Gravitational Waves from a Supermassive Black Hole Binary in M87?

This paper showed up on the arXiv last week: Gravitational Waves from a Supermassive Black Hole Binary in M87 (Yonemaru et al.). The authors posit that the supermassive black hole (SMBH) hosting AGN activity near the core of the giant elliptical galaxy M87 (I'll call this the primary black hole) may be in a binary with another large black hole. If this is the case, since M87 is less than 20 megaparsecs away, it may be an enticing source of gravitational waves detectable by pulsar timing arrays (PTAs).

The argument that the primary black hole is in a binary is based on the AGN activity originating approximately a parsec from the centroid of the galaxy. It is feasible that this offset is caused by the perturbative influence of other massive black holes in the galactic core, but it could also be because of a kick from a previous black hole merger or a rocket like thrust from an asymmetric relativistic jet.

If you suppose that the offset is because the primary black hole is in a binary, it has to be a pretty wide, long-period orbit to account for the scale of the offset---like a 2000 year orbital period. This would lead to a 1000 year gravitational wave period which is much, much longer than the 10-year spans of modern PTA data sets. With this in mind, the authors make the perfectly reasonable approximation that any gravitational waves from this hypothetical system can be well approximated as having a linear dependence on time. They then go about making estimates for the scale of the time derivative of the gravitational waves ($\dot{h}$) from this system for a variety of semi-plausible companion parameters (see the figure below).

Figure 3 from Yonemaru et al.

What would a linearly changing gravitational wave look like in a PTA experiment? For every pulsar you're observing, the gravitational wave would cause the apparent rotational frequency of the pulsar to drift linearly in time. The rate of the drift would be proportional to $\dot{h}$ and some projection factors that vary from pulsar to pulsar. If this drift were to go on for the entire 10-year span of the PTA experiment, the rotational frequency of some pulsars could change by as much as a part in $10^{16}$ or $10^{15}$ (see the right axis of the figure). The magnitude of this change is right in the ballpark of what PTA papers typically say are needed to make a detection. Sounds good.

But, there is a major flaw with all of this. Pulsar rotational frequencies slowly change all by themselves without the intervention of gravitational waves. In fact, shortly after the discovery of pulsars, Tommy Gold predicted that the rotational frequency of pulsars should decrease slowly in time. It was an important prediction that, when confirmed, helped support the idea that pulsars were rapidly rotating highly magnetized compact objects. Unfortunately, there is no way to assess the rate of change of a pulsars rotational frequency a priori, so to do high-precision pulsar timing, we fit out linear (and sometimes higher order) trends in the rotational frequency. There is no way for the linear-in-time gravitational waves these authors discuss to ever be differentiated from perfectly vanilla pulsar behavior. It's a really basic fact of pulsar timing. As a pretty solid rule of thumb, never trust a claim that PTAs can detect gravitational waves with frequencies well below the inverse of the PTA's data span.