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Tyler D. Robinson

Publications and source records attributed to Tyler D. Robinson.

At least 19 recordsLinked to original sources

Retrieving Ocean Glint Reflectance Signatures from Directly Imaged Earth-like Exoplanets

Future space telescopes searching for extraterrestrial life require methods to detect environments that can potentially support life. Liquid water is considered essential for life as we know it and its presence is therefore an important observable when characterizing potentially Earth-like exoplanets. Remotely inferring the presence of surface liquid water on a world from spatially unresolved observations is an outstanding challenge where the detection of ocean glint could provide supporting evidence. This study assesses the feasibility of detecting ocean glint from Earth-like exoplanets using simulated data from NASA's Habitable World Observatory (HWO). We conducted retrievals on these simulated observations using a model that included a glint contribution and performed model selection against retrievals that did not include glint. We find that over a range of spectral signal-to-noise ratios from 5 to 25, a phase angle of at least 120 deg is necessary for glint detection. Our results offer the opportunity to shape mission development by providing constraints on key telescope observing requirements.

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Impacts of Correlated Noise on Retrievals of Exo-Earth Atmospheres

The Habitable Worlds Observatory (HWO) aims to accomplish high-contrast imaging and spectroscopy of true Earth analogs for the first time. However, high-contrast spectroscopy with HWO may be limited by residual speckles which persist after deformable mirror correction and post-processing, hindering atmospheric characterization. Previous studies of self-luminous giant planets showed that neglecting spectrally correlated errors due to speckles results in biased inferences of planetary parameters. Currently, HWO retrieval studies generate spectra without noise spectral correlations. We present a Gaussian Process model of correlated noise of known properties in simulated HWO exo-Earth spectra, and the integration of this noise source into the forward and inverse modeling tool \texttt{rfast}. We quantify the impact of correlated noise on inferred molecular abundances and planetary properties across the ultraviolet/visible/near-infrared bandpass, for varying spectral resolutions (R), signal-to-noise ratios (SNR), and noise correlation length-scales (L). We find that, at the fiducial UV/Vis/NIR R=7/140/70 and SNR=10, including spectrally correlated noise at L=200 nm and L=10 nm yields a 57\% and 161\% higher average uncertainty on log oxygen abundance, compared to uncorrelated noise. Consequently, it is critical for both instrument design and post-processing algorithms to minimize short length-scale chromaticity. Additionally, we find that a moderate resolution can constrain carbon dioxide (R$\geq 280$) and weakly detect methane (R$\geq2800$) abundances, demonstrating the benefit of a moderate resolution near-infrared spectrograph. These findings can aid the interpretation of future HWO reflectance spectra and set requirements on optical quality, instrument stability, and observing configurations.

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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.

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Characterizing Earth analogs may require a moderate or high-resolution spectrograph

A primary goal of the Habitable Worlds Observatory (HWO) is to detect and measure the abundance of biosignature molecules, such as water (H2O) and oxygen (O2), in the atmosphere of Earth analogs. This is expected to require deep spectroscopic observations lasting hundreds of hours per planet. In this context, it is essential to optimize the spectral resolution of the spectrograph to both maximize the number of planets that can be studied over the lifetime of the mission, and also to reduce the risks of false detections. The purpose of this work is to provide a framework to explore the spectral resolution design trade-space for HWO. This framework must be valid and comparable across all spectral resolutions from low (R<100) to high resolutions (R>10,000), and account for the spectral correlation of the residual starlight (i.e., speckle noise chromaticity). Leveraging the concept of "template matching", we develop a simulation toolkit based on the Python package EXOSIMS to compute the detection significance of planets and molecules. We then simulate observations of Earth analogs around 164 stars using representative mission parameters to explore the effects of the detector noise and the correlated speckle noise floor. Our findings suggest that a moderate or high resolution spectrograph (R>1,000) will provide higher sensitivity to critical molecules compared to a low resolution spectroscopy mode (e.g., R~140). The correlated speckle noise may also entirely suppress our ability to detect bio-signatures at low spectral resolutions. We conclude that a more comprehensive study combined with detailed models of its stability, and other sources of correlated noise, is necessary to fully explore the trade space of spectral resolution and detectability of key species.

