arXiv subjects

Natasha E. Batalha

Publications and source records attributed to Natasha E. Batalha.

At least 73 records · Page 4Linked to original sources

arXiv2023

Spherical Harmonics for the 1D Radiative Transfer Equation II: Thermal Emission

Approximate methods to estimate solutions to the radiative transfer equation are essential for the understanding of atmospheres of exoplanets and brown dwarfs. The simplest and most popular choice is the "two-stream method" which is often used to produce simple yet effective models for radiative transfer in scattering and absorbing media. Toon et al. (1989) (Toon89) outlined a two-stream method for computing reflected light and thermal spectra and was later implemented in the open-source radiative transfer model PICASO. In Part~I of this series, we developed an analytical spherical harmonics method for solving the radiative transfer equation for reflected solar radiation (Rooney et al. 2023), which was implemented in PICASO to increase the accuracy of the code by offering a higher-order approximation. This work is an extension of this spherical harmonics derivation to study thermal emission spectroscopy. We highlight the model differences in the approach for thermal emission and benchmark the 4-term method (SH4) against Toon89 and a high-stream discrete-ordinates method, CDISORT. By comparing the spectra produced by each model we demonstrate that the SH4 method provides a significant increase in accuracy, compared to Toon89, which can be attributed to the increased order of approximation and to the choice of phase function. We also explore the trade-off between computational time and model accuracy. We find that our 4-term method is twice as slow as our 2-term method, but is up to five times more accurate, when compared with CDISORT. Therefore, SH4 provides excellent improvement in model accuracy with minimal sacrifice in numerical expense.

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arXiv2023

Spherical Harmonics for the 1D Radiative Transfer Equation I: Reflected Light

A significant challenge in radiative transfer theory for atmospheres of exoplanets and brown dwarfs is the derivation of computationally efficient methods that have adequate fidelity to more precise, numerically demanding solutions. In this work, we extend the capability of the first open-source radiative transfer model for computing the reflected light of exoplanets at any phase geometry, PICASO: Planetary Intensity Code for Atmospheric Spectroscopy Observations. Until now, PICASO has implemented two-stream approaches to the solving the radiative transfer equation for reflected light, in particular following the derivations of Toon et al. (1989) (Toon89). In order to improve the model accuracy, we have considered higher-order approximations of the phase functions, namely, we have increased the order of approximation from 2 to 4, using spherical harmonics. The spherical harmonics approximation decouples spatial and directional dependencies by expanding the intensity and phase function into a series of spherical harmonics, or Legendre polynomials, allowing for analytical solutions for low-order approximations to optimize computational efficiency. We rigorously derive the spherical harmonics method for reflected light and benchmark the 4-term method (SH4) against Toon89 and two independent and higher-fidelity methods (CDISORT & doubling-method). On average, the SH4 method provides an order of magnitude increase in accuracy, compared to Toon89. Lastly, we implement SH4 within PICASO and observe only modest increase in computational time, compared to two-stream methods (20% increase).

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arXiv2023

Photochemically-produced SO$_2$ in the atmosphere of WASP-39b

Photochemistry is a fundamental process of planetary atmospheres that regulates the atmospheric composition and stability. However, no unambiguous photochemical products have been detected in exoplanet atmospheres to date. Recent observations from the JWST Transiting Exoplanet Early Release Science Program found a spectral absorption feature at 4.05 $μ$m arising from SO$_2$ in the atmosphere of WASP-39b. WASP-39b is a 1.27-Jupiter-radii, Saturn-mass (0.28 M$_J$) gas giant exoplanet orbiting a Sun-like star with an equilibrium temperature of $\sim$1100 K. The most plausible way of generating SO$_2$ in such an atmosphere is through photochemical processes. Here we show that the SO$_2$ distribution computed by a suite of photochemical models robustly explains the 4.05 $μ$m spectral feature identified by JWST transmission observations with NIRSpec PRISM (2.7$σ$) and G395H (4.5$σ$). SO$_2$ is produced by successive oxidation of sulphur radicals freed when hydrogen sulphide (H$_2$S) is destroyed. The sensitivity of the SO$_2$ feature to the enrichment of the atmosphere by heavy elements (metallicity) suggests that it can be used as a tracer of atmospheric properties, with WASP-39b exhibiting an inferred metallicity of $\sim$10$\times$ solar. We further point out that SO$_2$ also shows observable features at ultraviolet and thermal infrared wavelengths not available from the existing observations.

