Verlindes emergent gravity versus MOND and the case of dwarf spheroidals

In a recent paper, Erik Verlinde has developed the interesting possibility that spacetime and gravity may emerge from the entangled structure of an underlying microscopic theory. In this picture, dark matter arises as a response to the standard model of particle physics from the delocalized degrees of freedom that build up the dark energy component of the Universe. Dark matter physics is then regulated by a characteristic acceleration scale $a_0$, identified with the radius of the (quasi)-de Sitter universe we inhabit. For a point particle matter source, or outside an extended spherically symmetric object, MONDs empirical fitting formula is recovered. However, Verlindes theory critically departs from MOND when considering the inner structure of galaxies, differing by a factor of 2 at the centre of a regular massive body. For illustration, we use the eight classical dwarf spheroidal satellites of the Milky Way. These objects are perfect testbeds for the model given their approximate spherical symmetry, measured kinematics, and identified missing mass. We show that, without the assumption of a maximal deformation, Verlindes theory can fit the velocity dispersion profile in dwarf spheroidals with no further need of an extra dark particle component. If a maximal deformation is considered, the theory leads to mass-to-light ratios that are marginally larger than expected from stellar population and formation history studies. We also compare our results with the recent phenomenological interpolating MOND function of McGaugh {it et al}, and find a departure that, for these galaxies, is consistent with the scatter in current observations.