I introduce batman, a Python package for modeling exoplanet transit light curves. The batman package supports calculation of light curves for any radially symmetric stellar limb darkening law, using a new integration algorithm for models that cannot be quickly calculated analytically. The code uses C extension modules to speed up model calculation and is parallelized with OpenMP. For a typical light curve with 100 data points in transit, batman can calculate one million quadratic limb-darkened models in 30 seconds with a single 1.7 GHz Intel Core i5 processor. The same calculation takes seven minutes using the four-parameter nonlinear limb darkening model (computed to 1 ppm accuracy). Maximum truncation error for integrated models is an input parameter that can be set as low as 0.001 ppm, ensuring that the community is prepared for the precise transit light curves we anticipate measuring with upcoming facilities. The batman package is open source and publicly available at https://github.com/lkreidberg/batman. Subject headings: methods: data analysis – methods: numerical

batman: BAsic Transit Model cAlculatioN in Python

Abstract Ultrahot Jupiters are gas giants that orbit so close to their host star that they are tidally locked, causing a permanent hot dayside and a cooler nightside. Signatures of their nonuniform atmospheres can be observed with high-resolution transit transmission spectroscopy by resolving time-dependent velocity shifts as the planet rotates and varying areas of the evening and morning terminator are probed. These asymmetric shifts were seen for the first time in iron absorption in WASP-76b. Here, we search for other atoms/ions in the planets transmission spectrum and study the asymmetries in their signals. We detect Li i , Na i , Mg i , Ca ii , V i , Cr i , Mn i , Fe i , Ni i , and Sr ii , and tentatively detect H i , K i , and Co i , of which V, Cr, Ni, Sr ii , and Co have not been reported before. We notably do not detect Ti or Al, even though these species should be readily observable, and hypothesize this could be due to condensation or cold trapping. We find that the observed signal asymmetries in the detected species can be explained in different ways. We find a relation between the expected condensation or ionization temperatures and the strength of the observed asymmetry, which could indicate rain-out or recombination on the nightside. However, we also find a dependence on the signal broadening, which could imply a two-zoned atmospheric model, in which the lower atmosphere is dominated by a day-to-night wind, while the upper atmosphere is dominated by a vertical wind or outflow. These observations provide a new level of modeling constraint and will aid our understanding of atmospheric dynamics in highly irradiated planets. 

An Atomic Spectral Survey of WASP-76b: Resolving Chemical Gradients and Asymmetries

Transmission spectroscopy is one of the premier methods used to probe the temperature, composition, and cloud properties of exoplanet atmospheres. Recent studies have demonstrated that the multidimensional nature of exoplanet atmospheres -- due to non-uniformities across the day-night transition and between the morning and evening terminators -- can strongly influence transmission spectra. However, the computational demands of 3D radiative transfer techniques have precluded their usage within atmospheric retrievals. Here we introduce TRIDENT, a new 3D radiative transfer model which rapidly computes transmission spectra of exoplanet atmospheres with day-night, morning-evening, and vertical variations in temperature, chemical abundances, and cloud properties. We also derive a general equation for transmission spectra, accounting for 3D atmospheres, refraction, multiple scattering, ingress/egress, grazing transits, stellar heterogeneities, and nightside thermal emission. After introducing TRIDENT's linear algebra-based approach to 3D radiative transfer, we propose new parametric prescriptions for 3D temperature and abundance profiles and 3D clouds. We show that multidimensional transmission spectra exhibit two significant observational signatures: (i) day-night composition gradients alter the relative amplitudes of absorption features; and (ii) morning-evening composition gradients distort the peak-to-wing contrast of absorption features. Finally, we demonstrate that these signatures of multidimensional atmospheres incur residuals > 100 ppm compared to 1D models, rendering them potentially detectable with JWST. TRIDENT's rapid radiative transfer, coupled with parametric multidimensional atmospheres, unlocks the final barrier to 3D atmospheric retrievals. 

TRIDENT: A Rapid 3D Radiative-transfer Model for Exoplanet Transmission Spectra

Aerosols have been found to be nearly ubiquitous in substellar atmospheres1–3. The precise temperature at which these aerosols begin to form in exoplanets has yet to be observationally constrained. Theoretical models and observations of muted spectral features indicate that silicate clouds play an important role in exoplanets between at least 950 and 2,100 K (ref. 4). Some giant planets, however, are thought to be hot enough to avoid condensation altogether5,6. Here we report the near-ultraviolet transmission spectrum of the ultra-hot Jupiter WASP-178b (approximately 2,450 K), which exhibits substantial absorption. Bayesian retrievals indicate the presence of gaseous refractory species containing silicon and magnesium, which are the precursors to condensate clouds at lower temperatures. SiO, in particular, has not previously, to our knowledge, been detected in exoplanets, but the presence of SiO in WASP-178b is consistent with theoretical expectations as the dominant Si-bearing species at high temperatures. These observations allow us to re-interpret previous observations of HAT-P-41b and WASP-121b that did not consider SiO, to suggest that silicate cloud formation begins on exoplanets with equilibrium temperatures between 1,950 and 2,450 K. Analysis is presented that indicates that there is strong evidence that SiO or Mg, the major constituents of silicate condensates, must be present in gaseous form in the atmosphere of ultra-hot Jupiter WASP-178b. 

