The Impact of Planetary Phase Functions on Exo-Earth Detectability with EXOSIMS

The under-development NASA Habitable Worlds Observatory (HWO) aims to provide breakthroughs in exoplanet science, yet the most effective approaches to modeling the detection and characterization of potentially Earth-like worlds with HWO remain uncertain despite being essential considerations for mission design. In this work, we aim to better model and understand detection metrics through the use of EXOSIMS (Exoplanet Open-Source Imaging Mission Simulator), an exoplanet yield modeling tool. Yield modeling requires representing planetary brightness via a planetary phase curve. Earth's true visual phase curve is non-Lambertian, deviating from the idealized Lambertian model in EXOSIMS, particularly at phase angles beyond 90 degrees (i.e., quadrature). This leads to underestimating Earth's brightness. To address this, we incorporate phase-dependent reflectance from a high-fidelity Earth model into EXOSIMS for physically motivated simulations. We explore and quantify differences in phase-dependent detections, finding that the realistic Earth phase function produces modest changes in the median number of detected exo-Earths and systematically redistributes detections towards medium to high phase angles where Earth is intrinsically brighter than a Lambertian approximation. Additionally, we explore the role of coronagraph inner working angle (IWA) by running simulations across multiple IWA values with both phase functions, revealing that smaller IWAs expand access to a broader range of orbital phases, altering the resulting phase-angle distribution of detections. Together, these results demonstrate that realistic phase functions and IWA parameters both have measurable impacts on yield estimates for an HWO-like mission and highlight the need to more realistically represent Earth-like worlds in yield modeling.