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 (RAR) 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 RAR 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 RAR.