Recovery of 150-250 MeV Cosmic Ray Proton Intensities Between 2004-2010 as Measured Near the Earth, at Voyager 2 and also in the Heliosheath at Voyager 1 - A Two Zone Heliosphere

The recovery of cosmic ray protons of energy ~150-250 MeV/nuc in solar cycle #23 from 2004 to 2010 has been followed at the Earth using IMP, ACE and balloon data and also at V2 between 74-92 AU and at V1 beyond the heliospheric termination shock (91-113 AU). The correlation coefficient between the intensities the Earth and V1 during this time period, is 0.936, allowing for a ~0.9 year delay due to the solar wind propagation time from the Earth to the outer heliosphere. To describe these intensity changes and to predict the absolute intensities measured at all three locations we have used a simple spherically symmetric (no drift) two-zone heliospheric transport model with specific values for the diffusion coefficient in both the inner and outer zones. The diffusion coefficient in the outer zone, from about 90 to 120 (130) AU, is determined to be ~5-10 times smaller than that in the inner zone out to 90 AU. This means that the outer zone acts much like a diffusing barrier in this model. The absolute magnitude of the intensities and the intensity changes at V1 and the Earth are described to within a few percent by a diffusion coefficient that varies with time by a factor ~4 in the inner zone and only ~1.8 (1.25) in the outer zone over the time period from 2004-2010. These diffusion coefficients and their variations are essentially the same as those derived earlier from a similar study using He nuclei of the same energy. This model and the diffusion coefficients used provide a total modulation potential at the Earth ~250 MV in 2009. The difference ~10-20% between calculated and observed intensities at V2 can be explained if the heliosphere is squashed by ~10% in distance (non-spherical) so that the HTS is closer to the Sun in the direction of V2 compared to V1.

💡 Research Summary

The paper investigates the recovery of 150‑250 MeV galactic cosmic‑ray (GCR) protons during solar cycle 23 (2004‑2010) as observed at three locations: near Earth (using IMP‑8, ACE, and balloon data), Voyager 2 (V2) between 74‑92 AU, and Voyager 1 (V1) beyond the heliospheric termination shock (HTS) between 91‑113 AU. A strong correlation (r = 0.936) is found between Earth and V1 intensities when a propagation delay of ~0.9 yr (the solar‑wind travel time) is applied, indicating that the modulation pattern propagates coherently throughout the heliosphere.

To interpret these observations, the authors employ a simple spherically symmetric, drift‑free, two‑zone transport model. The inner zone extends from the Sun to ~90 AU (approximately the average HTS distance) and the outer zone from ~90 AU to an outer boundary taken as 120 AU (or 130 AU in an alternative case) representing the heliosheath up to the heliopause. The diffusion coefficient is separated into a rigidity‑dependent part K₁(P) and a radial part K₂(r). In the inner zone K₁ varies with time by a factor of about 4, while in the outer zone it varies only by a factor of ~1.8 (or 1.25). Crucially, the absolute value of the diffusion coefficient in the outer zone is 5‑10 times smaller than in the inner zone, so the outer heliosheath acts as a diffusive barrier.

The local interstellar spectrum (LIS) used is the Webber‑Higbie (2009) parametrization, which at 200 MeV yields an intensity of ~9.8 (p m⁻² sr⁻¹ s⁻¹ MeV⁻¹). With the chosen diffusion parameters the model reproduces the Earth intensity in 2009 with a total modulation potential of ~250 MV, consistent with the unusually low solar activity of that year. At V1 (≈114 AU) the calculated intensity is within a few percent of the measured value (≈7.6 units), i.e., about 25 % below the LIS. At V2 the model underestimates the observed intensity by 10‑20 %. This discrepancy can be largely removed by assuming a modest north‑south asymmetry of the heliosphere: a ~10 % squashing in the V2 direction brings the HTS closer to the Sun, effectively reducing the radial distance that particles must traverse.

The authors demonstrate that a single‑zone model cannot simultaneously fit the Earth, V1, and V2 data; the inner‑zone diffusion alone would predict too rapid a recovery at V1, while an outer‑zone‑only model would miss the Earth’s modulation depth. The two‑zone approach, with a much smaller diffusion coefficient in the heliosheath, successfully captures the observed intensity gradients and temporal evolution. Sensitivity tests show that modest adjustments (≈10 %) to the diffusion coefficients or the outer boundary radius (120 AU vs. 130 AU) can fine‑tune the fit, especially for V2.

Key insights from the study are: (1) The heliosheath functions as a significant diffusive barrier, limiting the propagation of GCRs from the interstellar medium into the inner heliosphere. (2) Temporal changes in solar activity primarily affect the inner‑zone diffusion coefficient, producing a factor‑four variation, whereas the outer‑zone coefficient changes more modestly, leading to a smoother, delayed response at large heliocentric distances. (3) The observed offset between V1 and V2 intensities is best explained by a non‑spherical heliosphere, with a ~10 % north‑south compression, rather than by changes in the diffusion parameters alone.

These results have important implications for space‑weather forecasting, radiation risk assessment for deep‑space missions, and the development of more realistic heliospheric transport models that incorporate spatially varying diffusion and heliospheric asymmetries. By quantifying the diffusion barrier properties of the heliosheath, the work provides a framework for predicting how future solar cycles will modulate GCR intensities throughout the solar system, which is essential for planning long‑duration interplanetary and interstellar missions.