A time dependent model for spicule flow

A time dependent model for the flow of gas in a spicule is studied. In this model, the flow occurs in a magnetic flux sheath. Starting from hydrostatic equilibrium, the flux sheath is allowed to collapse normal to itself. The collapse induces a flow of gas along the magnetic field and this flow is identified as a spicule. A variety of sheath geometries and velocity patterns for the normal flow have been studied. It is observed that a large curvature in the field geometry and a large initial value for the normal flow are necessary to achieve spicule-like velocities. The duration for which a large velocity of normal flow is required is much shorter than the average lifetime of a spicule. It is proposed that the initial rapid collapse occurs during an impulsive spicule phase and it is the subsequent gradual relaxation of the flow which is observed as a spicule.     

Dynamical instability in accreting white dwarfs

We study the evolution of solid, CO white dwarfs after explosive carbon ignition at central densities around 10¹⁰ g cm^–3 triggered by steady accretion in a close binary system, in order to elucidate whether these stars can collapse to form a neutron star. We show that as long as the velocity of the burning front remains below a critical value of 0.006c _s (60 km s^–1), gravitational collapse is the final fate. These calculations support the accretion-induced collapse (AIC) scenario for the origin of a fraction of low-mass X-ray binaries.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Kepler's problem in constant curvature spaces

In this article the generalization of the motion of a particle in a central field to the case of a constant curvature space is investigated. We found out that orbits on a constant curvature surface are closed in two cases: when the potential satisfies Iaplace-Beltrami equation and can be regarded as an analogue of the potential of the gravitational interaction, and in the case when the potential is the generalization of the potential of an elastic spring. Also the full integrability of the generalized two-centre problem on a constant curvature surface is discovered and it is shown that integrability remains even if elastic forces are added.     

New open-source approaches to the modeling of stellar collapse and the formation of black holes

We present new approaches to the simulation of stellar collapse, the formation of black holes, and explosive core-collapse supernova nucleosynthesis that build upon open-source codes and microphysics. We discuss the new spherically-symmetric general-relativistic (GR) collapse code GR1D that is endowed with an approximate 1.5D treatment of rotation, comes with multiple nuclear equations of state, and handles neutrinos with a multi-species leakage scheme. Results from a first set of spinning black hole formation simulations are presented. We go on to discuss the derivative code GR1D+N which is tuned for calculations of explosive nucleosynthesis and includes a NSE/non-NSE equation of state treatment, and a nuclear reaction network. We present sample results showing GR1D+N??s performance in reproducing previous results with thermal-bomb-driven explosions. Finally, we introduce the 3?+?1 GR Zelmani core collapse simulation package and present first results obtained in its application to the 3D modeling of failing core-collapse supernovae.     

Role of primordial black holes in the direct collapse scenario of supermassive black hole formation at high redshifts

In this paper, we explore the possibility of accreting primordial black holes as the source of heating for the collapsing gas in the context of the direct collapse black hole scenario for the formation of super-massive black holes (SMBHs) at high redshifts, \(z\sim \) 6–7. One of the essential requirements for the direct collapse model to work is to maintain the temperature of the in-falling gas at \(\approx \)10\(^4\) K. We show that even under the existing abundance limits, the primordial black holes of masses \(\gtrsim \)10\(^{-2}M_\odot \), can heat the collapsing gas to an extent that the \(\mathrm{H}_2\) formation is inhibited. The collapsing gas can maintain its temperature at \(10^4\) K till the gas reaches a critical density \(n_{{c}} \,{\approx }\, 10^3~\hbox {cm}^{-3}\), at which the roto-vibrational states of \(\mathrm{H}_2\) approaches local thermodynamic equilibrium and \(\mathrm{H}_2\) cooling becomes inefficient. In the absence of \(\mathrm{H}_2\) cooling, the temperature of the collapsing gas stays at \(\approx \)10\(^4\) K even as it collapses further. We discuss scenarios of subsequent angular momentum removal and the route to find collapse through either a supermassive star or a supermassive disk.     

‘Nomadic’ nuclei of galaxies

In this paper we discuss observational and theoretical arguments in favour of hypothesis on nomad life of active nuclei inside and outside galaxies as well as its consequences. It may be the anisotropic collapse of a supermassive star, or the disruption of a supermassive binary system after the collapse of one companion that would give birth to such nuclei. We predict the existence of veritable quasi-stellar active objects without any ghost gagalies.     

