[Paper Review] Cosmic Ray Modulation studied with HelMod Monte Carlo tool and comparison with Ulysses Fast Scan Data during consecutive Solar Minima

P. Bobík, G. Boella+10 more|arXiv (Cornell University)|Jul 19, 2013

Solar and Space Plasma Dynamics3 citations

TL;DR

This study uses the HelMod 2D Monte Carlo code to simulate cosmic ray modulation during consecutive solar minima (2006–2009), incorporating time-dependent diffusion parameters derived from neutron monitors and including magnetic drift effects. The model successfully reproduces observed proton and electron latitudinal intensity gradients in the heliosphere, demonstrating that particle charge and interplanetary magnetic field polarity (qA > 0 vs. qA < 0) control the anisotropic penetration of cosmic rays into polar regions.

ABSTRACT

The Cosmic Rays propagation was studied in details using the HelMod-2D Monte Carlo code, that includes a general description of the diffusion tensor, and polar magnetic-field. The Numerical Approach used in this work is based on a set of Stochastic Differential Equations fully equivalent to the well know Parker Equation for the transport of Cosmic Rays. In our approach the Diffusion tensor in the frame of the magnetic field turbolence does not depends explicitly by Solar Latitude but varies with time using a diffusion parameter obtained by Neutron Monitors. The parameters of the Model were tuned using data during the solar Cycle 23 and Ulysses latitudinal Fast Scan in 1995. The actual parametrization is able to well reproduce the observed latitudinal gradient of protons and the southward shift of the minimum of latitudinal intensity. The description of the model is also available online at website www.helmod.org. The model was then applied on Pamela/Ulysses proton intensity from 2006 up to 2009. The model during this 4-year continous period agree well with both PAMELA (at 1 AU) and Ulysses data (at various solar distance and solar latitude). The agreement improves when considering the ratio between this data. Studies done also with particles with different charge (e.g. electrons) allow us to explain the presence (or not) of protons and electrons latitudinal gradients observed by Ulysses during the Latitudinal Fast Scan in 1995 and 2007.

Motivation & Objective

• To extend the HelMod Monte Carlo model beyond the ecliptic plane to study cosmic ray modulation during solar minima.
• To validate the model against Ulysses fast-scan data from 2006–2009 and PAMELA measurements at 1 AU.
• To investigate the role of magnetic drift and interplanetary magnetic field polarity in shaping latitudinal cosmic ray intensity gradients.
• To determine whether the model can reproduce the observed asymmetry in proton and electron intensity gradients during opposite IMF polarity phases.
• To assess the influence of particle charge and rigidity on cosmic ray distribution across heliospheric latitudes.

Proposed method

• Numerical solution of the Parker transport equation via a stochastic differential equation approach using the HelMod Monte Carlo code.
• Incorporation of time-dependent diffusion coefficients derived from neutron monitor data, with radial dependence ∝ r and rigidity dependence ∝ P/1 GV.
• Inclusion of magnetic drift velocity components (radial, latitudinal, and neutral sheet drift) scaled by the tilt angle of the heliospheric current sheet.
• Use of a 2D (radial and co-latitude) heliospheric geometry with boundary conditions at 100 AU and inward integration to Earth’s orbit.
• Simulation of proton and electron intensities at 1.7 GV rigidity across Ulysses’ orbit, normalized to Earth-orbit values and averaged at the south pole.
• Comparison of model outputs with Ulysses KET and PAMELA data, focusing on relative intensity ratios to minimize systematic errors.

Experimental results

Research questions

• RQ1 How well does the HelMod Monte Carlo model reproduce the latitudinal gradient of cosmic ray proton intensities observed by Ulysses during the 2006–2009 solar minimum?
• RQ2 What is the role of magnetic drift in shaping the anisotropic distribution of cosmic rays across heliospheric latitudes?
• RQ3 How does the sign of the product of particle charge and interplanetary magnetic field polarity (qA) affect cosmic ray penetration into polar regions?
• RQ4 Can the model reproduce the observed reversal of the latitudinal intensity gradient between protons and electrons at the same rigidity?
• RQ5 How does the model's performance compare to observational data during opposite IMF polarity phases (A > 0 and A < 0) in the 2007 fast scan?

Key findings

• The HelMod model successfully reproduces the observed latitudinal gradient of proton intensities during the 2006–2009 solar minimum, with good agreement to Ulysses and PAMELA data.
• For protons at 1.7 GV rigidity, the model predicts no significant latitudinal gradient when drift effects are excluded, but a strong gradient emerges when drifts are included.
• When particle charge and IMF polarity are considered (qA > 0), the model predicts enhanced cosmic ray penetration into the polar regions, consistent with observations during the 2007 fast scan.
• For electrons at the same rigidity, the model predicts a reversed gradient compared to protons, confirming the charge-dependent modulation effect observed by Ulysses.
• The model shows that the condition qA > 0 favors polar access for cosmic rays, while qA < 0 leads to a more uniform distribution across latitudes.
• The ratio of Ulysses to Earth-orbit intensities is well reproduced by the model, with normalized values close to unity at closest approach, confirming robustness against systematic errors.