arXiv subjects

Emily Rauscher

Publications and source records attributed to Emily Rauscher.

At least 37 records · Page 2Linked to original sources

arXiv2024

Radiatively Active Clouds and Magnetic Effects Explored in a Grid of Hot Jupiter GCMs

Cloud formation and magnetic effects are both expected to significantly impact the structures and observable properties of hot Jupiter atmospheres. For some hot Jupiters, thermal ionization and condensation can coexist in a single atmosphere, and both processes are important. We present a grid of general circulation models across a wide range of irradiation temperatures with and without incorporating the effects of magnetism and cloud formation to investigate how these processes work in tandem. We find that clouds are present in the atmosphere at all modeled irradiation temperatures, while magnetic effects are negligible for planets with irradiation temperatures cooler than 2000 K. At and above this threshold, clouds and magnetic fields shape atmospheres together, with mutual feedback. Models that include magnetism, through their influence on the temperature structure, produce more longitudinally symmetric dayside cloud coverage and more equatorially concentrated clouds on the nightside and morning terminator. To indicate how these processes would affect observables, we generate bolometric thermal and reflected phase curves from these models. The combination of clouds and magnetic effects increases thermal phase curve amplitudes and decreases peak offsets more than either process does individually.

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arXiv2024

Building a Planet Atmosphere: Fundamental Physics and Chemistry

This chapter provides an overview of the basic concepts foundational to atmospheric physics and chemistry. We discuss the retention of atmospheres against thermal evaporation and the global energy balance of planets. We present simple derivations of the vertical profile of an atmosphere, which may be shaped by convective and radiative transport. We then briefly touch upon the three-dimensional atmospheric structure, as shaped by circulation patterns. We describe how the abundances of chemical species in the atmosphere are determined, starting with the assumption of chemical equilibrium and then expanding to various disequilibrium effects. We introduce the particles that can be important components of atmospheres (clouds and hazes) and sketch out some of their complexity. Finally, we review some of the differences between atmospheres of terrestrial and gaseous worlds.

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arXiv2024

The Roasting Marshmallows Program with IGRINS on Gemini South II -- WASP-121 b has super-stellar C/O and refractory-to-volatile ratios

A primary goal of exoplanet science is to measure the atmospheric composition of gas giants in order to infer their formation and migration histories. Common diagnostics for planet formation are the atmospheric metallicity ([M/H]) and the carbon-to-oxygen (C/O) ratio as measured through transit or emission spectroscopy. The C/O ratio in particular can be used to approximately place a planet's initial formation radius from the stellar host, but a given C/O ratio may not be unique to formation location. This degeneracy can be broken by combining measurements of both the C/O ratio and the atmospheric refractory-to-volatile ratio. We report the measurement of both quantities for the atmosphere of the canonical ultra hot Jupiter WASP-121 b using the high resolution (R=45,000) IGRINS instrument on Gemini South. Probing the planet's direct thermal emission in both pre- and post-secondary eclipse orbital phases, we infer that WASP-121 b has a significantly super-stellar C/O ratio of 0.70$^{+0.07}_{-0.10}$ and a moderately super-stellar refractory-to-volatile ratio at 3.83$^{+3.62}_{-1.67} \times$ stellar. This combination is most consistent with formation between the soot line and H$_2$O snow line, but we cannot rule out formation between the H$_2$O and CO snow lines or beyond the CO snow line. We also measure velocity offsets between H$_2$O, CO, and OH, potentially an effect of chemical inhomogeneity on the planet day side. This study highlights the ability to measure both C/O and refractory-to-volatile ratios via high resolution spectroscopy in the near-infrared H and K bands.

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arXiv2024

Comparative Planetology of Magnetic Effects in Ultrahot Jupiters: Trends in High Resolution Spectroscopy

Ultrahot Jupiters (UHJs), being the hottest class of exoplanets known, provide a unique laboratory for testing atmospheric interactions with internal planetary magnetic fields at a large range of temperatures. Thermal ionization of atmospheric species on the dayside of these planets results in charged particles becoming embedded in the planet's mostly neutral wind. The charges will resist flow across magnetic field lines as they are dragged around the planet and ultimately alter the circulation pattern of the atmosphere. We model this process to study this effect on high resolution emission and transmission spectra in order to identify observational signatures of the magnetic circulation regime that exist across multiple UHJs. Using a state-of-the-art kinematic MHD/active drag approach in a 3D atmospheric model, we simulate three different ultrahot Jupiters with and without magnetic effects. We post-process these models to generate high resolution emission and transmission spectra and explore trends in net Doppler shift as a function of phase. In emission spectra, we find that the net Doppler shift before and after secondary eclipse can be influenced by the presence of magnetic drag and wavelength choice. Trends in transmission spectra show our active drag models consistently produce a unique shape in their Doppler shift trends that differs from the models without active drag. This work is a critical theoretical step to understanding how magnetic fields shape the atmospheres of UHJs and provides some of the first predictions in high resolution spectroscopy for observing these effects.