A differential equation for the classical collapse problem

The classical gravitational collapse problem is analysed on the basis of an integral equation connecting the evolutionary time (defined as dt/d log ) with the density and the collapse function , or by an equivalent first-order non-linear differential equation. The general behaviour of solutions is discussed, and some particular cases are studied.     

GeV-TeV $\gamma $-ray energy spectral break of BL Lac objects

In this paper, we compile the very-high-energy and high-energy spectral indices of 43 BL Lac objects from the literature. Based on a simple math model, \(\Delta \Gamma_{obs}= \alpha {{{z}}}+\beta \), we present evidence for the origin of an observed spectral break that is denoted by the difference between the observed very-high-energy and high-energy spectral indices, \(\Delta \Gamma_{obs}\). We find by linear regression analysis that \(\alpha \ne 0\) and \(\beta \ne 0\). These results suggest that the extragalactic background light attenuation and the intrinsic curvature dominate on the GeV-TeV \(\gamma \)-ray energy spectral break of BL Lac objects. We argue that the extragalactic background light attenuation is an exclusive explanation for the redshift evolution of the observed spectral break.     

The extreme initial kinetic energy allowed by a collapsing turbulent core

We present high-resolution hydrodynamical simulations aimed at following the gravitational collapse of a gas core, in which a turbulent spectrum of velocity is implemented only initially. We determine the maximal value of the ratio of kinetic energy to gravitational energy, denoted here by \((\frac{E_{\mathrm{kin}} }{E_{\mathrm{grav}}} )_{\max}\), so that the core (i) will collapse around one free-fall time of time evolution or (ii) will expand unboundedly, because it has a value of \(\frac{E_{\rm kin}}{E_{\mathrm{grav}}}\) larger than \(( \frac{E_{\mathrm{kin}}}{E_{\mathrm{grav}}} )_{\mathrm{max}}\). We consider core models with a uniform or centrally condensed density profile and with velocity spectra composed of a linear combination of one-half divergence-free turbulence type and the other half of a curl-free turbulence type. We show that the outcome of the core collapse are protostars forming either (i) a multiple system obtained from the fragmentation of filaments and (ii) a single primary system within a long filament. In addition, some properties of these protostars are also determined and compared with those obtained elsewhere.     

cD galaxies of apparent supergiant sizes due to the curvature of space

By combining two two-dimensional subspaces, closed into themselves due to curvature, it is possible to create a model of three-dimensional space of the same properties. If the Universe is a space of this type, its effect is that of a monstrous lens. Close objects are observed to diminish according to the normal law of perspective; however, the remote galaxies are seen to be very highly magnified.The apparent angular size² of a galaxy is more than the size¹ in flat space according to relation:² =¹ cosec , where is the angular distance from the observer to the galaxy. The diameter² d of a galaxy in curved space must be in the same relation to a diameter¹ d with no curvature of space:² d=¹ d cosec . The apparent angular size² and diameter² d are distorted shapes in consequence of an optical illusion caused by the spatial curvature.It is necessary to distribute the multitude of galaxies into two parts in accordance with their location on the close or reverse hemihypersphere of the Universe. The minimum of apparent angular size² of a galaxy of diameter¹ d is at the equatorial zone.The most likely candidates for location in the reverse hemi-hypersphere are cD's of apparent supergiant sizes due, probably, to the curvature of space. The existence of supergiant sizes of galaxies is the second indirect proof, besides superluminal velocities, that the Universe is closed into itself through curvature. The third indirect evidence, i.e., inductive confirmation of the same fact, is the superposition of galaxies which need not inevitably be a new alternative to the present theories of collisions, cannibalism, merger, etc.The fourth indirect proof of the positive curvature of the Universe is the occurrence of background radiation, because that must vanish in hyperbolic space irrespective of its origin. The gravitational lens effect acquires another theoretical form, as usual, in the case of remote galaxies, because it is impossible to distinguish between gravitator and lensing image.     

