The Eddington Limit in Cosmic Rays: An Explanation for the Observed Lack
  of Low-Mass Radio-Loud Quasars and the M_{BH}-M_{Bulge} Relation
  We present a feedback mechanism for supermassive black holes and their host
bulges that operates during epochs of radio-loud quasar activity. In the radio
cores of relativistic quasar jets, internal shocks convert a fraction of
ordered bulk kinetic energy into randomized relativistic ions, or in other
words cosmic rays. By employing a phenomenologically-motivated jet model, we
show that enough 1-100 GeV cosmic rays escape the radio core into the host
galaxy to break the Eddington limit in cosmic rays. As a result, hydrostatic
balance is lost and a cosmic ray momentum-driven wind develops, expelling gas
from the host galaxy and thus self-limiting the black hole and bulge growth.
Although the interstellar cosmic ray power is much smaller than the quasar
photon luminosity, cosmic rays provide a stronger feedback than UV photons,
since they exchange momentum with the galactic gas much more efficiently. The
amount of energy released into the host galaxy as cosmic rays, per unit of
black hole rest mass energy, is independent of black hole mass. It follows that
radio-loud jets should be more prevalent in relatively massive systems since
they sit in galaxies with relatively deep gravitational potentials. Therefore,
jet-powered cosmic ray feedback not only self-regulates the black hole and
bulge growth, but also provides an explanation for the lack of radio-loud
activity in relatively small galaxies. By employing basic known facts regarding
the physical conditions in radio cores, we approximately reproduce both the
slope and the normalization of the M_{BH}-M_{Bulge} relation.
