A super-massive black hole ( SMBH ) binary in the core of the blazar OJ 287 has been invoked in previous works to explain its observed optical flare quasi-periodicity .
Following this picture , we investigate a hadronic origin for the X-ray and \gamma -ray counterparts of the December 2015 major optical flare of this source .
An impact outflow must result after the lighter SMBH ( the secondary ) , crosses the accretion disc of the heavier one ( the primary ) .
We then consider acceleration of cosmic-ray ( CR ) protons in the shock driven by the impact outflow as it expands and collides with the active galactic nucleus ( AGN ) wind of the primary SMBH .
We show that the emission of these CRs can reproduce the X-ray and \gamma -ray flare data self-consistently with the the optical component of the December 2015 major flare .
We derive different emission profiles explaining the observed flare data having magnetic fields in the range B = 0.3 - 3 G in the emission region and power-law indices of q = 2.2 - 2.4 for the energy distribution of the emitting CRs .
The mechanical luminosity of the AGN wind represents \lesssim 10 \% of the mass accretion power of the primary SMBH in all the derived emission profiles .