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UV absorption by silicate cloud precursors in ultra-hot Jupiter WASP-178b

The technique of transmission spectroscopy -- the variation of the planetary radius with wavelength due to opacity sources in the planet's terminator region -- has been to date one of the most successful in the characterization of exoplanet atmospheres, providing key insights into the composition and structure of these distant worlds. A common assumption made when using this technique, however, is that the variations are the same in the entire terminator region. In reality, the morning and evening terminators might have distinct temperature, pressure and thus compositional profiles due to the inherent 3-D nature of the planet which would, in turn, give rise to different spectra on each side of it. Constraining those might be fundamental for our understanding of not only the weather patterns in these distant worlds, but also of planetary formation signatures which might only be possible to extract once these features are well understood. Motivated by this physical picture, in this work we perform a detailed study on the observational prospects of detecting this effect. We present an open-source semi-analytical framework with which this information can be extracted directly from transit lightcurves, and perform a detailed study on the prospects of detecting the effect with current missions such as TESS and upcoming ones such as JWST. Our results show that these missions show great promise for the detection of this effect. Transmission spectroscopy studies with JWST, in particular, could provide spectra of each of the limbs allowing us to convey 3-D information previously accessible only via phase-curves.

Constraining mornings & evenings on distant worlds: a new semi-analytical approach and prospects with transmission spectroscopy

When exoplanets pass in front of their stars, they imprint a transit signature on the stellar light curve which to date has been assumed to be symmetric in time, owing to the planet being modelled as a circular area occulting the stellar surface. However, this signature might be asymmetric due to different temperature/pressure and/or chemical compositions in the different terminator regions of the transiting planet. catwoman is a Python package that allows to model these asymmetric transit lightcurves, calculating lightcurves for any radially symmetric stellar limb darkening law, and where planets are modelled as two semi-circles, of different radii, using the integration algorithm developed in arXiv:1507.08285 and implemented in the batman library, from which catwoman builds upon.

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catwoman: A transit modelling Python package for asymmetric light curves

/pdf/catwoman-a-transit-modelling-python-package-for-asymmetric-udkxi7fprp.pdf

Catwoman: A transit modelling Python package for asymmetric light curves

Thermal phase curves of exoplanet atmospheres have revealed temperature maps as a function of planetary longitude, often by sinusoidal decomposition of the phase curve. We construct a framework for describing two-dimensional temperature maps of exoplanets with mathematical basis functions derived for a fluid layer on a rotating, heated sphere with drag/friction, which are generalizations of spherical harmonics. These basis functions naturally produce physically-motivated temperature maps for exoplanets with few free parameters. We investigate best practices for applying this framework to temperature maps of hot Jupiters by splitting the problem into two parts: (1) we constrain the temperature map as a function of latitude by tuning the basis functions to reproduce general circulation model (GCM) outputs, since disk-integrated phase curve observations do not constrain this dimension; and (2) we infer the temperature maps of real hot Jupiters using original reductions of several Spitzer phase curves, which directly constrain the temperature variations with longitude. The resulting phase curves can be described with only three free parameters per bandpass -- an efficiency improvement over the usual five or so used to describe sinusoidal decompositions of phase curves. Upon obtaining the hemispherically averaged dayside and nightside temperatures, the standard approach would be to use zero-dimensional box models to infer the Bond albedo and redistribution efficiency. We elucidate the limitation of these box models by demonstrating that negative Bond albedos may be obtained due to a choice of boundary condition on the nightside temperature. We propose generalized definitions for the Bond albedo and heat redistribution efficiency for use with two-dimensional (2D) temperature maps. Open-source software called kelp is provided to efficiently compute these phase curves.

Kathryn Jones

Papers

Constraining mornings & evenings on distant worlds: a new semi-analytical approach and prospects with transmission spectroscopy

catwoman: A transit modelling Python package for asymmetric light curves

Catwoman: A transit modelling Python package for asymmetric light curves

Physically-motivated basis functions for temperature maps of exoplanets

Constraining Mornings and Evenings on Distant Worlds: A new Semianalytical Approach and Prospects with Transmission Spectroscopy