The steady-state gamma-ray emission from the Sun is thought to consist of two emission components due to interactions with Galactic cosmic rays: (1) a hadronic disk component, and (2) a leptonic extended component peaking at the solar edge and extending into the heliosphere. The flux of these components is expected to vary with the 11 yr solar cycle, being highest during solar minimum and lowest during solar maximum, as it varies with the cosmic-ray flux. No study has yet analyzed the flux variation of each component over solar cycles. In this work, we measure the temporal variations of the flux of each component over 15 yr of Fermi Large Area Telescope observations and compare them with the sunspot number and Galactic cosmic-ray flux from AMS-02 near Earth. We find that the flux variation of the disk anticorrelates with the sunspot number and correlates with cosmic-ray protons, as expected, confirming its emission mechanism. In contrast, the extended component exhibits a more complex variation: despite an initial anticorrelation with the sunspot number, we find neither anticorrelation with the sunspot number nor correlation with cosmic-ray electrons over the full 15 yr period. This most likely suggests that cosmic-ray transport and modulation in the inner heliosphere are unexpectedly complex and may differ for electrons and protons or, alternatively, that there is an additional, unknown component of gamma rays or cosmic rays. These findings impact space weather research and emphasize the need for close monitoring of Cycle 25 and the ongoing polarity reversal.