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arXiv2024

Up, Up, and Away: Winds and Dynamical Structure as a Function of Altitude in the Ultra-Hot Jupiter WASP-76b

Due to the unprecedented signal strengths offered by the newest high-resolution spectrographs on 10-m class telescopes, exploring the 3D nature of exoplanets is possible with an unprecedented level of precision. In this paper, we present a new technique to probe the vertical structure of exoplanetary winds and dynamics using ensembles of planet absorption lines of varying opacity, and apply it to the well-studied ultra-hot Jupiter WASP-76b. We then compare these results to state-of-the-art global circulation models (GCMs) with varying magnetic drag prescriptions. We find that the known asymmetric velocity shift in Fe I absorption during transit persists at all altitudes, and observe tentative trends for stronger blueshifts and more narrow line profiles deeper in the atmosphere. By comparing three different model prescriptions (a hydrodynamical model with no drag, a magnetic drag model, and a uniform drag model) we are able to rule out the uniform drag model due to inconsistencies with observed trends in the data. We find that the magnetic model is slightly favored over the the hydrodynamic model, and note that this 3-Gauss kinematic magnetohydrodynamical GCM is also favored when compared to low-resolution data. Future generation high-resolution spectrographs on Extremely large telescopes (ELTs) will greatly increase signals and make methods like these possible with higher precision and for a wider range of objects.

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arXiv2024

A Comprehensive Analysis Spitzer 4.5 $μ$m Phase Curve of Hot Jupiters

Although exoplanetary science was not initially projected to be a substantial part of the Spitzer mission, its exoplanet observations set the stage for current and future surveys with JWST and Ariel. We present a comprehensive reduction and analysis of Spitzer's 4.5 micron phase curves of 29 hot Jupiters on low-eccentricity orbits. The analysis, performed with the Spitzer Phase Curve Analysis (SPCA) pipeline, confirms that BLISS mapping is the best detrending scheme for most, but not all, observations. Visual inspection remains necessary to ensure consistency across detrending methods due to the diversity of phase curve data and systematics. Regardless of the model selection scheme - whether using the lowest-BIC or a uniform detrending approach - we observe the same trends, or lack thereof. We explore phase curve trends as a function of irradiation temperature, orbital period, planetary radius, mass, and stellar effective temperature. We discuss the trends that are robustly detected and provide potential explanations for those that are not observed. While it is almost tautological that planets receiving greater instellation are hotter, we are still far from confirming dynamical theories of heat transport in hot Jupiter atmospheres due to the sample's diversity. Even among planets with similar temperatures, other factors like rotation and metallicity vary significantly. Larger, curated sample sizes and higher-fidelity phase curve measurements from JWST and Ariel are needed to firmly establish the parameters governing day-night heat transport on synchronously rotating planets.

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arXiv2024

Inhomogeneous terminators on the exoplanet WASP-39 b

Transmission spectroscopy has been a workhorse technique over the past two decades to constrain the physical and chemical properties of exoplanet atmospheres. One of its classical key assumptions is that the portion of the atmosphere it probes -- the terminator region -- is homogeneous. Several works in the past decade, however, have put this into question for highly irradiated, hot ($T_{eq}\gtrsim 1000$ K) gas giant exoplanets both empirically and via 3-dimensional modelling. While models predict clear differences between the evening (day-to-night) and morning (night-to-day) terminators, direct morning/evening transmission spectra in a wide wavelength range has not been reported for an exoplanet to date. Under the assumption of precise and accurate orbital parameters on WASP-39 b, here we report the detection of inhomogeneous terminators on the exoplanet WASP-39 b, which allows us to retrieve its morning and evening transmission spectra in the near-infrared ($2-5\ μ$m) using JWST. We observe larger transit depths in the evening which are, on average, $405 \pm 88$ ppm larger than the morning ones, also having qualitatively larger features than the morning spectrum. The spectra are best explained by models in which the evening terminator is hotter than the morning terminator by $177^{+65}_{-57}$ K with both terminators having C/O ratios consistent with solar. General circulation models (GCMs) predict temperature differences broadly consistent with the above value and point towards a cloudy morning terminator and a clearer evening terminator.