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Exomoons and Exorings with the Habitable Worlds Observatory II: Finding Endor with Lunar Eclipses

Giant planets in the habitable zone may host exomoons with conditions conducive to life. In this paper we describe a method by which the Habitable Worlds Observatory (HWO) could detect such moons: broadband reflected-light lunar eclipses (e.g., the moon passing into the shadow of the planet). We find that an Earth-like moon orbiting a Jovian-size planet at 1au can outshine its host planet near 1 micron, producing frequent (days time-scale) lunar eclipses with depths of order 50%. We determine that single eclipse events out to $\sim$12pc may be detectable for Earth-like moons around giant planets, down to $0.9R_\oplus$. Detection of smaller moons, $\sim$0.5$R_\oplus$ (corresponding to about the size of Mars or Ganymede), may be possible, but would generally require multiple events for most systems. These several-hour events provide a clear pathway to detecting habitable moons with HWO, given sufficient stare-time on each system to detect lunar eclipses. The occurrence rate of habitable exomoons remains unconstrained, however, making the ultimate yield uncertain. HWO will be capable of placing the first meaningful constraints on the frequency of habitable exomoons around giant planets; if it is non-negligible, HWO could also search for life on these worlds, possibly with lunar eclipse spectroscopy.

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Inferring and Interpreting the Visual Geometric Albedo and Phase Function of Earth

Understanding reflectance-related quantities for worlds enables effective comparative planetology and strengthens mission planning and execution. Measurements of these properties for Earth, especially its geometric albedo and phase function, have been difficult to achieve due to our Terrestrial situation -- it is challenging to obtain planetary-scale brightness measurements for the world we stand on. Using a curated dataset of visual (0.4--0.7 um) phase-dependent, disk-averaged observations of Earth taken from the ground and spacecraft, alongside a physical-statistical model, this work arrives at a definitive value for the visual geometric albedo of our planet: $0.242^{+0.005}_{-0.004}$. This albedo constraint is up 30--40% smaller than earlier, widely-quoted values. The physical-statistical model enables retrieval-like inferences to be performed on phase curves, and includes contributions from optically thick clouds, optically thin aerosols, Rayleigh scattering, ocean glint, gas absorption, and Lambertian surface reflectance. Detailed application of this inverse model to Earth's phase curve quantifies contributions of these different processes to the phase-dependent brightness of the Pale Blue Dot. Model selection identifies a scenario where aerosol forward scattering results in a false negative for surface habitability detection, which implies that aerosol forward scattering can effectively mimic an ocean glint signature in broadband visual phase curves. Observations of phase curves for Earth at redder-optical or near-infrared wavelengths could disentangle ocean glint effects from aerosol forward scattering. Finally, a review of albedos and planetary photometry is provided as well as a simple two-parameter fit to Earth's visual phase curve to ease adoption into other tools.

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Shedding Light on Large Space-Based Telescopes: Modeling Stray Light due to Primary Mirror Damage from Micrometeoroid Impacts

A large space-based telescope aimed at detecting and characterizing the atmospheres of Earth-like planets orbiting Sun-like stars will require unprecedented contrast and stability. However, damage to the primary mirror due to micrometeoroid impacts will provide a stochastic, time-dependent source of stray light in the coronagraph's field of view that could significantly lengthen exposure times and reduce the expected science yield. To better quantify the impact of stray light and inform the Habitable Worlds Observatory mission design process, we present estimates of stray light in different micrometeoroid damage scenarios for a broad range of targets, and use that to find the expected decrease in science yield (i.e., the expected number of detected exoEarth candidates). We find that stray light due to micrometeoroid damage may significantly reduce yield, by 30% -- 60% in some cases, but significant uncertainties remain due to the unknown maximum expected impactor energy, and the relationship between impact energy and expected crater size. Micrometeoroid damage therefore needs further exploration, as it has the potential to reduce scientific yield, and in turn drive the development of mitigation strategies, selection of telescope designs, and selection of observing priorities in the future.

