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 (AGN) is believed to vary periodically, on
timescales 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 face-on 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 AGN. 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 micrometer)
bands. We constrain the dust torus to be thin (aspect ratio ~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.
