Kevin Heng

University of Notre Dame, South Bend, Indiana, United States

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Publications (79)378.52 Total impact

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    ABSTRACT: Optical phase curves have become one of the common probes of exoplanetary atmospheres, but the information they encode has not been fully elucidated. Building on a diverse body of work, we upgrade the Flexible Modeling System (FMS) to include scattering in the two-stream, dual-band approximation and generate plausible, three-dimensional structures of irradiated atmospheres to study the radiative effects of aerosols or condensates. In the optical, we treat the scattering of starlight using a generalisation of Beer's law that allows for a finite Bond albedo to be prescribed. In the infrared, we implement the two-stream solutions and include scattering via an infrared scattering parameter. We present a suite of four-parameter general circulation models for Kepler-7b and demonstrate that its climatology is expected to be robust to variations in optical and infrared scattering. The westward and eastward shifts of the optical and infrared phase curves, respectively, are shown to be robust outcomes of the simulations. Assuming micron-sized particles and a simplified treatment of local brightness, we further show that the peak offset of the optical phase curve is sensitive to the composition of the aerosols or condensates. However, to within the measurement uncertainties, we cannot distinguish between aerosols made of silicates (enstatite or forsterite), iron, corundum or titanium oxide, based on a comparison to the measured peak offset ($41^\circ \pm 12^\circ$) of the optical phase curve of Kepler-7b. Measuring high-precision optical phase curves will provide important constraints on the atmospheres of cloudy exoplanets and reduce degeneracies in interpreting their infrared spectra.
    No preview · Article · Jan 2016
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    ABSTRACT: Over the duration of the Kepler mission, KIC 8462852 was observed to undergo irregularly shaped, aperiodic dips in flux down to below the 20% level. The dipping activity can last for between 5 and 80 days. We characterize the object with high-resolution spectroscopy, spectral energy distribution fitting, and Fourier analyses of the Kepler light curve. We determine thatKIC 8462852 is a main-sequence F3 V/IV star, with a rotation period ~0.88 d, that exhibits no significant IR excess. In this paper, we describe various scenarios to explain the mysterious events in the Kepler light curve, most of which have problems explaining the data in hand. By considering the observational constraints on dust clumps orbiting a normal main-sequence star, we conclude that the scenario most consistent with the data is the passage of a family of exocomet fragments, all of which are associated with a single previous breakup event. We discuss the necessity of future observations to help interpret the system.
    Full-text · Article · Sep 2015 · Monthly Notices of the Royal Astronomical Society
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    ABSTRACT: The science of extra-solar planets is one of the most rapidly changing areas of astrophysics and since 1995 the number of planets known has increased by almost two orders of magnitude. A combination of ground-based surveys and dedicated space missions has resulted in 560-plus planets being detected, and over 1200 that await confirmation. NASA's Kepler mission has opened up the possibility of discovering Earth-like planets in the habitable zone around some of the 100,000 stars it is surveying during its 3 to 4-year lifetime. The new ESA's Gaia mission is expected to discover thousands of new planets around stars within 200 parsecs of the Sun. The key challenge now is moving on from discovery, important though that remains, to characterisation: what are these planets actually like, and why are they as they are? In the past ten years, we have learned how to obtain the first spectra of exoplanets using transit transmission and emission spectroscopy. With the high stability of Spitzer, Hubble, and large ground-based telescopes the spectra of bright close-in massive planets can be obtained and species like water vapour, methane, carbon monoxide and dioxide have been detected. With transit science came the first tangible remote sensing of these planetary bodies and so one can start to extrapolate from what has been learnt from Solar System probes to what one might plan to learn about their faraway siblings. As we learn more about the atmospheres, surfaces and near-surfaces of these remote bodies, we will begin to build up a clearer picture of their construction, history and suitability for life. The Exoplanet Characterisation Observatory, EChO, will be the first dedicated mission to investigate the physics and chemistry of Exoplanetary Atmospheres. By characterising spectroscopically more bodies in different environments we will take detailed planetology out of the Solar System and into the Galaxy as a whole.