Mean field escapers in non-equilibrium systems

We present some results of our study on non-equilibriumN-body systems that undergo initial collapse. This collapse is followed by global pulsations of the system. During these pulsations, the mean gravitational field fluctuates violently. Some particles pick up enough energy to be ejected from the system into the halo or even fly off to infinity. We discuss the region in phase space from which these mean field escapers originate and their energy frequency distribution for the illustrative case of a uniform spherical initial state. The pulsations lead to the production of shells in the halo.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

The gravitational collapse of iron-oxygen stars with masses of 2M ⊙ and 10M ⊙ II

The collapse of iron-oxygen stars with masses of 2M has been calculated. The commencement of the collapse is due to dissociation of iron-group nuclei into free nucleons. After a while, the collapse proceeds in consequence of intensive energy losses due to neutrino volume radiation. At an intermediate stage of the collapse, the core — opaque with respect to neutrino radiation (neutrino core) — is formed inside the collapsing star. Both the gradual increase of the mass of the neutrino core and the partial absorption of neutrinos radiated from the surface of the neutrino core by the stellar envelope (deposition) were taken into account in our calculations. The kinetics of oxygen burning in the outer layers of the envelope was also allowed for. Neither the deposition, nor the oxygen burning, result in ejection of stellar envelopes.     

Mirages on Mars

The possibility of observing mirages on Mars from the Viking lander cameras is examined. A simple model for the production of both inferior and superior mirages is developed. Assuming the atmospheric index of refraction to be a linear function of density (i.e., temperature), ray curvatures are calculated through layers of large, expected thermal gradient.Assuming the Martian morning inversions of Gierasch and Goody (1968), calculations of ray curvature show the superior mirage to be an unlikely occurrence on Mars since the downward curvature of the ray through the inversion layer is less than the downward curvature of the planet. In order to examine the nature of inferior mirages we select a reasonable expression for temperature profile in the surface layer fitted to the midafternoon, midlatitude summer results of Gierasch and Goody. Integration of the expression for ray curvature yields a relation for the minimum distance between the lander cameras and an inferior mirage as a function of the surface superadiabatic lapse rate. Such calculations indicate that the Viking lander cameras will record inferior mirages at horizontal distances of a kilometer or so from the lander. Given the appearance of an inferior mirage at a measured minimum distance from the observer it should be a simple matter to calculate the corresponding mean temperature lapse rate at the surface.     

Towards solution of the pulsar problem

The 24-year-old pulsar problem is reconsidered. New results are obtained by replacing the assumption of steady-state discharges near the polar caps by oscillatory discharges, and by creating the neutral-excess pair plasma via inverse-Compton collisions rather than via curvature radiation. As a result, the electrons and positrons which compose the pulsar wind have different bulk velocities and an oscillating space density, and (strong) coherent curvature radiation is implied (without invoking the excitation of instabilities, and contrary to existing proofs of its impossibility). The magnetospheres of young pulsars are likely to have considerable higher-order multipole components, in particular octupole. Radiation transfer through the pulsar magnetosphere results in fan beams whose polarization is dictated by the bottom of the radiation zone, hence, looks like curvature radiation from dipole-like polar caps.Wind generation depends mainly on the quantityB² which takes similar values for the ms pulsars; the latter compensate for (somewhat) weaker fields by wider polar caps and smaller curvature radii.     

Laboratory study of coherent curvature radiation as a pulsar emission mechanism

To simulate some of the major physical processes occurring in pulsars, we performed experiments using a relativistic electron beam propatating helically through a magnetized plasma. Microwave radiation with 1 cm emerged when the predicted resonance conditions were satisfied. Power exceeded 1 MW and radiation lasted as long as the electron beam pulse. The spectrum, harmonics, power and scalings were consistent with a model of coherent curvature radiation from electrons which are bunched by a beam-plasma streaming instability. Brightness temperature was 10²⁰ degrees. Polarization was that of single-particle emission, but with some evidence for diffraction patterns due to the beam bunches themselves. The Razin effect does not apply to our experiments and was not observed. The fundamental two-step process of electrostatic bunching followed by curvature emission describes well all our results.     

Relations between integrable systems in plane and curved spaces

We consider trajectory isomorphisms between various integrable systems on an n-dimensional sphere S ⁿ and a Euclidean space . Some of the systems are classical integrable problems of Celestial Mechanics in plane and curved spaces. All the systems under consideration have an additional first integral quadratic in momentum and can be integrated analytically by using the separation of variables. We show that some integrable problems in constant curvature spaces are not essentially new from the viewpoint of the theory of integration, and they can be analyzed using known results of classical Celestial Mechanics.     

