Stability of the equilibrium distributions of interstellar gas,cosmic rays,and magnetic field in an external gravitational field

An interstellar medium consisting of regular and turbulent magnetic fields, thermal gas and cosmic rays is tested for stability in a stellar gravitational field. Cosmic rays are described by the diffusion-convection equation and the stability region of the system is determined. It is shown that the presence of cosmic rays is a stabilizing factor if the cosmic-ray diffusion coefficient is sufficiently small. The dependence of the maximum growth rate of instability on the cosmic-ray diffusion coefficient is qualitatively determined.     

Structure and Instabilities of Irradiated Protoplanetary Disks: Effects of Dust Particle Growth

We have constructed self-consistent temperature and density profiles of irradiated active protoplanetary disks, using a two-dimensional radiative transfer calculation. By means of these profiles we have studied the stabilization of the convective instability by radiative heating and the magnetorotational instability (MRI) via ohmic dissipation, taking into account the effect of dust particle growth. Simple chemistry such as ionization by cosmic rays and recombination on dust grains are used to calculate the ionization degree of gas in the disks. Our results show that the dust growth stabilizes the convective instability due to the 2D effect of radiative transfer, while it enhances the MRI through the decrease in the recombination of ions on the dust grains. In addition, the influences of the dust settling toward the midplane of the disks on the instabilities are discussed.     

Thermal instability and the effects of cosmic-ray diffusion

We study the dynamical effects of cosmic rays (CRs) on thermal instability in the linear regime. CRs and the thermal plasma are treated as two different interacting fluids, in which CRs can diffuse along the magnetic field lines. We show that the growth rate of the magnetothermal condensation mode is reduced because of the existence of CRs, and this stabilizing effect depends on the diffusion coefficient and the ratio of CR pressure to gas pressure. Thus, a slower rate of structure formation via thermal instability is predicted when CRs are considered.     

Magnetorotational instability in stratified, weakly ionized accretion discs

We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionized accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and is assumed to be constant with height.
We obtained solutions for the structure and growth rate of global unstable modes for different conductivity regimes, strengths of the initial magnetic field and coupling between ionized and neutral components of the fluid. The envelopes of short-wavelength perturbations are determined by the action of competing local growth rates at different heights, driven by the vertical stratification of the disc. Ambipolar diffusion perturbations peak consistently higher above the midplane than modes including Hall conductivity. For weak coupling, perturbations including the Hall effect grow faster and act over a more extended cross-section of the disc than those obtained using the ambipolar diffusion approximation.
Finally, we derived an approximate criterion for when Hall diffusion determines the growth of the magnetorotational instability. This is satisfied over a wide range of radii in protostellar discs, reducing the extent of the magnetic 'dead zone'. Even if the magnetic coupling is weak, significant accretion may occur close to the midplane, rather than in the surface regions of weakly ionized discs.     

Saturated magnetic field amplification at supernova shocks

Cosmic ray streaming instabilities at supernova shocks are discussed in the quasi-linear diffusion formalism which takes into account the feedback effect of wave growth on the cosmic ray streaming motion. In particular, the non-resonant instability that leads to magnetic field amplification in the short wavelength regime is considered. The linear growth rate is calculated using kinetic theory for a streaming distribution. We show that the non-resonant instability is actually driven by a compensating current in the background plasma. The non-resonant instability can develop into a non-linear regime generating turbulence. The saturation of the amplified magnetic fields due to particle diffusion in the turbulence is derived analytically. It is shown that the evolution of parallel and perpendicular cosmic ray pressures is predominantly determined by non-resonant diffusion. However, the saturation is determined by resonant diffusion which tends to reduce the streaming motion through pitch angle scattering. The saturated level can exceed the mean background magnetic field.     

Instability of the structure of strong oblique MHD cosmic-ray shocks

A criterion of the instability of a flow of a thermal plasma and cosmic rays in front of an oblique MHD shock wave with respect to short-wavelength magnetosonic disturbances is derived. The dependence of a cosmic-ray diffusion tensor on a plasma density and a large-scale magnetic field is taken into account. The most unstable disturbances propagate at an angle to the magnetic field if diffusion is strongly anisotropic. In some cases the most strong instability connects with the off-diagonal terms of the diffusion tensor.     

Extragalactic UHE proton spectrum and prediction for iron-nuclei flux at 10–10 GeV

We investigate the problem of transition from galactic cosmic rays to extragalactic ultra-high energy cosmic rays. Using the model for extragalactic ultra-high energy cosmic rays and observed all-particle cosmic ray spectrum, we calculate the galactic spectrum of iron nuclei in the energy range 10⁸–10⁹ GeV. The flux and spectrum predicted at lower energies agree well with the KASCADE data. The transition from galactic to extragalactic cosmic rays is distinctly seen in spectra of protons and iron nuclei, when they are measured separately. The shape of the predicted iron spectrum agrees with the Hall diffusion.     

Building the Fast Galactic Dynamo

In this paper we demonstrate the importance of cosmic rays for the dynamics of the interstellar medium. We present the first 3D-MHD numerical simulations of the Parker instability triggered by cosmic rays accelerated in randomly distributed supernova remnants. We show that in the presence of galactic rotation a net radial magnetic field is produced as a result of the cosmic ray injection and Coriolis force. This process provides a possibility of very efficient magnetic field amplification within the general frame of so called fast galactic dynamo proposed by Parker (1992).     

