On the evidence of a dark matter density spike around the primary black hole in OJ 287

Abstract: The central engine of blazar OJ~287 is arguably the most notable supermassive black hole (SMBH) binary candidate that emits nano-Hertz (nHz) gravitational waves. This inference is mainly due to our ability to predict and successfully monitor certain quasi-periodic doubly peaked high brightness flares with a period of $\sim$12 years from this blazer. The use of post-Newtonian accurate SMBH binary orbital description that includes the effects of higher order GW emission turned out to be a crucial ingredient for accurately predicting the epochs of such Bremsstrahlung flares in our SMBH binary central engine description for OJ~287. It was very recently argued that one should include the effects of dynamical friction, induced by certain dark matter density spikes around the primary SMBH, to explain the {\it observed} decay of SMBH binary orbit in OJ~287. Invoking binary pulsar timing-based arguments, measurements, and OJ~287's orbital description, we show that observationally relevant SMBH binary orbital dynamics in OJ~287 are insensitive to dark matter-induced dynamical friction effects. This implies that we could only provide an upper bound on the spike index parameter rather than obtaining an observationally derived value, as argued by \cite{Chan2024}.