Nonlinear thin shell instabilities in molecular clouds

Observations of molecular clouds point to the existence of supersonic, turbulent flows. Therefore, any theory which attempts to describe molecular cloud evolution and star formation must include a consideration of the dynamics of colliding flows. Previous studies have considered the collision of supersonic streams or clouds. The resultant instabilities provide a mechanism which may give rise to observable cloud morphologies and enhance the star formation rate. One such instability is the nonlinear thin shell instability (NTSI) of a shock-bounded slab. This process is driven by ram pressure and efficient cooling. In this study, I use numerical simulations to examine the head-on collision of supersonic gas streams in a cold, molecular gas. A dense slab forms in the collision midplane and is prone to a number of instabilities, including the NTSI. The thermodynamic processes involved are found to have a controlling influence upon the instability and fragmentation of the slab. Although some minimal amount of cooling is needed to drive the instability, too rapid a cooling rate gives rise to smaller wavelength instabilities which wipe out the NTSI. The growth rate of the NTSI in a gas undergoing molecular cooling corresponds to a timescale of order 10¹² s, in general agreement with the theoretical value for an isothermal gas. The NTSI may provide a viable mechanism for the instigation of rapid star formation.     

Numerical simulations of fast MHD waves in a coronal plasma

A method is presented for the numerical study of the temporal evolution of nonlinear periodic waves in solar coronal loops which are approximated by smoothed slabs of enhanced gas density embedded within a uniform magnetic field. This method uses a fast Fourier transform technique to calculate spatial derivatives and a modified Euler algorithm for the time scheme for solving cold magnetohydrodynamic equations that govern nonlinear perturbations. The numerical results show that nonlinearity can play a significant role, leading to wave breaking of the kink wave and slab demolition for the sausage one. The kink periodic wave adjusts better to the smoothed slab than the sausage wave.     

The time-scale for core collapse in spherical star clusters

The collapse time for a cluster of equal-mass stars is usually stated to be either 330 central relaxation times (t_rc) or 12-19 half-mass relaxation times (t_rh). But the first of these times applies only to the late stage of core collapse, and the second only to low-concentration clusters. To clarify how the time depends on the density profile, the Fokker-Planck equation is solved for the evolution of a variety of isotropic cluster models, including King models, models with power-law density cusps of ρ ∼ r^−γ, and models with nuclei. The collapse times for King models vary considerably with the cluster concentration when expressed in units of t_rc or t_rh, but vary much less when expressed in units of t_rc divided by a dimensionless measure of the temperature gradient in the core. Models with cusps have larger temperature gradients and evolve faster than King models, but not all of them collapse: those with 0 < γ < 2 expand because they start with a temperature inversion. Models with nuclei collapse or expand as the nuclei would in isolation if their central relaxation times are short; otherwise their evolution is more complicated. Suggestions are made for how the results can be applied to globular clusters, galaxies, and clusters of dark objects in the centers of galaxies.Scott D. Tremaine     

Time signatures of impulsively generated waves in a coronal plasma

Impulsively generated waves in solar coronal loops are numerically simulated in the frame-work of cold magnetohydrodynamics. Coronal inhomogeneities are approximated by gas density slabs embedded in a uniform magnetic field. The simulations show that an initially excited pulse results in the propagation of wave packets which correspond to both trapped and leaky waves. Whereas the leaky waves propagate outside the slab, the trapped waves occur as a result of a total reflection from the slab walls. Time signatures of these waves are made by a detection of the trapped waves at a fixed spatial location. For waves excited within the slab, time signatures exhibit periodic, quasi-periodic and decay phases. The time signatures for waves excited outside the slab, or for a multi-series of variously shaped impulses generated at different places and times, can possess extended quasi-periodic phases. The case of parallel slabs, when the presence of a second slab influences the character of wave propagation in the first slab, exhibits complex time signatures as a result of solitary waves interaction.     