The role of Cosmic rays in hydrostatic equilibrium of the galactic halo

The hydrostatic equilibrium of the gas field system is studied in the halo. Cosmic-ray distribution is considered independently from the magnetic field on the basis of the diffusion model of the propagation of cosmic rays. We show that the cosmic rays extend in the halo to distances of a few kiloparsecs. The magnetic field decreases slowly with height above the galactic plane.     

The dynamical coupling of cosmic rays and magnetic field in galactic disks

In this paper we demonstrate the importance of cosmic rays for the dynamics of the interstellar medium. We present the first 3D-MHD numerical simulations of the Parker instability triggered by cosmic rays accelerated in supernova remnants. We show that in the presence of galactic rotation a net radial magnetic field is produced as a result of the cosmic ray injection. This process provides a very efficient magnetic field amplification within the general frame of so called fast galactic dynamo proposed by Parker (1992). This revised version was published online in September 2006 with corrections to the Cover Date.     

Influence of cosmic rays on propagation of long magneto hydrodynamic waves

The influence of relativistic particles on the dispersion properties of a cosmic plasma are considered. Use is made of the equation of magneto-hydrodynamics for the thermal plasma and the diffusion equation for cosmic rays. The mechanism of dissipation of the waves due to the diffusion of cosmic rays is shown to be predominant for magneto acoustic waves in the interstellar medium.     

Gamma rays from molecular clouds

It is believed that the observed diffuse gamma-ray emission from the galactic plane is the result of interactions between cosmic rays and the interstellar gas. Such emission can be amplified if cosmic rays penetrate into dense molecular clouds. The propagation of cosmic rays inside a molecular cloud has been studied assuming an arbitrary energy and space dependent diffusion coefficient. If the diffusion coefficient inside the cloud is significantly smaller compared to the average one derived for the galactic disk, the observed gamma-ray spectrum appears harder than the cosmic ray spectrum, mainly due to the slower penetration of the low energy particles towards the core of the cloud. This may produce a great variety of gamma-ray spectra.     

Drag Instability

With the ionization rate of neutral particles caused by cosmic rays and balanced by the recombination rate of ions for a cold, weakly ionized fluid threaded by stressed magnetic fields, we show that a local perturbation can evolve to a traveling wave with its perturbed quantities growing with time so long as the drift velocity between neutrals and ions is comparable to the Alfven speed of the fluid. Since the large drift velocity is one of the key assumptions to drive this instability, we name it the “drag instability”. We suggest that the drag instability might occur in the regions where magnetic fields are highly stressed such as a C-shock front or a collapsing proto-stellar cloud.     

Effect of shocks on interstellar turbulence and cosmic-ray dynamics

A theoretical model for the interstellar turbulence is developed. In this model the fluctuation spectrum is formed due to reflection of shocks, produced by supernovae, on interstellar clouds. The spectra of turbulence and the diffusion coefficient of cosmic rays are derived. It is demonstrated that local enhancements of the ionization rate by cosmic rays accelerated by supernova shocks may be responsible for fast renewal of warm ionized envelopes around cores of standard ISM clouds.     

Cosmic rays in a large-scale strongly turbulent magnetic field

A modification of the diffusional motion of cosmic rays in a large scale turbulent field is considered. The partial dragging of particles in the arbitrarily wandering magnetic field lines may lead to the creation of a new regime of diffusion of cosmic rays in the Galaxy.     

Galactic and Anomalous Cosmic Rays in the Heliosphere

We discuss the present status of our understanding of the transport and acceleration of anomalous cosmic rays and the transport of galactic and CIR-accelerated particles in the heliosphere. Currently, two- and three-dimensional numerical codes can accurately model many of the observed phenomena – with the major current uncertainties being the values of the parameters such as the diffusion coefficients and the effects of the poorly understood structure beyond the termination shock. We illustrate the nature of the phenomena by discussing in detail the response of energetic particles to co-rotating interaction regions, the acceleration of singly- and multiply-charged anomalous cosmic rays, and the effects of galactic cosmic rays on the structure of the solar wind and its termination shock. This revised version was published online in July 2006 with corrections to the Cover Date.     

Growth of the MRI in accretion discs – the influence of radiation transport

In this paper, we investigate the influence of radiative transport on the growth of the magnetorotational instability (MRI) in accretion discs. The analysis is performed by the use of analytical and numerical means. We provide a general dispersion relation together with the corresponding eigenfunctions describing the growth rates of small disturbances on a homogeneous background shear flow. The dispersion relation includes compressibility and radiative effects in the flux-limited diffusion approximation. By introducing an effective speed of sound, all the effects of radiation transport can be subsumed into one single parameter. It can be shown that the growth rates of the vertical modes – which are the fastest growing ones – are reduced by radiative transport. For the case of non-vertical modes, the growth rates may instead be enhanced. We quantify the effects of compressibility and radiative diffusion on the growth rates for the gas-pressure dominated case. The analytical discussion is supplemented by numerical simulations, which are also used for a first investigation of the non-linear stage of the MRI in gas-pressure dominated accretion discs with radiation transport included.     

Statistical acceleration and spatial diffusion of cosmic rays in turbulent medium

Statistical acceleration of cosmic rays in a turbulent medium is considered. Charged particles are assumed to acquire energy in a bounded region of space and leave the acceleration region due to spatial diffusion caused by the scattering of cosmic rays in turbulent magnetic fields. Analytical solutions of the cosmic ray transport equation are obtained and equilibrium space-energy distributions of high-energy particles are studied in the acceleration region and beyond.