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arXiv2023

A Catalogue of Exoplanet Atmospheric Retrieval Codes

Exoplanet atmospheric retrieval is a computational technique widely used to infer properties of planetary atmospheres from remote spectroscopic observations. Retrieval codes typically employ Bayesian sampling algorithms or machine learning approaches to explore the range of atmospheric properties (e.g., chemical composition, temperature structure, aerosols) compatible with an observed spectrum. However, despite the wide adoption of exoplanet retrieval techniques, there is currently no systematic summary of exoplanet retrieval codes in the literature. Here, we provide a catalogue of the atmospheric retrieval codes published to date, alongside links to their respective code repositories where available. Our catalogue will be continuously updated via a Zenodo archive.

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arXiv2022

Early Release Science of the exoplanet WASP-39b with JWST NIRCam

Measuring the metallicity and carbon-to-oxygen (C/O) ratio in exoplanet atmospheres is a fundamental step towards constraining the dominant chemical processes at work and, if in equilibrium, revealing planet formation histories. Transmission spectroscopy provides the necessary means by constraining the abundances of oxygen- and carbon-bearing species; however, this requires broad wavelength coverage, moderate spectral resolution, and high precision that, together, are not achievable with previous observatories. Now that JWST has commenced science operations, we are able to observe exoplanets at previously uncharted wavelengths and spectral resolutions. Here we report time-series observations of the transiting exoplanet WASP-39b using JWST's Near InfraRed Camera (NIRCam). The long-wavelength spectroscopic and short-wavelength photometric light curves span 2.0 - 4.0 $μ$m, exhibit minimal systematics, and reveal well-defined molecular absorption features in the planet's spectrum. Specifically, we detect gaseous H$_2$O in the atmosphere and place an upper limit on the abundance of CH$_4$. The otherwise prominent CO$_2$ feature at 2.8 $μ$m is largely masked by H$_2$O. The best-fit chemical equilibrium models favour an atmospheric metallicity of 1-100$\times$ solar (i.e., an enrichment of elements heavier than helium relative to the Sun) and a sub-stellar carbon-to-oxygen (C/O) ratio. The inferred high metallicity and low C/O ratio may indicate significant accretion of solid materials during planet formation or disequilibrium processes in the upper atmosphere.

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arXiv2022

Early Release Science of the Exoplanet WASP-39b with JWST NIRSpec G395H

Measuring the abundances of carbon and oxygen in exoplanet atmospheres is considered a crucial avenue for unlocking the formation and evolution of exoplanetary systems. Access to an exoplanet's chemical inventory requires high-precision observations, often inferred from individual molecular detections with low-resolution space-based and high-resolution ground-based facilities. Here we report the medium-resolution (R$\sim$600) transmission spectrum of an exoplanet atmosphere between 3-5 $μ$m covering multiple absorption features for the Saturn-mass exoplanet WASP-39b, obtained with JWST NIRSpec G395H. Our observations achieve 1.46x photon precision, providing an average transit depth uncertainty of 221 ppm per spectroscopic bin, and present minimal impacts from systematic effects. We detect significant absorption from CO$_2$ (28.5$σ$) and H$_2$O (21.5$σ$), and identify SO$_2$ as the source of absorption at 4.1 $μ$m (4.8$σ$). Best-fit atmospheric models range between 3 and 10x solar metallicity, with sub-solar to solar C/O ratios. These results, including the detection of SO$_2$, underscore the importance of characterising the chemistry in exoplanet atmospheres, and showcase NIRSpec G395H as an excellent mode for time series observations over this critical wavelength range.

