Dark Matter Constraints from the Eccentric Supermassive Black Hole Binary OJ 287

OJ 287 is a binary system containing a 18 billion solar mass primary black hole accompanied by
a 150 million solar mass secondary black hole in an eccentric orbit, which triggers electromagnetic
flares twice in every 12 year orbital period when it traverses the accretion disk of the primary.
The times of these emissions are consistent with the predictions of general relativity calculated to
the 4.5th post-Newtonian order. The orbit of the secondary black hole samples the gravitational
field at distances between O(10) and O(50) Schwarzschild radii around the primary, and hence is
sensitive to the possible presence of a dark matter spike around it. We find that the agreement
of general-relativistic calculations with the measured timings of flares from OJ 287 constrains the
mass of such a spike to < 3% of the primary mass, and discuss the prospects for refining this
constraint via observations of the next flare, which is expected later in July 2022.