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Earth Analogs in Reflected Light: Insights from Early Spectral Characterization in Unconstrained Orbits

A next generation of space-based observatories aims to detect and characterize potentially Earth-like exoplanets around Sun-like stars using reflected light spectroscopy. However, it remains unclear how such direct imaging observations$-$limited in spectral coverage and signal-to-noise ratio (S/N)$-$translate into constraints on atmospheric composition and habitability. Coronagraphs used for high-contrast imaging typically operate over narrow bandpasses, and exposure time limits can restrict data quality. To optimize observing strategies and instrument design, we use our atmospheric retrieval tool, $\texttt{rfast}$, to assess the performance of a $\mathit{Habitable\ Worlds\ Observatory}$-type mission across different spectral bandpasses ("Red", "Blue", "Visible", "NIR", and their combination) and S/N levels (10, 15, and 20; from moderate to moderate-high observation quality) in retrieving a wide range of 17 atmospheric, surface, bulk, and orbital parameters of a habitable Earth analog. We outline the observation requirements for each parameter and the detection capabilities of each case, within a novel scenario where spectral data are taken "early", prior to achieving orbit constraints (which may require repeat visits to a system). For coronagraph-restricted and NIR-only bandpasses, most of the limited retrievable information is already captured at S/N = 10, with little improvement at higher S/N. For broader spectral coverage, the quality and quantity of retrieved information improve with increasing S/N, but combining visible and NIR ranges provides the most comprehensive characterization, even at moderate S/N. To maximize returns, wider spectral coverage should be prioritized over improving S/N when spectral access is limited.

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The Open-Source Photochem Code: A General Chemical and Climate Model for Interpreting (Exo)Planet Observations

With the launch of the James Webb Space Telescope, we are firmly in the era of exoplanet atmosphere characterization. Understanding exoplanet spectra requires atmospheric chemical and climate models that span the diversity of planetary atmospheres. Here, we present a more general chemical and climate model of planetary atmospheres. Specifically, we introduce the open-source, one-dimensional photochemical and climate code Photochem, and benchmark the model against the observed compositions and climates of Venus, Earth, Mars, Jupiter and Titan with a single set of kinetics, thermodynamics and opacities. We also model the chemistry of the hot Jupiter exoplanet WASP-39b. All simulations are open-source and reproducible. To first order, Photochem broadly reproduces the gas-phase chemistry and pressure-temperature profiles of all six planets. The largest model-data discrepancies are found in Venus's sulfur chemistry, motivating future experimental work on sulfur kinetics and spacecraft missions to Venus. We also find that clouds and hazes are important for the energy balance of Venus, Earth, Mars and Titan, and that accurately predicting aerosols with Photochem is challenging. Finally, we benchmark Photochem against the popular VULCAN and HELIOS photochemistry and climate models, finding excellent agreement for the same inputs; we also find that Photochem simulates atmospheres 2 to 100 time more efficiently. These results show that Photochem provides a comparatively general description of atmospheric chemistry and physics that can be leveraged to study Solar System worlds or interpret telescope observations of exoplanets.

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Progress toward a demonstration of high contrast imaging at ultraviolet wavelengths

NASA's Habitable Worlds Observatory (HWO) aims to achieve starlight suppression to the $10^{-10}$ level for the detection and spectral characterization of Earth-like exoplanets. Broadband ozone absorption features are key biosignatures that appear in the 200-400nm near-ultraviolet (UV) regime. Extending coronagraphy from visible wavelengths to the UV, however, brings with it a number of challenges, including tighter requirements on wavefront sensing and control, optical surface quality, scattered light, and polarization aberrations, among other things. We aim to partially quantify and address these challenges with a combination of modeling, high-resolution metrology to the scales required for UV coronagraphy, and ultimately a demonstration of UV coronagraphy on the Space Coronagraph Optical Bench (SCoOB) vacuum testbed. In these proceedings, we provide a status update on our modeling and contrast budgeting efforts, characterization efforts to understand performance limitations set by key optical components, and our plans to move toward a demonstration of UV coronagraphy.