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arXiv2024

Multiple Clues for Dayside Aerosols and Temperature Gradients in WASP-69 b from a Panchromatic JWST Emission Spectrum

WASP-69 b is a hot, inflated, Saturn-mass planet 0.26 Mjup with a zero-albedo equilibrium temperature of 963 K. Here, we report the JWST 2 to 12 um emission spectrum of the planet consisting of two eclipses observed with NIRCam grism time series and one eclipse observed with MIRI LRS. The emission spectrum shows absorption features of water vapor, carbon dioxide and carbon monoxide, but no strong evidence for methane. WASP-69 b's emission spectrum is poorly fit by cloud-free homogeneous models. We find three possible model scenarios for the planet: 1) a Scattering Model that raises the brightness at short wavelengths with a free Geometric Albedo parameter 2) a Cloud Layer model that includes high altitude silicate aerosols to moderate long wavelength emission and 3) a Two-Region model that includes significant dayside inhomogeneity and cloud opacity with two different temperature-pressure profiles. In all cases, aerosols are needed to fit the spectrum of the planet. The Scattering model requires an unexpectedly high Geometric Albedo of 0.64. Our atmospheric retrievals indicate inefficient redistribution of heat and an inhomogeneous dayside distribution, which is tentatively supported by MIRI LRS broadband eclipse maps that show a central concentration of brightness. Our more plausible models (2 and 3) retrieve chemical abundances enriched in heavy elements relative to solar composition by 6x to 14x solar and a C/O ratio of 0.65 to 0.94, whereas the less plausible highly reflective scenario (1) retrieves a slightly lower metallicity and lower C/O ratio.

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arXiv2024

Sulfur Dioxide and Other Molecular Species in the Atmosphere of the Sub-Neptune GJ 3470 b

We report observations of the atmospheric transmission spectrum of the sub-Neptune exoplanet GJ 3470 b taken using the Near-Infrared Camera (NIRCam) on JWST. Combined with two archival HST/WFC3 transit observations and fifteen archival Spitzer transit observations, we detect water, methane, sulfur dioxide, and carbon dioxide in the atmosphere of GJ 3470 b, each with a significance of >3-sigma. GJ 3470 b is the lowest mass -- and coldest -- exoplanet known to show a substantial sulfur dioxide feature in its spectrum, at $M_{p}$=11.2${\,{\rm M}_{\oplus}}$ and $T_{eq}$=600$\,$K. This indicates disequilibrium photochemistry drives sulfur dioxide production in exoplanet atmospheres over a wider range of masses and temperatures than has been reported or expected. The water, carbon dioxide, and sulfur dioxide abundances we measure indicate an atmospheric metallicity of approximately $100\times$ Solar. We see further evidence for disequilibrium chemistry in our inferred methane abundance, which is significantly lower than expected from equilibrium models consistent with our measured water and carbon dioxide abundances.

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arXiv2024

The metallicity and carbon-to-oxygen ratio of the ultra-hot Jupiter WASP-76b from Gemini-S/IGRINS

