Soliton solution for the central dark mass in 47-Tuc globular cluster and implications for the axiverse

Abstract

We offer a standing wave explanation for the rising proper motions of stars at the center of the globular cluster 47-Tucanae, amounting to $\ensuremath{\simeq}0.44%$ of the total mass. We show that this can be explained as a solitonic core of dark matter composed of light bosons, $m\ensuremath{\ge}{10}^{\ensuremath{-}18}\text{ }\text{ }\mathrm{eV}$, corresponding to $\ensuremath{\le}0.27\text{ }\text{ }\mathrm{pc}$, as an alternative to a single black hole (BH) or a concentration of stellar BH remnants proposed recently. This is particularly important because having a concentrated stellar BH remnant with the above radii is very challenging without the heavy core since the three-body encounters would prevent the BHs from being that concentrated. We propose that this core develops from dark matter captured in the deep gravitational potential of this globular cluster as it orbits the dark halo of our Galaxy. This boson may be evidence for a second light axion, additional to a lighter boson of ${10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$, favored for the dominant dark matter implied by the large dark cores of dwarf spheroidal galaxies. The identification of two such light bosonic mass scales favors the generic string theory prediction of a wide, discrete mass spectrum of axionic scalar fields.