A new scale in the quasi-static limit of Aether Scalar Tensor Theory

One of the aims of Aether Scalar Tensor Theory (AeST) is to reproduce the successes of Modified Newtonian Dynamics (MOND) on galactic scales. Indeed, the quasi-static limit of AeST achieves precisely this, assuming that the vector field $\vec{A}$ vanishes and that the so-called ghost condensate can be neglected. The effects of the ghost condensate were investigated in detail in previous studies. Here, we focus on the assumption of a vanishing vector field. We argue that this assumption is not always justified and show how to correctly take into account the vector field, finding that the quasi-static limit depends on a model parameter $m_\times$. In the limit $m_\times \to 0$, one recovers the quasi-static limit with a vanishing vector field. In particular, one finds a two-field version of MOND. In the opposite limit, $m_\times \to \infty$, one finds a single-field version of MOND. We show that, in practice, much of the phenomenology of the quasi-static limit depends only very little on the value of $m_\times$. Still, for some observational tests, such as those involving wide binaries, $m_\times$ has percent-level effects that may be important.