Stability analysis of two-dimensional models of quiescent prominences

Using the MHD energy principle of Bernstein et al. (1958) we develop a formalism in order to analyze the stability properties of two-dimensional magnetostatic plasma equilibria. We apply this to four models of quiescent prominences, namely those of Menzel (1951), Dungey (1953), Kippenhahn and Schlüter (1957), and finally Lerche and Low (1980). For the observed parameter range, all models are stable and they explain reasonably well the reported flare-initiated oscillations in quiescent prominences. We also investigate other parameters regions, which may be relevant in some stellar atmospheres. It is found that, with the exception of the Kippenhahn and Schlüter model, all models become unstable. The instabilities that occur show simultaneously several features of well-known MHD-instabilities. However, an unequivocal assignment of the instabilities to specific instability prototypes is not possible. Our formalism allows one to investigate not only more realistic prominence equilibria, but also arbitrary one- and two-dimensional static ideal MHD-equilibria.     

The importance of experiments: Constraints on chondrule formation models

Abstract— We review a number of constraints that have been placed on the formation of chondrules and show how these can be used to test chondrule formation models. Four models in particular are examined: the “X‐wind” model (sudden exposure to sunlight <0.1 AU from the proto‐Sun, with subsequent launching in a magnetocentrifugal outflow); solar nebula lightning; nebular shocks driven by eccentric planetesimals; and nebular shocks driven by diskwide gravitational instabilities. We show that constraints on the thermal histories of chondrules during their melting and crystallization are the most powerful constraints and provide the least ambiguous tests of the chondrule formation models. Such constraints strongly favor melting of chondrules in nebular shocks. Shocks driven by gravitational instabilities are somewhat favored over planetesimal bow shocks.     

Self-gravity driven instabilities of interfaces in the interstellar medium

In order to understand star formation it is important to understand the dynamics of atomic and molecular clouds in the interstellar medium (ISM). Non-linear hydrodynamic flows are a key component to the ISM. One route by which non-linear flows arise is the onset and evolution of interfacial instabilities. Interfacial instabilities act to modify the interface between gas components at different densities and temperatures. Such an interface may be subject to a host of instabilities, including the Rayleigh–Taylor, Kelvin–Helmholtz, and Richtmyer–Meshkov instabilities. Recently, a new density interface instability was identified. This self-gravity interfacial instability (SGI) causes any displacement of the interface to grow on roughly a free-fall time-scale, even when the perturbation wavelength is much less than the Jeans length. In previous work, we used numerical simulations to confirm the expectations of linear theory and examine the non-linear evolution of the SGI. We now continue our study by generalizing our initial conditions to allow the acceleration due to self-gravity to be non-zero across the interface. We also consider the behaviour of the SGI for perturbation wavelengths near the Jeans wavelength. We conclude that the action of self-gravity across a density interface may play a significant role in the ISM either by fuelling the growth of new instabilities or modifying the evolution of existing instabilities.     

Streaming Instability in the Gas-Dust Medium of the Protoplanetary Disc and the Formation of Fractal Dust Clusters

The sequence of evolution of the protoplanetary gas-and-dust disk around the parent star includes, according to modern concepts, its compression in the central plane and decay into separate dust condensations (clusters) due to the occurrence of various types of instabilities. The interaction of dust clusters of a fractal structure during their collisions is considered as a key mechanism for the formation and growth of primary solids, which serve as the basis for the subsequent formation of planetesimals and embryos of planets. Among the mechanisms contributing to the formation of planetesimals, an important place belongs, along with gravitational instability, hydrodynamic instabilities, in particular, the socalled streaming instability of the two-phase gas-dust layer due to its ability to concentrate dispersed particles in dense clots. In contrast to a number of existing models of streaming instability, in which dust particles are considered structurally compact and monodisperse, this paper proposes a more realistic model of polydisperse particles of fractal nature, forming dust clusters as a result of coagulation. The instability of the dust layer in the central plane of the protoplanetary disk under linear axisymmetric perturbations of its parameters is considered. A preliminary conclusion can be drawn that the proposed model of dust fractal aggregates of different scales increases the efficiency of linear growth of hydrodynamic instabilities, including the streaming instabilities associated with the difference between the velocities of the dust and gas phases.