Measurements of the carbon-to-oxygen (C/O) ratios of exoplanet atmospheres can reveal details about their formation and evolution. Recently, high-resolution cross-correlation analysis has emerged as a method of precisely constraining the C/O ratios of hot Jupiter atmospheres. We present two transits of the ultra-hot Jupiter WASP-76b observed between 1.4-2.4 $μ$m with Gemini-S/IGRINS. We detected the presence of H$_{2}$O, CO, and OH at signal-to-noise ratios of 6.93, 6.47, and 3.90, respectively. We performed two retrievals on this data set. A free retrieval for abundances of these three species retrieved a volatile metallicity of $\left[\frac{\mathrm{C}+\mathrm{O}} {\mathrm{H}}\right]=-0.70^{+1.27}_{-0.93}$, consistent with the stellar value, and a super-solar carbon-to-oxygen ratio of C/O$=0.80^{+0.07}_{-0.11}$. We also ran a chemically self-consistent grid retrieval, which agreed with the free retrieval within $1σ$ but favored a slightly more sub-stellar metallicity and solar C/O ratio ($\left[\frac{\mathrm{C}+\mathrm{O}} {\mathrm{H}}\right]=-0.74^{+0.23}_{-0.17}$ and C/O$=0.59^{+0.13}_{-0.14}$). A variety of formation pathways may explain the composition of WASP-76b. Additionally, we found systemic ($V_{sys}$) and Keplerian ($K_{p}$) velocity offsets which were broadly consistent with expectations from 3D general circulation models of WASP-76b, with the exception of a redshifted $V_{sys}$ for H$_{2}$O. Future observations to measure the phase-dependent velocity offsets and limb differences at high resolution on WASP-76b will be necessary to understand the H$_{2}$O velocity shift. Finally, we find that the population of exoplanets with precisely constrained C/O ratios generally trends toward super-solar C/O ratios. More results from high-resolution observations or JWST will serve to further elucidate any population-level trends.

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arXiv2024

A High Internal Heat Flux and Large Core in a Warm Neptune Exoplanet

Interactions between exoplanetary atmospheres and internal properties have long been hypothesized to be drivers of the inflation mechanisms of gaseous planets and apparent atmospheric chemical disequilibrium conditions. However, transmission spectra of exoplanets has been limited in its ability to observational confirm these theories due to the limited wavelength coverage of HST and inferences of single molecules, mostly H$_2$O. In this work, we present the panchromatic transmission spectrum of the approximately 750 K, low-density, Neptune-sized exoplanet WASP-107b using a combination of HST WFC3, JWST NIRCam and MIRI. From this spectrum, we detect spectroscopic features due to H$_2$O (21$σ$), CH$_4$ (5$σ$), CO (7$σ$), CO$_2$ (29$σ$), SO$_2$ (9$σ$), and NH$_3$ (6$σ$). The presence of these molecules enable constraints on the atmospheric metal enrichment (M/H is 10--18$\times$ Solar), vertical mixing strength (log$_{10}$K$_{zz}$=8.4--9.0 cm$^2$s$^{-1}$), and internal temperature ($>$345 K). The high internal temperature is suggestive of tidally-driven inflation acting upon a Neptune-like internal structure, which can naturally explain the planet's large radius and low density. These findings suggest that eccentricity driven tidal heating is a critical process governing atmospheric chemistry and interior structure inferences for a majority of the cool ($<$1,000K) super-Earth-to-Saturn mass exoplanet population.

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arXiv2024

Two-Dimensional Eclipse Mapping of the Hot Jupiter WASP-43b with JWST MIRI/LRS

We present eclipse maps of the two-dimensional thermal emission from the dayside of the hot Jupiter WASP-43b, derived from an observation of a phase curve with the JWST MIRI/LRS instrument. The observed eclipse shapes deviate significantly from those expected for a planet emitting uniformly over its surface. We fit a map to this deviation, constructed from spherical harmonics up to order $\ell_{\rm max}=2$, alongside the planetary, orbital, stellar, and systematic parameters. This yields a map with a meridionally-averaged eastward hot-spot shift of $(7.75 \pm 0.36)^{\circ}$, with no significant degeneracy between the map and the additional parameters. We show the latitudinal and longitudinal contributions of the day-side emission structure to the eclipse shape, finding a latitudinal signal of $\sim$200 ppm and a longitudinal signal of $\sim$250 ppm. To investigate the sensitivity of the map to the method, we fix the non-mapping parameters and derive an "eigenmap" fitted with an optimised number of orthogonal phase curves, which yields a similar map to the $\ell_{\rm max}=2$ map. We also fit a map up to $\ell_{\rm max}=3$, which shows a smaller hot-spot shift, with a larger uncertainty. These maps are similar to those produced by atmospheric simulations. We conclude that there is a significant mapping signal which constrains the spherical harmonic components of our model up to $\ell_{\rm max}=2$. Alternative mapping models may derive different structures with smaller-scale features; we suggest that further observations of WASP-43b and other planets will drive the development of more robust methods and more accurate maps.

