Surfaces of zero kinetic energy in a general three-body problem

We generalize the concept of zero-velocity surface and construct zero-kinetic-energy surfaces. In the space of three mutual distances, we determine the regions where motion is possible; these regions are in the shape of an infinitely long tripod. Motions in the three-body problem are shown to be unstable according to Hill.     

Axisymmetric dusty gas jet in the inner coma of a comet

The behavior of expanding pure and dusty gas jets is investigated in the inner coma of an H₂O-dominated comet by numerically solving the axisymmetric, time-dependent, coupled hydrodynamic equations for H₂O gas and single-sized dust (0.65 μ) in polar coordinates (r, θ, φ). The jet profile is assumed to be Gaussian on the surface of a nucleus. The viscosity of the gas is taken into account. Two-dimensional distributions of the densities, velocities in the r and θ directions, and temperatures for the gas and dust have been obtained. For the dusty jet, the axisymmetric transonic solution for the gas has been calculated time-dependently. For a narrow dusty gas jet (i.e., of breadth 10°), the gas density peaks shift from the central axis of the jet (θ = 0°) to its wings (θ ∼ 30°) with the gas flowing away from the cometary nucleus, owing to a steep density gradient in the θ direction. Dragged by this laterally expanding gas outflow, the dust particles are swept away from the central axis and are also concentrated more sharply at θ ∼ 35° than the gas particles. This lateral expansion of the jet is overwhelming only within the innermost region (r ≦ 10 km). The jet feature for the gas becomes indiscernible by the time the flow reaches the outer boundary (r = 100 km), while the corresponding dust feature remains even at the outer boundary. The radial velocities of the gas and dust are enhanced inside the jet, compared with those in the background. For a broad pure gas jet (i.e., of breadth 30°), on the other hand, the gas density peaks do not shift to the wings and the jet feature can still be seen at the outer boundary, in contrast to the narrow case.     

Self-similar flows of a self-gravitating gas with increasing energy in uniform atmosphere

Self-similar flows of a gas, moving under the gravitational force of attraction behind a spherical shock wave, which are driven out by a propelling contact surface and propagating into a uniform atmosphere at rest are investigated. The energy of the expanding wave has been assumed to be time-dependent, obeying a power law. In the last section the self-similar homothermal flows of self-gravitating gas has been also discussed. A comparative study has been made between the nature of flow variables for adiabatic and homothermal flows.     

Propagation of ion-acoustic waves in a warm dusty plasma with electron inertia

The KdV equation is derived for weakly nonlinear ion-acoustic waves in an unmagnetized warm dusty plasma with electron inertia. It has been shown that the inclusion of electron inertia and pressure variation of the species not only significantly modifies the basic features (width and amplitude) of dust ion-acoustic solitions, but also introduces a new parametric regime for the existence of positive and negative solitons.     

A self-similar flow of self-gravitating gas behind a shock wave with increasing energy,I

Self-similar flows of self-gravitating gas behind a spherical shock wave which are driven out by a propelling contact surface, propagating in a nonuniform atmosphere at rest, are investigated. The total energy content of the flow between a shock front and contact surface is taken to be time-dependent. In brief, the self-similar homothermal flows of self-gravitating gas behind a shock wave and Roche's model case are also studied in the present paper.     

Magnetohydrodynamic behaviour of a finite amplitude disturbance in the solar magnetic field

In this paper, dynamic processes in the solar atmosphere are studied numerically from a complete set of MHD equations. Dynamic evolution of the non-linear magnetic field is produced by the finite amplitude of the azimuthai magnetic field at the base of the flux tube of the solar atmosphere. It is assumed that the initial configuration of the magnetic field is a force-free and potential field, the magnetic field is disturbed at the base, the plasma is driven and a part of the magnetic energy is transformed into the kinetic energy of the plasma.The compressed flow of the plasma has the features of fast MHD waves. The computation results give quantitatively the non-linear evolution of strong magnetic fields. These results could be used in an explanation of coronal transients, surge, spray and eruptive prominence events in the solar atmosphere, as well as in a modelling of plasma behaviour in high-β structure experiments in the laboratory.     

