  The ion foreshock is highly dynamic, disturbing the bow shock and the
magnetosphere-ionosphere system. To forecast foreshock-driven space weather
effects, it is necessary to model foreshock ions as a function of upstream
shock parameters. Case studies in the accompanying paper show that
magnetosheath ions sometimes exhibit strong field-aligned anisotropy towards
the upstream direction, which may be responsible for enhancing magnetosheath
leakage and therefore foreshock ion density. To understand the conditions
leading to such an anisotropy and the potential for enhanced leakage, we
perform case studies and a statistical study of magnetosheath and foreshock
region data surrounding ~500 THEMIS bow shock crossings. We quantify the
anisotropy using the heat flux along the field-aligned direction. We show that
the strong field-aligned heat flux persists across the entire magnetosheath
from the magnetopause to the bow shock. Ion distribution functions reveal that
the strong heat flux is caused by a secondary thermal population. We find that
stronger anisotropy events exhibit heat flux preferentially towards the
upstream direction near the bow shock and occur under larger IMF strength and
larger solar wind dynamic pressure and/or energy flux. Additionally, we show
that near the bow shock, magnetosheath leakage is a significant contributor to
foreshock ions, and through enhancing the leakage the magnetosheath ion
anisotropy can modulate the foreshock ion velocity and density. Our results
imply that likely due to field line draping and compression against the
magnetopause that leads to a directional mirror force, modeling the foreshock
ions necessitates a more global accounting of downstream conditions.