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Detecting Land with Reflected Light Spectroscopy to Rule Out Waterworld O$_2$ Biosignature False Positives

The search for life outside our solar system is at the forefront of modern astronomy, and telescopes such as the Habitable Worlds Observatory (HWO) are being designed to identify biosignatures. Molecular oxygen, O$_2$, is considered a promising indication of life, yet substantial abiotic O$_2$ may accumulate from H$_2$O photolysis and hydrogen escape on a lifeless, fully (100%) ocean-covered terrestrial planet when surface O$_2$ sinks are suppressed. This so-called waterworld false positive scenario could be ruled out with land detection because exposed land precludes extremely deep oceans (~50 Earth oceans) given topographic limits set by the crushing strength of rocks. Land detection is possible because plausible geologic surfaces exhibit increasing reflectance with wavelength in the visible, whereas liquid water and ice/snow have flat or decreasing reflectance, respectively. Here, we present reflected light retrievals to demonstrate that HWO could detect land on an exo-Earth in the disk-averaged spectrum. Given a signal-to-noise ratio of 20 spectrum, Earth-like land fractions can be confidently detected with 0.3-1.1 $μ$m spectral coverage (resolution R~140 in the visible, R~7 in the UV, with Earth-like atmosphere and clouds). We emphasize the need for UV spectroscopy down to at least 0.3 $μ$m to break an O$_3$-land degeneracy. We find that the SNR and resolution requirements in the visible/UV imply that a larger aperture (~8 m) will be necessary to ensure the observing times required for land detection are feasible for most HWO terrestrial habitable zone targets. These results strongly inform the HWO minimum requirements to corroborate possible oxygen biosignatures.

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Extreme Forward Scattering Observed in Disk-Averaged Near-Infrared Phase Curves of Titan

Titan, with its thick and hazy atmosphere, is a key world in our solar system for understanding light scattering processes. NASA's Cassini mission monitored Titan between 2004 and 2017, where the derived dataset includes a large number of whole disk observations. Once spatially integrated, these whole disk observations reveal Titan's phase-dependent brightness which can serve as an analog for how hazy worlds might appear around other stars. To explore Titan's phase curve, we present a pipeline for whole disk Titan observations acquired by the Cassini Visual and Infrared Mapping Spectrometer (VIMS) spanning 0.9--5.1 $μ$m. Application of the pipeline finds over 4,400 quality spatially- and spectrally-resolved datacubes that were then integrated over Titan's disk to yield phase curves spanning 2\degree--165\degree in phase angle. Spectra at near-full phase provide a useful approximation for Titan's geometric albedo, thus extending the spectral coverage of previous work. Crescent phase brightness enhancements in the Cassini VIMS phase curves are often more extreme than analogous results seen at optical wavelengths, which can be explained by atmospheric transparency and haze scattering processes. These results provide validation opportunities for exoplanet-focused spectral models and also shed light on how extreme aerosol forward scattering could influence exoplanet observations and interpretations.

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Detecting Surface Liquid Water on Exoplanets

Planets with large bodies of water on their surface will have more temperate and stable climates, and such planets are the ideal places for life-as-we-know-it to arise and evolve. A key science case for the Habitable Worlds Observatory (HWO) is to determine which planets host surface liquid water. Aside from its implications for planetary climate and astrobiology, detecting surface water on terrestrial exoplanets would place important constraints on our theories of planet formation and volatile delivery. Rotational variability in the reflectance of an exoplanet may reveal surface features rotating in and out of view, including oceans. Orbital changes in reflectance and polarization, meanwhile, are sensitive to the scattering phase function of the planetary surface, including specular reflection from large bodies of water. Although these techniques are applicable to all temperate terrestrial exoplanets, we focus in this document on the directly-imaged planets that are more likely to drive the HWO coronagraph design. Identification of water oceans relies on detecting a liquid, and using other lines of evidence to narrow that liquid down to being water. Liquids have smoother surfaces than most solids, and hence exhibit specular reflection instead of diffuse reflection. In practice, this makes lakes and oceans look dark from most illumination angles, but mirror-like at glancing angles. HWO is uniquely capable of identifying surface liquid oceans via their optical properties. Given that discovering an ocean on an exoplanet would confirm its status as a habitable world, this science case is literally the raison d'etre of the Habitable Worlds Observatory.

