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