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arXiv2024

Report of the Working Group on Strategic Exoplanet Initiatives with HST and JWST

This STScI Working Group (WG) was charged with soliciting community feedback and evaluating the strategic planning for exoplanet science with JWST and HST given the high quality of exoplanet observations, the significantly lengthened mission lifetime for JWST, and the pronounced expansion of the field over the last decade. We were charged with identifying key science themes, providing recommendations on issues associated with optimal timing and scale of resources, as well as providing a recommended DDT concept achievable with 500 hours of JWST time. We recommend a DDT concept to survey the atmospheres of rocky-M dwarf exoplanets. It is critical to quickly survey a wide sample of such targets to ascertain if they indeed host significant atmospheres, i.e., define the cosmic shoreline, and to identify high priority targets for future follow-up. It is important for this effort to occur early in the mission lifetime. In the context of strategic planning of exoplanet observations, it is useful to estimate the expected exoplanet observational commitment over JWST's lifetime. Given the current usage associated with exoplanets, extended over 20 cycles, it is anticipated that JWST will dedicate $\approx$30,000 hours to exoplanet observations. We recommend efforts to support GO-driven programs that will contribute to this unprecedented data product of JWST. Of the $\approx$30,000 hours of anticipated JWST full-mission time dedicated to exoplanets, we expect that 1/3 of it could, and perhaps inevitably would, form a comprehensive, high S/N, panchromatic, 10$^4$ hour atmospheric survey of planets. Such an observational sample would be a legacy archive that would address a broad range of science questions across various populations of planets. It would also bridge the direct imaging and transit communities and involve a multitude of techniques to detect and characterize exoplanets.

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arXiv2024

A Direct Comparison between the use of Double Gray and Multiwavelength Radiative Transfer in a General Circulation Model with and without Radiatively Active Clouds

Inhomogeneous cloud formation and wavelength-dependent phenomena are expected to shape hot Jupiter atmospheres. We present a General Circulation Model (GCM) with multiwavelength "picket fence" radiative transfer and radiatively active, temperature dependent clouds, and compare the results to a double gray routine. The double gray method inherently fails to model polychromatic effects in hot Jupiter atmospheres, while picket fence captures these non-gray aspects and performs well compared to fully wavelength-dependent methods. We compare both methods with radiatively active clouds and cloud-free models, assessing the limitations of the double gray method. Although there are broad similarities, the picket fence models have larger day-night side temperature differences, non-isothermal upper atmospheres, and multiwavelength effects in the presence of radiatively active clouds. We model the well-known hot Jupiters HD 189733 b and HD 209458 b. For the hotter HD 209458 b, the picket fence method prevents clouds from thermostating dayside temperatures, resulting in hotter upper atmospheres and the dissipation of dayside clouds. Differences in the temperature structures are then associated with nuanced differences in the circulation patterns and clouds. Models of the cooler HD 189733 b have global cloud coverage, regardless of radiative transfer scheme, whereas there are larger differences in the models of HD 209458 b, particularly in the extent of the partial cloud coverage on its dayside. This results in minor changes to the thermal and reflected light phase curves of HD 189733 b, but more significant differences for the picket fence and double gray versions of HD 209458 b.

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arXiv2024

Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b

Hot Jupiters are among the best-studied exoplanets, but it is still poorly understood how their chemical composition and cloud properties vary with longitude. Theoretical models predict that clouds may condense on the nightside and that molecular abundances can be driven out of equilibrium by zonal winds. Here we report a phase-resolved emission spectrum of the hot Jupiter WASP-43b measured from 5-12 $μ$m with JWST's Mid-Infrared Instrument (MIRI). The spectra reveal a large day-night temperature contrast (with average brightness temperatures of 1524$\pm$35 and 863$\pm$23 Kelvin, respectively) and evidence for water absorption at all orbital phases. Comparisons with three-dimensional atmospheric models show that both the phase curve shape and emission spectra strongly suggest the presence of nightside clouds which become optically thick to thermal emission at pressures greater than ~100 mbar. The dayside is consistent with a cloudless atmosphere above the mid-infrared photosphere. Contrary to expectations from equilibrium chemistry but consistent with disequilibrium kinetics models, methane is not detected on the nightside (2$σ$ upper limit of 1-6 parts per million, depending on model assumptions).

