Anisotropy

Introduction The propagation of relativistic charged particles in the heliosphere and interstellar magnetic fields is calculated using the ptracing code. This code was originally developed for the studies described in Desiati & Zweibel (2014). It includes several analytical magnetic and electric field configurations and interfaces to different heliospheric numerical models. Additionally, it supports multithreading, allowing it to take full advantage of computers with a large number of CPU cores and shared memory. Trajectories are calculated by numerically integrating the following set of 6–dimensional ordinary differential equations $$\frac{d\mathbf{p}}{dt} = q \left(\mathbf{v}\times\mathbf{B} \right), \, \frac{d\mathbf{r}}{dt} = \mathbf{v},$$ describing the Lorentz force exerted by the magnetic field $\mathbf{B}(\mathbf{r})$ on particles with electric charge $q$ and velocity $\mathbf{v}$, where $\mathbf{r}$ is their position vector and $\mathbf{p}$ the momentum. Momentum is expressed in units of $mc$; $\hat{\mathbf{p}}\equiv\mathbf{p}/mc$. The particle velocity $\mathbf{v}$ is related to $\hat{\mathbf{p}}$ by $\mathbf{v} = \hat{\mathbf{p}}/\sqrt{1+\hat p^2}$ and the particle Lorentz factor $\gamma = \sqrt{1+\hat p^2}$. In these units, the dimensionless particle gyroradius is $\hat r_g = \hat p_{\perp}$, and the dimensionless gyro-frequency is $\hat \omega_g = 1/\gamma$. %We denote normalized variables with a hat. The equations of motion can be numerically integrated using various stepping algorithms. The code supports an adaptive time step size in these calculations, with a tolerance level denoted by a parameter $\epsilon$ to ensure that truncation errors remain sufficiently small. The integration of particle trajectories concludes when either the maximum integration time, $t_\mathrm{max}$, is reached or when the particles have attained a radius of $r_\mathrm{max}$. The figure demonstrates how protons are affected by the heliosphere and the modified magnetic field near its boundary. One challenge in calculating trajectories within open boundary systems is that particles propagating from outside the heliosphere have a very low probability of reaching Earth or passing near it. To address this, we plan to generate 100 million anti-proton trajectories, propagating backward from Earth to a distance of 50,000 AU from the Sun. We compute the trajectories using the Boris Push stepping method. This algorithm has become a standard for this purpose. Although the Boris algorithm is not symplectic, it does conserve phase space volume, and its energy error is globally bounded, comparable to that of symplectic algorithms. To ensure the accuracy of our results and as part of our validation procedure, we will perform additional checks by varying the integration tolerance parameters and comparing the outcomes with the explicit fourth-order Runge-Kutta method. Additionally, we will conduct cross-validation with limited statistics using third-party tools such as CRPropa. We calculate trajectories using heliospheric models provided by our collaborator, Prof. Nikolai Pogorelov, to investigate the systematic effects of model parameters on our data interpretation. According to Liouville’s Theorem, we can interpret the calculated back-propagated anti-proton trajectories as protons traveling from the ISM to Earth. A preliminary study utilized numerically computed particle trajectories from a computational heliospheric model to assess the experimental biases introduced by ground-based experiments and their impact on interpretations. Our intention is to conduct thorough investigations into this experimental dimension of cosmic-ray physics, which will aid in developing the analytical tools needed to explore the origins of cosmic-ray anisotropy and its propagation through the interstellar medium and the heliosphere.

Feb 7, 2025

Cosmic-ray Anisotropy

Introduction The IceCube and the HAWC observatories have established themselves as leaders in studying Galactic cosmic-ray anisotropy in the TeV–PeV energy range. IceCube captures anisotropy amplitudes with high precision by mapping cosmic-ray arrival directions relative to an isotropic reference. The IceTop surface array detects showers above 500 TeV, while the deep in-ice array records muons down to 10 TeV, both closely aligning with primary cosmic-ray directions. HAWC gamma-ray array detects showers above 1-10 TeV. IceCube and HAWC’s continuous sky observation enhances measurement stability, enabling energy-dependent anisotropy studies and spherical harmonic expansion analysis. Recent findings highlight the dipole component’s amplitude and phase as indicators of cosmic-ray diffusion in interstellar plasma. The angular power spectrum at different energies reflects pitch angle scattering processes. IceCube has submitted results from 12 years (2011–2023) of cosmic-ray muon data, refining event selection for improved stability. High-resolution sky maps will explore temporal anisotropy variations and cross-check muon and shower data consistency. IceCube also analyzes the Compton-Getting effect for calibration and cosmic-ray spectral index measurement. Given individual experiments’ limited sky coverage, full-sky measurements via collaborations with HAWC, GRAPES-3, TALE, and KASCADE aim to provide a comprehensive view of anisotropy. These efforts will improve understanding of cosmic-ray diffusion and heliospheric influence on observed distributions. Publications This is the list of cosmic-ray anisotropy results published by the team: citation title DOI arXiv ApJ (2010) 718 L194 Measurement of the Anisotropy of Cosmic Ray Arrival Directions with IceCube 10.1088/2041-8205/718/2/L194 1005.2960 ApJ (2011) 740 16 Observation of Anisotropy in the Arrival Directions of Galactic Cosmic Rays at Multiple Angular Scales with IceCube 10.1088/0004-637X/740/1/16 1105.2326 ApJ (2012) 746 33 Observation of an Anisotropy in the Galactic Cosmic Ray arrival direction at 400 TeV with IceCube 10.1088/0004-637X/746/1/33 1109.1017 ApJ (2013) 765 55 Observation of Cosmic Ray Anisotropy with the IceTop Air Shower Array 10.1088/0004-637X/765/1/55 1210.5278 ApJ (2016) 826 220 Anisotropy in Cosmic-Ray Arrival Directions in the Southern Hemisphere with Six Years of Data from the IceCube Detector 10.3847/0004-637X/826/2/220 1603.01227 ApJ (2019) 871 96 All-Sky Measurement of the Anisotropy of Cosmic Rays at 10 TeV and Mapping of the Local Interstellar Magnetic Field 10.3847/1538-4357/aaf5cc 1812.05682 ApJ (2025) Observation of Cosmic-Ray Anisotropy in the Southern Hemisphere with Twelve Years of Data Collected by the IceCube Neutrino Observatory 2412.05046

Feb 1, 2025

Using TeV Cosmic Rays to probe the Heliosphere's Boundary with the Local Interstellar Medium

The outer heliosphere regulates cosmic ray penetration into near-Earth space, reduces space radiation, and makes life possible in our solar system. Voyager and IBEX in-situ and remote observations of the outer heliosphere and the distorted local interstellar magnetic are important for heliospheric modeling. TeV cosmic rays provide a new tool to study the heliosphere interstellar medium boundary.

Jul 1, 2023