Plasma jet and shock formation during current loop coalescence in solar flares

We report on the results of plasma jet and shock formation during the current loop coalescence in solar flares. It is shown by a theoretical model based on the ideal MHD equation that the spiral, two-sided plasma jet can be explosively driven by the plasma rotational motion induced during the two current loop coalescence process. The maximum velocity of the jet can exceed the Alfvén velocity, depending on the plasma (= c _s ² v _A ² ) ratio. The acceleration time getting to the maximum jet velocity is quite short and le than 1 s. The rebound following the plasma collapse driven by magnetic pinch effect can strongly induce super-Alfvénic flow. We present the condition of the shock formation. We briefly discuss the high-energy particle acceleration during the plasma collapse as well as by the shocks.     

The formation and evolution of low mass protostars

A review is presented of the earliest stages of protostellar evolution. Observations of prestellar cores, which are believed to represent the initial conditions for protostellar collapse, depart significantly from the scale-free density distribution which is usually taken as the starting point for the formation of a low-mass protostar. Pre-stellar cores are observed to have radial density profiles which have flat inner regions, steepening towards their edges. This is seen to qualitatively match the predictions of the Bonnor-Ebert stability criterion for pressure-bounded self-gravitating gas clouds. From these initial conditions, theoretical modelling of cores threaded by magnetic fields predicts that quasi-static evolution by the process of ambipolar diffusion will lead to a significantly different starting point for collapse than the static singular isothermal sphere.This departure from a scale-free density distribution for the initial conditions has recently been shown to produce an ensuing protostellar collapse which has a non-constant accretion rate. Recently published observations of low-mass protostars in the Ophiuchi cluster are demonstrated to be consistent with such a non-constant protostellar mass accretion rate, contrary to the standard protostellar collapse model. Instead, the data appear consistent with an initially high accretion rate, which subsequently decays. The initial phase of high accretion rate is labelled the main accretion phase, during which 50 per cent of the circumstellar envelope mass is accreted in 10 per cent of the total accretion time, and which is equated observationally with Class 0 objects. The subsequent phase with roughly an order of magnitude lower accretion rate is labelled the late accretion phase, during which the remainder of the envelope mass is accreted in the remaining 90 per cent of the total accretion time, at an order of magnitude lower accretion rate, and which is equated observationally with Class I objects. The growth of circumstellar discs begins in the Class 0 stage, and proceeds through the Class I and II stages. Published data of the Taurus star-forming region currently available appear also to be consistent with this scenario.     

The Third Integral in a Self-consistent Galactic Model

We apply the theory of the third integral to a self-consistent galactic model, generated by the collapse of a N-body system. The final configuration after the collapse is a stationary triaxial system, that represents an almost prolate non-rotating elliptical galaxy with its longest axis in the z-direction. This system is represented by an axisymmetric potential V plus a small triaxial perturbation V ₁. The orbits in the potential V are of three types: box orbits, tube orbits (corresponding to various resonances), and chaotic orbits.The intersections of the box and tube orbits by a Poincaré surface of section z=0 are closed invariant curves. The main tube orbits are like ellipses and form an island of stability on the (R,R) plane.We calculated the third integral I in the potential V for the general non-resonant case and for various resonant cases. The agreement between the invariant curves of the orbits and the level curves of the third integral is good for the box and tube orbits, if we truncate the third integral at an appropriate level. As expected the third integral fails in the case of chaotic orbits. The most important result is the form of the number density F on the Poincaré surface of section. This function decreases exponentially outwards for the box orbits, like Fexp(–bI), while it is constant, as expected, for the chaotic orbits. In the case of the island of the main tube orbits it has a minimum at the center of the island. This can be explained by the form of the near elliptical orbits that are elongated along R, thus they fail to support a self-consistent galaxy, which is elongated along the z-axis.     

Exact solution to radiation-filled Brans-Dicke closed space cosmology

Under the assumption of a power law (k·R ⁿ=C,C=const.) between the gravitational constantk and the radius of curvatureR of the Universe and forP=1/3 the exact solution is sought for the cosmological equations of Brans and Dicke. The solution turns out to be valid for closed space and the parameter of the scalar-tensor theory is necessarily negative. The radius of curvature increases linearly with respect to the age of the Universe while the gravitational constant grows with the square of the radius of curvature. It has been shown (Lessner, 1974) that in this case (KR ²) the spatial component of the field equations is independent of the remaining equations. However, our solution satisfies this independent equation. This solution for the radiation-dominated era corresponds to the solution for the matter-dominated era found by Dehnen and one of the authors (Dehnen and Obregón, 1971). Our solution, as is the solution previously obtained for the matter-dominated era, is in contradiction to Dirac's hypothesis in which the gravitational constant should decrease with time in an expanding Universe.