Study of Lobster and Kirkpatrick-Baez Designs for a Small Mission dedicated to Gravitational Wave Transient Localization

Abstract: The localization of X-ray counterparts to gravitational wave events requires a telescope with accurate localization capability in a field of view comparable to the region constrained by the gravitational wave detectors. In the context of a small, dedicated, mission, we investigate which optical design could satisfy this capability. We compare the possible optical designs that have been proposed for X-rays: the Lobster Eye design (both in the Angel and Schmidt variant) - inspired by the eyes of crustaceans - consisting of many small capillaries where grazing incidence reflection occurs, the Kirkpatrick-Baez design, where double reflection occurs on two orthogonal parabolic mirrors, and the standard Wolter-I design. We find that the first two designs, compared to the latter, can achieve a significantly larger field of view, and have a good localization capability if the focal length is longer than existing Lobster Eye designs. The Kirkpatrick-Baez design presents the best angular resolution, but the best overall field of view is obtained with a Lobster system: we present a small optical module able to achieve an effective area $>$100 cm$^2$ at 1 keV in a field of view of 10 deg$^2$.