Dissipation of MHD waves in an inhomogeneous streaming plasma

The investigation of instabilities adopting the point of view of inhomogeneous mass flow, physically corresponds to consideration of stability of the perturbations whose wavelengths in the direction of plasma inhomogeneities are much larger than the characteristic plasma scale length. The dissipation of hydromagnetic-waves and instabilities takes place due to the inhomogeneous plasma flow. Both the velocity and plasma density vary in the direction perpendicular to the magnetic field. It is found that the Alfvén wave branch and magnetosonic branch may be driven unstable by the velocity shear. Instability, oscillatory modes, marginal instability and overstability are worked out.     

Reflectance spectra of iron meteorites: Implications for spectral identification of their parent bodies

Abstract– The 0.35–2.5 μm reflectance spectra of iron meteorite powders and slabs have been studied as a function of composition, surface texture (for slabs), grain size (for powders), and viewing geometry (for powders). Powder spectra are invariably red‐sloped over this wavelength interval and have a narrow range of visible albedos (approximately 10–15% at 0.56 μm). Metal (Fe:Ni) compositional variations have no systematic effect on the powder spectra, increasing grain size results in more red‐sloped spectra, and changes in viewing geometry have variable effects on overall reflectance and spectral slope. Roughened metal slab spectra have a wider, and higher, range of visible albedos than powders (22–74% at 0.56 μm), and are also red‐sloped. Smoother slabs exhibit greater differences from iron meteorite powder spectra, exhibiting wider variations in overall reflectance, spectral slopes, and spectral shapes. No unique spectral parameters exist that allow for powder and slab spectra to be fully separated in all cases. Spectral differences between slabs and powders can be used to constrain possible surface properties, and causes of rotational spectral variations, of M‐asteroids. The magnitude of spectral variations between M‐asteroids and rotational and spectral variability does not necessarily imply a dramatic change in surface properties, as the differences in albedo and/or spectral slope can be accommodated by modest changes in grain size (for powders), small changes in surface roughness (for slabs), or variations in viewing geometry. Since metal powders exhibit much less spectral variability than slabs, M‐asteroid spectral variability requires larger changes in either powder properties or viewing geometry than for slabs for a given degree of spectral variation.     

Numerical simulations of fast MHD waves in a coronal plasma

The temporal evolution of ducted waves under coronal conditions is studied in the framework of linearized low MHD by means of numerical simulations. Coronal loops are represented by smoothed slabs of enhanced gas density embedded within a uniform magnetic field. The simulations show that for a smoothed density profile there is an energy leakage from the slab, associated with the propagation of sausage and kink waves. Wave energy leakage in the kink wave is generally small, whereas the wave energy in sausage waves leaks more strongly for long wavelengths and smoother slabs.     

The strength of the lunar lithosphere

A self-gravitating, elastic, spherical thick shell model is used to derive the present state of the lateral variations of density and stress differences within the lunar lithosphere. The model is allowed to deform under the load of an initial surface topography and internal density distribution, such that the resulting deformed body gives rise to the observed surface topography and gravity specified by the spherical harmonics of degree up to 70. Two main models are considered, Model A and Model B, with elastic lithospheres of thickness 300 and 210 km, respectively. Model A displays density perturbations of generally less than ±200 kg/m³ within the crustal layers, reducing rapidly to less than ±20 kg/m³ at the base of the lithosphere. The density perturbations in Model B are similar in the crust and marginally higher at the base of the lithosphere. The major stress differences in the mantle are associated with the mascon basins and are found to reach maximums of 8-10 MPa within the lower lithosphere (150-270 km) of Model A and maximums of 12-16 MPa at 150 to 180 km depth for Model B. A moderate correlation exists between the modeled stress distributions and shallow moonquake epicenters. However, the overall results of this study imply that other remnant stresses, due to processes other than density perturbations, exist and play a critical role in the large shallow moonquakes.     

Dynamical supersymmetric inflation

We propose a new class of inflationary models in which the scalar field potential governing inflation is generated by the same nonperturbative gauge dynamics that may lead to supersymmetry breaking. Such models satisfy constraints from cosmic microwave background measurements for natural values of the fundamental parameters in the theory. In addition, they have two particularly interesting characteristics: a “blue” spectrum of scalar perturbations, and an upper bound on the total amount of inflation possible.     

