[Paper Review] Antiproton modulation in the Heliosphere and AMS-02 antiproton over proton ratio prediction

P. Bobík, M. Boschini+7 more|arXiv (Cornell University)|Feb 1, 2011

Solar and Space Plasma Dynamics28 references3 citations

TL;DR

This study presents a quasi time-dependent 2D stochastic model of cosmic ray modulation in the heliosphere, using stochastic differential equations to simulate antiproton and proton transport. The model successfully reproduces the observed antiproton-to-proton ratio using identical heliospheric parameters, predicting a good agreement with BESS-97 and PAMELA data and forecasting for AMS-02.

ABSTRACT

We implemented a quasi time-dependent 2D stochastic model of solar modulation describing the transport of cosmic rays (CR) in the heliosphere. Our code can modulate the Local Interstellar Spectrum (LIS) of a generic charged particle (light cosmic ions and electrons), calculating the spectrum at 1AU. Several measurements of CR antiparticles have been performed. Here we focused our attention on the CR antiproton component and the antiproton over proton ratio. We show that our model, using the same heliospheric parameters for both particles, fit the observed anti-p/p ratio. We show a good agreement with BESS-97 and PAMELA data and make a prediction for the AMS-02 experiment.

Motivation & Objective

• To develop a quasi time-dependent 2D stochastic model of cosmic ray transport in the heliosphere, accounting for solar modulation effects.
• To simulate the modulation of antiprotons and protons using the same heliospheric parameters to test consistency in the antiproton-to-proton ratio.
• To validate the model against existing experimental data from BESS-97 and PAMELA on the antiproton flux and ratio.
• To provide a prediction for the antiproton-to-proton ratio at 1 AU as measured by the AMS-02 experiment.

Proposed method

• The model solves the Parker equation via stochastic differential equations (SDEs) to simulate particle transport in the heliosphere.
• The SDEs include radial and latitudinal diffusion, convection by the solar wind, adiabatic energy loss, and drifts due to magnetic field gradients and curvature.
• The model incorporates a tilted heliospheric current sheet and includes both regular and neutral sheet drifts, with rigidity-dependent diffusion coefficients.
• The radial and latitudinal diffusion coefficients are derived from parallel diffusion, with perpendicular components scaled by rigidity-dependent factors.
• The integration uses a time step proportional to $ r^2 $ to optimize computational efficiency in the outer heliosphere.
• The model uses measured solar wind velocity, tilt angle, and estimated diffusion parameters ($ k_0 $) to simulate particle spectra at 1 AU.

Experimental results

Research questions

• RQ1 Can a single set of heliospheric parameters simultaneously reproduce the observed antiproton-to-proton ratio across different energy ranges?
• RQ2 How well does the 2D stochastic model with drift and diffusion effects reproduce the BESS-97 and PAMELA measurements of the antiproton flux and ratio?
• RQ3 What is the predicted antiproton-to-proton ratio at 1 AU as measured by AMS-02 under the same modulation conditions?
• RQ4 How do solar modulation effects, including drift and convection, influence the energy spectrum of antiprotons relative to protons?

Key findings

• The model achieves good agreement with BESS-97 and PAMELA data for the antiproton-to-proton ratio across the energy range from ~60 MeV to ~180 GeV.
• The same heliospheric parameters (solar wind velocity, tilt angle, and diffusion coefficient $ k_0 $) successfully describe the modulation of both antiprotons and protons.
• The inclusion of both regular and neutral sheet drifts significantly improves the model's ability to reproduce observed latitudinal and energy-dependent gradients.
• The model predicts a stable antiproton-to-proton ratio at 1 AU that aligns with the expected AMS-02 measurement, supporting the consistency of the solar modulation framework.
• The use of a variable perpendicular diffusion coefficient, increasing toward the poles, improves the reproduction of observed proton and electron latitudinal gradients.
• The simulation results confirm that the antiproton-to-proton ratio is robustly modulated by solar activity, with minimal dependence on particle charge beyond the modulation parameters.