One answer to that is observation: eventually a nHz-GW-bright source should be localized to a bright electromagnetic source (e+e- synchrotron radiation of a jet

One answer to that is observation: eventually a nHz-GW-bright source should be localized to a bright electromagnetic source (e+e- synchrotron radiation of a jet from one member of the smbh binary, for instance). If we can't trace a bright source to an SMBHB candidate eventually, back to the drawing board. > Why not have periodically distributed dark matter Big warning: I don't do galactic dynamics! That will colour my approach to answering your question. It's a neat question though. Second big warning: in no way is this rigorous, and I won't feel bad if someone blows me up with math. Think Lorentzian rather than Euclidean. The dark matter (DM) blobs have to move around the pulsar timing array (PTA) members in order to induce longitudinal redshift and blueshift, and also (because the beamline is dragged by the other polarization) brightening and dimming. DM is famously bad at dimming background objects... DM is also really hard to compactify (you need it to couple with gravitationally collapsing hot baryons and get the latter to cool fast) and has tiny bulk viscosity. So you're going to need really weird initial conditions to get the overdensities you want in place. Cold DM is also really hard to lift to a higher gravitational potential. Around the PTA pulsars its even hard to lift baryonic clouds since our galaxy is super-quiet (no AGN outflow or feedback) and the PTA millisecond pulsars are well out of the central bulge. That ties your hands a bit on Lorentzian periodicity, and my bet is that from generic initial values you end up with a pulsar with a sparse but fat ~spherical "atmosphere" of DM. Euclidean v Lorentzian in a nutshell. Euclid: take an equilateral tetrahedron (to keep things nice and simple), spatial lengths in lightseconds (and setting c=1). You and three friends at the vertices stay put with respect to each other. Lorentz equilateral tetrahedron: put one vertex a second in the future, and its opposite side in the present. You and two friends at the vertices of that past side move at c to the future vertex. We can take you and your two friends' movement timelike and to the non-relativistic limit through rescaling. We can rotate the E vs L tetrahedra or change the areas of one or more sides so that the points trace out the worldlines of some DM masses. Thinking E-style you arrange four blobs of dark matter at the vertices of a tetrahedron around the pulsar enclosed by a (not necessarily equilateral and not necessarily unchanging in edge length or face area or volume) tetrahedron. Invites Kepler thinking. But we don't have Euclidean symmetries in our universe, we have Lorentzian ones. Thinking L-style you arrange three blobs of dark matter around the pulsar enclosed by the L-tetrahdron, and blobs and the pulsar eventually collide (that's basically Raychaudhuri's focusing theorem). Evading eventual Raychaudhuri collision is hard because there's basically no contact forces within the DM blobs or between them and the pulsar (so no outward acceleration), therefore you need to rely on vorticity to oppose collapse. And the point of the exercise is to introduce or at least mimic nonzero shear (sphere->ellipsoid), which acts against vorticity. It's not quite "CRUNCH" because the DM blobs will sail through each other and the pulsar, but the pulsar won't move the way you want and dynamical drag effects will settle the DM blobs into an atmosphere around (and through!) the pulsar. Thanks to the pulsar spin, high frequency multipole gravitational radiation from bumps on the crust and interior quakes and things (yay, pulsar glitches) will dominate the GW spectrum. Lots of wiggling, and not obviously the wiggling you want. I'm inclined to demand a description of initial conditions that leads to the wiggling you want (in-flight frequency and brightness evolution of the emitted beam), because in all honesty I don't trust my intuition that the IVs would be really non-generic in angular momentum but I'd think it's really really cool if I were wrong on the "there's no way that would work" reaction to the DM blobs mimicking nHz GW background idea. Final two things: I kept editing in and out dissipation and viscosity, because I don't do and don't want to do galactic dynamics. However, subgalactic DM overdensity blobs are unlikely to stay blobs.