Effects of gyroviscosity and hall currents on the stability of a stratified rotating self-gravitating plasma

Instability in a horizontal layer of a stratified rotating self-gravitating plasma is studied to include simultaneously the effects of Hall currents and the finiteness of the ion Larmor radius. Proper solutions have been obtained through the variational methods for a semi-infinite plasma in which the density has an exponential gradient along the vertical. The dispersion relation obtained has been solved numerically and it is found that the growth rate of the unstable perturbations decreases with both coriolis forces and gyroviscous effects. The influence of the effects of gyroviscosity as well as of Coriolis forces is consequently stabilizing. Hall currents are found to have a destabilizing influence as the growth rate is found to increase with this effect.     

Stability of an anisotropic plasma jet

The instability arising in a slab model of a jet moving in an external plasma is investigated, assuming the plasmas to be governed by the Chew, Goldberger, and Low (CGL) equations. Numerical results on the growth rates of unstable modes are obtained both for symmetric and asymmetric perturbations for equal aligned and transverse fields in wide and slender jet approximations. Special cases of an incompressible jet moving in a static CGL plasma and of a CGL plasma jet moving in an incompressible environment are also considered and conditions of instability derived.     

Early star formation and galaxy formation triggered by the evolution of large-scale density perturbations

The evolution of small-scale density perturbations on the background of increasing large-scale perturbations of supercluster size will be considered. In the case that the characteristic length scales of both perturbation modes differ significantly, the interaction between both modes has to be taken into account already within lowest order of approximation. It will be shown that in this case an effective amplification for the smaller-scale perturbations occurs. For these perturbations the characteristic times of evolution decreases in dependence on the considered mass-scales more or less rapidly. Therefore, the growth of adiabatic density perturbations on mass-scales up to galaxy masses seems to be triggered by the density evolution of superclusters which the smaller-mass perturbations are embedded in. A model for the formation of observed condensed matter distribution will be proposed.     

Effects of rotation on Rayleigh-Taylor instabilities of an accelerating,compressible, perfectly conducting plane layer

The stability of a plane-stratified slab of perfectly conducting, rotating, compressible, inviscid plasma accelerated by a magnetic field is considered. Exact solutions for the growth rates of the unstable modes are determined for a -law gas when the undisturbed equilibrium is an isothermal atmosphere of semi-infinite extent with no frozen-in field. It is shown that the rotation has no effect on the region of unstable modes which has wavelengths long compared with the atmospheric scale height. On the other side, the growth rates in the presence of rotation are less than those in the absence of rotation for unstable modes.     

Magnetothermal condensation modes including the effects of charged dust particles

We study thermal instability in a magnetized and partially ionized plasma with charged dust particles. Our linear analysis shows that the growth rate of the unstable modes in the presence of dust particles strongly depends on the ratio of the cooling rate and the modified dust-cyclotron frequency. If the cooling rate is less than the modified dust-cyclotron frequency, then the growth rate of the condensation modes does not modify due to the existence of the charged dust particles. But, when the cooling rate is greater than (or comparable to) the modified dust-cyclotron frequency, the growth rate of unstable modes increases because of the dust particles. Also, the wavenumber of the perturbations corresponding to the maximum growth rate shifts to the smaller values (larger wavelengths) as the cooling rate becomes larger than the modified dust-cyclotron frequency. We show that the growth rate of the condensation modes increases with the electrical charge of the dust particles.     

Formation of Intensive Magnetic Flux Tubes in a Converging Flow of Partially Ionized Solar Photospheric Plasma

Theoretical model, explaining a phenomenon of formation of Intensive Magnetic Flux Tube (IMFT) in a converging flow of partially ionized solar photospheric plasma is considered. Special attention is paid to the fact of weak ionization (n/n _n ∼ 10^-4) of plasma in the photosphere. The cases of 2D magnetic slab and cylindric magnetic tube are considered. It was shown that in a converging flow of photospheric plasma thin magnetic tubes, or slabs with the characteristic scale L ₀ ∼ (1 ÷ 5) ċ 10⁷ cm and magnetic field 1000 ÷ 2000 G can be generated. By this 2D magnetic slabs could be unstable with respect to an exchange instability and appear as an intermediate step during IMFT formation on the boundary of two supergranulation cells. Formation of compact strong magnetic field structures, and their energy balance are discussed. Stationary Joule energy dissipation taking place on the photospheric levels in the models of magnetic slab or IMFT under consideration increases towards the periphery of these objects and can exceed radiation looses. This can cause the occurrence of magnetic tubes with hot external envelopes, and modification of plasma temperature and density distribution, with respect to ones in a quiet atmosphere. This revised version was published online in July 2006 with corrections to the Cover Date.     