    Full-text · Article · Sep 2015
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    Kevin Heng · James R. Lyons
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    ABSTRACT: We present a comprehensive study of the abundance of carbon dioxide in exoplanetary atmospheres. We construct analytical models of systems in chemical equilibrium that include carbon monoxide, carbon dioxide, water, methane and acetylene and relate the equilibrium constants of the chemical reactions to temperature and pressure via the tabulated Gibbs free energies. We prove that such chemical systems may be described by a quintic equation for the mixing ratio of methane. By examining the abundances of these molecules across a broad range of temperatures (spanning equilibrium temperatures from 600 to 2500 K), pressures (via temperature-pressure profiles that explore albedo and opacity variations) and carbon-to-oxygen ratios (from 0.1 to 100), we conclude that carbon dioxide is subdominant compared to carbon monoxide and water. Atmospheric mixing does not alter this conclusion if carbon dioxide is subdominant everywhere in the atmosphere. Carbon dioxide and carbon monoxide may attain comparable abundances if the metallicity is greatly enhanced, but this property is negated by temperatures above 1000 K. For hydrogen-dominated atmospheres, our generic result has the implication that retrieval studies need to set the subdominance of carbon dioxide as a prior of the calculation and not let its abundance completely roam free as a fitting parameter, because it directly affects the inferred value of the carbon-to-oxygen ratio and may produce unphysical conclusions. We discuss the relevance of these implications for the hot Jupiter WASP-12b and suggest that some of the previous results are chemically impossible. The relative abundance of carbon dioxide to acetylene is potentially a sensitive diagnostic of the carbon-to-oxygen ratio.
    Full-text · Article · Jul 2015 · The Astrophysical Journal
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    ABSTRACT: Ocean planets are volatile-rich planets, not present in our Solar system, which are thought to be dominated by deep, global oceans. This results in the formation of high-pressure water ice, separating the planetary crust from the liquid ocean and, thus, also from the atmosphere. Therefore, instead of a carbonate–silicate cycle like on the Earth, the atmospheric carbon dioxide concentration is governed by the capability of the ocean to dissolve carbon dioxide (CO2). In our study, we focus on the CO2 cycle between the atmosphere and the ocean which determines the atmospheric CO2 content. The atmospheric amount of CO2 is a fundamental quantity for assessing the potential habitability of the planet's surface because of its strong greenhouse effect, which determines the planetary surface temperature to a large degree. In contrast to the stabilizing carbonate–silicate cycle regulating the long-term CO2 inventory of the Earth atmosphere, we find that the CO2 cycle feedback on ocean planets is negative and has strong destabilizing effects on the planetary climate. By using a chemistry model for oceanic CO2 dissolution and an atmospheric model for exoplanets, we show that the CO2 feedback cycle can severely limit the extension of the habitable zone for ocean planets.
    Preview · Article · Jul 2015 · Monthly Notices of the Royal Astronomical Society
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    Kevin Heng · James R. Lyons · Shang-Min Tsai
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    ABSTRACT: We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets. Starting from the first law of thermodynamics, we demonstrate that the van't Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients) and procedures associated with the Gibbs free energy (minimisation, rescaling) have a common physical and mathematical origin. We correct an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and rigorously derive its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. To avoid confusion, we simply term them the dimensionless and dimensional equilibrium constants. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously thought without recourse to tagging on ad hoc functional forms. Our formulation of the evolution equations for chemical kinetics correctly enforces the book-keeping of elemental abundances, reproduces chemical equilibrium in the steady-state limit and is able to explain why photochemistry is an intrinsically disequilibrium effect. Finally, we derive analytical models of chemical systems with only hydrogen and with carbon, hydrogen and oxygen. For the latter, we include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.
    Full-text · Article · Jun 2015 · The Astrophysical Journal
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    ABSTRACT: We present imaging and spectroscopic observations with HST and VLT of the ring of SN 1987A from 1994 to 2014. After an almost exponential increase of the shocked emission from the hotspots up to day ~8,000 (~2009), both this and the unshocked emission are now fading. From the radial positions of the hotspots we see an acceleration of these up to 500-1000 km/s, consistent with the highest spectroscopic shock velocities from the radiative shocks. In the most recent observations (2013 and 2014), we find several new hotspots outside the inner ring, excited by either X-rays from the shocks or by direct shock interaction. All of these observations indicate that the interaction with the supernova ejecta is now gradually dissolving the hotspots. We predict, based on the observed decay, that the inner ring will be destroyed by ~2025.
    Full-text · Article · May 2015
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    Kevin Heng · Joshua Nathan Winn
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    ABSTRACT: What strange new worlds will our next-generation telescopes find?
