The global features of the modulation of galactic cosmic ray protons and helium nuclei in a very quiet heliosphere are studied with a comprehensive, three-dimensional, drift model and compared to proton and helium observations measured by PAMELA from 2006 to 2009. Combined with accurate very local interstellar spectra (VLIS) for protons and helium nuclei, this provides the opportunity to study in detail how differently cosmic ray species with dissimilar mass-to-charge ratio ( $A/Z$ ) are modulated down to a few GV. The effects at Earth of the difference in their VLIS’s and those caused by the main modulation mechanisms are illustrated. We find that both the PAMELA proton and helium spectra are reproduced well with the numerical model, assuming the same set of modulation parameters and diffusion coefficients. A comparative study of 3He2 (He-3) and 4He2 (He-4) modulated spectra reveals that they do not undergo identical spectral changes below 3 GV mainly due to differences in their VLIS’s. This result is important to uncover and investigate the effects on the proton to total helium ratio ( $p$ /He) caused by the difference in their VLIS’s and those by $A/Z$ . The computed $p$ /He displays three modulation regimes, reflecting the complex interplay of modulation processes in the heliosphere. At rigidities above ∼3 GV, the $p$ /He ratio at the Earth is found to deviate modestly from a value of ∼5.5, largely independent of the assumed modulation conditions. This result indicates that the PAMELA measurement of $p$ /He reveals at these rigidities the shapes of their VLIS’s. Below ∼0.6 GV, $p$ /He increases with decreasing rigidity from 2006 to 2009 and significant variations are predicted depending on the assumed solar modulation conditions. This result indicates that as modulation levels decreased from 2006 to 2009, the contribution of adiabatic energy changes dissipated faster for protons than for helium nuclei at the same rigidity mainly due to different slopes of their VLIS’s. The differences between modulation effects for protons and helium are found to be the consequence of how the combined interplaying modulation mechanisms in the heliosphere affect the modulated spectra based on their $A/Z$ and particularly on their VLIS’s.

中文翻译：

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与 PAMELA 在 2006 年至 2009 年间的观测相关的银河质子和氦核的太阳调制的 3D 数值模拟

使用全面的三维漂移模型研究了在非常安静的日光层中银河宇宙射线质子和氦核调制的全局特征，并与 PAMELA 在 2006 年至 2009 年期间测量的质子和氦观测值进行了比较。结合准确的非常质子和氦核的局部星际光谱 (VLIS)，这提供了详细研究具有不同质荷比 ($A/Z$) 的不同宇宙射线物种如何被调制到几个 GV 的机会。说明了它们的 VLIS 差异和主要调制机制引起的差异在地球上的影响。我们发现 PAMELA 质子和氦光谱都可以用数值模型很好地再现，假设调制参数和扩散系数相同。对 3He2 (He-3) 和 4He2 (He-4) 调制光谱的比较研究表明，它们在低于 3 GV 的情况下不会发生相同的光谱变化，这主要是由于它们的 VLIS 的差异。这一结果对于揭示和研究由 VLIS 和 $A/Z$ 的差异对质子与总氦比 ($p$/He) 的影响很重要。计算出的 $p$ /He 显示了三种调制方式，反映了日光层中调制过程的复杂相互作用。在刚度高于~3 GV 时，发现地球上的 $p$/He 比值略微偏离 ~5.5，很大程度上与假设的调制条件无关。该结果表明，$p$/He 的 PAMELA 测量揭示了在这些刚性下其 VLIS 的形状。低于~0.6 GV，$p$ /He 从 2006 年到 2009 年随着刚性的降低而增加，并且根据假定的太阳能调制条件预测会有显着变化。该结果表明，从 2006 年到 2009 年，随着调制水平的降低，质子的绝热能变化的贡献比相同刚度的氦原子核耗散得更快，这主要是由于其 VLIS 的斜率不同。质子和氦的调制效应之间的差异被发现是日球层中组合的相互作用调制机制如何影响基于它们的 A/Z 的调制光谱的结果，特别是它们的 VLIS。在相同刚度下，质子的绝热能量变化的贡献比氦原子核耗散得更快，这主要是由于它们的 VLIS 的斜率不同。质子和氦的调制效应之间的差异被发现是日球层中组合的相互作用调制机制如何影响基于它们的 A/Z 的调制光谱的结果，特别是它们的 VLIS。在相同刚度下，质子的绝热能量变化的贡献比氦原子核耗散得更快，这主要是由于它们的 VLIS 的斜率不同。质子和氦的调制效应之间的差异被发现是日球层中组合的相互作用调制机制如何影响基于它们的 A/Z 的调制光谱的结果，特别是它们的 VLIS。