The Radial Acceleration Relation and a Magnetostatic Analogy in
  Quasilinear MOND
  Recently a remarkable relation has been demonstrated between the observed
radial acceleration in disk galaxies and the acceleration predicted on the
basis of baryonic matter alone. Here we study this relation within the
framework of the modified gravity model MOND. The field equations of MOND
automatically imply the radial acceleration relation for spherically symmetric
galaxies, but for disk galaxies deviations from the relation are expected. Here
we investigate whether these deviations are of sufficient magnitude to bring
MOND into conflict with the observed relation. In the quasilinear formulation
of MOND, to calculate the gravitational field of a given distribution of
matter, an intermediate step is to calculate the "pristine field", which is a
simple nonlinear function of the Newtonian field corresponding to the same
distribution of matter. Hence, to the extent that the quasilinear gravitational
field is approximately equal to the pristine field, the radial acceleration
relation will be satisfied. We show that the difference between the quasilinear
and pristine fields obeys the equations of magnetostatics, the curl of the
pristine field serves as the source for the difference in the two fields, much
as currents serve as sources for the magnetic field. Using the magnetostatic
analogy we numerically study the difference between the pristine and
quasilinear fields for simple model galaxies with a Gaussian profile. Our
principal finding is that the difference between the fields is small compared
to the observational uncertainties and that quasilinear MOND is therefore
compatible with the observed radial acceleration relation.
