Lighthouse in the dust: infrared echoes of periodic emission from massive black hole binaries

The optical and UV emission from sub-parsec massive black hole binaries (MBHBs) in active galactic nuclei (AGNs) is believed to vary periodically, on time-scales comparable to the binary's orbital time. If driven by accretion rate fluctuations, the variability could be isotropic. If dominated by relativistic Doppler modulation, the variability should instead be anisotropic, resembling a rotating forward-beamed lighthouse. We consider the infrared (IR) reverberation of either type of periodic emission by pc-scale circumbinary dust tori. We predict the phase and amplitude of IR variability as a function of the ratio of dust light crossing time to the source variability period, and of the torus inclination and opening angle. We enumerate several differences between the isotropic and anisotropic cases. Interestingly, for a nearly faceon binary with an inclined dust torus, the Doppler boost can produce IR variability without any observable optical/UV variability. Such orphan-IR variability would have been missed in optical searches for periodic AGNs. We apply our models to time-domain WISE IR data from the MBHB candidate PG 1302-102 and find consistency with dust reverberation by both isotropically emitting and Doppler-boosted sources in the shorter wavelength W1-W2 (2.8 -> 5.3 mu m) bands. We constrain the dust torus to be thin (aspect ratio similar to 0.1), with an inner radius at 1-5 pc. More generally, our dust-echo models will aid in identifying new MBHB candidates, determining their nature and constraining the physical properties of MBHBs and their dust tori.