  OAO 1657-415 is an atypical supergiant X-ray binary among wind-fed and
disk-fed systems, showing alternate spin-up/spin-down intervals lasting on the
order of tens of days. We study different torque states of OAO 1657-415 based
on the spin history monitored by {\it Fermi}/GBM, together with fluxes from
{\it Swift}/BAT and {\it MAXI}/GSC. Its spin frequency derivatives are well
correlated with {\it Swift}/BAT fluxes during rapid spin-up episodes,
anti-correlated with {\it Swift}/BAT fluxes during rapid spin-down episodes,
and not correlated in between. The orbital profile of spin-down episodes is
reduced by a factor of 2 around orbital phases of 0.2 and 0.8 compared to that
of spin-up episodes. The orbital hardness ratio profile of spin-down episodes
is also lower than that of spin-up episodes around phases close to the
mid-eclipse, implying that there is more material between the neutron star and
the observer for spin-down episodes than for spin-up episodes around these
phases. These results indicate that the torque state of the neutron star is
connected with the material flow on orbital scale and support the
retrograde/prograde disk accretion scenario for spin-down/spin-up torque
reversal.