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arXiv2023

A Combined Ground-based and JWST Atmospheric Retrieval Analysis: Both IGRINS and NIRSpec Agree The Atmosphere of WASP-77A b is Metal-Poor

Ground-based, high-resolution and space-based, low-resolution spectroscopy are the two main avenues through which transiting exoplanet atmospheres are studied. Both methods provide unique strengths and shortcomings, and combining the two can be a powerful probe into an exoplanet's atmosphere. Within a joint atmospheric retrieval framework, we combined JWST NIRSpec/G395H secondary eclipse spectra and Gemini South/IGRINS pre- and post-eclipse thermal eclipse observations of the hot Jupiter WASP-77A b. Our inferences from the IGRINS and NIRSpec data sets are consistent with each other, and combining the two allows us to measure the gas abundances of H$_2$O and CO as well as the vertical thermal structure with higher precision than either data set provided individually. We confirm WASP-77A b's subsolar metallicty ([(C+O)/H]=-0.61$^{+0.10}_{-0.09}$) and solar C/O ratio (C/O = 0.57$^{+0.06}_{-0.06}$). The two types of data are complementary, and our abundance inferences are mostly driven by the IGRINS data while inference of the thermal structure is driven by the NIRSpec data. Our ability to draw inferences from the post-eclipse IGRINS data is highly sensitive to the number of singular values removed in the detrending process, potentially due to high and variable humidity. We also search for signatures for atmospheric dynamics in the IGRINS data and find that propagated ephemeris error can manifest as both an orbital eccentricity or a strong equatorial jet. Neither are detected when using more up-to-date ephemerides. However, we find moderate evidence of thermal inhomogeneity and measure a cooler nightside that presents itself in the later phases after secondary eclipse.

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arXiv2023

Ground-breaking Exoplanet Science with the ANDES spectrograph at the ELT

In the past decade the study of exoplanet atmospheres at high-spectral resolution, via transmission/emission spectroscopy and cross-correlation techniques for atomic/molecular mapping, has become a powerful and consolidated methodology. The current limitation is the signal-to-noise ratio during a planetary transit. This limitation will be overcome by ANDES, an optical and near-infrared high-resolution spectrograph for the ELT. ANDES will be a powerful transformational instrument for exoplanet science. It will enable the study of giant planet atmospheres, allowing not only an exquisite determination of atmospheric composition, but also the study of isotopic compositions, dynamics and weather patterns, mapping the planetary atmospheres and probing atmospheric formation and evolution models. The unprecedented angular resolution of ANDES, will also allow us to explore the initial conditions in which planets form in proto-planetary disks. The main science case of ANDES, however, is the study of small, rocky exoplanet atmospheres, including the potential for biomarker detections, and the ability to reach this science case is driving its instrumental design. Here we discuss our simulations and the observing strategies to achieve this specific science goal. Since ANDES will be operational at the same time as NASA's JWST and ESA's ARIEL missions, it will provide enormous synergies in the characterization of planetary atmospheres at high and low spectral resolution. Moreover, ANDES will be able to probe for the first time the atmospheres of several giant and small planets in reflected light. In particular, we show how ANDES will be able to unlock the reflected light atmospheric signal of a golden sample of nearby non-transiting habitable zone earth-sized planets within a few tenths of nights, a scientific objective that no other currently approved astronomical facility will be able to reach.

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arXiv2023

The Sensitivity of Eclipse Mapping to Planetary Rotation

Mapping exoplanets across phases and during secondary eclipse is a powerful technique for characterizing Hot Jupiters in emission. Since these planets are expected to rotate about axes normal to their orbital planes, with rotation periods synchronized with their orbital periods, mapping provides a direct correspondence between orbital phase and planetary longitude. We develop a framework to understand the information content of planets where their rotation states are not well constrained, by constructing bases of light curves across different rotation rates and obliquities that are orthogonal in integrated flux across secondary eclipse. These demonstrate that brightness variability during eclipse may arise from a variety of rotation rates, obliquities, and map structures, requiring priors to properly disentangle each of these components. By modeling eclipse observations of the Warm Jupiter HAT-P-18 b we demonstrate that, at a signal-to-noise equivalent to $\sim 10$ orbits with JWST, confusion about map structure is likely a concern only at the upper physical limits of possible rotation rates. Even without priors, one may nevertheless be able to put an order-of-magnitude constraint on rotation rate by determining at what rates the fitted map complexity is minimized, a prescription whose efficacy increases if out-of-eclipse data are available to isolate the effects of rotation. Finally, in the limit of maps with longitudinal symmetry, the projected obliquity in the plane of the sky determines the information available during eclipse, ranging from non-detections of structure to a basic constraint on hemispherical asymmetry and orientation depending on the obliquity angle.

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