    Preview · Article · Apr 2015 · American Scientist
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    ABSTRACT: We present a theory for interpreting the sodium lines detected in transmission spectra of exoplanetary atmospheres. Previous analyses employed the isothermal approximation and dealt only with the transit radius. By recognising the absorption depth and the transit radius as being independent observables, we develop a theory for jointly interpreting both quantities, which allows us to infer the temperatures and number densities associated with the sodium lines. We are able to treat a non-isothermal situation with a constant temperature gradient. Our novel diagnostics take the form of simple-to-use algebraic formulae and require measurements of the transit radii (and their corresponding absorption depths) at line center and in the line wing for both sodium lines. We apply our diagnostics to the HARPS data of HD 189733b, confirm the upper atmospheric heating reported by Huitson et al. (2012), derive a temperature gradient of $0.4376 \pm 0.0154$ K km$^{-1}$ and find densities $\sim 1$ to $10^4$ cm$^{-3}$.
    Full-text · Article · Mar 2015
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    Simon L. Grimm · Kevin Heng
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    ABSTRACT: We present an ultrafast opacity calculator for application to exoplanetary atmospheres, which we name HELIOS-K. It takes a line list as an input, computes the shape of each spectral line (e.g., a Voigt profile) and provides an option for grouping an enormous number of lines into a manageable number of bins. We implement a combination of Algorithm 916 and Gauss-Hermite quadrature to compute the Voigt profile, write the code in CUDA and optimise the computation for graphics processing units (GPUs). We use the k-distribution method to reduce $\sim 10^5$ to $10^8$ lines to $\sim 10$ to $10^4$ wavenumber bins, which may then be used for radiative transfer, atmospheric retrieval and general circulation models. We demonstrate that the resampling of the k-distribution function, within each bin, is an insignificant source of error across a broad range of wavenumbers and column masses. By contrast, the choice of line-wing cutoff for the Voigt profile is a significant source of error and affects the value of the computed flux by $\sim 10\%$. This is an outstanding physical (rather than computational) problem, due to our incomplete knowledge of pressure broadening of spectral lines in the far line wings. We emphasize that this problem remains regardless of whether one performs line-by-line calculations or uses the k-distribution method and affects all calculations of exoplanetary atmospheres requiring the use of wavelength-dependent opacities. We provide a checklist for reviewing radiative transfer and retrieval studies that require computations of the opacity function. Using a NVIDIA K20 GPU, HELIOS-K is capable of computing an opacity function with $\sim 10^5$ spectral lines in $\sim 1$ second and is publicly available as part of the Exoclimes Simulation Platform (ESP; www.exoclime.org).
    Preview · Article · Mar 2015 · The Astrophysical Journal
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    ABSTRACT: Exoplanet science is now in its full expansion, particularly after the CoRoT and Kepler space missions that led us to the discovery of thousands of extra-solar planets. The last decade has taught us that UV observations play a major role in advancing our understanding of planets and of their host stars, but the necessary UV observations can be carried out only by HST, and this is going to be the case for many years to come. It is therefore crucial to build a treasury data archive of UV exoplanet observations formed by a dozen "golden systems" for which observations will be available from the UV to the infrared. Only in this way we will be able to fully exploit JWST observations for exoplanet science, one of the key JWST science case.
    Full-text · Article · Mar 2015
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    ABSTRACT: We present new Hubble Space Telescope images of high-velocity Hα and Lyα emission in the outer debris of SN 1987 A. The Hα images are dominated by emission from hydrogen atoms crossing the reverse shock (RS). For the first time we observe emission from the RS surface well above and below the equatorial ring (ER), suggesting a bipolar or conical structure perpendicular to the ring plane. Using the Hα imaging, we measure the mass flux of hydrogen atoms crossing the RS front, in the velocity intervals (−7500 < Vobs < −2800 km s−1) and (1000 < Vobs < 7500 km s−1), = 1.2 × 10−3M yr−1. We also present the first Lyα imaging of the whole remnant and new Chandra X-ray observations. Comparing the spatial distribution of the Lyα and X-ray emission, we observe that the majority of the high-velocity Lyα emission originates interior to the ER. The observed Lyα/Hα photon ratio, ≈ 17, is significantly higher than the theoretically predicted ratio of ≈5 for neutral atoms crossing the RS front. We attribute this excess to Lyα emission produced by X-ray heating of the outer debris. The spatial orientation of the Lyα and X-ray emission suggests that X-ray heating of the outer debris is the dominant Lyα production mechanism in SN 1987 A at this phase in its evolution.
