Title:Verlinde's emergent gravity vs MOND and the case of dwarf spheroidals

Abstract:In a recent paper, Erik Verlinde has further developed the interesting possibility that spacetime and gravity may emerge from the entanglement structure of an underlying microscopic theory. In this picture dark matter arises as the response to the standard model of particle physics from the delocalized low energy degrees of freedom that build up the dark energy component of the Universe. Physics is then regulated by a characteristic acceleration scale $a_0$, identified in this model with the dark energy de Sitter radius by $a_0=cH_0\approx 5.4\times 10^{-10}\,\textrm{m/s}^2$ (using {\it Planck} data). For a point particle, or outside an extended spherically symmetric massive object, Milgrom's empirical fitting formula is recovered. However, Verlinde's theory critically departs from MOND when considering the inner structure of galaxies. For illustration, we use the the eight classical dwarf spheroidal satellites of the Milky Way. These objects are perfect testbeds for the model given their spherical symmetry, measured kinematics, and large identified missing mass. As a consistency check we show that, for reasonable stellar mass-to-light ratios, Verlinde's theory can fit the velocity dispersion profile in dwarf spheroidals with no further need of an extra dark particle component. Finally we compare our results with the recent phenomenological interpolating MOND function of McGaugh {\it et al}, and find a departure of up to 50 percent in the innermost region of these galaxies.