     

A simple model for solar isorotational contours

The solar convective zone, or SCZ, is nearly adiabatic and marginally convectively unstable. But, the SCZ is also in a state of differential rotation, and its dynamical stability properties are those of a weakly magnetized gas. This renders it far more prone to rapidly growing rotational baroclinic instabilities than a hydrodynamical system would be. These instabilities should be treated on the same footing as convective instabilities. If isentropic and isorotational surfaces coincide in the SCZ, the gas is marginally (un)stable to both convective and rotational disturbances. This is a plausible resolution for the instabilities associated with these more general rotating convective systems. This motivates an analysis of the thermal wind equation in which isentropes and isorotational surfaces are identical. The characteristics of this partial differential equation correspond to isorotation contours, and their form may be deduced even without precise knowledge of how the entropy and rotation are functionally related. Although the exact solution of the global SCZ problem in principle requires this knowledge, even the simplest models produce striking results in broad agreement with helioseismology data. This includes horizontal (i.e. quasi-spherical) isorotational contours at the poles, axial contours at the equator and approximately radial contours at mid-latitudes. The theory does not apply directly to the tachocline, where a simple thermal wind balance is not expected to be valid. The work presented here is subject to tests of self-consistency, among them the prediction that there should be a good agreement between isentropes and isorotational contours in sufficiently well-resolved large-scale numerical magnetohydrodynamics simulations.     

NLTE wind models of hot subdwarf stars

We calculate NLTE models of stellar winds of hot compact stars (central stars of planetary nebulae and subdwarf stars). The studied range of subdwarf parameters is selected to cover a large part of these stars. The models predict the wind hydrodynamical structure and provide mass-loss rates for different abundances. Our models show that CNO elements are important drivers of subdwarf winds, especially for low-luminosity stars. We study the effect of X-rays and instabilities on these winds. Due to the line-driven wind instability, a significant part of the wind could be very hot.     

The linear stability of dilute particulate rings

Irregular structure in planetary rings is often attributed to the intrinsic instabilities of a homogeneous state undergoing Keplerian shear. Previously these have been analysed with simple hydrodynamic models. We instead employ a kinetic theory, in which we solve the linearised moment equations derived in Shu and Stewart 1985 for a dilute ring. This facilitates an examination of velocity anisotropy and non-Newtonian stress, and their effects on the viscous and viscous/gravitational instabilities thought to occur in Saturn's rings. Because we adopt a dilute gas model, the applicability of our results to the actual dense rings of Saturn are significantly curtailled. Nevertheless this study is a necessary preliminary before an attack on the difficult problem of dense ring dynamics. We find the Shu and Stewart formalism admits analytic stability criteria for the viscous overstability, viscous instability, and thermal instability. These criteria are compared with those of a hydrodynamic model incorporating the effective viscosity and cooling function computed from the kinetic steady state. We find the two agree in the ‘hydrodynamic limit’ (i.e., many collisions per orbit) but disagree when collisions are less frequent, when we expect the viscous stress to be increasingly non-Newtonian and the velocity distribution increasingly anisotropic. In particular, hydrodynamics predicts viscous overstability for a larger portion of parameter space. We also numerically solve the linearised equations of the more accurate Goldreich and Tremaine 1978 kinetic model and discover its linear stability to be qualitatively the same as that of Shu and Stewart's. Thus the simple collision operator adopted in the latter would appear to be an adequate approximation for dilute rings, at least in the linear regime.     

Dynamical aspects of electrostatic double layers

Electrostatic double layers have been proposed as an acceleration mechanism in solar flares and other astrophysical objects. They have been extensively studied in the laboratory and by means of computer simulations. The theory of steady-state double layers implies several existence criteria, in particular the Bohm criteria, restricting the conditions under which double layers may form. In the present paper several already published theoretical models of different types of double layers are discussed. It is shown that the existence conditions often imply current-driven instabilities in the ambient plasma, at least for strong double layers, and it is argued that such conditions must be used with care when applied to real plasmas. Laboratory double layers, and by implication those arising in astrophysical plasmas often produce instabilities in the surrounding plasma and are generally time-dependent structures. Naturally occuring double layers should, therefore, be far more common than the restrictions deduced from idealised time-independent models would imply. In particular it is necessary to understand more fully the time-dependent behaviour of double layers. In the present paper the dynamics of weak double layers is discussed. Also a model for a moving strong double layer, where an associated potential minimum plays a significant role, is presented.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

The role of turbulent convection in the primitive solar nebula: I. Theory

The theoretical framework for modeling the primordial solar nebula is presented in which convection is assumed to be the sole source of turbulence that causes the nebula to evolve. We use a new model of convective turbulence that takes into account the important effects of radiative dissipation, rotation, and anisotropy of convective motions. This model is based on a closure for the nonlinear interactions that employs the growth rates of hydrodynamic instabilities, a procedure that allows one to compute turbulence coefficients for instabilities other than convection. The vertical structure equations in the thin-disk approximation are developed for this new model, and a detailed comparison and critique of previous convective models of the solar nebula are presented. Numerical results are presented in a subsequent paper.     

