PIERNIK mhd code - a multi-fluid, non-ideal extension of the relaxing-TVD scheme (I)

We present a new multi-fluid, grid MHD code PIERNIK, which is based on the Relaxing TVD scheme. The original scheme has been extended by an addition of dynamically independent, but interacting fluids: dust and a diffusive cosmic ray gas, described within the fluid approximation, with an option to add other fluids in an easy way. The code has been equipped with shearing-box boundary conditions, and a selfgravity module, Ohmic resistivity module, as well as other facilities which are useful in astrophysical fluid-dynamical simulations. The code is parallelized by means of the MPI library. In this paper we shortly introduce basic elements of the Relaxing TVD MHD algorithm, following Trac & Pen (2003) and Pen et al. (2003), and then focus on the conservative implementation of the shearing box model, constructed with the aid of the Masset's (2000) method. We present results of a test example of a formation of a gravitationally bounded object (planet) in a self-gravitating and differentially rotating fluid.Comment: 6 pages, 3 figures, conference proceedings of the Torun Exoplanets 200

Cosmic-ray driven dynamo in galaxies

We present recent developments of global galactic-scale numerical models of the Cosmic Ray (CR) driven dynamo, which was originally proposed by Parker (1992). We conduct a series of direct CR+MHD numerical simulations of the dynamics of the interstellar medium (ISM), composed of gas, magnetic fields and CR components. We take into account CRs accelerated in randomly distributed supernova (SN) remnants, and assume that SNe deposit small-scale, randomly oriented, dipolar magnetic fields into the ISM. The amplification timescale of the large-scale magnetic field resulting from the CR-driven dynamo is comparable to the galactic rotation period. The process efficiently converts small-scale magnetic fields of SN-remnants into galactic-scale magnetic fields. The resulting magnetic field structure resembles the X-shaped magnetic fields observed in edge-on galaxies.Comment: 6 pages, 4 figures, to appear in Proceedings of IAU Symp. 274, Advances in Plasma Astrophysics, ed. A. Bonanno, E. de Gouveia dal Pino and A. Kosoviche

Global galactic dynamo driven by cosmic-rays and exploding magnetized stars

We report first results of first global galactic-scale CR-MHD simulations of cosmic-ray-driven dynamo. We investigate the dynamics of magnetized interstellar medium (ISM), which is dynamically coupled with the cosmic-ray (CR) gas. We assume that exploding stars deposit small-scale, randomly oriented, dipolar magnetic fields into the differentially rotating ISM, together with a portion of cosmic rays, accelerated in supernova shocks. We conduct numerical simulations with the aid of a new parallel MHD code PIERNIK. We find that the initial magnetization of galactic disks by exploding magnetized stars forms a favourable conditions for the cosmic-ray-driven dynamo. We demonstrate that dipolar magnetic fields supplied on small SN-remnant scales, can be amplified exponentially, by the CR-driven dynamo, to the present equipartition values, and transformed simultaneously to large galactic-scales. The resulting magnetic field structure in an evolved galaxy appears spiral in the face-on view and reveals the so called X-shaped structure in the edge-on view.Comment: 11 pages, 4 figure

3D model of magnetic fields evolution in dwarf irregular galaxies

Radio observations show that magnetic fields are present in dwarf irregular galaxies (dIrr) and its strength is comparable to that found in spiral galaxies. Slow rotation, weak shear and shallow gravitational potential are the main features of a typical dIrr galaxy. These conditions of the interstellar medium in a dIrr galaxy seem to unfavourable for amplification of the magnetic field through the dynamo process. Cosmic-ray driven dynamo is one of the galactic dynamo model, which has been successfully tested in case of the spiral galaxies. We investigate this dynamo model in the ISM of a dIrr galaxy. We study its efficiency under the influence of slow rotation, weak shear and shallow gravitational potential. Additionally, the exploding supernovae are parametrised by the frequency of star formation and its modulation, to reproduce bursts and quiescent phases. We found that even slow galactic rotation with a low shearing rate amplifies the magnetic field, and that rapid rotation with a low value of the shear enhances the efficiency of the dynamo. Our simulations have shown that a high amount of magnetic energy leaves the simulation box becoming an efficient source of intergalactic magnetic fields.Comment: 4 pages, 4 figures, to appear in Proceedings of IAU Symp. 274, Advances in Plasma Astrophysics, ed. A. Bonanno, E. de Gouveia dal Pino and A. Kosoviche

Kelvin-Helmholtz instability of relativistic jets - the transition from linear to nonlinear regime

The observed wiggles and knots in astrophysical jets as well as the curvilinear motion of radio emitting features are frequently interpreted as signatures of the Kelvin-Helmholtz (KH) instability (eg. Hardee 1987). We investigate the KH instability of a hydrodynamic jet composed of a relativistic gas, surrounded by a nonrelativistic external medium and moving with a relativistic bulk speed. We show basic nonlinear effects, which become important for a finite amplitude KH modes. Since the KH instability in supersonic jets involves acoustic waves over-reflected on jet boundaries, the basic nonlinear effect relies on the steepening of the acoustic wave fronts, leading to the formation of shocks. It turns our that the shocks appear predominantly in the external nonrelativistic gas, while the internal acoustic waves remain linear for a much longer time. In addition, the external medium "hardens" as soon as the boundary oscillation velocity becomes comparable to the external sound speed. On the other hand, the amplification of internal waves due to the over-reflection is limited by a nonlinearity of the Lorentz $\gamma$ factor. This implies that the sidereal oscillations of the jet boundary, resulting from the K-H instability, are limited to very small amplitudes comparable to a fraction of the jet radius.Comment: TeX, 5 pages, no figures, lecproc.cmm included, To appear in Proceedings of ``Relativistic jets in AGNs'', Krakow, Poland, 27-30 May 1997, M.Ostrowski, M.Sikora, G.Madejski, M. Begelman (eds.

