Chandrasekhar's integral stability criterion for an equilibrium spherical cloud of a protostar, modified in the framework of non-Gaussian kappa-statistics

Within the framework of the non-extensive statistical mechanics of Kanyadakis, a generalization of the integral stability theorem of Chandrasekhar for the spherically symmetric distribution of matter and black radiation in an exoplanetary cloud in a state of gravitational equilibrium is obtained. For this purpose, the elements of deformed thermodynamics for an ideal gas, deformed canonical Gibbs distribution, as well as the effective gravitational constant, calculated in the formalisms of Kanyadakis and Verlinde, are used. In this, the deformation parameter κ (kappa) measures the so-called degree of nonextensiveness of the cloud system. In addition, the modified thermodynamic properties of blackbody radiation, in particular, the analogue of Stefan's law for radiation energy and generalized expressions for the entropy, heat capacity and radiation pressure, are discussed in the context of κ -statistics. The presented method of combining the indicated anomalous physical processes provides an alternative to the classical procedure of Chandrasekhar's derivation of the well-known integral theorems for gas configurations in gravitational equilibrium, and restores all standard expressions in the limit κ → 0. The results obtained will be able, according to the author, to explain some astrophysical problems of stellar-planetary cosmogony, associated, in particular, with modeling the processes of joint formation and evolution of a protosun and an exoplanetary cloud from a single nebula.

Interaction of an accelerating layer with a cloud: formation of tails and cumulative jets

ABSTRACT We consider the penetration of spherical dense cloud into a planar layer of gas that is in gravitational equilibrium in a constant field of gravity with acceleration W. We take into account the compressibility of the medium in contrast to the classical problem of a drop falling on the surface of an incompressible fluid. Our goal is to study the formation of cumulative jets in relation to the conditions on the borders of H ii regions. We determine those features of motion that would distinguish jet streams from inhomogeneities of a different origin. Our simulation has shown that cumulative jets may arise in the presence of an acceleration layer W. The gas in jet moves in the direction opposite to the initial velocity Vc. At the same time, there are both a cumulative jet and tails, teardrop-shaped condensations, caused, respectively, by gas inflow in the wake behind the cloud and the classical Rayleigh–Taylor instability. We assume the model, according to which the H ii RCW 82 region formed in an initially homogeneous cloud. In framework of this model, we estimated the characteristic time of a cumulative jet formation ts ≈ 0.15 Myr. This is less than the present age of the H ii RCW 82 region, which is about 0.4 Myr. From the obtained estimates, it follows that the conditions at the periphery of the H ii RCW 82 region are favourable for the manifestation of cumulative effects on scales of ∼1.4 × 1017 cm, which are significantly smaller than the layer thickness.

Siesmic Activity and its Periphery

Earthquake is a series of vibrations within the earth's crust. It occurs when the earth's crust break due to geological forces on the rock and adjoining plate. Earthquake refers to a movement or tremor of the earth’s crust that originates naturally and below the surface. An earthquake is a vibration or oscillation of the surface of the earth caused by a transient disturbance of the elastic or gravitational equilibrium of the rocks at or beneath the surface. There are two causes of earthquakes. One is religious concept and the other is modern concept. Earthquakes are of different types according to their place of origin and location. There are so many effects of earthquakes.The Himalayan Physics Vol. 6 & 7, April 2017 (86-91)

An Alternative to the Alcubierre Theory: Warp Fields by the Gravitation via Accelerated Particles Assertion

<p class="1Body">A summarization of the Alcubierre metric is given in comparison to a new metric that has been formulated based on the theoretical assertion of a recently published paper entitled “gravitational space-time curve generation via accelerated particles”. The new metric mathematically describes a warp field where particle accelerators can theoretically generate gravitational space-time curves that compress or contract a volume of space-time toward a hypothetical vehicle traveling at a sub-light velocity contingent upon the amount of voltage generated. Einstein’s field equations are derived based on the new metric to show its compatibility to general relativity. The “time slowing” effects of relativistic gravitational time dilation inherent to the gravitational field generated by the particle accelerators is mathematically shown to be counteracted by a gravitational equilibrium point between an arrangement of two equal magnitude particle accelerators. The gravitational equilibrium point produces a volume of flat or linear space-time to which the hypothetical vehicle can traverse the region of contracted space-time without experiencing time slippage. The theoretical warp field possessing these attributes is referred to as the two gravity source warp field which is mathematically described by the new metric.</p>

Estimation of the physical parameters of planets and stars in the gravitational equilibrium model

The motion equations of matter in a gravitational field, acceleration field, pressure field, and other fields are considered based on the field theory. This enables us to derive simple formulas in the framework of the gravitational equilibrium model, which allow us to estimate the physical parameters of cosmic bodies. The acceleration field coefficient, η, and the pressure field coefficient, σ, are a function of the state of matter, and their sum is close in magnitude to the gravitational constant, G. In the presented model the dependence is found of the internal temperature and pressure on the current radius. The central temperatures and pressures are calculated for the Earth and the Sun, for a typical neutron star and a white dwarf. The heat flux and the thermal conductivity coefficient of these objects’ matter are found, and the formula for estimating the entropy is provided. All the quantities are compared with the calculation results in different models of cosmic bodies. The discovered good agreement with these data proves the effectiveness and universality of the proposed model for estimating the parameters of planets and stars and for more precise calculation of physical quantities.

SELF-GRAVITATING SYSTEM OF SEMIDEGENERATED FERMIONS AS CENTRAL OBJECTS AND DARK MATTER HALOS IN GALAXIES

We propose a unified model for dark matter haloes and central galactic objects as a self-gravitating system of semidegenerated fermions in thermal equilibrium. We consider spherical symmetry and then we solve the equations of gravitational equilibrium using the Fermi integrals in a dimensionless manner, obtaining the density profile and velocity curve. We also obtain scaling laws for the observables of the system and show that, for a wide range of our parameters, our model is consistent with the so called universality of the surface density of dark matter.