arXiv subjects

Daniel Kitzmann

Publications and source records attributed to Daniel Kitzmann.

At least 55 records · Page 3Linked to original sources

arXiv2022

Astrometric Accelerations as Dynamical Beacons: Discovery and Characterization of HIP 21152 B, the First T-Dwarf Companion in the Hyades

Benchmark brown dwarf companions with well-determined ages and model-independent masses are powerful tools to test substellar evolutionary models and probe the formation of giant planets and brown dwarfs. Here, we report the independent discovery of HIP~21152~B, the first imaged brown dwarf companion in the Hyades, and conduct a comprehensive orbital and atmospheric characterization of the system. HIP~21152 was targeted in an ongoing high-contrast imaging campaign of stars exhibiting proper motion changes between Hipparcos and Gaia, and was also recently identified by Bonavita et al. (2022) and Kuzuhara et al. (2022). Our Keck/NIRC2 and SCExAO/CHARIS imaging of HIP~21152 revealed a comoving companion at a separation of $0.37^{\prime\prime}$ (16 au). We perform a joint orbit fit of all available relative astrometry and radial velocities together with the Hipparcos-Gaia proper motions, yielding a dynamical mass of $24^{+6}_{-4}\,\mathrm{M_{Jup}}$, which is $1{-}2σ$ lower than evolutionary model predictions. Hybrid grids that include the evolution of cloud properties best reproduce the dynamical mass. We also identify a comoving wide-separation ($1837^{\prime\prime}$ or $7.9 \times 10^4 \, \mathrm{au}$) early-L dwarf with an inferred mass near the hydrogen-burning limit. Finally, we analyze the spectra and photometry of HIP~21152~B using the Saumon & Marley (2008) atmospheric models and a suite of retrievals. The best-fit grid-based models have $f_{\mathrm{sed}}=2$, indicating the presence of clouds, $T_{\mathrm{eff}}=1400 \, \mathrm{K}$, and $\log{g}=4.5 \, \mathrm{dex}$. These results are consistent with the object's spectral type of $\mathrm{T0\pm1}$. As the first benchmark brown dwarf companion in the Hyades, HIP~21152~B joins the small but growing number of substellar companions with well-determined ages and dynamical masses.

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arXiv2022

The Mantis Network II: Examining the 3D high-resolution observable properties of the UHJs WASP-121b and WASP-189b through GCM modelling

The atmospheres of ultra hot Jupiters (UHJs) are prime targets for the detection of molecules and atoms at both low and high spectral resolution. We study the atmospheres of the UHJs WASP-121b and WASP-189b by performing 3D general circulation models (GCMs) of these planets using high temperature correlated-k opacity schemes with ultra-violet (UV) absorbing species included. The GCM results are then post-processed at low and high spectral resolutions and compared to available data. The high resolution results are cross-correlated with molecular and atomic templates to produce mock molecular detections. Our GCM models produce similar temperature-pressure (T-p) structure trends to previous 1D radiative-convective equilibrium models of UHJs. Furthermore, the inclusion of UV opacities greatly shapes the thermal and dynamical properties of the high-altitude, low-pressure regions of the UHJ atmospheres, with sharp T-p inversions due to the absorption of UV light. This suggests that optical wavelength, high-resolution observations probe a dynamically distinct upper atmospheric region, rather than the deeper jet forming layers.

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arXiv2022

FastChem 2: An improved computer program to determine the gas-phase chemical equilibrium composition for arbitrary element distributions