A simulation of a jet with the hiccups

We present results of a numerical simulation of a stellar jet from a source with supersonic variations in the outflow velocity. The simulation is compared with both analytical predictions and observations.     

Fully nonlinear ion-acoustic solitary waves in a warm magnetized plasma with electron inertia

Ion-acoustic solitary waves in a warm, magnetized plasma with electron inertia have been investigated through Sagdeev pseudopotential method. It has been established the existence of both compressive supersonic solitons, and rarefactive subsonic and supersonic solitons within the parametric domains. The effect of the external magnetic field for generation of the supersonic compressive solitons of constant amplitudes appears to be passive after some critical direction of propagation of the wave. However, up to the critical direction of propagation, the magnetic resistance is found to be quite active to drastically reduce the soliton amplitudes. The generation of rarefactive solitons in this warm magnetized plasma is rather more feasible to be supersonic without electron inertia.     

A systematic study on energy dependence of quasi-periodic oscillation frequency in GRS 1915+105

Systematically studying all the RXTE/PCA observations for GRS 1915+105 before November 2010, we have discovered three additional patterns in the relation between Quasi-Periodic Oscillation (QPO) frequency and photon energy, extending earlier outcomes reported by Qu et al. (Astrophys. J. 710:836, 2010). We have confirmed that as QPO frequency increases, the relation evolves from the negative correlation to positive one. The newly discovered patterns provide new constraints on the QPO models.     

Gravitation and inertia; a rearrangement of vacuum in gravity

We address gravitation and inertia in the framework of a general gauge principle (GGP) which accounts for the gravitation gauge group G _R generated by a hidden local internal symmetry implemented on the flat space. Following the method of phenomenological Lagrangians, we connect the group G _R to a non-linear realization of the Lie group of the distortion G _D of the local internal properties of six-dimensional flat space, M ₆, which is assumed as a toy model underlying four-dimensional Minkowski space. We study the geometrical structure of the space of parameters and derive the Maurer–Cartan’s structure equations. We treat distortion fields as Goldstone fields, to which the metric and connection are related, and we infer the group invariants and calculate the conserved currents. The agreement between the proposed gravitational theory and available observational verifications is satisfactory. Unlike the GR, this theory is free of fictitious forces, which prompts us to address separately the inertia from a novel view point. We construct a relativistic field theory of inertia, which treats inertia as a distortion of local internal properties of flat space M ₂ conducted under the distortion inertial fields. We derive the relativistic law of inertia (RLI) and calculate the inertial force acting on the photon in a gravitating system. In spite of the totally different and independent physical sources of gravitation and inertia, the RLI furnishes a justification for the introduction of the Principle of Equivalence. Particular attention is given to the realization of the group G _R by the hidden local internal symmetry of the abelian group U ^loc=U(1) _Y ×diag[SU(2)], implemented on the space M ₆. This group has two generators, the third component T ³ of isospin and the hypercharge Y, implying Q ^d =T ³+Y/2, where Q ^d is the distortion charge operator assigning the number −1 to particles, but +1 to anti-particles. This entails two neutral gauge bosons that coupled to T ³ and Y. We address the rearrangement of the vacuum state in gravity resulting from these ideas. The neutral complex Higgs scalar breaks the vacuum symmetry leaving the gravitation subgroup intact. The resulting massive distortion field component may cause an additional change of properties of the spacetime continuum at huge energies above the threshold value.     

Axisymmetric dusty gas jet in the inner coma of a comet: II. The case of isolated jets

