  An intergalactic magnetic field stronger than $3\times10^{-13}$~G would
explain the lack of a bright, extended degree-scale, GeV-energy inverse Compton
component in the gamma-ray spectra of TeV-blazars. A robustly predicted
consequence of the presence of such a field is the existence of degree-scale
GeV-energy gamma-ray halos -- gamma-ray bow ties -- about TeV-bright active
galactic nuclei, corresponding to more than half of all radio galaxies.
However, the emitting regions of these halos are confined to and aligned with
the direction of the relativistic jets associated with gamma-ray sources. Based
on the orientation of radio jets, we align and stack corresponding degree-scale
gamma-ray images of isolated Fanaroff-Riley class I and II objects and exclude
the existence of these halos at overwhelming confidence, limiting the
intergalactic field strength to $<10^{-15}$~G for large-scale fields and
progressively larger in the diffusive regime when the correlation length of the
field becomes small in comparison to 1 Mpc. When combined with prior limits on
the strength of the intergalactic magnetic field, this excludes a purely
magnetic explanation for the absence of halos. Thus, it requires the existence
of novel physical processes that preempt the creation of halos, e.g., the
presence of beam-plasma instabilities in the intergalactic medium or a drastic
cutoff of the very high energy spectrum of these sources.