The computation of complex neutral/ionised chemical equilibrium compositions is invaluable to obtain scientific insights of, for example, the atmospheres of extrasolar planets and cool stars. We present FastChem 2, a new version of the established semi-analytical thermochemical equilibrium code FastChem. Whereas the original version is limited to atmospheres containing a significant amount of hydrogen, FastChem 2 is also applicable to chemical mixtures dominated by any other species, such as CO$_2$ or N$_2$. The new C++ code and an optional Python module are publicly available under the GPLv3 license at https://github.com/exoclime/FastChem. The program is backward compatible so that the previous version can be easily substituted. We updated the thermochemical database by adding HNC, FeH, TiH, Ca$^-$, and some organic molecules. In total 523 species are now in the thermochemical database including 28 chemical elements. The user can reduce the total number of species to, for example, increase the computation performance or can add further species if the thermochemical data are available. The program is validated against its previous version and extensively tested over an extended pressure-temperature grid with pressures ranging from $10^{-13}\,\mathrm{bar}$ up to $10^3\,\mathrm{bar}$ and temperatures between $100\,\mathrm{K}$ and $6000\,\mathrm{K}$. FastChem 2 is successfully applied to a number of different scenarios including nitrogen, carbon, and oxygen-dominated atmospheres as well as test cases without hydrogen and helium. Averaged over the extended pressure-temperature grid FastChem 2 is up to 50 times faster than the previous version and is also applicable to situations not treatable with version 1.

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arXiv2022

Retrieval Study of Brown Dwarfs Across the L-T Sequence

A large suite of 228 atmospheric retrievals is performed on a curated sample of 19 brown dwarfs spanning the L0 to T8 spectral types using the open-source Helios-r2 retrieval code, which implements the method of short characteristics for radiative transfer and a finite-element description of the temperature-pressure profile. Surprisingly, we find that cloud-free and cloudy (both gray and non-gray) models are equally consistent with the archival SpeX data from the perspective of Bayesian model comparison. Only upper limits for cloud properties are inferred if log-uniform priors are assumed, but the cloud optical depth becomes constrained if a uniform prior is used. Water is detected in all 19 objects and methane is detected in all of the T dwarfs, but no obvious trend exists across effective temperature. As carbon monoxide is only detected in a handful of objects, the inferred carbon-to-oxygen ratios are unreliable. The retrieved radius generally decreases with effective temperature, but the values inferred for some T dwarfs are implausibly low and may indicate missing physics or chemistry in the models. For the early L dwarfs, the retrieved surface gravity depends on whether the gray or non-gray cloud model is preferred. Future data are necessary for constraining cloud properties and the vertical variation of chemical abundances, the latter of which is needed for distinguishing between the chemical instability versus traditional cloud interpretation of the L-T transition.

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arXiv2022

The PEPSI Exoplanet Transit Survey (PETS) I: Investigating the presence of a silicate atmosphere on the super-Earth 55 Cnc e

The study of exoplanets and especially their atmospheres can reveal key insights on their evolution by identifying specific atmospheric species. For such atmospheric investigations, high-resolution transmission spectroscopy has shown great success, especially for Jupiter-type planets. Towards the atmospheric characterization of smaller planets, the super-Earth exoplanet 55 Cnc e is one of the most promising terrestrial exoplanets studied to date. Here, we present a high-resolution spectroscopic transit observation of this planet, acquired with the PEPSI instrument at the Large Binocular Telescope. Assuming the presence of Earth-like crust species on the surface of 55 Cnc e, from which a possible silicate-vapor atmosphere could have originated, we search in its transmission spectrum for absorption of various atomic and ionized species such as Fe , Fe+, Ca , Ca+, Mg and K , among others. Not finding absorption for any of the investigated species, we are able to set absorption limits with a median value of 1.9 x RP. In conclusion, we do not find evidence of a widely extended silicate envelope on this super-Earth reaching several planetary radii.

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arXiv2022

Sunbathing under white light -- 3D modelling of brown dwarf - white dwarf atmospheres with strong UV irradiation

The atmospheres of brown dwarfs orbiting in close proximity to their parent white dwarf represent some of the most extreme irradiated environments known. Understanding their complex dynamical mechanisms pushes the limits of theoretical and modelling efforts, making them valuable objets to study to test contemporary understanding of irradiated atmospheres. We use the Exo-FMS GCM to simulate the brown dwarfs WD0137-349B, SDSS J141126.20+200911.1B and EPIC212235321B, first coupled to a multi-banded grey radiative-transfer scheme then a spectral correlated-k scheme with high temperature opacity tables. We then post-process the GCM results using gCMCRT to compare to available observational data. Our GCM models predict strongly temperature inverted atmospheres, spanning many decades in pressure due to impact of UV band heating. Post-processing of our models suggest that the day-night contrast is too small in the GCM results. We therefore suggest that the formation of cloud particles as well as atmospheric drag effects such as magnetic drag are important considerations in setting the day-night temperature contrast for these objects.

