Cometary Flow Research Articles

Existence theorems for the initial value problem of the cometary flow equation with an external force

The initial value problem of the cometary flow equation with a given external force is investigated. By assuming that the initial microscopic density has finite mass and finite momentum and belongs to Lp for some p>1, three existence results of weak solutions with mass conservation and local estimates for the kinetic energy are established for different external forces, each of which is assumed to be divergence free with respect to particle velocities. The first result deals with a bounded smooth force and a Lorentz force with bounded smooth electric and magnetic intensities, and the second one concerns a force belonging to Lq with 1p+1q=1. In the third theorem, we discuss a force that can be divided into two parts: one is in Lq and the other is linearly growing at infinity; in this case we need to assume further that the initial density has finite first order spatial moment.

Cometary flow equation with a self-consistent electromagnetic field

We study the Cauchy problem of a three-dimensional cometary flow equation with a self-consistent electromagnetic field. This kinetic model comes from the theory of astrophysical plasmas and can be viewed as a perturbation by a wave-particle collision operator of the classical Vlasov-Maxwell system. The main result is a global existence theorem of a non-negative weak solution for initial data meeting the physical significance, namely, for initial data having finite mass and total energy and verifying some compatibility conditions.

On the cometary flow equations with force fields

The Cauchy problem of a nonlinear kinetic equation modeling the time evolution of a cometary flow interacting with a force field is discussed, two kinds of existence results for weak solutions are established for initial data having finite mass and finite kinetic energy. The first one concerns a given force field which is assumed to be divergence free with respect to the velocity variable, it is shown that there exists a nonnegative weak solution to the Cauchy problem when the initial datum and the force field have reasonable integrability. As a special case, we also consider a Lorentz field and give another type of existence result. The second one deals with self-consistent electrostatic field, we show that when the initial datum has an L2 integrability the system has a global nonnegative solution which extends a previous result obtained by one of the authors.

MASSIVE STAR FORMATION OF THE SGR A EAST H II REGIONS NEAR THE GALACTIC CENTER

A group of four compact HII regions associated with the well-known 50 km/s molecular cloud is the closest site of on-going star formation to the dynamical center of the Galaxy, at a projected distance of ~6 pc. We present a study of ionized gas based on the [NeII] (12.8 micron) line, as well as multi-frequency radio continuum, HST Pa alpha and Spitzer IRAC observations of the most compact member of the HII group, Sgr A East HII D. The radio continuum image at 6cm shows that this source breaks up into two equally bright ionized features, D1 and D2. The SED of the D source is consistent with it being due to a 25\pm3 solar mass, star with a luminosity of 8\pm3x10^4 solar luminosity. The inferred mass, effective temperature of the UV source and the ionization rate are compatible with a young O9-B0 star. The ionized features D1 and D2 are considered to be ionized by UV radiation collimated by an accretion disk. We consider that the central massive star photoevaporates its circumstellar disk on a timescale of 3x10^4 years giving a mass flux ~3x10^{-5} solar mass per yr and producing the ionized material in D1 and D2 expanding in an inhomogeneous medium. The ionized gas kinematics, as traced by the [Ne II] emission, is difficult to interpret, but it could be explained by the interaction of a bipolar jet with surrounding gas along with what appears to to be a conical wall of lower velocity gas. The other HII regions, Sgr A East A-C, have morphologies and kinematics that more closely resemble cometary flows seen in other compact HII regions, where gas moves along a paraboloidal surface formed by the interaction of a stellar wind with a molecular cloud.

Global weak solutions to the cometary flow equation with a self-generated electric field

We study the Cauchy problem of a cometary flow equation with a self-generated electric field. This kinetic model originates from the theory of astrophysical plasmas and can be viewed as a perturbation, by a wave-particle collision operator, of the classical Vlasov–Poisson system. By asymptotic methods in kinetic theory, global existence of nonnegative weak solutions to the Cauchy problem in three space variables is established for bounded initial data having finite second order velocity moments.

Diffusive Limit of a Kinetic Model for Cometary Flows

A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on the moments of the distribution function. Under a diffusive and low Mach number scaling the macroscopic limit is a generalization of the incompressible Navier-Stokes equations, where the momentum equations are coupled to a diffusive equation for an energy distribution function. By a moment approximation, this system can be related to a low Mach number model of fluid mechanics, which already appeared in the literature. Finally, for a linearized version corresponding to Stokes flow an existence result for initial value problems is proved.

Classification of Equilibrium Solutions of the Cometary Flow Equation and Explicit Solutions of the Euler Equations for Monatomic Ideal Gases

The set of smooth equilibrium solutions of a kinetic model for cometary flows is split into equivalence classes according to similarity transformations. For each equivalence class in the two- and three-dimensional cases a normal form is computed. Each such equilibrium solution gives rise to an explicit solution of the compressible Euler equations for monatomic gases. The set of these solutions is discussed with special emphasis on solutions containing vacuum regions.

Convergence to Equilibrium for the Linearized Cometary Flow Equation

We study convergence to equilibrium for certain spatially inhomogenous kinetic equations, such as discrete velocity models or a linearization of a kinetic model for cometary flow. For such equations, the convergence to a unique equilibrium state is the result of, first, the dissipative effects of the collision operator, which morphs the solution towards an entropy‐minimizing local equilibrium state, and second, the transport operator as well as the imposed periodic boundary conditions, which repulse the solution from the set of local equilibria as long as the approached local equilibrium is not the global one. This behavior is quantified in a system of differential inequalities of relative entropies with respect to different (sub)classes of local equilibria, respectively, the global equilibrium. We introduce projection operators leading to a convenient notation.

Existence and Convergence to Equilibrium of a Kinetic Model for Cometary Flows

A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on moments of the distribution function. An earlier existence result is extended to bounded domains with reflecting boundaries and to initial conditions permitting vacuum regions. The long time behaviour is investigated. Convergence on compact time intervals (shifted to infinity) to the set of equilibrium solutions is proven. The set of smooth equilibrium solutions is computed.

Existence of Solutions of a Kinetic Equation Modeling Cometary Flows

A global existence theorem is presented for a kinetic problem of the form ∂ t f+v·∇ x f=Q(f), f(t=0)=f 0, where Q(f) is a simplified model wave–particle collision operator extracted from quasilinear plasma physics. Evaluation of Q(f) requires the computation of the mean velocity of the distribution f. Therefore, the assumptions on the data are such that vacuum regions, where the mean velocity is not well defined, are excluded. Also the initial data are assumed to have bounded total energy. As additional results conservation laws for mass, momentum, and energy are derived, as well as an entropy dissipation law and the propagation of higher order moments.

Numerical methods for astrophysical plasmas

This review covers some numerical methods used for astrophysical plasmas and centers mainly on methods developed for astrophysical problems. After general remarks on ▿·B in astrophysical MHD calculations, a first-order, one-sided finite-difference formulation is derived for spherical and cylindrical geometries, respectively, where for any given vector field A the expression ▿·( ▿ × A) vanishes. The artificial tensor viscosity to broaden nonplanar shock fronts is briefly discussed. The major part illustrates several numerical methods used for cometary flows, solar MHD problems, pulsar magnetospheres, equilibrium and collapse of interstellar clouds and, finally, supernova shock interactions with clouds. The sections on solar physics and pulsar magnetospheres are kept very short. At the end conclusions are drawn concerning astrophysical MHD calculations.