Convective instability in the martian middle atmosphere

Dry convective instabilities in Mars’s middle atmosphere are detected and mapped using temperature retrievals from Mars Climate Sounder observations spanning 1.5 martian years. The instabilities are moderately frequent in the winter extratropics. The frequency and strength of middle atmospheric convective instability in the northern extratropics is significantly higher in MY 28 than in MY 29. This may have coupled with changes to the northern hemisphere mid-latitude and tropical middle atmospheric temperatures and contributed to the development of the 2007 global dust storm. We interpret these instabilities to be the result of gravity waves saturating within regions of low stability created by the thermal tides. Gravity wave saturation in the winter extratropics has been proposed to provide the momentum lacking in general circulation models to produce the strong dynamically-maintained temperature maximum at 1-2 Pa over the winter pole, so these observations could be a partial control on modeling experiments.     

Loop models of solar flares: Revisions and comparisons

Due to developments in solar flare observations which appear to show that a particular class of solar flares result from instabilities occurring in magnetic loops we re-examine the Alfvén-Carlqvist flare model to show that it is workable and we update the Spicer loop model of a flare. It is noted that the Alfvén-Carlqvist model of necessity requires an external current driver which must maintain the current driven instability at marginal stability during the duration of the flare. In addition, it is argued that if the Alfvén-Carlqvist model is to work the current density must rise in a time shorter than an MHD or resistive tearing mode time scale. Otherwise, the dominant flare mechanism must be an ideal MHD or tearing type instability. Further, the distinctions between the two models are highlighted and a new hybrid model of the Alfvén-Carlqvist and Spicer models is introduced.     

Accretion Flows: Aspects of Gas Dynamic Modeling

We present our view on the application of numerical models to accretion flows in astrophysics. Special attention is paid to the problem of existence of steady-state solutions in time-dependent calculations and to origin of numerically induced instabilities. The problem is considered of the supersonic wind accretion onto gravitating objects. We also present the results of the gas dynamic simulation of accretion on a body imitating the shape of the star magnetosphere with holes in its polar regions. This shape can occur as a result of the cusp disintegration owing to theRayleigh–Taylor instability in the equatorial region of the magnetosphere. This revised version was published online in July 2006 with corrections to the Cover Date.     

Black hole spin and radio loudness in a Λ cold dark matter universe

We use a combination of a cosmological N -body simulation of the concordance Λ cold dark matter paradigm and a semi-analytic model of galaxy formation to investigate the spin development of central supermassive black holes (BHs) and its relation to the BH host galaxy properties. In order to compute BH spins, we use the α model of Shakura & Sunyaev and consider the King et al. warped disc alignment criterion. The orientation of the accretion disc is inferred from the angular momentum of the source of accreted material, which bears a close relationship to the large-scale structure in the simulation. We find that the final BH spin depends almost exclusively on the accretion history and only weakly on the warped disc alignment. The main mechanisms of BH spin-up are found to be gas cooling processes and disc instabilities, a result that is only partially compatible with Monte Carlo models where the main spin-up mechanisms are major mergers and disc instabilities; the latter results are reproduced when implementing randomly oriented accretion discs in our model. Regarding the BH population, we find that more massive BHs, which are hosted by massive ellipticals, have higher spin values than less massive BHs, hosted by spiral galaxies. We analyse whether gas accretion rates and BH spins can be used as tracers of the radio loudness of active galactic nuclei (AGN). We find that the current observational indications of an increasing trend of radio-loud AGN fractions with stellar and BH mass can be easily obtained when placing lower limits on the BH spin, with a minimum influence from limits on the accretion rates; a model with random accretion disc orientations is unable to reproduce this trend. Our results favour a scenario where the BH spin is a key parameter to separate the radio-loud and radio-quiet galaxy populations.     

Instabilities in a nonstationary model of self-gravitating disks. II. Warp modes of vertical oscillations

Gravitational instabilities with respect to warp modes of vertical oscillations are examined for nonlinearly nonequilibrium disk models with isotropic and anisotropic velocity diagrams. Nonstationary analogs of the dispersion relations for vertical oscillations in these models are derived in a general form. A detailed study is made of the major large scale oscillatory modes, which correspond primarily to the most common type of warp in the form of an integral sign, as well as to dome-shaped, U-shaped, and precessional warps. Critical diagrams showing the initial virial relation as a function of the rotation parameter for the nonstationary model are constructed for each of these vertical oscillation modes. A comparative analysis is made of the growth rates of the instabilities for these modes in order to determine the dependence of the characteristic times for their appearance on the basic physical parameters of the two models.     

