Effects of galactic magnetic field on the UHECR correlation studies with starburst galaxies

We estimate the biases caused by the coherent deflection of cosmic rays due to the Galactic magnetic field (GMF) in maximum-likelihood analysis for searches of ultrahigh-energy cosmic ray (UHECR) sources in the literature. We simulate mock event datasets with a set of assumptions for the starburst galaxy (SBG) source model (arXiv:1801.06160), coherent deflection by a GMF model (arXiv:1204.3662,arXiv:1210.7820), and mixed-mass composition (arXiv:1901.03338); we then conduct a maximum-likelihood analysis without accounting for the GMF in the same manner as previous studies. We find that the anisotropic fraction $f_{\mathrm{a}\mathrm{n}\mathrm{i}}$ is estimated systematically lower than the true value. We estimate the true parameters which are compatible with the best-fit parameters reported in (arXiv:1801.06160), and find that except for a narrow region with a large anisotropic fraction and small separation angular scale a wide parameter space is still compatible with the experimental results. We also develop a maximum-likelihood method that takes into account the GMF model and confirm in the MC simulations that we can estimate the true parameters within a 1$\sigma$ contour under the ideal condition that we know the event-by-event mass and the GMF.