The galactic dynamo effect due to Parker-shearing instability of magnetic flux tubes. II. Numerical simulations and the nonlinear evolution

In this paper we continue investigations of the Parker-shearing instability performing numerical simulations of the magnetic flux tube dynamics in the thin flux-tube approximation. We show that evolution of flux tubes resulting from numerical simulations is very similar to that of linear solutions if the vertical displacements are smaller than the vertical scale height $H$ of the galactic disc. If the vertical displacements are comparable to $H$, the vertical growth of perturbations is faster in the nonlinear range than in the linear one and we observe a rapid inflation of the flux tube at its top, which leads to a singularity in numerical simulations, if only the cosmic rays are taken into account. Then we perform simulations for the case of nonuniform external medium, which show that the dominating wavelength of the Parker instability is the same as the wavelength of modulations of external medium. As a consequence of this fact, in the case of dominating cosmic ray pressure, the dynamo $\alpha$ effect related to these short wavelength modulations is much more efficient than that related to the linearly most unstable long wavelengths modes of the Parker instability. Under the influence of differential forces resulting from differential rotation and the density waves, the $\alpha$-effect is essentially magnified in the spiral arms and diminished in the interarm regions, what confirms our previous results obtained in the linear approximation.Comment: LaTeX, 13 pages, 15 ps figures, uses l-aa.sty and epsf.sty. Published in Astronomy & Astrophysics, 327, 81

Parker-Jeans Instability of Gaseous Disks Including the Effect of Cosmic Rays

We use linear analysis to examine the effect of cosmic rays (CRs) on the Parker-Jeans instability of magnetized self-gravitating gaseous disks. We adopt a slab equilibrium model in which the gravity (including self-gravity) is perpendicular to the mid-plane, the magnetic field lies along the slab. CR is described as a fluid and only along magnetic field lines diffusion is considered. The linearised equations are solved numerically. The system is susceptible to Parker-Jeans instability. In general the system is less unstable when the CR diffusion coefficient is smaller (i.e., the coupling between the CRs and plasma is stronger). The system is also less unstable if CR pressure is larger. This is a reminiscence of the fact that Jeans instability and Parker instability are less unstable when the gas pressure is larger (or temperature is higher). Moreover, for large CR diffusion coefficient (or small CR pressure), perturbations parallel to the magnetic field are more unstable than those perpendicular to it. The other governing factor on the growth rate of the perturbations in different directions is the thickness of the disk or the strength of the external pressure on the disk. In fact, this is the determining factor in some parameter regimes.Comment: 19pages, 14figures submitted to Ap

The galactic dynamo effect due to Parker-shearing instability of magnetic flux tubes. I. General formalism and the linear approximation

In this paper we investigate the idea of Hanasz & Lesch 1993 that the galactic dynamo effect is due to the Parker instability of magnetic flux tubes. In addition to the former approach, we take into account more general physical conditions in this paper, by incorporating cosmic rays and differential forces due to the axisymmetric differential rotation and the density waves as well. We present the theory of slender magnetic flux tube dynamics in the thin flux tube approximation and the Lagrange description. This is the application of the formalism obtained for solar magnetic flux tubes by Spruit (1981), to the galactic conditions. We perform a linear stability analysis for the Parker-shearing instability of magnetic flux tubes in galactic discs and then calculate the dynamo coefficients. We present a number of new effects which are very essential for cosmological and contemporary evolution of galactic magnetic fields. First of all we demonstrate that a very strong dynamo $\alpha$-effect is possible in the limit of weak magnetic fields in presence of cosmic rays. Second, we show that the differential force resulting from axisymmetric differential rotation and the linear density waves causes that the $\alpha$-effect is essentially magnified in galactic arms and switched off in the interarm regions. Moreover, we predict a non-uniform magnetic field in spiral arms and well aligned one in interarm regions. These properties are well confirmed by recent observational results by Beck & Hoernes (1996)Comment: LaTeX, 15 pages, 8 figures, uses l-aa.sty and epsf.sty, minor corrections to match the published version, Published in Astronomy & Astrophysics, 321, 100

Initial Magnetization of Galaxies by Exploding, Magnetized Stars

We conduct a series of magnetohydrodynamical (MHD) simulations of magnetized interstellar medium (ISM) disturbed by exploding stars. Each star deposits a randomly oriented, dipolar magnetic field into ISM. The simulations are performed in a Cartesian box, in a reference frame that is corotating with the galactic disk. The medium is stratified by vertical galactic gravity. The resulting turbulent state of ISM magnetized by the stellar explosions is processed with the aid of Fourier analysis. The results leads to the conclusion that the input of magnetic energy from exploding stars is additionally multiplied by differential rotation. The resulting magnetic field appears to grow up in small-scale component, while the total magnetic flux remains limited. Our results indicate that magnetic field originating from exploding stars can be a source of initial magnetic fields for a subsequent dynamo process.Comment: Published in Proceedings of the 14th Young Scientists Conference on Astronomy and Space Physics, Kyiv, Ukraine, April 23-28, 200

Hydrodynamical instability of extragalactic stratified jets

The recent development of tomographic analysis of radio data shows the presence of sheaths around several extragalactic jets. We have studied the Kelvin-Helmholtz instability of such stratified jets, describing them as inner relativistic beams embedded in slower plasma envelopes. We find that the para- meters of the envelope generally determine the Kelvin-Helmholtz properties of the jet which thus appears isolated from any ambient external medium.Comment: LaTeX, 5 pages, 1 figure and crckapb.sty, epsf.sty included, To appear in the proceedings of Girona Conference ``Blazars, Black Holes and Jets'', 9-12 September 1996, Girona, Spai