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arXiv2022

Early Release Science of the exoplanet WASP-39b with JWST NIRISS

Transmission spectroscopy provides insight into the atmospheric properties and consequently the formation history, physics, and chemistry of transiting exoplanets. However, obtaining precise inferences of atmospheric properties from transmission spectra requires simultaneously measuring the strength and shape of multiple spectral absorption features from a wide range of chemical species. This has been challenging given the precision and wavelength coverage of previous observatories. Here, we present the transmission spectrum of the Saturn-mass exoplanet WASP-39b obtained using the SOSS mode of the NIRISS instrument on the JWST. This spectrum spans $0.6 - 2.8 μ$m in wavelength and reveals multiple water absorption bands, the potassium resonance doublet, as well as signatures of clouds. The precision and broad wavelength coverage of NIRISS-SOSS allows us to break model degeneracies between cloud properties and the atmospheric composition of WASP-39b, favoring a heavy element enhancement ("metallicity") of $\sim 10 - 30 \times$ the solar value, a sub-solar carbon-to-oxygen (C/O) ratio, and a solar-to-super-solar potassium-to-oxygen (K/O) ratio. The observations are best explained by wavelength-dependent, non-gray clouds with inhomogeneous coverage of the planet's terminator.

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arXiv2022

Importance of Sample Selection in Exoplanet Atmosphere Population Studies

Understanding planet formation requires robust population studies, which are designed to reveal trends in planet properties. In this work, we aim to determine if different methods for selecting populations of exoplanets for atmospheric characterization with JWST could influence population-level inferences. We generate three hypothetical surveys of super-Earths/sub-Neptunes, each spanning a similar radius-insolation flux space. The survey samples are constructed based on three different selection criteria (evenly-spaced-by-eye, binned, and a quantitative selection function). Using an injection-recovery technique, we test how robustly individual-planet atmospheric parameters and population-level parameters can be retrieved. We find that all three survey designs result in equally suitable targets for individual atmospheric characterization, but not equally suitable targets for constraining population parameters. Only samples constructed with a quantitative method or that are sufficiently evenly-spaced-by-eye result in robust population parameter constraints. Furthermore, we find that the sample with the best targets for individual atmospheric study does not necessarily result in the best constrained population parameters. The method of sample selection must be considered. We also find that there may be large variability in population-level results with a sample that is small enough to fit in a single JWST cycle ($\sim$12 planets), suggesting that the most successful population-level analyses will be multi-cycle. Lastly, we infer that our exploration of sample selection is limited by the small number of transiting planets with measured masses around bright stars. Our results can guide future development of programs that aim to determine underlying trends in exoplanet atmospheric properties and, by extension, formation and evolution processes.

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arXiv2022

Effects of Rotation on the Spectra of Brown Dwarfs

Measured rotational speeds of giant planets and brown dwarfs frequently constitute appreciable fractions of the breakup limit, resulting in centrifugal expansion of these objects at the equator. According to models of internal energy transport, this expansion ought to make the poles of a rotator significantly hotter than the equator, so that inclination of the rotational axis greatly affects both spectral shape and total flux. In this article, we explore the dependence of a substellar object's observables on its rotational speed and axis inclination. To do so, we combine PICASO (a Planetary Intensity Code for Atmospheric Spectroscopy Observations) with software PARS (Paint the Atmospheres of Rotating Stars). The former computer program models radiative transfer within plane-parallel planetary atmospheres, while the latter computes disk-integrated spectra of centrifugally deformed gaseous masses. We find that the specific flux of a typical fast-rotating brown dwarf can increase by as much as a factor of 1.5 with movement from an equator-on to a pole-on view. On the other hand, the distinctive effect of rotation on spectral shape increases toward the equator-on view. The latter effect also increases with lower effective temperature. The bolometric luminosity estimate for a typical fast rotator at extreme inclinations has to be adjusted by as much as about 20% due to the anisotropy of the object's observed flux. We provide a general formula for the calculation of the corresponding adjustment factor in terms of rotational speed and inclination.

