The final state of charged collapsing core and its optical appearance

We discuss the optical appearance of a charged collapsing stellar core. In the case Q < M , the collapse leads to the formation of a black hole and the phenomenon will be qualitatively similar to the uncharged case, that is, an exponentially increasing redshift and an exponentially decreasing intensity but the time-constant may be very much greater. In the case Q >M, if the collapse ends in a singularity, then infinite redshift and vanishing of light will be seen optically within a finite time. But the formation of singularity does not seem to be a real possibility. More probably, a steady, vibrating configuration will form, which will show very large redshift if Q is close to M.     

The accretion of matter by a collapsing star in the presence of a magnetic field

The exact nonstationary solution for the variation of the magnetic field in the Schwarzschild metric with a given spherically symmetric flow is obtained. Initially a homogeneous magnetic field increases with time, changing into a quasi-radial field. On the assumption of equipartition between the magnetic and kinetic energies of a falling gas, in the relativistic case, estimates of the stationary field and the intensity of synchrotron radiation are presented. A considerable part of the radiation is formed in the relativistic regionr?(2.5 to 7.7)r _g (r _g is the gravitational radius of a black hole). Estimates are made for radiation from the relativistic region in the case of disc type accretion.     

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.     

Deflection of near-Earth asteroids by kinetic energy impacts from retrograde orbits

Previous studies of non-nuclear diversion of near Earth asteroids have largely ignored the use of pure kinetic energy impacts, partly due to apparent limits on impact speeds of 10-. Here, I will consider the use of a near-term solar sail to deliver an inert projectile onto a retrograde solar orbit, thus raising impact speeds to at least . Such high-energy orbits increase the energy liberated during impact by a factor of 40 or more, while reducing the required projectile mass by at least 95%. This considerable reduction in projectile mass allows kilometre-sized asteroids to be diverted with current launch vehicles, near-term technologies and at a cost comparable to a modest deep space mission.     

Quasi-elastic neutrino scattering by nuclei in superdense matter of a collapsing star

The interaction of neutrinos with nuclei in the superdense matter of a collapsing star is studied, taking into account the collective modes and thermal fluctuations of the medium density. It is shown that the elastic neutrino scattering by nuclei with a momentum transfer less than or of the order of the inverse distance between the ions in the nonideal Coulomb plasma, differs considerably from the analogous scattering by a single nucleus. The weak A interaction screening by medium electrons is taken into account. The collision integral and transport cross section of neutrino scattering by nuclei are calculated in terms of macroscopic medium parameters.     

The accretion of matter by a collapsing star in the presence of a magnetic field. II. Selfconsistent stationary picture

The stationary two-dimensional magnetohydrodynamic solution for the accretion of the matter without pressure into a gravitating centre of a black hole is obtained. It is assumed that the magnetic field far from the collapsed star is homogeneous and its influence on the flow is negligible. Around the star, at the plane perpendicular to the direction of the magnetic field, the dense quasistationary disc is formed, the structure of which in a large extent is determined by dissipation processes. The structure is calculated for (a) a laminar disc with the Coulomb mechanism of dissipation; and (b) a turbulent disc.The estimations of the parameters of the shock which result from the infall of the matter onto the disc are given. In the last section the numerical estimation and approximate character of the radiation spectrum of the disc and the shock are obtained for two cases of 10M and 10⁵ M . The luminosity of collapsed objects withM=10M appears to be about solar, thus its observation is possibly only at the distances less than 300–1000 pc. The collapsed objects in the Galaxy withM=10⁵ M could constitute very bright sources in spectral regions from optical up to X-ray. The spectra of a laminar and a turbulent disc for 10M black hole are very different. The laminar disc radiates primarily in the ultraviolet. The turbulent disc radiates a large part of its flux in the infrared. Therefore, one cannot exclude the possibility that some of the galactic infrared star-like sources are individual black holes in the accretion state.     

The radiation of energy by a current in a plasma

The derivation of the differential power emitted in any given direction by a current J in a linear, homogeneous and non-absorbing plasma is reviewed in detail. The conventional derivation is shown to give the poweremitted; a formalism for the powerreceived is established by evaluating the Poynting vector in terms of the far field. It is pointed out that the two power expressions differ because the same energy dE is emitted in a time dt _e but received over a different time dt _r . Moreover, a careful scrutiny of both the formalism for the power emission and for the power reception exposes implicit assumptions which do not hold if the plasma is anisotropic. The necessary steps for establishing a valid formalism for anisotropic media are briefly sketched.     

