2017MNRAS.469.1630H

Under a MONDian view, astrophysical systems are expected to follow Newtonian dynamics whenever the local acceleration is above the critical a₀ = 1.2 x 10^–10 m s^–2, and enter a modified regime for accelerations below this critical value. Indeed, the dark matter phenomenology on galactic and subgalactic scales appears always, and only, at low accelerations. It is standard to find the a < a₀ regime towards the low density outskirts of astronomical systems, where under a Newtonian interpretation, dark matter becomes conspicuous. Thus, it is standard to find, and to think, of the dense central regions of observed systems as purely Newtonian. However, under spherical symmetry in the MONDian as in the Newtonian case, the local acceleration will tend to zero as one approaches the very centre of a mass distribution. It is clear that for spherically symmetric systems, an inner a < a₀ region will necessarily appear interior to a critical radius, which will depend on the details of the density profile in question. Here, we calculate analytically such a critical radius for a constant-density core, and numerically for a cored isothermal profile. Under a Newtonian interpretation, such a central MONDian region will be interpreted as extra mass, analogous to the controversial black holes sometimes inferred to lie at the centres of globular clusters, despite an absence of nuclear activity detected to date. We calculate this effect and give predictions for the 'central black hole' mass to be expected under Newtonian interpretations of low density Galactic globular clusters.