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arXiv2022

Probing the Extent of Vertical Mixing in Brown Dwarf Atmospheres with Disequilibrium Chemistry

Evidence of disequilibrium chemistry due to vertical mixing in the atmospheres of many T and Y-dwarfs has been inferred due to enhanced mixing ratios of CO and reduced NH$_3$. Atmospheric models of planets and brown dwarfs typically parameterize this vertical mixing phenomenon with the vertical eddy diffusion coefficient, $K_{\rm zz}$. While $K_{\rm zz}$ can perhaps be approximated in the convective regions in the atmosphere with mixing length theory, in radiative regions the strength of vertical mixing is uncertain by many orders of magnitude. With a new grid of self-consistent 1D model atmospheres from $T_{\rm eff}$ of 400 - 1000 K, computed with a new radiative-convective equilibrium python code PICASO 3.0, we aim to assess how molecular abundances and corresponding spectra can be used as a probe of depth-dependent $K_{\rm zz}$. At a given surface gravity, we find non-monotonic behavior in the CO abundance as a function of $T_{\rm eff}$, as chemical abundances are sometimes quenched in either of two potential atmospheric convective zones, or quenched in either of two possible radiative zones. The temperature structure and chemical quenching behavior also changes with gravity. We compare our models with available near-infrared and M-band spectroscopy of several T and Y-dwarfs and assess their atmospheric vertical mixing profiles. We also compare to color-magnitude diagrams and make predictions for JWST spectra. This work yields new constraints, and points the way to significant future gains, in determining $K_{\rm zz}$, a fundamental atmospheric parameter in substellar atmospheres, with significant implications for chemistry and cloud modeling.

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arXiv2022

Identification of carbon dioxide in an exoplanet atmosphere

Carbon dioxide (CO2) is a key chemical species that is found in a wide range of planetary atmospheres. In the context of exoplanets, CO2 is an indicator of the metal enrichment (i.e., elements heavier than helium, also called "metallicity"), and thus formation processes of the primary atmospheres of hot gas giants. It is also one of the most promising species to detect in the secondary atmospheres of terrestrial exoplanets. Previous photometric measurements of transiting planets with the Spitzer Space Telescope have given hints of the presence of CO2 but have not yielded definitive detections due to the lack of unambiguous spectroscopic identification. Here we present the detection of CO2 in the atmosphere of the gas giant exoplanet WASP-39b from transmission spectroscopy observations obtained with JWST as part of the Early Release Science Program (ERS). The data used in this study span 3.0 to 5.5 μm in wavelength and show a prominent CO2 absorption feature at 4.3 μm (26σ significance). The overall spectrum is well matched by one-dimensional, 10x solar metallicity models that assume radiative-convective-thermochemical equilibrium and have moderate cloud opacity. These models predict that the atmosphere should have water, carbon monoxide, and hydrogen sulfide in addition to CO2, but little methane. Furthermore, we also tentatively detect a small absorption feature near 4.0 μm that is not reproduced by these models.

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arXiv2022

PICASO 3.0: A One-Dimensional Climate Model for Giant Planets and Brown Dwarfs

Upcoming James Webb Space Telescope (JWST) observations will allow us to study exoplanet and brown dwarf atmospheres in great detail. The physical interpretation of these upcoming high signal-to-noise observations requires precise atmospheric models of exoplanets and brown dwarfs. While several one-dimensional and three-dimensional atmospheric models have been developed in the past three decades, these models have often relied on simplified assumptions like chemical equilibrium and are also often not open-source, which limits their usage and development by the wider community. We present a python-based one-dimensional atmospheric radiative-convective equilibrium model. This model has heritage from the Fortran-based code (Marley et al.,1996} which has been widely used to model the atmospheres of Solar System objects, brown dwarfs, and exoplanets. In short, the basic capability of the original model is to compute the atmospheric state of the object under radiative-convective equilibrium given its effective or internal temperature, gravity, and host--star properties (if relevant). In the new model, which has been included within the well-utilized code-base PICASO, we have added these original features as well as the new capability of self-consistently treating disequilibrium chemistry. This code is widely applicable to Hydrogen-dominated atmospheres (e.g., brown dwarfs and giant planets).

