the observed jets are near equipartition, with extremely relativistic, monoenergetic e^±-pairs of bulk Lorentz factor γ ≲ 10⁴, and are first-order stable. We describe plausible mechanisms for the jets’ (i) formation, (ii) propagation, and (iii) termination. Wherever a beam meets with resistance, its frozen-in Poynting flux transforms the delta-shaped energy distribution of the pairs into an almost white power law,E ² N _E ∼E ^−∫ with ∫ ≳ 0, via single-step falls through the huge convected potential.     

Calculation of effective optical depth of absorption line formation in homogeneous semi-infinite planetary atmosphere during anisotropic scattering

The algorithm for determining effective optical thickness of absorption line formation in a plane-parallel homogeneous planetary atmosphere is presented. The case of anisotropic scattering is considered. The results of numerical calculations of τ _e (μ₀) at the scattering angle γ = π for some values of the single scattering albedo λ and the parameter of the Heyney-Greenstein scattering indicatrix g are given. The refined equation for the function T ^m (−μ, μ₀) is presented.     

On most general exact solution for Vaidya-Tikekar isentropicsuperdense star

The energy density of Vaidya-Tikekar isentropic superdense star is found to be decreasing away from the center, only if the parameter K is negative. The most general exact solution for the star is derived for all negative values of K in terms of circular and inverse circular functions. Which can further be expressed in terms of algebraic functions for K = 2-(n/δ)² < 0 (n being integer andδ = 1,2,3 4). The energy conditions 0 ≤ p ≤ αρc ², (α = 1 or 1/3) and adiabatic sound speed conditiondp dρ ≤ c ², when applied at the center and at the boundary, restricted the parameters K and α such that .18 < −K −2287 and.004 ≤ α ≤ .86. The maximum mass of the star satisfying the strong energy condition (SEC), (α = 1/3) is found to be3.82 Mq_· at K=−2/3, while the same for the weak energy condition (WEC), (α =1) is 4.57 M_ _⊙ atK=−>5/2. In each case the surface density is assumed to be 2 × 10¹⁴ gm cm^-3. The solutions corresponding to K>0 (in fact K>1) are also made meaningful by considering the hypersurfaces t= constant as 3-hyperboloid by replacing the parameter R ² by −R² in Vaidya-Tikekar formalism. The solutions for the later case are also expressible in terms of algebraic functions for K=2-(n/δ² > 1 (n being integer or zero and δ =1,2,3 4). The cases for which 0 < K < 1 do not possess negative energy density gradient and therefore are incapable of representing any physically plausible star model. In totality the article provides all the physically plausible exact solutions for the Buchdahl static perfect fluid spheres. This revised version was published online in July 2006 with corrections to the Cover Date.     

Structure and stability of rotating fluid disks around massive objects. I. Newtonian formulation

In this paper we have presented a very general class of solutions for rotating fluid disks around massive objects (neglecting the self gravitation of the disk) with density as a function of the radial coordinate only and pressure being nonzero. Having considered a number of cases with different density and velocity distributions, we have analysed the stability of such disks under both radial and axisymmetric perturbations. For a perfect gas disk with γ= 5/3 the disk is stable with frequency (MG/r³)^1/2 for purely radial pulsation with expanding and contracting boundary. In the case of axisymmetric perturbation the critical γ_c for neutral stability is found to be much less than 4/3 indicating that such disks are mostly stable under such perturbations. On leave of absence from Government College, Jagdalpur 494005.