Evidence of Intermediate-Scale Energy Spectrum Anisotropy of Cosmic Rays E$geq$10$^{19.2}$ eV with the Telescope Array Surface Detector

An intermediate-scale energy spectrum anisotropy has been found in the arrival directions of ultra-high energy cosmic rays of energies above $10^{19.2}$ eV in the northern hemisphere, using 7 years of data from the Telescope Array surface detector. A relative energy distribution test is done comparing events inside oversampled spherical caps of equal exposure, to those outside, using the Poisson likelihood ratio. The center of maximum significance is at $9^h$$16^m$, $45^{circ}$. and has a deficit of events with energies $10^{19.2}$$leq$$E$$<$$10^{19.75}$ eV and an excess for $E$$geq$$10^{19.75}$ eV. The post-trial probability of this energy anisotropy, appearing by chance anywhere on an isotropic sky, is found by Monte Carlo simulation to be $9$$times$$10^{-5}$ ($3.74$$sigma_{global}$).