  We consider monochromatic and isotropic photon emission from circular
equatorial Kerr orbiters. We derive analytic expressions for the photon escape
probability and the redshift-dependent total flux collected on the celestial
sphere as a function of emission radius and black hole parameters. These
calculations crucially involve the critical curve delineating the region of
photon escape from that of photon capture in each emitter's sky. This curve
generalizes to finite orbital radius the usual Kerr critical curve and displays
interesting features in the limit of high spin, which we investigate by
developing a perturbative expansion about extremality. Although the innermost
stable circular orbit appears to approach the event horizon for very rapidly
spinning black holes, we find in this regime that the photon escape probability
tends to $5/12+1/(\sqrt{5}\pi)\arctan\sqrt{5/3}\approx54.65\%$. We also obtain
a simple formula for the flux distribution received on the celestial sphere,
which is nonzero. This confirms that the near-horizon geometry of a high-spin
black hole is in principle observable. These results require us to introduce a
novel type of near-horizon double-scaling limit. We explain the dip observed in
the total flux at infinity as an imprint of the black hole: the black hole
"bite".
