I. Büsching

MODELING THE MODULATION OF GALACTIC AND JOVIAN ELECTRONS BY STOCHASTIC PROCESSES

We present a newly developed numerical modulation model to study the transport of galactic and Jovian electrons in the heliosphere. The model employs stochastic differential equations (SDEs) to solve the corresponding transport equation in five dimensions (time, energy, and three spatial dimensions) which is difficult to accomplish with the numerical schemes used in finite difference models. Modeled energy spectra for galactic electrons are compared for the two drift cycles to observations at Earth. Energy spectra and radial intensity profiles of galactic and Jovian electrons are compared successfully to results from previous studies. In line with general drift considerations, it is found that most 100 MeV electrons observed at Earth enter the heliosphere near the equatorial regions in the A > 0 cycle, while they enter mainly over the polar regions in the A < 0 cycle. Our results indicate that 100 MeV electrons observed at Earth originate at the heliopause with ~600 MeV undergoing adiabatic cooling during their transport to Earth. The mean propagation time of these particles varies between ~180 and 300 days, depending on the drift cycle. For 10 MeV Jovian electrons observed at Earth, a mean propagation time of ~40 days is obtained. During this time, the azimuthal position of the Jovian magnetosphere varies by ~1°. At a 50 AU observational point, the mean propagation time of these electrons increases to ~370 days with an azimuthal position change of Jupiter of ~20°. The SDE approach is very effective in calculating these propagation times.

A Cosmic-Ray Positron Anisotropy due to Two Middle-Aged, Nearby Pulsars?

Geminga and B0656+14 are the closest pulsars with characteristic ages in the range of 100 kyr to 1 Myr. They both have spin-down powers of the order 3 × 1034 ergs s−1 at present. The winds of these pulsars had most probably powered pulsar wind nebulae (PWNe) that broke up less than about 100 kyr after the birth of the pulsars. Assuming that leptonic particles accelerated by the pulsars were confined in the PWNe and were released into the interstellar medium (ISM) on breakup of the PWNe, we show that, depending on the pulsar parameters, both pulsars make a nonnegligible contribution to the local cosmic ray (CR) positron spectrum, and they may be the main contributors above several GeV. The relatively small angular distance between Geminga and B0656+14 thus implies an anisotropy in the local CR positron flux at these energies. We calculate the contribution of these pulsars to the locally observed CR electron and positron spectra depending on the pulsar birth period and the magnitude of the local CR diffusion coefficient. We further give an estimate of the expected anisotropy in the local CR positron flux. Our calculations show that within the framework of our model, the local CR positron spectrum imposes constraints on pulsar parameters for Geminga and B0656+14, notably the pulsar period at birth, and also the local interstellar diffusion coefficient for CR leptons.

A stochastic differential equation code for multidimensional Fokker-Planck type problems

Abstract We present a newly developed numerical code that integrates Fokker–Planck type transport equations in four to six spatial dimensions (configuration plus momentum space) and time by means of stochastic differential equations. In contrast to other, similar approaches our code is not restricted to any special configuration or application, but is designed very generally with a modular structure and, moreover, allows for Cartesian, cylindrical or spherical coordinates. Depending on the physical application the code can integrate the equations forward or backward in time. We exemplify the mathematical ideas the method is based upon and describe the numerical realisation and implementation in detail. The code is validated for both cases against an established finite-differences explicit numerical code for a scenario that includes particle sources as well as a linear loss term. Finally we discuss the new possibilities opened up with respect to general applications and newly developed hardware.

On the propagation times and energy losses of cosmic rays in the heliosphere

[1] We present calculations of the propagation times and energy losses of cosmic rays as they are transported through the heliosphere. By calculating these quantities for a spatially 1D scenario, we benchmark our numerical model, which uses stochastic differential equations to solve the relevant transport equation, with known analytical solutions. The comparison is successful and serves as a vindication of the modeling approach. A spatially 3D version of the modulation model is subsequently used to calculate the propagation times and energy losses of galactic electrons and protons in different drift cycles. We find that the propagation times of electrons are longer than those of the protons at the same energy. Furthermore, the propagation times are longer in the drift cycle when the particles reach the Earth by drifting inward along the heliospheric current sheet. The calculated energy losses follow this same general trend. The energy losses suffered by the electrons are comparable to those of the protons, which is in contrast to the generally held perception that electrons experience little energy losses during their propagation through the heliosphere.

