  The broadband spectrum of a BL Lac object, OJ 287, from radio to
$\gamma$-rays obtained during a major $\gamma$-ray flare detected by
\emph{Fermi} in 2009 are studied to understand the high energy emission
mechanism during this episode. Using a simple one-zone leptonic model,
incorporating synchrotron and inverse Compton emission processes, we show that
the explanation of high energy emission from X-rays to $\gamma$-rays, by
considering a single emission mechanism, namely, synchrotron self-Compton (SSC)
or external Compton (EC) requires unlikely physical conditions. However, a
combination of both SSC and EC mechanisms can reproduce the observed high
energy spectrum satisfactorily. Using these emission mechanisms we extract the
physical parameters governing the source and its environment. Our study
suggests that the emission region of OJ 287 is surrounded by a warm infrared
(IR) emitting region of $\sim 250 \, K$. Assuming this region as a spherical
cloud illuminated by an accretion disk, we obtain the location of the emission
region to be $\sim 9 pc$. This supports the claim that the $\gamma$-ray
emission from OJ 287 during the 2009 flare arises from a location far away from
the central engine as deduced from millimeter-gamma ray correlation study and
very long baseline array images.
