Weak lensing by a galactic dark matter halo
We obtain an analytic expression of the weak-field deflection angle of a model galactic halo through the application of the Gauss-Bonnet theorem on the optical metric, a method suggested by Gibbons and Werner. Our model makes use of the Navarro-Frank-White (NFW) density profile up to some galactic halo length scale a. Beyond this radius, the energy density falls proportional to r-n so that the mass function is rendered finite at spatial infinity. We find that the deflection angle is finite for any value of the impact parameter and behaves comparable to the deflection due to a Plummer sphere.
By submitting their manuscript to the Samahang Pisika ng Pilipinas (SPP) for consideration, the Authors warrant that their work is original, does not infringe on existing copyrights, and is not under active consideration for publication elsewhere.
Upon acceptance of their manuscript, the Authors further agree to grant SPP the non-exclusive, worldwide, and royalty-free rights to record, edit, copy, reproduce, publish, distribute, and use all or part of the manuscript for any purpose, in any media now existing or developed in the future, either individually or as part of a collection.
All other associated economic and moral rights as granted by the Intellectual Property Code of the Philippines are maintained by the Authors.