The Martian Planetary Boundary Layer: Turbulent kinetic energy and fundamental similarity scales

We review selected in situ measurements and models aimed at the study of the Martian Planetary Boundary Layer (PBL). We also discuss critically the advantages and limitations of applying similarity theories to the Martian PBL and calculate the fundamental scales predicted by these theories. Finally, we obtain values of the turbulent kinetic energy (TKE) and address its budget by weighting the significance of the different terms involved in it. In situ measurements taken by the Viking and Pathfinder missions along with similarity theories conveniently adapted to Mars are used to obtain the fundamental scales, the TKE and its budget.     

The variation of the angle between the magnetic and rotation axes in a collapsing star

We derive the formula for the variation of the magnetic axis in a collapsing oblique rotator. Our results of calculation show that the case of the magnetic axis coincident with the rotation axis is unstable, and the angle between the two axes will grow on any small perturbation.     

Suppression of resonant field line oscillations by a turbulent background

Stochastic fluctuations of the magnetospheric plasma and background magnetic field, especially intense during geomagnetically active periods, can provide an additional mechanism of damping of Alfvén field line oscillations. To quantify this hypothesis, we consider a driven Alfvén field line resonator with stochastic fluctuations of the Alfvén resonant frequency. This problem is first considered analytically for a low level of fluctuations, then a more general numerical approach is introduced. The results of analytical calculations and numerical modeling both indicate the deterioration of resonant properties of the resonator owing to stochastic background fluctuations.     

The dynamics of dust in a collapsing protostellar cloud and its possible role in planet formation

First results are presented of a calculation describing the collapse of a rotating dusty protostellar cloud. The dust and gas components are calculated separately, although their interaction (e.g., radiation transport, friction, etc.) is taken into account. In the early stages of the collapse the dust is dynamically unimportant. The evolution of the dust cloud is strongly influenced by dust-dust collisions: rapid sedimentation into an equatorial dust disc is found to take place as a result of accumulative dust-dust collisions and the corresponding grain growth. Treating the dust separately from the gas allows us to compare our results with solar-system cosmochemical measurements, with celestial mechanics information and to draw conclusions about the time and place of planet formation in the collapsing cloud.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Stellar occultations by turbulent planetary atmospheres: The Beta Scorpii events

Possible manifestationsof turbulent scattering in the 1971 Beta Scorpii occultations by Jupiter are critically examined. Lack of detailed correlation between light curves observed at 60-km separations on the Jovian limb argues against a detailed layering hypothesis. An approximate calculation shows that the observed features of the light cuves can be explained in terms of a model for which “spikes” are scintillations caused by Jovian atmospheric turbulence. A significant number of paired spikes are a consequence of the model if the occulted star is binary with an appropriate orientation. The statistical properties of spikes for Beta Scorpii A and C are predicted from Rytov theory for Kolmogorov turbulence and compared with the available observations. Finally, we discuss the effects of turbulent scattering on the temperature profile which is obtained by averaging over the effect of the spikes.     

The rotation of Io with a liquid core

In a previous paper (Henrard, Celest. Mech. Dyn. Astron. 178, 144–153, 2005c) we have developed an analytical theory of the rotation of the Galilean satellite Io, considered as a rigid body and based on a synthetic theory of its orbital motion due to Lainey (Théorie Dynamique des Satellites Galiléens. PhD dissertation, Observatoire de Paris, 2002) (see also Lainey et al., A&A, 420, 1171–1183 2004a; A&A, 427, 371–376, 2004b). One of the most important causes of departure of the actual rotation from the rigid theory is thought to be the existence of a liquid core, the size of which is unknown but would be an important piece of information concerning the structure of the interior of the satellite. In this contribution we develop the analytical theory of a liquid core contained in a cavity filled by an inviscid fluid of constant uniform density and vorticity. The theory is based on Poincaré (Bull. Astron. 27, 321–356, 1910) model and is developed by a Lie transform perturbation method, very much like in our previous contribution. Our main conclusion is that the addition of a degree of freedom (the spin of the core) with a frequency close to the orbital frequency multiplies the possibility of resonances and that for some particular size of the core one may expect a (possibly small) region of chaotic behaviour in the vicinity of the Cassini state.     

The possible protogalactic role of eddies in a turbulent early universe

It is shown that eddies, present in a turbulent early universe, can form excellent galaxies upon collapse of the eddies and a small amount of viscous evolution. The resulting model galaxies display realistically flat rotation curves as well as exponential-like luminosity profiles. The dark mass is allowed to be non-baryonic in this model.Work performed under the auspices of the U.S. Department of Energy.     

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.)     

Charged shell supported by a phantom energy

This paper discusses the evolution of a thin spherically symmetric self gravitating phantom shell around the charged shell. The general equations describing the motion of shell with a general form of equation of state are derived. The different types of space-time R _± and T _± regions and shell motion are classified depending on the parameters of the problem. The mechanical stability analysis of this spherically symmetric thin shell with charge in Reissner-Nordstrom (RN) to linearized spherically symmetric perturbation about static equilibrium solution is carried out.