Probing solar modulation analytic models with cosmic ray periodic spectra
Physical Review D(2024)
Abstract
The AMS02 experiment has published the periodic spectra of proton, helium and
helium isotopes across the majority of the 24 solar cycle. These precise data
exhibit temporal structures that correlate with solar modulation. In this
study, we utilize these data to probe three analytic solar modulation models,
including the force-field approximation, the convection-diffusion model and the
extended force-field approximation with a drift effect. We adopt a method that
eliminates the influence of interstellar cosmic ray spectra, and use the
Earth-observed spectra at time t_1 to predict those at time t_2. In order
to explore the rigidity-dependence of solar modulation models, we substitute
the conventional potential parameter ϕ with a modified parameter
ϕ'=R/ k_2(R)ϕ for our analysis. Combining with the χ^2
minimization method, the best-fit modulation parameter ϕ' can be
evaluated. First, we test the validity of a rigidity-independent ϕ' and
find that both the force-field approximation (FFA) and the extended force-field
approximation (EFFA) agree well with data near the solar minimum period.
However, all models significantly deviate from the data during the solar
maximum. Consequently, we assume a constant ϕ'(t_1) at solar minimum and
calculate Δϕ'=ϕ'(t_2)-ϕ'(t_1) for each rigidity bin at time
t_2. It is found that Δϕ' generally adheres to a linear-logarithm
relationship with rigidity at any given time. By adopting a linear-logarithm
formula of Δϕ', we further discover that both the modified FFA and
EFFA can reconcile the observations during solar maxima. This suggests that at
solar maximum, the parameter ϕ', which correlates with the diffusion
pattern in the heliospheric magnetic fields, exhibits a rigidity dependence.
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