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arXiv2022

3D radiative-transfer for exoplanet atmospheres. gCMCRT: a GPU accelerated MCRT code

Radiative-transfer (RT) is a key component for investigating atmospheres of planetary bodies. With the 3D nature of exoplanet atmospheres being important in giving rise to their observable properties, accurate and fast 3D methods are required to be developed to meet future multi-dimensional and temporal data sets. We develop an open source GPU RT code, gCMCRT, a Monte Carlo RT forward model for general use in planetary atmosphere RT problems. We aim to automate the post-processing pipeline, starting from direct global circulation model (GCM) output to synthetic spectra. We develop albedo, emission and transmission spectra modes for 3D and 1D input structures. We include capability to use correlated-k and high-resolution opacity tables, the latter of which can be Doppler shifted inside the model. We post-process results from several GCM groups including ExoRad, SPARC/MITgcm THOR, UK Met Office UM, Exo-FMS and the Rauscher model. Users can therefore take advantage of desktop and HPC GPU computing solutions. gCMCRT is well suited for post-processing large GCM model grids produced by members of the community and for high-resolution 3D investigations.

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arXiv2022

Titanium oxide and chemical inhomogeneity in the atmosphere of the exoplanet WASP-189b

The temperature of an atmosphere decreases with increasing altitude, unless a shortwave absorber exists that causes a temperature inversion. Ozone plays this role in the Earth`s atmosphere. In the atmospheres of highly irradiated exoplanets, shortwave absorbers are predicted to be titanium oxide (TiO) and vanadium oxide (VO). Detections of TiO and VO have been claimed using both low and high spectral resolution observations, but later observations have failed to confirm these claims or overturned them. Here we report the unambiguous detection of TiO in the ultra-hot Jupiter WASP-189b using high-resolution transmission spectroscopy. This detection is based on applying the cross-correlation technique to many spectral lines of TiO from 460 to 690 nm. Moreover, we report detections of metals, including neutral and singly ionised iron and titanium, as well as chromium, magnesium, vanadium and manganese (Fe, Fe+, Ti, Ti+, Cr, Mg, V, Mn). The line positions of the detected species differ, which we interpret as a consequence of spatial gradients in their chemical abundances, such that they exist in different regions or dynamical regimes. This is direct observational evidence for the three-dimensional thermo-chemical stratification of an exoplanet atmosphere derived from high-resolution ground-based spectroscopy.

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arXiv2021

TOI-2109b: An Ultrahot Gas Giant on a 16 hr Orbit

We report the discovery of an ultrahot Jupiter with an extremely short orbital period of $0.67247414\,\pm\,0.00000028$ days ($\sim$16 hr). The $1.347 \pm 0.047$ $R_{\rm Jup}$ planet, initially identified by the Transiting Exoplanet Survey Satellite (TESS) mission, orbits TOI-2109 (TIC 392476080): a $T_{\rm eff} \sim 6500$ K F-type star with a mass of $1.447 \pm 0.077$ $M_{\rm Sun}$, a radius of $1.698 \pm 0.060$ $R_{\rm Sun}$, and a rotational velocity of $v\sin i_* = 81.9 \pm 1.7$ km s$^{-1}$. The planetary nature of TOI-2109b was confirmed through radial velocity measurements, which yielded a planet mass of $5.02 \pm 0.75$ $M_{\rm Jup}$. Analysis of the Doppler shadow in spectroscopic transit observations indicates a well-aligned system, with a sky-projected obliquity of $λ= 1\overset{\circ}{.}7 \pm 1\overset{\circ}{.}7$. From the TESS full-orbit light curve, we measured a secondary eclipse depth of $731 \pm 46$ ppm, as well as phase-curve variations from the planet's longitudinal brightness modulation and ellipsoidal distortion of the host star. Combining the TESS-band occultation measurement with a $K_s$-band secondary eclipse depth ($2012 \pm 80$ ppm) derived from ground-based observations, we find that the dayside emission of TOI-2109b is consistent with a brightness temperature of $3631 \pm 69$ K, making it the second hottest exoplanet hitherto discovered. By virtue of its extreme irradiation and strong planet-star gravitational interaction, TOI-2109b is an exceptionally promising target for intensive follow-up studies using current and near-future telescope facilities to probe for orbital decay, detect tidally driven atmospheric escape, and assess the impacts of H$_2$ dissociation and recombination on the global heat transport.

