The External Field Dominated Solution In QUMOND & AQUAL: Application To Tidal Streams

Abstract

The standard $\Lambda$CDM paradigm seems to describe cosmology and large scale structure formation very well. However, a number of puzzling observations remain on galactic scales. An example is the anisotropic distribution of satellite galaxies in the Local Group. This has led to suggestions that a modified gravity theory might provide a better explanation than Newtonian gravity supplemented by dark matter. One of the leading modified gravity theories is Modified Newtonian Dynamics (MOND). For an isolated point mass, it boosts gravity by an acceleration-dependent factor of $\nu$. Recently, a much more computer-friendly quasi-linear formulation of MOND (QUMOND) has become available. We investigate analytically the solution for a point mass embedded in a constant external field of ${\mathbf{g}}_{ext}$. We find that the potential is $\Phi =-\frac{GM{\nu }_{ext}}{r}\left(1+\frac{K_0}{2}{\sin }^2\theta \right)$, where $r$ is distance from the mass $M$ which is in an external field that `saturates' the $\nu$ function at the value ${\nu }_{ext}$, leading to a fixed value of $K_0\equiv \frac{\partial Ln\nu }{\partial Ln{g}_{ext}}$. In a very weak gravitational field $\left(\left|{\mathbf{g}}_{ext}\right|\ll a_0\right)$, $K_0=-\frac{1}{2}$. The angle $\theta$ is that between the external field direction and the direction towards the mass. Our results are quite close to the more traditional aquadratic Lagrangian (AQUAL) formulation of MOND. We apply both theories to a simple model of the Sagittarius tidal stream. We find that they give very similar results, with the tidal stream seeming to spread slightly further in AQUAL.

5 pages, 2 figures, 1 table. References updated, typos fixed

Cited by in corpus (9)

• Declining rotation curves of galaxies as a test of gravitational theory
• Testing Gravity with wide binary stars like $\alpha$ Centauri
• Origin of the Local Group satellite planes
• Testing Modified Gravity Theories via Wide Binaries and GAIA
• A Plane of High Velocity Galaxies Across the Local Group
• Probing the radial acceleration relation and the strong equivalence principle with the Coma cluster ultra-diffuse galaxies
• The Kennicutt-Schmidt law and the main sequence of galaxies in Newtonian and Milgromian dynamics
• The underlying radial acceleration relation
• Distinguishing Standard from Modified Gravity in the Local Group and beyond