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

TL;DR

The study tackles the problem of localizing gravitational wave X-ray counterparts within a wide field using a small mission. It compares Lobster Eye (Angel and Schmidt variants), Kirkpatrick-Baez, and Wolter-I optical designs via ray-tracing, optimizing a Lobster Eye Angel configuration for a target of $A_{eff}>100$ cm$^{2}$ and a $10$ deg$^{2}$ field with HEW between $50$ and $100$ arcsec. Key findings show Lobster Eye designs can deliver wide-field performance with steady HEW (~$50$ arcsec) over the field when equipped with a longer focal length ($f=2.5$ m) and appropriately sized mirrors; Kirkpatrick-Baez offers superior on-axis resolution but degrades off-axis more slowly than Wolter-I, while Wolter-I is less favorable for wide-field localization. The conclusion favors a single Lobster Eye telescope as the simplest and most capable option to meet the stated localization requirements for a small mission, with stray-light considerations and PSF characterization highlighted for final design readiness.

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$^2$.

Figures (8)

• Figure 1: Schematic (not to scale) of a portion of a Lobster Eye mirror module and conventions used in this work. Left: top view; right: side view. In the Schmidt case, the $R$ and $f$ represented correspond to $R_{inner}$ and $f_{inner}$, while the outer curvature and focal point are shown in light blue. On the right only a section is shown, so only one of the two orthogonal reflections is represented.
• Figure 2: Distribution of photons in the image formed from a Lobster Eye. Left: the different colors indicate the number of reflections of photons (but not the density per pixel); the fractional distributions of photons depends on the optical configuration (see for example Figures \ref{['fig:L_optimization']} and \ref{['fig:Lobsters_comparison']} below). Right: pixel-binned map of the image, showing the density per pixel of the different components.
• Figure 3: Effective area and half energy width in a Lobster Angel telescope, for different focal distances. The continuous blue curve refers to an on-axis source, the dashed orange curve to a source 1.8 deg off-axis. The optical parameters are reported in Table \ref{['tab:Optical-parameters-used']}; the green vertical lines indicate the value used in the remaining of this work.
• Figure 4: Fraction of rays reflected on-axis for each reflection order, for the Angel case, as a function of mirror length. The continuous curves refer to an on-axis source, the dashed curves to a source 1.8 deg off-axis. For the remaining of this work we chose a length of 40 mm (indicated by the the green vertical lines). The optical parameters are reported in Table \ref{['tab:Optical-parameters-used']}.
• Figure 5: Performance in effective area, half energy widths and fractions of rays, for the Angel case, as a function of mirror length. The continuous blue curve refers to an on-axis source, the dashed orange curve to a source 1.8 deg off-axis. The fractions of rays refer to, from top to bottom, rays that do not reflect on any surface (stray light), rays reflected once (forming the arms of the cross), rays double reflected to the focusing center and rays double reflected outside of the focusing center (in the "clouds", see Figure \ref{['fig:Color-coded-simulation']}). For the remaining of this work we chose a length of 40 mm (indicated by the the green vertical lines). The optical parameters are reported in Table \ref{['tab:Optical-parameters-used']}.