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arXiv2021

Physically-motivated basis functions for temperature maps of exoplanets

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.

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arXiv2021

A Comparative Study of Atmospheric Chemistry with VULCAN

We present an update of the open-source photochemical kinetics code VULCAN (Tsai et al. 2017; https://github.com/exoclime/VULCAN) to include C-H-N-O-S networks and photochemistry. Additional new features are advection transport, condensation, various boundary conditions, and temperature-dependent UV cross-sections. First, we validate our photochemical model for hot Jupiter atmospheres by performing an intercomparison of HD 189733b models between Moses et al. (2011), Venot et al. (2012), and VULCAN, to diagnose possible sources of discrepancy. Second, we set up a model of Jupiter extending from the deep troposphere to upper stratosphere to verify the kinetics for low temperature. Our model reproduces hydrocarbons consistent with observations, and the condensation scheme successfully predicts the locations of water and ammonia ice clouds. We show that vertical advection can regulate the local ammonia distribution in the deep atmosphere. Third, we validate the model for oxidizing atmospheres by simulating Earth and find agreement with observations. Last, VULCAN is applied to four representative cases of extrasolar giant planets: WASP-33b, HD 189733b, GJ 436b, and 51 Eridani b. We look into the effects of the C/O ratio and chemistry of titanium/vanadium species for WASP-33b; we revisit HD 189733b for the effects of sulfur and carbon condensation; the effects of internal heating and vertical mixing ($K_{\textrm{zz}}$) are explored for GJ 436b; we test updated planetary properties for 51 Eridani b with S$_8$ condensates. We find sulfur can couple to carbon or nitrogen and impact other species such as hydrogen, methane, and ammonia. The observable features of the synthetic spectra and trends in the photochemical haze precursors are discussed for each case.

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arXiv2021

Closed-formed ab initio solutions of geometric albedos and reflected light phase curves of exoplanets

Studying the albedos of the planets and moons of the Solar System dates back at least a century. Of particular interest is the relationship between the albedo measured at superior conjunction, known as the ``geometric albedo", and the albedo considered over all orbital phase angles, known as the ``spherical albedo". Determining the relationship between the geometric and spherical albedos usually involves complex numerical calculations and closed-form solutions are restricted to simple reflection laws. Here we report the discovery of closed-form solutions for the geometric albedo and integral phase function, which apply to any law of reflection that only depends on the scattering angle. The shape of a reflected light phase curve, quantified by the integral phase function, and the secondary eclipse depth, quantified by the geometric albedo, may now be self-consistently inverted to retrieve globally averaged physical parameters. Fully Bayesian phase curve inversions for reflectance maps and simultaneous light curve detrending may now be performed due to the efficiency of computation. Demonstrating these innovations for the hot Jupiter Kepler-7b, we infer a geometric albedo of $0.25^{+0.01}_{-0.02}$, a phase integral of $1.77 \pm0.07$, a spherical albedo of $0.44^{+0.02}_{-0.03}$ and a scattering asymmetry factor of $0.07^{+0.12}_{-0.11}$.

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arXiv2021

Atmospheric characterization of terrestrial exoplanets in the mid-infrared: biosignatures, habitability & diversity

Exoplanet science is one of the most thriving fields of modern astrophysics. A major goal is the atmospheric characterization of dozens of small, terrestrial exoplanets in order to search for signatures in their atmospheres that indicate biological activity, assess their ability to provide conditions for life as we know it, and investigate their expected atmospheric diversity. None of the currently adopted projects or missions, from ground or in space, can address these goals. In this White Paper we argue that a large space-based mission designed to detect and investigate thermal emission spectra of terrestrial exoplanets in the MIR wavelength range provides unique scientific potential to address these goals and surpasses the capabilities of other approaches. While NASA might be focusing on large missions that aim to detect terrestrial planets in reflected light, ESA has the opportunity to take leadership and spearhead the development of a large MIR exoplanet mission within the scope of the "Voyage 2050" long-term plan establishing Europe at the forefront of exoplanet science for decades to come. Given the ambitious science goals of such a mission, additional international partners might be interested in participating and contributing to a roadmap that, in the long run, leads to a successful implementation. A new, dedicated development program funded by ESA to help reduce development and implementation cost and further push some of the required key technologies would be a first important step in this direction. Ultimately, a large MIR exoplanet imaging mission will be needed to help answer one of mankind's most fundamental questions: "How unique is our Earth?"