The destruction of a continuous ring revolving around a gravitating center

In article by Morozov and Fridman (1984) the general equation of motion of an elastic thread in an external gravitational field was formulated and also instability of an elastic thread rotating around a gravitating center was established.On this basis, in the present article we show that the classical model of a hypothetical continous ice ring around Saturn, proposed by Laplace and Maxwell, was incorrectly interpreted by them. Specifically, supposing the ring to be infinitely hard and firm, they came to the conclusion that it will fall on the planet's surface. However, in reality such a ring would be destroyed due to internal stresses under displacements which are three orders of magnitude smaller than the distance between the ring and the planet. We also note that accounting for this effect is important under discussions of cosmogonical models.In conclusion, estimates are given which show that the steel ring (thread) revolving the Earth and rotating around it at the distance of 200 km from the surface would be torn, due to its instability before it falls on the Earth. Meanwhile, for threads of firm aluminium fusions the opposite picture is to be expected. It is noted that the instabilities indicated may be stabilized by using follow-up (cybernetic) systems with power plants.     

Magnetorotational and Tayler Instabilities in the Pulsar Magnetosphere

The magnetospheres around neutron stars should be very particular because of their strong magnetic field and rapid rotation. A study of the pulsar magnetospheres is of crucial importance since it is the key issue to understand how energy outflow to the exterior is produced. In this paper, we discuss magnetohydrodynamic processes in the pulsar magnetosphere. We consider in detail the properties of magnetohydrodynamic waves that can exist in the magnetosphere and their instabilities. These instabilities lead to formation of magnetic structures and can be responsible for short-term variability of the pulsar emission.     

The Monitor project: JW 380 – a 0.26-, 0.15-M⊙, pre-main-sequence eclipsing binary in the Orion nebula cluster

We present a general recipe for constructing N -body realizations of galaxies comprising near spherical and disc components. First, an exact spherical distribution function for the spheroids (halo and bulge) is determined, such that it is in equilibrium with the gravitational monopole of the disc components. Second, an N -body realization of this model is adapted to the full disc potential by growing the latter adiabatically from its monopole. Finally, the disc is sampled with particles drawn from an appropriate distribution function, avoiding local-Maxwellian approximations. We performed test simulations and find that the halo and bulge radial density profile very closely match their target model, while they become slightly oblate due to the added disc gravity. Our findings suggest that vertical thickening of the initially thin disc is caused predominantly by spiral and bar instabilities, which also result in a radial re-distribution of matter, rather than scattering off interloping massive halo particles.     

The formation of Ganymede's grooved terrain: Numerical modeling of extensional necking instabilities

Ganymede's grooved terrain likely formed during an epoch of global expansion, when unstable extension of the lithosphere resulted in the development of periodic necking instabilities. Linear, infinitesimal-strain models of extensional necking support this model of groove formation, finding that the fastest growing modes of an instability have wavelengths and growth rates consistent with Ganymede's grooves. However, several questions remain unanswered, including how nonlinearities affect instability growth at large strains, and what role instabilities play in tectonically resurfacing preexisting terrain. To address these questions we numerically model the extension of an icy lithosphere to examine the growth of periodic necking instabilities over a broad range of strain rates and temperature gradients. We explored thermal gradients up to 45 K km⁻¹ and found that, at infinitesimal strain, maximum growth rates occur at high temperature gradients (45 K km⁻¹) and moderate strain rates (10⁻¹³ s⁻¹). Dominant wavelengths range from 1.8 to 16.4 km (post extension). Our infinitesimal growth rates are qualitatively consistent with, but an order of magnitude lower than, previous linearized calculations. When strain exceeds ∼10% growth rates decrease, limiting the total amount of amplification that can result from unstable extension. This fall-off in growth occurs at lower groove amplitudes for high-temperature-gradient, thin-lithosphere simulations than for low-temperature-gradient, thick-lithosphere simulations. At large strains, this shifts the ideal conditions for producing large amplitude grooves from high temperature gradients to more moderate temperature gradients (15 K km⁻¹). We find that the formation of periodic necking instabilities can modify preexisting terrain, replacing semi-random topography up to 100 m in amplitude with periodic ridges and troughs, assisting the tectonic resurfacing process. Despite this success, the small topographic amplification produced by our model presents a formidable challenge to the necking instability mechanism for groove formation. Success of the necking instability mechanism may require rheological weakening or strain localization by faulting, effects not included in our analysis.