Generalizations of Quasilinear MOND (QUMOND)

Abstract

I present a class of theories that generalize quasilinear MOND (QUMOND). Like QUMOND, these GQUMOND theories require solving only the linear Poisson equation (twice). Unlike QUMOND, their Lagrangian depends on higher derivatives of the Newtonian potential. They thus dictate different "phantom" densities as virtual sources in the Poisson equation for the MOND potential. These theories might open new avenues to more fundamental theories, and have much heuristic value. I use them to demonstrate that even within limited classes of modified-gravity formulations of MOND, theories can differ substantially on lower-tier MOND predictions. Such GQUMOND theories force, generically, the introduction of dimensioned constants other than the MOND acceleration, $a_0$, such as a length, a frequency, etc. As a result, some of these theories reduce to QUMOND itself only, e.g., on length scales (or, in other versions, dynamical times) larger than some critical value. But in smaller systems (or, alternatively, in ones with shorter dynamical times), MOND effects are screened, even if their internal accelerations are smaller than $a_0$. In such theories it is possible that MOND (expressed as QUMOND) applies on galactic scales, but its departures from Newtonian dynamics are substantially suppressed in some subgalactic systems -- such as binary stars, and open, or globular star clusters. The same holds for the effect of the galactic field on dynamics in the inner solar system, which can be greatly suppressed compared with what QUMOND predicts. Tidal effects of a galaxy on smaller subsystems are the same as in QUMOND, for the examples I consider. I also describe briefly versions that do not involve dimensioned constants other than $a_0$, and yet differ from QUMOND in important ways.