R. Kissmann

PICARD: A novel code for the Galactic Cosmic Ray propagation problem

Abstract In this manuscript we present a new approach for the numerical solution of the Galactic Cosmic Ray propagation problem. We introduce a method using advanced contemporary numerical algorithms while retaining the general complexity of other established codes. In this paper we present the underlying numerical scheme in conjunction with tests showing the correctness of the scheme. Finally we show the solution of a first example propagation problem using the new code to show its applicability to Galactic Cosmic Ray propagation.

Vertical Structure and Turbulent Saturation Level in Fully Radiative Protoplanetary Disc Models

We investigate a massive (Σ ~ 10 000 g cm -2 at 1 au) protoplanetary disc model by means of 3D radiation magnetohydrodynamic simulations. The vertical structure of the disc is determined self-consistently by a balance between turbulent heating caused by the magnetorotational turbulence and radiative cooling. Concerning the vertical structure, two different regions can be distinguished: a gas-pressure-dominated, optically thick mid-plane region where most of the dissipation takes place, and a magnetically dominated, optically thin corona which is dominated by strong shocks. At the location of the photosphere, the turbulence is supersonic (M ~ 2), which is consistent with previous results obtained from the fitting of spectra of young stellar objects. It is known that the turbulent saturation level in simulations of MRI-induced turbulence does depend on numerical factors such as the numerical resolution and the box size. However, by performing a suite of runs at different resolutions (using up to 64 x 128 x 512 grid cells) and with varying box sizes (with up to 16 pressure scaleheights in the vertical direction), we find that both the saturation levels and the heating rates show a clear trend to converge once a sufficient resolution in the vertical direction has been achieved.

Local turbulence simulations for the multiphase ISM

In this paper, we show results of numerical simulations for the turbulence in the interstellar medium (ISM). These results were obtained using a Riemann solver-free numerical scheme for high-Mach number hyperbolic equations. Here, we especially concentrate on the physical properties of the ISM. That is, we do not present turbulence simulations trimmed to be applicable to the ISM. The simulations are rather based on physical estimates for the relevant parameters of the interstellar gas. Applying our code to simulate the turbulent plasma motion within a typical interstellar molecular cloud, we investigate the influence of different equations of state (isothermal and adiabatic) on the statistical properties of the resulting turbulent structures. We find slightly different density power spectra and dispersion maps, while both cases yield qualitatively similar dissipative structures, and exhibit a departure from the classical Kolmogorov case towards a scaling described by the She-Leveque model. Solving the full energy equation with realistic heating/cooling terms appropriate for the diffuse interstellar gas (DIG), we are able to reproduce a realistic two-phase distribution of cold and warm plasma. When extracting maps of polarized intensity from our simulation data, we find encouraging similarity to actual observations. Finally, we compare the actual magnetic field strength of our simulations to its value inferred from the rotation measure. We find these to be systematically different by a factor of about 1.15, thus highlighting the often-underestimated influence of varying line-of-sight particle densities on the magnetic field strength derived from observed rotation measures.

Spiral arms as cosmic ray source distributions

Abstract The Milky Way is a spiral galaxy with (or without) a bar-like central structure. There is evidence that the distribution of suspected cosmic ray sources, such as supernova remnants, are associated with the spiral arm structure of galaxies. It is yet not clearly understood what effect such a cosmic ray source distribution has on the particle transport in our Galaxy. We investigate and measure how the propagation of Galactic cosmic rays is affected by a cosmic ray source distribution associated with spiral arm structures. We use the PICARD code to perform high-resolution 3D simulations of electrons and protons in galactic propagation scenarios that include four-arm and two-arm logarithmic spiral cosmic ray source distributions with and without a central bar structure as well as the spiral arm configuration of the NE2001 model for the distribution of free electrons in the Milky Way. Results of these simulation are compared to an axisymmetric radial source distribution. Also, effects on the cosmic ray flux and spectra due to different positions of the Earth relative to the spiral structure are studied. We find that high energy electrons are strongly confined to their sources and the obtained spectra largely depend on the Earth’s position relative to the spiral arms. Similar finding have been obtained for low energy protons and electrons albeit at smaller magnitude. We find that even fractional contributions of a spiral arm component to the total cosmic ray source distribution influences the spectra on the Earth. This is apparent when compared to an axisymmetric radial source distribution as well as with respect to the Earth’s position relative to the spiral arm structure. We demonstrate that the presence of a Galactic bar manifests itself as an overall excess of low energy electrons at the Earth. Using a spiral arm geometry as a cosmic ray source distributions offers a genuine new quality of modeling and is used to explain features in cosmic ray spectra at the Earth that are else-wise attributed to other propagation effects. We show that realistic cosmic ray propagation scenarios have to acknowledge non-axisymmetric source distributions.

Global structure of magnetorotationally turbulent protoplanetary discs

The aim of this paper is to investigate the spatial structure of a protoplanetary disc whose dynamics is governed by magnetorotational turbulence. We perform a series of local three-dimensional chemoradiative magnetohydrodynamic simulations located at different radii of a disc which is twice as massive as the standard minimum mass solar nebula of Hayashi. The ionization state of the disc is calculated by including collisional ionization, stellar X-rays, cosmic rays and the decay of radionuclides as ionization sources, and by solving a simplified chemical network which includes the effect of the absorption of free charges by μm-sized dust grains. In the region where the ionization is too low to ensure good coupling between matter and magnetic fields, a non-turbulent central ‘dead zone’ forms, which ranges approximately from a distance of 2 to 4 au from the central star. The approach taken in this work allows for the first time to derive the global spatial structure of a protoplanetary disc from a set of physically realistic numerical simulations.