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Paths to Robust Exoplanet Science Yield Margin for the Habitable Worlds Observatory

The Habitable Worlds Observatory (HWO) will seek to detect and characterize potentially Earth-like planets around other stars. To ensure that the mission achieves the Astro2020 Decadal's recommended goal of 25 exoEarth candidates (EECs), we must take into account the probabilistic nature of exoplanet detections and provide "science margin" to budget for astrophysical uncertainties with a reasonable level of confidence. In this study, we explore the probabilistic distributions of yields to be expected from a blind exoEarth survey conducted by such a mission. We identify and estimate the impact of all major known sources of astrophysical uncertainty on the exoEarth candidate yield. As expected, eta_Earth uncertainties dominate the uncertainty in EEC yield, but we show that sampling uncertainties inherent to a blind survey are another important source of uncertainty that should be budgeted for during mission design. We adopt the Large UV/Optical/IR Surveyor Design B (LUVOIR-B) as a baseline and modify the telescope diameter to estimate the science margin provided by a larger telescope. We then depart from the LUVOIR-B baseline design and identify six possible design changes that, when compiled, provide large gains in exoEarth candidate yield and more than an order of magnitude reduction in exposure times for the highest priority targets. We conclude that a combination of telescope diameter increase and design improvements could provide robust exoplanet science margins for HWO.

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Potential technosignature from anomalously low deuterium/hydrogen (D/H) in planetary water depleted by nuclear fusion technology

Deuterium-deuterium (DD) fusion is viewed as an ideal energy source for humanity in the far future, given a vast seawater supply of D. Here, we consider long-lived, extraterrestrial, technological societies that develop DD fusion. If such a society persists over geologic timescales, oceanic deuterium would diminish. For an ocean mass and initial D/H that are Earth-like, fusion power use of only $\sim$10 times that projected for humankind next century would deplete the deuterium-hydrogen ratio (D/H) in $\sim$(a few)$\times 10^8$ years to values below that of the local Interstellar Medium (ISM). Ocean masses of a few percent Earth's would reach anomalously low D/H in $\sim10^6$ to $10^7$ years. The timescale shortens with greater energy consumption, smaller oceans, or lower initial D/H. Here, we suggest that anomalous D/H in planetary water below local ISM values of $\sim16\times 10^{-6}$ (set by Big Bang nucleosynthesis plus deuterium loss onto dust or small admixtures of deuterium-poor stellar material) may be a technosignature. Unlike SETI from radio signals, anomalous D/H would persist for eons, even if civilizations perish or relocate. We discuss wavelengths of strong absorption features for detecting D/H anomalies in atmospheric water vapor. These are vibrational O-D stretching at 3.7 $μ$m in transmission spectroscopy of Earth-like worlds, $\sim1.5$ $μ$m (in the wings of the 1.4 $μ$m water band) in the shorter near-infrared for direct imaging by Habitable Worlds Observatory, and 3.7 $μ$m or $\sim7.5$ $μ$m (in the wings of the broad 6.3 $μ$m bending vibration of water) for concepts like the Large Interferometer for Exoplanets (LIFE).

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HWO Yield Sensitivities in the NIR and NUV

Habitable Worlds Observatory (HWO) will search for biosignatures from Earth-size exoplanets in the habitable zones of nearby stars. The wavelength range for biosignatures used by the HabEx and LUVOIR mission concept studies was 200 nm to 2 microns and, as such, this is a candidate wavelength range for HWO. The visible wavelength range (500-1000 nm) provides for detection of water, oxygen, and Raleigh scattering; the near-ultraviolet is valuable for detection of ozone; and the near-infrared enables detection of carbon dioxide and methane for Earth-like atmospheres. Damiano et al. 2023 showed the significant improvement in spectral retrieval reliability when the NUV and NIR are both used with the visible. However, the challenge of the NUV, in addition to the technological and engineering challenges of starlight suppression in the NUV, is the drop in flux of host stars. In the NIR, the challenge is the geometric access to the habitable zone due to the wavelength dependency of the inner working angle limit of coronagraphs. For these reasons, exoplanet yields are lower in the NUV and NIR than in the visible (Morgan et al. 2023, Morgan et al. 2024) and some instrument parameters are more critical for improving NUV and NIR yields than others. In this paper we present a new capability for performing a large number of end-to-end yield modeling simulations to enable large, multivariate parameter sweeps. We utilize this capability to calculate the Visible, NIR, and NUV yield sensitivities to the instrument parameters: aperture diameter, coronagraph core throughput, contrast, and inner working angle (IWA). We find that parameter interactions are important in determining yield, the most important of which is the interaction between contrast and IWA, but that the strength of that interaction is different in each of the three wavebands.

