[Paper Review] Three dimensional modeling of CR propagation

Daniele Gaggero, Luca Maccione+3 more|arXiv (Cornell University)|Jun 28, 2013

Astrophysics and Cosmic Phenomena3 citations

TL;DR

This paper presents a major upgrade to the DRAGON code, introducing full 3D anisotropic diffusion modeling for cosmic ray (CR) propagation in the Galaxy, with position- and rigidity-dependent diffusion coefficients parallel and perpendicular to the regular magnetic field. For the first time, it demonstrates that the Sun's location in an interarm region, combined with enhanced energy losses, naturally steepens the electron spectrum, enabling a consistent fit to AMS-02 and PAMELA data with a primary injection index of 2.38 compatible with shock acceleration theory.

ABSTRACT

We present here a major upgrade of DRAGON, a numerical package that computes the propagation of a wide set of CR species from both astrophysical and exotic origin in the Galaxy in a wide energy range from tens of MeV to tens of TeV. DRAGON takes into account all relevant processes in particular diffusion, convection, reacceleration, fragmentation and energy losses. For the first time, we present a full 3D version of DRAGON with anisotropic position-dependent diffusion. In this version, the propagation is calculated within a 3D cartesian grid and the user is able to implement realistic and structured three dimensional source, gas and regular magnetic field distributions. Moreover, it is possible to specify an arbitrary function of position and rigidity for the diffusion coefficients in the parallel and perpendicular direction to the regular magnetic field of the Galaxy. The code opens many new possibilities in the study of CR physics. In particular, we can study for the first time the impact of the spiral arm structure on the leptonic spectra: taking into account the fact that we live in an interarm region, far from most sources, we obtain - due to increased energy losses - a steeper electron spectrum compared to the assumption of a smooth source term. We discuss the implications of these results on our understanding on leptonic spectra and we briefly mention future studies that can be performed with our new 3D code.

Motivation & Objective

• To develop a 3D, anisotropic cosmic ray propagation model that accounts for realistic Galactic structures and anisotropic diffusion.
• To address the limitations of previous models that assume isotropic diffusion and smooth source distributions.
• To investigate how the Sun's location in an interarm region affects electron and positron spectra due to enhanced energy losses.
• To reproduce high-precision electron and positron data from AMS-02 and PAMELA with a physically motivated injection spectrum.
• To enable future studies of local anisotropic diffusion and its impact on CR transport in the heliosphere and local interstellar medium.

Proposed method

• The code solves the 3D cosmic ray transport equation in Cartesian coordinates with position- and rigidity-dependent diffusion coefficients in parallel and perpendicular directions relative to the Galactic magnetic field.
• It allows arbitrary 3D distributions for CR sources, interstellar gas, and regular magnetic fields, enabling realistic modeling of spiral arms and local structures.
• The diffusion tensor is constructed from $ D_{\parallel} $, $ D_{\bot} $, and magnetic field unit vectors, with separable spatial and energy dependence.
• The code uses operator splitting and finite difference methods to numerically solve the transport equation with source, convection, reacceleration, energy losses, and fragmentation.
• It incorporates solar modulation via the HelioProp code, accounting for charge-dependent drifts and time-dependent heliospheric parameters.
• The model is tested using Green's functions for pure parallel and perpendicular diffusion, confirming numerical accuracy.

Experimental results

Research questions

• RQ1 How does the Sun's location in an interarm region affect the predicted electron spectrum due to enhanced energy losses?
• RQ2 Can a single primary electron injection spectrum with $ \gamma_0 = 2.38 $ be consistent with AMS-02 and PAMELA data when 3D source structure and energy losses are properly modeled?
• RQ3 What role does anisotropic diffusion play in shaping the high-energy cosmic ray electron spectrum in the local Galactic environment?
• RQ4 Can the observed positron fraction rise be explained without requiring a dominant, hard-spectrum extra component, given realistic 3D source distributions?
• RQ5 How do local structures such as the Local Bubble and spiral arm overdensities influence the propagation of high-energy leptons?

Key findings

• The model reproduces the AMS-02 positron fraction and PAMELA electron data with a primary electron injection index of $ \gamma_0 = 2.38 $, consistent with shock acceleration theory.
• The observed steepening of the electron spectrum at high energies is naturally explained by the Sun's location in an interarm region with enhanced energy losses, without requiring a hard-spectrum extra component.
• A secondary component with a 10 TeV cutoff and $ \gamma_0 = 1.7 $ provides a good fit to the positron fraction, with cutoffs as low as 1 TeV also yielding acceptable fits.
• The Fermi-LAT electron spectrum above 200 GeV is underpredicted by the model, suggesting a possible contribution from a nearby local source such as the Vela SNR.
• A single nearby electron accelerator with $ E_{\text{cut}} = 1~\text{TeV} $ and $ \gamma = 2.1 $ yields a good combined fit to Fermi-LAT and AMS-02 data, indicating local sources may explain the high-energy excess.