Simulating three-dimensional nonthermal high-energy photon emission in colliding-wind binaries

Massive stars in binary systems have long been regarded as potential sources of high-energy γ rays. The emission is principally thought to arise in the region where the stellar winds collide and accelerate relativistic particles which subsequently emit γ rays. On the basis of a three-dimensional distribution function of high-energy particles in the wind collision region—as obtained by a numerical hydrodynamics and particle transport model—we present the computation of the three-dimensional nonthermal photon emission for a given line of sight. Anisotropic inverse Compton emission is modeled using the target radiation field of both stars. Photons from relativistic bremsstrahlung and neutral pion decay are computed on the basis of local wind plasma densities. We also consider photon-photon opacity effects due to the dense radiation fields of the stars. Results are shown for different stellar separations of a given binary system comprising of a B star and a Wolf-Rayet star. The influence of orbital orientation with respect to the line of sight is also studied by using different orbital viewing angles. For the chosen electron-proton injection ratio of 10–2, we present the ensuing photon emission in terms of two-dimensional projections maps, spectral energy distributions, and integrated photon flux values in various energy bands. Here, we find a transition from hadron-dominated to lepton-dominated high-energy emission with increasing stellar separations. In addition, we confirm findings from previous analytic modeling that the spectral energy distribution varies significantly with orbital orientation.

HIGH-ENERGY PARTICLE TRANSPORT IN THREE-DIMENSIONAL HYDRODYNAMIC MODELS OF COLLIDING-WIND BINARIES

Massive stars in binary systems (such as WR 140, WR 147, or η Carinae) have long been regarded as potential sources of high-energy γ-rays. The emission is thought to arise in the region where the stellar winds collide and produce relativistic particles that subsequently might be able to emit γ-rays. Detailed numerical hydrodynamic simulations have already offered insight into the complex dynamics of the wind collision region (WCR), while independent analytical studies, albeit with simplified descriptions of the WCR, have shed light on the spectra of charged particles. In this paper, we describe a combination of these two approaches. We present a three-dimensional hydrodynamical model for colliding stellar winds and compute spectral energy distributions of relativistic particles for the resulting structure of the WCR. The hydrodynamic part of our model incorporates the line-driven acceleration of the winds, gravity, orbital motion, and the radiative cooling of the shocked plasma. In our treatment of charged particles, we consider diffusive shock acceleration in the WCR and the subsequent cooling via inverse Compton losses (including Klein-Nishina effects), bremsstrahlung, collisions, and other energy loss mechanisms.

Propagation in 3D spiral-arm cosmic-ray source distribution models and secondary particle production using Picard

Abstract We study the impact of possible spiral-arm distributions of Galactic cosmic-ray sources on the flux of various cosmic-ray nuclei throughout our Galaxy. We investigate model cosmic-ray spectra at the nominal position of the sun and at different positions within the Galaxy. The modelling is performed using the recently introduced numerical cosmic ray propagation code P icard . Assuming non-axisymmetric cosmic-ray source distributions yields new insights on the behaviour of primary versus secondary nuclei. We find that primary cosmic rays are more strongly confined to the vicinity of the sources, while the distribution of secondary cosmic rays is much more homogeneous compared to the primaries. This leads to stronger spatial variation in secondary to primary ratios when compared to axisymmetric source distribution models. A good fit to the cosmic-ray data at Earth can be accomplished in different spiral-arm models, although leading to decisively different spatial distributions of the cosmic-ray flux. These lead to different cosmic ray anisotropies, where even reproducing the data becomes possible. Consequently, we advocate directions to seek best fit propagation parameters that take into account the higher complexity introduced by the spiral-arm structure on the cosmic-ray distribution. We specifically investigate whether the flux at Earth is representative for a large fraction of the Galaxy. The variance among possible spiral-arm models allows us to quantify the spatial variation of the cosmic-ray flux within the Galaxy in presence of non-axisymmetric source distributions.

First results of a new 3-D model of the time-dependent modulation of electrons in the heliosphere

Abstract We employ our recently developed ansatz for the time-dependent 3-D modelling of Jovian and galactic electrons in the inner heliosphere. The main goal of the study is to check whether the form of the diffusion tensofi as determined recently by Ferreira et al. (2001a,b) with an extended parameter study of the steady state is also useful for comparison with observations for which the time-dependence cannot be neglected, like long-term modulation due to solar cycle activity and short-term modulation, e.g., due to corotating interaction regions. We apply the model to compare the simulation results with time series of electron intensities as observed with the SOHO, the IMP 8 and the Ulysses spacecraft and discuss the findings.

A central conservative scheme for general rectangular grids

We present an extension of the genuinely multi-dimensional semi-discrete central scheme developed in [A. Kurganov, S. Noelle, G. Petrova, Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J. Sci. Comput. 23 (3) (2001) 707-740.] to arbitrary orthogonal grids. The presented algorithm is constructed to yield the geometric scaling factors in a self-consistent way. Additionally, the order of the scheme is not fixed during the derivation of the basic algorithm. Based on the resulting general scheme it is possible to construct methods of any desired order, just by considering the corresponding reconstruction polynomial. We demonstrate how a second order scheme in plane polar coordinates and cylindrical coordinates can be derived from our general formulation. Finally, we demonstrate the correctness of this second order scheme through application to several numerical experiments.