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arXiv2021

Simulating gas giant exoplanet atmospheres with Exo-FMS: Comparing semi-grey, picket fence and correlated-k radiative-transfer schemes

Radiative-transfer (RT) is a fundamental part of modelling exoplanet atmospheres with general circulation models (GCMs). An accurate RT scheme is required for estimates of the atmospheric energy transport and for gaining physical insight from model spectra. We implement three RT schemes for Exo-FMS: semi-grey, non-grey `picket fence', and real gas with correlated-k. We benchmark the Exo-FMS GCM using these RT schemes to hot Jupiter simulation results from the literature. We perform a HD 209458b-like simulation with the three schemes and compare their results. These simulations are then post-processed to compare their observable differences. The semi-grey scheme results show qualitative agreement with previous studies in line with variations seen between GCM models. The real gas model reproduces well the temperature and dynamical structures from other studies. After post-processing our non-grey picket fence scheme compares very favourably with the real gas model, producing similar transmission spectra, emission spectra and phase curve behaviours. Exo-FMS is able to reliably reproduce the essential features of contemporary GCM models in the hot gas giant regime. Our results suggest the picket fence approach offers a simple way to improve upon RT realism beyond semi-grey schemes.

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arXiv2021

Visible-light Phase Curves from the Second Year of the TESS Primary Mission

We carried out a systematic study of full-orbit phase curves for known transiting systems in the northern ecliptic sky that were observed during Year 2 of the TESS primary mission. We applied the same methodology for target selection, data processing, and light-curve fitting as we did in our Year 1 study. Out of the 15 transiting systems selected for analysis, seven - HAT-P-7, KELT-1, KELT-9, KELT-16, KELT-20, Kepler-13A, and WASP-12 - show statistically significant secondary eclipses and day-night atmospheric brightness modulations. Small eastward dayside hotspot offsets were measured for KELT-9b and WASP-12b. KELT-1, Kepler-13A, and WASP-12 show additional phase-curve variability attributed to the tidal distortion of the host star; the amplitudes of these signals are consistent with theoretical predictions. We combined occultation measurements from TESS and Spitzer to compute dayside brightness temperatures, TESS-band geometric albedos, Bond albedos, and phase integrals for several systems. The new albedo values solidify the previously reported trend between dayside temperature and geometric albedo for planets with $1500<T_{\mathrm{day}}<3000$ K. For Kepler-13Ab, we carried out an atmospheric retrieval of the full secondary eclipse spectrum, which revealed a non-inverted temperature-pressure profile, significant H$_{2}$O and K absorption in the near-infrared, evidence for strong optical atmospheric opacity due to sodium, and a confirmation of the high geometric albedo inferred from our simpler analysis. We explore the implications of the phase integrals (ratios of Bond to geometric albedos) for understanding exoplanet clouds. We also report updated transit ephemerides for all of the systems studied in this work.

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arXiv2021

HELIOS-K 2.0 Opacity Calculator and Open-source Opacity Database for Exoplanetary Atmospheres