The behavior of isolated pure and dusty gas jets ejected from an active spot on the sunlit side of the nucleus surface is hydrodynamically investigated in the inner coma of an H₂O-dominated comet that is assumed to have no ambient ejection of the gas and dust from the dust-covered surface except the active spot. Steady-state solutions of the expanding jets are obtained by numerically solving the axisymmetric, time-dependent, coupled hydrodynamic equations of H₂O gas and the dust in polar coordinates (r, θ, φ). The dust particles are treated as multicomponents composed of the three radii of a = 0.01, 0.1, and 1 μm. The boundary conditions of a slip wall are applied to the dust-covered surface. Discussion is given on the no-slip-wall conditions. Compared with the previous study on the jets surrounded by ambient gas and dust ejected from a nonactive region by Y. Kitamura (1986, Icarus 66, 241–257), the jet features can be clearly discerned even at large distances from the nucleus center, and the shift of the density peaks from the central axis to the wings, which was seen in the previous study, does not occur, because the jets can freely expand in the θ direction without being decelerated by the ambient gas and dust. The gas flow in the θ direction is supersonic, and consequently it is predicted that the shock waves are formed in the interactive regions among several jets. For the isolated jets with no ambient ejection, it is to be noted that the flow of the gas and dust along the nucleus surface arises in spite of the radial ejection from the active spot, and that this flow may change the surface structure. In the dusty case, the gas temperature increases immediately from 200 to ∼275°K in the vicinity of the surface owing to strong heating by the fine dust particles with the radius as small as 0.01 μm. In addition to the fine dust, the hot dust mantle (300–400°K) on the surface may considerably heat the gas near the mantle.     

The effects of deformation inertia (kinetic energy) in the orbital and spin evolution of close-in bodies

The purpose of this work is to evaluate the effect of deformation inertia on tide dynamics, particularly within the context of the tide response equations proposed independently by Boué et al. (Celest Mech Dyn Astron 126:31–60, 2016) and Ragazzo and Ruiz (Celest Mech Dyn Astron 128(1):19–59, 2017). The singular limit as the inertia tends to zero is analyzed, and equations for the small inertia regime are proposed. The analysis of Love numbers shows that, independently of the rheology, deformation inertia can be neglected if the tide-forcing frequency is much smaller than the frequency of small oscillations of an ideal body made of a perfect (inviscid) fluid with the same inertial and gravitational properties of the original body. Finally, numerical integration of the full set of equations, which couples tide, spin and orbit, is used to evaluate the effect of inertia on the overall motion. The results are consistent with those obtained from the Love number analysis. The conclusion is that, from the point of view of orbital evolution of celestial bodies, deformation inertia can be safely neglected. (Exceptions may occur when a higher-order harmonic of the tide forcing has a high amplitude.)     

The entropy and energy of intergalactic gas in galaxy clusters

Studies of the X-ray surface brightness profiles of clusters, coupled with theoretical considerations, suggest that the breaking of self-similarity in the hot gas results from an 'entropy floor', established by some heating process, which affects the structure of the intracluster gas strongly in lower-mass systems. By fitting analytical models for the radial variation in gas density and temperature to X-ray spectral images from the ROSAT PSPC and ASCA GIS, we have derived gas entropy profiles for 20 galaxy clusters and groups. We show that, when these profiles are scaled such that they should lie on top of one another in the case of self-similarity, the lowest-mass systems have higher-scaled entropy profiles than more massive systems. This appears to be due to a baseline entropy of depending on the extent to which shocks have been suppressed in low-mass systems. The extra entropy may be present in all systems, but is detectable only in poor clusters, where it is significant compared with the entropy generated by gravitational collapse. This excess entropy appears to be distributed uniformly with radius outside the central cooling regions.
We determine the energy associated with this entropy floor, by studying the net reduction in binding energy of the gas in low-mass systems, and find that it corresponds to a pre-heating temperature of 0.3 keV. Since the relationship between entropy and energy injection depends upon gas density, we are able to combine the excesses of 70140 keV cm² and 0.3 keV to derive the typical electron density of the gas into which the energy was injected. The resulting value of implies that the heating must have happened prior to cluster collapse but after a redshift z 710. The energy requirement is well matched to the energy from supernova explosions responsible for the metals which now pollute the intracluster gas.     

Cooling and energy loss of partially ionized hydrogen gas behind a shock wave

We studied the difference in behavior of total energy and its thermal component during the radiative cooling of partially ionized hydrogen gas. Our calculations were fulfilled for the conditions in the atmosphere of a cool star. It is shown that the attenuation of total energy loss does not interfere with the cooling rate.     

