Daniel Garrett

WFIRST-AFTA coronagraph science yield modeling with EXOSIMS

Abstract. We present and discuss the design details of an extensible, modular, open-source software framework called EXOSIMS (Exoplanet Open-Source Imaging Mission Simulator), which creates end-to-end simulations of space-based exoplanet imaging missions. We motivate the development and baseline implementation of the component parts of this software with models of the wide-field infrared survey telescope-astrophysics focused telescope assets (WFIRST-AFTA) coronagraph and present initial results of mission simulations for various iterations of the WFIRST-AFTA coronagraph design. We present and discuss two sets of simulations. The first compares the science yield of completely different instruments in the form of early competing coronagraph designs for WFIRST-AFTA. The second set of simulations evaluates the effects of different operating assumptions, specifically the assumed postprocessing capabilities and telescope vibration levels. We discuss how these results can guide further instrument development and the expected evolution of science yields.

ANALYTICAL FORMULATION OF THE SINGLE-VISIT COMPLETENESS JOINT PROBABILITY DENSITY FUNCTION

We derive an exact formulation of the multivariate integral representing the single-visit obscurational and photometric completeness joint probability density function for arbitrary distributions for planetary parameters. We present a derivation of the region of nonzero values of this function, which extends previous work, and discuss the time and computational complexity costs and benefits of the method. We present a working implementation and demonstrate excellent agreement between this approach and Monte Carlo simulation results.

A comparison of analytical depth of search metrics with mission simulations for exoplanet imagers

While new, advanced, ground-based instrumentation continues to produce new exoplanet discoveries and provide further insights into exoplanet formation and evolution, our desire to discover and characterize planets of Earth size about stars of all types and ages necessitates dedicated, imaging space instruments. Given the high costs and complexities of space observatories, it is vital to build confidence in a proposed instrument’s capabilities during its design phase, and much effort has been devoted to predicting the performance of various flavors of space- based exoplanet imagers. The fundamental problem with trying to answer the question of how many exoplanets a given instrument will discover is that the number of discoverable planets is unknown, and so all results are entirely dependent on the assumptions made about the population of planets being studied. Here, we explore an alternate approach, which involves explicitly separating instrumental and mission biasing from the assumptions made about planet distributions. This allows us to calculate a mission’s ‘depth of search’-a metric independent of the planetary population and defined as the fraction of the contrast–projected separation space reached by a given instrument for a fixed planetary radius and semi-major axis. When multiplied by an assumed occurrence rate for planets at this radius and semi-major axis (derived from an assumed planetary population), this yields the expected number of detections by the instrument for that population. Integrating over the full ranges of semi-major axis and planetary radius provides estimates of planet yield for a full mission. We use this metric to evaluate the coronagraphs under development for the WFIRST mission under different operating assumptions. We also compare the results of convolving the depth of search with an assumed planetary population to those derived by running full mission simulations based on that same population.

Multi-mission modeling for space-based exoplanet imagers

In addition to the Wide-Field Infrared Survey Telescope Coronagraphic Imager (WFIRST CGI), which is currently scheduled for launch in the mid 2020s, there is an extensive, ongoing design effort for next-generation, space-based, exoplanet imaging instrumentation. This work involves mission concepts such as the Large UV/ Optical/Infrared Surveyor (LUVOIR), the Habitable Exoplanet Imaging Misson (HabEx), and a starshade rendezvous mission for WFIRST, among others. While each of these efforts includes detailed mission analysis targeted at the specifics of each design, there is also interest in being able to analyze all such concepts in a unified way (to the extent that this is possible) and to draw specific comparisons between projected concept capabilities. Here, we discuss and compare two fundamental approaches to mission analysis, full mission simulation and depth of search analysis, in the specific context of simulating and comparing multiple different mission concepts. We present strategies for mission analysis at varying stages of concept definition, using WFIRST as a motivating example, and discuss useful metrics for cross-mission comparison, as well as strategies for evaluating these metrics.

Scheduling and target selection optimization for exoplanet imaging spacecraft

Space-based extrasolar planet imaging mission performance is dependent on selection of optimal targets, integration times, and scheduling each observation. We use the WFIRST space telescopes stellar coronagraphic instrument as a baseline to compare simulated exoplanet detection yield of multiple target selection and scheduling algorithms. Using completeness as a reward metric and integration time plus overhead time as a cost metric, we simultaneously optimize the observation list and integration times. To schedule these observations, we present different dynamic planning and static planning algorithms and validate their performance in “realistic” Monte Carlo simulations using the Exoplanet Open-Source Imaging Mission Simulator (EXOSIMS) software package. We test these algorithms with completeness generated from different assumed planet populations to demonstrate robustness in deviation of the actual planet population from the planned planet population.

Optimal starshade observation scheduling

An exoplanet direct imaging mission using an external occulter for starlight suppression could potentially achieve higher contrasts and throughputs than an equivalently sized telescope with an internal coronagraph. We consider a formation flying mission where the starshade must station-keep with a telescope, assumed to be on a halo orbit about the Sun-Earth L2 point, during observations and slew between observations as the telescope re-orients to target the next star. We use a parameterization of the slew fuel cost calculation based on interpolation of exact solutions of boundary value problem in the circular restricted three body formalism. Time constraints are imposed based on when stars are observable due to the motion of bright sources in the solar system, integration times, and mission lifetime constraints. Finally, we present a comprehensive cost function incorporating star completeness values as a reward heuristic and retargeting fuel costs to sequentially select the next best star to observe. Ensembles of simulations are conducted for different selection schemes; for a 3 year mission, taking two steps of the linear cost function produces the most unique detections with an average of 7.08± 2.55.

Planet Occurrence Rate Density Models Including Stellar Effective Temperature

We present planet occurrence rate density models fit to Kepler data as a function of semi-major axis, planetary radius, and stellar effective temperature. We find that occurrence rates for M type stars with lower effective temperature do not follow the same trend as F, G, and K type stars when including a polynomial function of effective temperature in an occurrence rate density model and a better model fit includes a break in effective temperature. Our model fit for M type stars consists of power laws on semi-major axis and planetary radius. Our model fit for F, G, and K type stars consists of power laws on semi-major axis and planetary radius broken at 2.771

Detected exoplanet population distributions found analytically

R_\oplus

Starshade orbital maneuver study for WFIRST

and a quadratic function of stellar effective temperature. Our models show agreement with published occurrence rate studies and are the first to explicitly include stellar effective temperature as a variable. By introducing stellar effective temperature into our occurrence rate density models, we enable more accurate occurrence rate predictions for individual stars in mission simulation and science yield calculations for future and proposed exoplanet finding missions.

ExEP yield modeling tool and validation test results

We present analytical methods for determining the distributions of planetary population parameters which would be detected from an assumed planetary population for a direct imaging instrument. We present detected distributions for projected separation, Δmag, semi-major axis, eccentricity, geometric albedo, and planetary radius. All of these distributions are validated against Monte Carlo simulation. For greater accuracy in Monte Carlo simulation, the number of sampled planets and computational cost must increase. Our analytical methods reduce the computational cost and more accurately determine these functions than Monte Carlo simulations.