Periodically modulated FRB as extreme mass ratio binaries

The activity of at least one repeating fast radio burst (FRB) source is periodically modulated. If this modulation is the result of precession of the rotation axis and throat of an accretion disc around a black hole, driven by a companion that is also the source of accreted mass, then it may be possible to constrain the mass of the black hole. The dynamics is analogous to that of superorbital periods in ordinary mass-transfer binaries in which the accreting object may be a stellar-mass black hole, a neutron star or a white dwarf, but in the FRB source it may be an intermediate-mass black hole. In a semidetached (mass-transferring) binary, the orbital period is nearly proportional to the -1/2 power of the mean density of the mass-losing star and nearly independent of the mass of the primary, but the ratio of precessional to orbital periods scales approximately as the -2/3 power of the mass ratio for small mass ratios (massive accretors). Assuming a value for the secondary's density and identifying the observed modulation period as a disc precession period would determine the mass ratio and the mass of the black hole. This model and magnetar-SNR (supernova remnant) models make distinguishable predictions of the evolution of the rotation measure that may soon be tested in FRB 121102.