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arXiv2022

Cloudy and Cloud-free Thermal Phase Curves with PICASO: Applications to WASP-43b

We present new functionality within PICASO, a state-of-the-art radiative transfer model for exoplanet and brown dwarf atmospheres, by developing a new pipeline that computes phase-resolved thermal emission (thermal phase curves) from three-dimensional (3D) models. Because PICASO is coupled to Virga, an open-source cloud code, we are able to produce cloudy phase curves with different sedimentation efficiencies ($f_{sed}$) and cloud condensate species. We present the first application of this new algorithm to hot Jupiter WASP-43b. Previous studies of the thermal emission of WASP-43b from Kataria et al. found good agreement between cloud-free models and dayside thermal emission, but an overestimation of the nightside flux, for which clouds have been suggested as a possible explanation. We use the temperature and vertical wind structure from the cloud-free 3D general circulation models of Kataria et al. and post-process it using PICASO, assuming that clouds form and affect the spectra. We compare our models to results from Kataria et al., including Hubble Space Telescope Wide-Field Camera 3 (WFC3) observations of WASP-43b from Stevenson et al. In addition, we compute phase curves for Spitzer at 3.6 and 4.5 $μm$ and compare them to observations from Stevenson et al. We are able to closely recover the cloud-free results, even though PICASO utilizes a coarse spatial grid. We find that cloudy phase curves provide much better agreement with the WFC3 and Spitzer nightside data, while still closely matching the dayside emission. This work provides the community with a convenient, user-friendly tool to interpret phase-resolved observations of exoplanet atmospheres using 3D models.

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arXiv2021

A New Sedimentation Model for Greater Cloud Diversity in Giant Exoplanets and Brown Dwarfs

The observed atmospheric spectrum of exoplanets and brown dwarfs depends critically on the presence and distribution of atmospheric condensates. The Ackerman & Marley (2001) methodology for predicting the vertical distribution of condensate particles is widely used to study cloudy atmospheres and has recently been implemented in an open-source python package virga. The model relies upon input parameter $f_{\text{sed}}$, the sedimentation efficiency, which until now has been held constant. The relative simplicity of this model renders it useful for retrieval studies due to its rapidly attainable solutions. However, comparisons with more complex microphysical models such as CARMA have highlighted inconsistencies between the two approaches, namely that the cloud parameters needed for radiative transfer produced by virga are dissimilar to those produced by CARMA. To address these discrepancies, we have extended the original Ackerman and Marley methodology in virga to allow for non-constant $f_{\text{sed}}$ values, in particular those that vary with altitude. We discuss one such parameterization and compare the cloud mass mixing ratio produced by virga with constant and variable $f_{\text{sed}}$ profiles to that produced by CARMA. We find that the variable $f_{\text{sed}}$ formulation better captures the profile produced by CARMA with heterogeneous nucleation, yet performs comparatively to constant $f_{\text{sed}}$ for homogeneous nucleation. In general, virga has the capacity to handle any $f_{\text{sed}}$ with an explicit anti-derivative, permitting a plethora of alternative cloud profiles that are otherwise unattainable by constant $f_{\text{sed}}$ values. The ensuing flexibility has the potential to better agree with increasingly complex models and observed data.

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arXiv2021

Modeling Polarization Signals from Cloudy Brown Dwarfs: Luhman 16 A and B in Three Dimensions

The detection of disk-integrated polarization from Luhman 16A and B in H-band, and subsequent modeling, has been interpreted in the framework of zonal cloud bands on these bodies. Recently, Tan and Showman (2021) investigated three-dimensional atmospheric circulation and cloud structures of brown dwarfs with general circulation models (GCMs), and their simulations yield complex cloud distributions showing some aspects of zonal jets, but also complex vortices that cannot be captured by a simple model. Here we use these 3D GCMs specific to Luhman 16A and B, along with the three-dimensional Monte Carlo radiative transfer code ARTES, to calculate their polarization signals. We adopt the 3D temperature-pressure and cloud profiles from the GCMs as our input atmospheric structures. Our polarization calculations at 1.6 $μ$m agree well with the measured degree of linear polarization from both Luhman 16 A and B. Our calculations reproduce the measured polarization for both the objects with cloud particle sizes between 0.5-1 \,$μ$m for Luhman 16 A and 5 \,$μ$m for Luhman 16 B. We find that the degree of linear polarization can vary on hour-long timescales over the course of a rotation period. We also show that models with azimuthally symmetric band-like cloud geometries, typically used for interpreting polarimetry observations of brown dwarfs, over-predict the polarization signal if the cloud patterns do not include complex vortices within these bands. This exploratory work shows that GCMs are promising for modeling and interpreting polarization signals of brown dwarfs.