Computing and using opacities is a key part of modeling and interpreting data of exoplanetary atmospheres. Since the underlying spectroscopic line lists are constantly expanding and currently include up to ~ 10^10 - 10^11 transition lines, the opacity calculator codes need to become more powerful. Here we present major upgrades to the HELIOS-K GPU-accelerated opacity calculator and describe the necessary steps to process large line lists within a reasonable amount of time. Besides performance improvements, we include more capabilities and present a toolbox for handling different atomic and molecular data sets: from downloading and pre-processing the data to performing the opacity calculations in a user-friendly way. HELIOS-K supports line lists from ExoMol, HITRAN, HITEMP, NIST, Kurucz and VALD3. By matching the resolution of 0.1 cm^-1 and cutting length of 25 cm^-1 used by the ExoCross code for timing performance (251 seconds excluding data read-in time), HELIOS-K can process the ExoMol BT2 water line list in 12.5 seconds. Using a resolution of 0.01 cm^-1, it takes 45 seconds - equivalent to about 10^7 lines per second. As a wavenumber resolution of 0.01 cm^-1 suffices for most exoplanetary atmosphere spectroscopic calculations, we adopt this resolution in calculating opacity functions for several hundred atomic and molecular species, and make them freely available on the open-access DACE database. For the opacity calculations of the database, we use a cutting length of 100 cm^-1 for molecules and no cutting length for atoms. Our opacities are available for downloading from https://dace.unige.ch/opacityDatabase and may be visualized using https://dace.unige.ch/opacity.

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arXiv2021

Lithologic Controls on Silicate Weathering Regimes of Temperate Planets

Weathering of silicate rocks at a planetary surface can draw down CO$_2$ from the atmosphere for eventual burial and long-term storage in the planetary interior. This process is thought to provide an essential negative feedback to the carbonate-silicate cycle (carbon cycle) to maintain clement climates on Earth and potentially similar temperate exoplanets. We implement thermodynamics to determine weathering rates as a function of surface lithology (rock type). These rates provide upper limits that allow estimating the maximum rate of weathering in regulating climate. This modeling shows that the weathering of mineral assemblages in a given rock, rather than individual minerals, is crucial to determine weathering rates at planetary surfaces. By implementing a fluid-transport controlled approach, we further mimic chemical kinetics and thermodynamics to determine weathering rates for three types of rocks inspired by the lithologies of Earth's continental and oceanic crust, and its upper mantle. We find that thermodynamic weathering rates of a continental crust-like lithology are about one to two orders of magnitude lower than those of a lithology characteristic of the oceanic crust. We show that when the CO$_2$ partial pressure decreases or surface temperature increases, thermodynamics rather than kinetics exerts a strong control on weathering. The kinetically- and thermodynamically-limited regimes of weathering depend on lithology, whereas, the supply-limited weathering is independent of lithology. Our results imply that the temperature-sensitivity of thermodynamically-limited silicate weathering may instigate a positive feedback to the carbon cycle, in which the weathering rate decreases as the surface temperature increases.

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arXiv2020

Exploring the atmospheric dynamics of the extreme ultra-hot Jupiter KELT-9b using TESS photometry

We carry out a phase-curve analysis of the KELT-9 system using photometric observations from NASA's Transiting Exoplanet Survey Satellite (TESS). The measured secondary eclipse depth and peak-to-peak atmospheric brightness modulation are $650^{+14}_{-15}$ ppm and $566\pm16$ ppm, respectively. The planet's brightness variation reaches maximum $31\pm5$ minutes before the midpoint of the secondary eclipse, indicating a $5\overset{\circ}{.}2\pm0\overset{\circ}{.}9$ eastward shift in the dayside hot spot from the substellar point. We also detect stellar pulsations on KELT-9 with a period of $7.58695\pm0.00091$ hours. The dayside emission of KELT-9b in the TESS bandpass is consistent with a blackbody brightness temperature of $4600\pm100$ K. The corresponding nightside brightness temperature is $3040\pm100$ K, comparable to the dayside temperatures of the hottest known exoplanets. In addition, we detect a significant phase-curve signal at the first harmonic of the orbital frequency and a marginal signal at the second harmonic. While the amplitude of the first harmonic component is consistent with the predicted ellipsoidal distortion modulation assuming equilibrium tides, the phase of this photometric variation is shifted relative to the expectation. Placing KELT-9b in the context of other exoplanets with phase-curve observations, we find that the elevated nightside temperature and relatively low day-night temperature contrast agree with the predictions of atmospheric models that include H$_{2}$ dissociation and recombination. The nightside temperature of KELT-9b implies an atmospheric composition containing about 50% molecular and 50% atomic hydrogen at 0.1 bar, a nightside emission spectrum that deviates significantly from a blackbody, and a 0.5-2.0 $μ$m transmission spectrum that is featureless at low resolution.

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