Order and chaos in spiral galaxies

Spiral galaxies contain both ordered and chaotic orbits. In normal spirals the perturbations are weak (of order 2–10%) and most orbits are ordered. The density wave theory refers mainly to linear perturbations. Nonlinear effects appear in the outer parts of the open spirals (S_b, S_c) and produce the termination of these spirals near the 4/1 resonance. On the other hand in barred spirals the perturbations are relatively strong (of order 100%). Then the outer spirals and the envelope of the bar are composed mainly of chaotic orbits, while the main body of the bar is composed of ordered orbits. The chaotic orbits of the spiral arms of strong barred galaxies are sticky, i.e. they do not escape from the galaxy for at least a Hubble time. The forms of these spirals are delineated by the unstable manifolds of the unstable periodic orbits L_1, L_2 near the ends of the bar and of other unstable periodic orbits inside and outside corotation.     

Perturbed Robe’s circular restricted three-body problem under an Oblate Primary

This paper examines the existence and linear stability of equilibrium points in the perturbed Robe’s circular restricted three-body problem under the assumption that the hydrostatic equilibrium figure of the first primary is an oblate spheroid. The problem is perturbed in the sense that small perturbations are given to the Coriolis and centrifugal forces are being considered. Results of the analysis found two axial equilibrium points on the line joining the centre of both primaries. It is further observed that under certain conditions, points on the circle within the first primary are also equilibrium points. And a special case where the density of the fluid and that of the infinitesimal mass are equal (D = 0) is discussed. The linear stability of this configuration is examined; it is observed that the first axial point is unstable while the second one is conditionally stable and the circular points are unstable.     

A ready-made code for the computation of prominence NLTE models

A computer code is proposed for the computation of simple NLTE models of solar prominences. These models consist of plane-parallel slabs, with constant pressure and temperature, standing vertically above the solar surface. Each model is defined by five parameters: temperature, density, geometrical thickness, microturbulent velocity and height above the solar surface. The code computes the electron density, hydrogen level populations inside the slab, and determines the line profiles and continua emitted by the slab. An example of application of this code is given.     

Instabilities of galactic discs in the presence of star formation

We discuss the stability of galactic discs in which the energy of interstellar clouds is gained in encounters with expanding supernova (SN) remnants and lost in inelastic collisions. Energy gain and loss processes introduce a phase difference between the pressure and density perturbations, making discs unstable on small scales for several recipes of star formation. This is in contrast to the standard stability analysis in which small-scale perturbations are stabilized by pressure. In the limit of small scales, the dispersion relation for the growth rate reduces to that of thermal instabilities in a fluid without gravity. If instabilities lead to star formation, then our results imply a secondary mode of star formation that operates on small scales and feeds on the existence of a primary mode on intermediate scales. This may be interpreted as positive feedback. Further, the standard stability criterion on intermediate scales is significantly modified.     

Corrugation Instability of a Coronal Arcade

We analyse the behaviour of linear magnetohydrodynamic perturbations of a coronal arcade modelled by a half-cylinder with an azimuthal magnetic field and non-uniform radial profiles of the plasma pressure, temperature, and the field. Attention is paid to the perturbations with short longitudinal (in the direction along the arcade) wavelengths. The radial structure of the perturbations, either oscillatory or evanescent, is prescribed by the radial profiles of the equilibrium quantities. Conditions for the corrugation instability of the arcade are determined. It is established that the instability growth rate increases with decreases in the longitudinal wavelength and the radial wave number. In the unstable mode, the radial perturbations of the magnetic field are stronger than the longitudinal perturbations, creating an almost circularly corrugated rippling of the arcade in the longitudinal direction. For coronal conditions, the growth time of the instability is shorter than one minute, decreasing with an increase in the temperature. Implications of the developed theory for the dynamics of coronal active regions are discussed.