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Microphysical Prescriptions for Parameterized Water Cloud Formation on Ultra-cool Substellar Objects

Water must condense into ice clouds in the coldest brown dwarfs and exoplanets. When they form, these icy clouds change the emergent spectra, temperature structure, and albedo of the substellar atmosphere. The properties of clouds are governed by complex microphysics but these complexities are often not captured by the simpler parameterized cloud models used in climate models or retrieval models. Here, we combine microphysical cloud modeling and 1D climate modeling to incorporate insights from microphysical models into a self-consistent, parameterized cloud model. Using the 1D Community Aerosol and Radiation Model for Atmospheres (CARMA), we generate microphysical water clouds and compare their properties with those from the widely-used EddySed cloud model (Ackerman & Marley 2001) for a grid of Y dwarfs. We find that the mass of water condensate in our CARMA water clouds is significantly limited by available condensation nuclei; in models without additional seed particles for clouds added, the atmosphere becomes supersaturated. We incorporate water latent heat release in the convective and radiative parts of the atmosphere and find no significant impact on water-ice cloud formation for typical gas giant compositions. Our analysis reveals the CARMA cloud profiles have a gradual decrease in opacity of approximately 4% per bar below the cloud base. Incorporating this gradual cloud base falloff and a variable $f_{sed}$ parameter allows spectra generated from the parameterized Eddysed model to better match those of the microphysical CARMA model. This work provides recommendations for efficiently generating microphysically-informed water clouds for future models of cold substellar objects with H/He atmospheres.

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Influence of Orbit and Mass Constraints on Reflected Light Characterization of Directly Imaged Rocky Exoplanets

Survey strategies for upcoming exoplanet direct imaging missions have considered varying assumptions of prior knowledge. Precursor radial velocity surveys could have detected nearby exo-Earths and provided prior orbit and mass constraints. Alternatively, a direct imaging mission performing astrometry could yield constraints on orbit and phase angle of target planets. Understanding the impact of prior mass and orbit information on planetary characterization is crucial for efficiently recognizing habitable exoplanets. To address this question, we use a reflected-light retrieval tool to infer the atmospheric and bulk properties of directly imaged Earth-analogs while considering varying levels of prior information and signal-to-noise ratio (SNR). Because of the strong correlation between the orbit-related parameters and the planetary radius, prior information on the orbital distance and planetary phase yield tight constraints on the planetary radius: from $R_{\rm{p}}=2.95^{+2.69}_{-1.95}~R_{\oplus}$ without prior knowledge, to $R_{\rm{p}}=1.01^{+0.33}_{-0.19}~R_{\oplus}$ with prior determination of the orbit for $\rm{SNR}=20$ in the visible/near-infrared spectral range, thus allowing size determination from reflected light observations. However, additional knowledge of planet mass does not notably enhance radius ($R_{\rm{p}}=0.98^{+0.17}_{-0.14}~R_{\oplus}$) or atmospheric characterization. Also, prior knowledge of the mass alone does not yield a tight radius constraint ($R_{\rm{p}}=1.64^{+1.29}_{-0.80}~R_{\oplus}$) nor improves atmospheric composition inference. By contrast, because of its sensitivity to gas column abundance, detecting a Rayleigh scattering slope or bounding Rayleigh opacity helps to refine gas mixing ratio inferences without requiring prior mass knowledge. Overall, apart from radius determination, increasing the SNR is more beneficial than additional prior observations.

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