Probing solar modulation analytic models with cosmic ray periodic spectra

The AMS02 experiment has published the periodic spectra of proton, helium, and helium isotopes across the majority of solar cycle 24. 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 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. with a modified parameter phi ' = R/k(2)(R)phi for our analysis. Combined with the chi(2) minimization method, the best-fit modulation parameter phi ' can be evaluated. First, we test the validity of a rigidity-independent phi ' 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 phi '(t(1)) at solar minimum and calculate Delta phi ' = phi '(t(2)) - phi '(t(1)) for each rigidity bin at time t(2). It is found that Delta phi ' generally adheres to a linearlogarithm relationship with rigidity at any given time. By adopting a linear-logarithm formula of Delta phi ', 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 phi ', which correlates with the diffusion pattern in the heliospheric magnetic fields, exhibits a rigidity dependence. Moreover, the modified EFFA enhances the concordance with data during periods of pronounced dips, as observed by AMS02. This implies that the drift effect could significantly contribute to these solar transient phenomena.