Quantum Tunneling of Ultralight Dark Matter Out of Satellite Galaxies

The idea of ultralight scalar (axion) dark matter is theoretically appealing and may resolve some small-scale problems of cold dark matter; so it deserves careful attention. In this work we carefully analyze tunneling of the scalar field in dwarf satellites due to the tidal gravitational force from the host halo. The tidal force is far from spherically symmetric; causing tunneling along the axis from the halo center to the dwarf, while confining in the orthogonal plane. We decompose the wave function into a spherical term plus higher harmonics, integrate out angles, and then numerically solve a residual radial Schr\"odinger-Poisson system. By demanding that the core of the Fornax dwarf halo can survive for at least the age of the universe places a bound on the dark matter particle mass $2\times 10^{-22}\,\mbox{eV}\lesssim m\lesssim 6\times 10^{-22}\,$eV. Interestingly, we show that if another very low density halo is seen, then it rules out the ultralight scalar as core proposal completely. Furthermore, the non-condensed particles likely impose an even sharper lower bound. We also determine how the residual satellites could be distributed as a function of radius.