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arXiv2021

A Snowball in Hell: The Potential Steam Atmosphere of TOI-1266c

TOI-1266c is a recently discovered super-Venus in the radius valley orbiting an early M dwarf. However, its notional bulk density ($\sim$2.2 g cm$^{-3}$) is consistent with a large volatile fraction, suggesting that it might have volatile reservoirs that have survived billions of years at more than twice the Earth's insolation. On the other hand, the upper mass limit paints a picture of a cool super Mercury dominated by >50\% iron core ($\sim$9.2 g cm$^{-3}$) that has tiptoed up to the collisional stripping limit and into the radius gap. Here, we examine several hypothetical states for TOI-1266c using a combination of new and updated open-source atmospheric escape, radiative-convective, and photochemical models. We find that water-rich atmospheres with trace amounts of H$_{2}$ and CO$_{2}$ are potentially detectable (SNR $>\sim 5$) in less than 20 hours of JWST observing time. We also find that water vapor spectral features are not substantially impacted by the presence of high-altitude water or ice clouds due the presence of a significant amount of water above the cloud-deck, although further work with self-consistent cloud models is needed. Regardless of its mass, however, TOI-1266c represents a unique proving ground for several hypotheses related to the evolution of sub-Neptunes and Venus-like worlds, particularly those near the radius valley.

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arXiv2021

On the Utility of Transmission Color Analysis I: Differentiating Super-Earths and Sub-Neptunes

The majority of exoplanets found to date have been discovered via the transit method, and transmission spectroscopy represents the primary method of studying these distant worlds. Currently, in-depth atmospheric characterization of transiting exoplanets entails the use of spectrographs on large telescopes, requiring significant observing time to study each planet. Previous studies have demonstrated trends for solar system worlds using color-color photometry of reflectance spectra, as well as trends within transmission spectra for hot Jupiters. Building on these concepts, we have investigated the use of transmission color photometric analysis for efficient, coarse categorization of exoplanets and for assessing the nature of these worlds, with a focus on resolving the bulk composition degeneracy to aid in discriminating super-Earths and sub-Neptunes. We present our methodology and first results, including spectrum models, model comparison frameworks, and wave band selection criteria. We present our results for different transmission "color" metrics, filter selection methods, and numbers of filters. Assuming noise-free spectra of isothermal atmospheres in chemical equilibrium, with our pipeline, we are able to constrain atmospheric mean molecular weight in order to distinguish between super-Earth and sub-Neptune atmospheres with >90$\%$ overall accuracy using as few as two specific low-resolution filter combinations. We also found that increasing the number of filters does not substantially impact this performance. This method could allow for broad characterization of large numbers of planets much more efficiently than current methods permit, enabling population and system-level studies. Additionally, data collected via this method could inform follow-up observing time by large telescopes for more detailed studies of worlds of interest.

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arXiv2021

Impacts of Water Latent Heat on the Thermal Structure of Ultra-Cool Objects: Brown Dwarfs and Free-Floating Planets

Brown dwarfs are essential targets for understanding planetary and sub-stellar atmospheres across a wide range of thermal and chemical conditions. As surveys continue to probe ever deeper, and as observing capabilities continue to improve, the number of known Y dwarfs -- the coldest class of sub-stellar objects, with effective temperatures below about 600 K -- is rapidly growing. Critically, this class of ultra-cool objects has atmospheric conditions that overlap with Solar System worlds and, as a result, tools and ideas developed from studying Earth, Jupiter, Saturn and other nearby worlds are well-suited for application to sub-stellar atmospheres. To that end, we developed a one-dimensional (vertical) atmospheric structure model for ultra-cool objects that includes moist adiabatic convection, as this is an important process for many Solar System planets. Application of this model across a range of effective temperatures (350, 300, 250, 200 K), metallicities ([M/H] of 0.0, 0.5, 0.7, 1.5), and gravities (log $g$ of 4.0, 4.5, 4.7, 5.0) demonstrates strong impacts of water latent heat release on simulated temperature-pressure profiles. At the highest metallicities, water vapor mixing ratios reach an Earth-like 3%, with associated major alterations to the thermal structure in the atmospheric regions where water condenses. Spectroscopic and photometric signatures of metallicity and moist convection should be readily detectable at near- and mid-infrared wavelengths, especially with James Webb Space Telescope observations, and can help indicate the formation history of an object.

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