Spatially resolved XMM-Newton analysis and a model of the nonthermal emission of MSH 15–52

We present an X-ray analysis and a model of the nonthermal emission of the pulsar wind nebula (PWN) MSH 15-52. We analyzed XMM-Newton data to obtain the spatially resolved spectral parameters around the pulsar PSR B1509―58. A steepening of the fitted power-law spectra and decrease in the surface brightness is observed with increasing distance from the pulsar. In the second part of this paper, we introduce a model for the nonthermal emission, based on assuming the ideal magnetohydrodynamic limit. This model is used to constrain the parameters of the termination shock and the bulk velocity of the leptons in the PWN. Our model is able to reproduce the spatial variation of the X-ray spectra. The parameter ranges that we found agree well with the parameter estimates found by other authors with different approaches. In the last part of this paper, we calculate the inverse Compton emission from our model and compare it to the emission detected with the HESS telescope system. Our model is able to reproduce the flux level observed with HESS, but not the spectral shape of the observed TeV γ-ray emission.

Cosmic-ray positrons from millisecond pulsars

Observations by the Fermi Large Area Telescope of gamma-ray millisecond pulsar light curves imply copious pair production in their magnetospheres, and not exclusively in those of younger pulsars. Such pair cascades may be a primary source of Galactic electrons and positrons, contributing to the observed enhancement in positron flux above ~10 GeV. Fermi has also uncovered many new millisecond pulsars, impacting Galactic stellar population models. We investigate the contribution of Galactic millisecond pulsars to the flux of terrestrial cosmic-ray electrons and positrons. Our population synthesis code predicts the source properties of present-day millisecond pulsars. We simulate their pair spectra invoking an offset-dipole magnetic field. We also consider positrons and electrons that have been further accelerated to energies of several TeV by strong intrabinary shocks in black widow and redback systems. Since millisecond pulsars are not surrounded by pulsar wind nebulae or supernova shells, we assume that the pairs freely escape and undergo losses only in the intergalactic medium. We compute the transported pair spectra at Earth, following their diffusion and energy loss through the Galaxy. The predicted particle flux increases for non-zero offsets of the magnetic polar caps. Pair cascades from the magnetospheres of millisecond pulsars are only modest contributors around a few tens of GeV to the lepton fluxes measured by AMS-02, PAMELA, and Fermi, after which this component cuts off. The contribution by black widows and redbacks may, however, reach levels of a few tens of percent at tens of TeV, depending on model parameters.

Obtaining Cosmic-Ray Propagation Parameters from Diffuse Very High Energy Gamma-Ray Emission from the Galactic Center Ridge

The recent discovery of diffuse, very high energy (VHE) γ-radiation from the Galactic center ridge by the HESS telescope allows for the first time the direct determination of the parameters of Galactic cosmic-ray propagation models. Whereas this discovery showed that the diffuse γ-radiation can be explained by the interaction of VHE cosmic-ray (CR) protons with the interstellar gas located in several giant molecular clouds, we show in this paper that the associated diffusion coefficient for the protons depends on the epoch of activity of the central source of protons: Assuming that the supernova remnant (SNR) Sgr A East was responsible for the particle acceleration, we infer a diffusion coefficient for the Galactic center region of κ = 1-5 kpc2 Myr-1 for a mean proton energy of ~3 TeV. More specifically, for impulsive injection in a 5-10 kyr SNR, we infer a value of κ = 1-2 kpc2 Myr-1, whereas for source activity timescales equal to the age of the SNR, the diffusion coefficient would increase to κ ~ 5 kpc2 Myr-1. These values are smaller than those inferred from local CR abundances. Finally, the above-mentioned values of κ for impulsive injection are equally valid if the required transient source of protons was due to an earlier epoch of stellar infall into the black hole Sgr A*.

Multi-wavelength modeling of globular clusters–the millisecond pulsar scenario

The potentially large number of millisecond pulsars (MSPs) in globular cluster (GC) cores makes these parent objects ideal laboratories for studying the collective properties of an ensemble of MSPs. Such a population is expected to radiate several spectral components in the radio through ?-ray waveband. First, pulsed emission is expected via curvature and synchrotron radiation (CR and SR) and possibly even via inverse Compton (IC) scattering inside the pulsar magnetospheres. Second, unpulsed emission should transpire through the continuous injection of relativistic leptons by the MSPs into the ambient region, which in turn produce SR and IC emission when they encounter the cluster magnetic field, as well as several background photon components. In this paper we continue to develop the MSP scenario for explaining the multi-wavelength properties of GCs by considering the entire modeling chain, including the full transport equation, refined emissivities of stellar and Galactic background photons, integration of the flux along the line of sight, and comparison with observations. As an illustration, we apply the model to Terzan 5, where we can reasonably fit both the (line-of-sight-integrated) X-ray surface flux and spectral energy density data, using the first to constrain the leptonic diffusion coefficient within the GC. We lastly discuss possible future extensions to and applications of this maturing model.