Irreversible thermodynamics of the universe with interacting modified Chaplygin gas as dark energy

The present work deals with irreversible thermodynamics of universe containing interacting dark fluids. Recent observational evidences reveal that the universe is dominated by two dark components-dark matter and dark energy. The interaction between them leads to spontaneous heat flow between the horizon and the fluid system and as a result the system will no longer be in thermal equilibrium. In this paper dark matter is chosen as pressureless dust while modified Chaplygin gas has been considered as dark energy. In two separate cases we have considered the universe to be bounded by apparent horizon and event horizon and the validity of generalized second law of thermodynamics in the context of irreversible thermodynamics has been studied for both the cases.     

Holographic dark energy model with linearly varying deceleration parameter and generalised Chaplygin gas dark energy model in Bianchi type-I universe

The paper deals with a spatially homogeneous and anisotropic Bianchi type-I universe filled with two minimally interacting fluids; matter and holographic dark energy components. The nature of the holographic dark energy for Bianchi type-I space time is discussed. An exact solution to Einstein’s field equations in Bianchi type-I line element is obtained using the assumption of linearly varying deceleration parameter. Under the suitable condition, it is observed that the anisotropy parameter of the universe approaches to zero for large cosmic time and the coincidence parameter increases with increasing time. We established a correspondence between the holographic dark energy models with the generalised Chaplygin gas dark energy model. We also reconstructed the potential and dynamics of the scalar field which describes the Chaplygin cosmology. Solution of the field equations shows that a big rip type future singularity will occur for this model. It has been observed that the solutions are compatible with the results of recent observations.     

Equilibria of a satellite subjected to gravitational and aerodynamic torques with pressure center in a principal plane of inertia

Attitude motion of a satellite subjected to gravitational and aerodynamic torques in a circular orbit is considered. In special case, when the center of pressure of aerodynamic forces is located in one of the principal central planes of inertia of the satellite, all equilibrium orientations are determined. Existence conditions of all equilibria are obtained and evolution of domains with a fixed number of equilibria is investigated in detail. All bifurcation values of the system’s parameters corresponding to the qualitative change of these domains are determined. Sufficient conditions of stability are obtained for each equilibrium orientation using generalized integral of energy.     

Magnetohydrodynamic study of shock waves in the current sheet of a solar coronal magnetic loop

A Lagrangian Remap (LareXd) Code is employed to investigate the shock wave formation in the current sheet of a solar coronal magnetic loop and its effect on the magnetic reconnection. We constructed the slow shock structure in the presence of viscosity and heat conduction parallel and perpendicular to the magnetic field and pairs of slow shocks propagate away from the central current sheet, the so-called diffusion region. Significant jumps in plasma density, pressure, velocity and magnetic field occur across the main shock while the temperature appears in the foreshock. In the presence of dissipative effects, the distinct jumps disappear and the shock profiles show smooth transition between the downstream and the upstream regions while the plasma density and the pressure show very narrow and a sharp decrease with time. These results can be applied to the heating of the solar corona, the structure of the magnetic reconnection and the solar wind.     

Suppression of resistive hose instability in a relativistic electron–positron flow

This paper presents the effects of electron–positron pair production on the linear growth of the resistive hose instability of a filamentary beam that could lead to snake-like distortion. For both the rectangular radial density profile and the diffuse profile reflecting the Bennett-type equilibrium for a self-collimating flow, the modified eigenvalue equations are derived from a Vlasov–Maxwell equation. While for the simple rectangular profile, current perturbation is localized at the sharp radial edge, for the realistic Bennett profile with an obscure edge, it is non-locally distributed over the entire beam, removing catastrophic wave–particle resonance. The pair production effects likely decrease the betatron frequency, and expand the beam radius to increase the resistive decay time of the perturbed current; these also lead to a reduction of the growth rate. It is shown that, for the Bennett profile case, the characteristic growth distance for a preferential mode can exceed the observational length-scale of astrophysical jets. This might provide the key to the problem of the stabilized transport of the astrophysical jets including extragalactic jets up to  Mpc (∼3 × 10²⁴ cm)  scales.