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.
Aims. To provide a significantly improved probability distribution for the H-test for periodicity in X-ray and γ-ray arrival times, which is already extensively used by the γ-ray pulsar community. ...Also, to obtain an analytical probability distribution for stacked test statistics in the case of a search for pulsed emission from an ensemble of pulsars where the significance per pulsar is relatively low, making individual detections insignificant on their own. This information is timely given the recent rapid discovery of new pulsars with the Fermi-LAT t γ-ray telescope. Methods. Approximately 1014 realisations of the H-statistic (H) for random (white) noise is calculated from a random number generator for which the repetition cycle is ≫1014. From these numbers the probability distribution P(>H) is calculated. Results. The distribution of H is found to be exponential with parameter λ = 0.4 so that the cumulative probability distribution P(>H)= $\exp$(-λ H). If we stack independent values for H, the sum of K such values would follow the Erlang-K distribution with parameter λ for which the cumulative probability distribution is also a simple analytical expression. Conclusions. Searches for weak pulsars with unknown pulse profile shapes in the Fermi-LAT, Agile or other X-ray data bases should benefit from the H-test since it is known to be powerful against a broad range of pulse profiles, which introduces only a single statistical trial if only the H-test is used. The new probability distribution presented here favours the detection of weaker pulsars in terms of an improved sensitivity relative to the previously known distribution.
Galactic transport models for cosmic rays involve the diffusive motion of these particles in the interstellar medium. Owing to the large-scale structured Galactic magnetic field, this diffusion is ...anisotropic with respect to the local field direction. We included this transport effect along with continuous loss processes in a quantitative model of Galactic propagation for cosmic ray protons that is based on stochastic differential equations. We calculated energy spectra at different positions along the Sun’s Galactic orbit and compared them to the isotropic diffusion case. The results show that a larger amplitude of variation and different spectral shapes are obtained in the introduced anisotropic diffusion scenario, which in turn emphasizes the need for accurate Galactic magnetic field models.
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.
Key Points
Heliospheric propagation times of cosmic ray protons & electrons are calculated
Exact calculations of energy losses for protons and electrons are presented
The SDE approach lends itself to the calculation of these quantities
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.
► SDE code for multidimensional Fokker–Planck-type equations. ► Transport equation includes source terms and sinks. ► Applicable to heliospheric as well as galactic problems. ► Code may be applied also to other fields of research. ► Designed also to run on GPUs.
The detection of fast variations of the tera-electron volt (TeV) (10¹² eV) γ-ray flux, on time scales of days, from the nearby radio galaxy M87 is reported. These variations are about 10 times as ...fast as those observed in any other wave band and imply a very compact emission region with a dimension similar to the Schwarzschild radius of the central black hole. We thus can exclude several other sites and processes of the γ-ray production. The observations confirm that TeV γ rays are emitted by extragalactic sources other than blazars, where jets are not relativistically beamed toward the observer.
Drifts are one of the major cosmic ray modulation mechanisms in the heliosphere. Three types of drifts occur in the background heliospheric magnetic field, namely curvature, gradient and current ...sheet drifts. The last component occurs because of the switch in magnetic field polarity across the heliospheric current sheet and is the main topic of study. We discuss and implement a new approach to model drifts in a numerical modulation model. The model employs stochastic differential equations to solve the relevant transport equation in five (three spatial, energy and time) dimensions. What is of interest is the fact that the model can handle current sheet tilt angles up to the theoretical maximum of
α
=90° and still remain numerically stable. We use the additional insights gained from the numerical model to investigate the effectiveness of drifts along the current sheet by examining the relationship between the current sheet path length and the cosmic ray propagation time. It is found that diffusion can disrupt the drift process very effectively, leading to diffusive short circuiting of the current sheet by the cosmic rays.
The measurement of an excess in the cosmic-ray electron spectrum between 300 and 800 GeV by the ATIC experiment has – together with the PAMELA detection of a rise in the positron fraction up to ...≈100 GeV – motivated many interpretations in terms of dark matter scenarios; alternative explanations assume a nearby electron source like a pulsar or supernova remnant. Here we present a measurement of the cosmic-ray electron spectrum with H.E.S.S. starting at 340 GeV. While the overall electron flux measured by H.E.S.S. is consistent with the ATIC data within statistical and systematic errors, the H.E.S.S. data exclude a pronounced peak in the electron spectrum as suggested for interpretation by ATIC. The H.E.S.S. data follow a power-law spectrum with spectral index of 3.0±0.1(stat.)± 0.3(syst.), which steepens at about 1 TeV.
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 x 10 super(34) ergs s super(-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.
Background Mental practice has been used in neurologic rehabilitation to improve motor performance. This study explored if mental practice targeting the hand modulates cortical excitability and ...improves function of the affected hand. Transcranial Magnetic Stimulation (TMS) was used to measure changes in the duration of the cortical Silent Period (cSP) and to analyze the amplitudes of motor evoked potentials (MEPs). Methods A number of 32 subacute stroke patients participated in the study ( n = 32; m = 19, f = 13; mean age = 62.8 ± 11.2 years; time since onset = 2.1 ± 1.1 months). Mental practice for the hand consisted of two interventions. Intervention 1 comprises a 30 min computer based Hand Identification Task (HIT). Intervention 2 includes repeated mental performance of the Box-and-Block Test (BBT) over 30 min. Those two kinds of intervention were administered in randomized order on different days. Before and after training, cortical excitability of the motor system as well as motor performance of the hands were measured. TMS was executed with a round coil, with electrical recordings from the Interosseus dorsalis I muscle on both sides. The hemispheres were stimulated one after the other, with a stimulus intensity of 130% of the resting motor threshold. During TMS, the patients performed a tonic pinch grip. Duration of cSP and MEP amplitudes were analyzed taking the mean of 5 stimulations. Motor function data were gathered using the BBT and a subtest of Jebsen Taylor Hand Function Test (JTHFT; nine men’s morris game stone task). Results Independent of the kind of the intervention, the duration of cSP on the affected side was significantly shorter after intervention ( p < 0.007). The cSP of the unaffected side did not change. Amplitudes of MEPs did not show changes on neither side. Motor performance of the affected hand significantly improved after both interventions (BBT p < 0.003; JTHFT subtest p < 0.001). The unaffected hand showed significant improvements in the JTHFT subtest ( p < 0.03), however not in the BBT. A significant correlation between the shortening of the cSP and the improvement of motor performance in the JTHFT subtest ( r = 0.51, p < 0.02) was found for the affected side only after intervention 2. Conclusions Mental practice for the hand reduced cortical inhibition on the affected side and improved motor performance, independently of the kind of mental intervention. Thus, to occupy oneself mentally with the hand seems to be more important than the specificity of the intervention. The correlation between reduced inhibition and improved motor performance suggests that an indirect fostering of excitability by reducing the activity of inhibitory neurons can improve motor function.
PDF
