  Galactic cosmic rays (GCRs), the highly energetic particles that may raise
critical health issues for astronauts in space, are modulated by solar activity
with their intensity lagging behind the sunspot number (SSN) variation by about
one year. Previously, this lag has been attributed to a combined effect of
outward convecting solar wind and inward propagating GCRs. However, the lag's
amplitude and its solar-cycle dependence are still not fully understood (Ross &
Chaplin, 2019). By investigating the solar surface magnetic field, we find that
the source of heliospheric magnetic field -- the open magnetic flux on the Sun,
already lags behind SSN before it convects into heliosphere along with the
solar wind. The delay during odd cycles is longer than that during sequential
even cycles. Thus, we propose that the GCR lag is primarily due to the greatly
late opening of the solar magnetic field with respect to SSN, though solar wind
convection and particle transport in the heliosphere also matter. We further
investigate the origin of the open flux from different latitudes of the Sun and
found that the total open flux is significantly contributed by that from low
latitudes where coronal mass ejections frequently occur and also show an
odd-even cyclic pattern. Our findings challenge existing theories, and may
serve as the physical basis of long-term forecasts radiation dose estimates for
manned deep-space exploration missions.