    No preview · Article · Mar 2015
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    ABSTRACT: We present new {\it Hubble Space Telescope} images of high-velocity H-$\alpha$ and Lyman-$\alpha$ emission in the outer debris of SN~1987A. The H-$\alpha$ images are dominated by emission from hydrogen atoms crossing the reverse shock. For the first time we observe emission from the reverse shock surface well above and below the equatorial ring, suggesting a bipolar or conical structure perpendicular to the ring plane. Using the H$\alpha$ imaging, we measure the mass flux of hydrogen atoms crossing the reverse shock front, in the velocity intervals ($-$7,500~$<$~$V_{obs}$~$<$~$-$2,800 km s$^{-1}$) and (1,000~$<$~$V_{obs}$~$<$~7,500 km s$^{-1}$), $\dot{M_{H}}$ = 1.2~$\times$~10$^{-3}$ M$_{\odot}$ yr$^{-1}$. We also present the first Lyman-$\alpha$ imaging of the whole remnant and new $Chandra$ X-ray observations. Comparing the spatial distribution of the Lyman-$\alpha$ and X-ray emission, we observe that the majority of the high-velocity Lyman-$\alpha$ emission originates interior to the equatorial ring. The observed Lyman-$\alpha$/H-$\alpha$ photon ratio, $\langle$$R(L\alpha / H\alpha)$$\rangle$ $\approx$~17, is significantly higher than the theoretically predicted ratio of $\approx$ 5 for neutral atoms crossing the reverse shock front. We attribute this excess to Lyman-$\alpha$ emission produced by X-ray heating of the outer debris. The spatial orientation of the Lyman-$\alpha$ and X-ray emission suggests that X-ray heating of the outer debris is the dominant Lyman-$\alpha$ production mechanism in SN 1987A at this phase in its evolution.
    Full-text · Article · Feb 2015
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    ABSTRACT: We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii as well as to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Our main conclusions are: (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are key constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. [...]
    Full-text · Article · Feb 2015 · Astronomy and Astrophysics
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    ABSTRACT: Exoplanet phase curves provide a wealth of information about atmospheric dynamics, energetics, and chemistry. Phase curves have been observed for relatively few planets, yet the current small sample already hints at the inadequacy of current atmospheric models. Our ultimate goal of understanding the global circulation patterns and their relation to atmospheric chemistry requires a larger and more homogenous sample. Here, we propose to more than double the sample of hot Jupiters with high S/N phase observations by targeting seven bright systems. Combined with the powerful new technique of high-resolution infrared Doppler spectroscopy, our observations will enable an unprecedented comparative study to relate global circulation patterns to atmospheric chemistry, and ultimately to facilitate retrieval of global abundance and temperature maps of extrasolar planets. The planets in our sample represent the best objects to leverage both space-based phase curves and ground-based spectroscopy in a combined analysis. Spectroscopic observations break the inclination degeneracy that plagued earlier non-transiting phase variations, while phase curves provide crucial information about the planetary thermal continuum that is lost in the inherently relative spectroscopic analysis. Our program uses Spitzer's recently-validated snapshot-phase curve mode to obtain high-precision photometry on long timescales with low data volumes and high scheduling flexibility, and our new retrieval approach will become a critical capability in an era of measurements at higher S/N and spectral resolution with JWST and Extremely Large ground-based telescopes.
    No preview · Article · Nov 2014
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    ABSTRACT: PLATO 2.0 is a mission candidate for ESA's M3 launch opportunity (2022/24). It addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, able to develop life? The PLATO 2.0 instrument consists of 34 small aperture telescopes providing a wide field-of-view and a large photometric magnitude range. It targets bright stars in wide fields to detect and characterize planets down to Earth-size by photometric transits, whose masses can then be determined by ground-based radial-velocity follow-up measurements. Asteroseismology will be performed for stars <=11mag to obtain highly accurate stellar parameters, including masses and ages. The combination of bright targets and asteroseismology results in high accuracy for the bulk planet parameters: 2%, 4-10% and 10% for planet radii, masses and ages, respectively. The foreseen baseline observing strategy includes two long pointings (2-3 years) to detect and bulk characterize planets reaching into the habitable zone (HZ) of solar-like stars and an additional step-and-stare phase to cover in total about 50% of the sky. PLATO 2.0 will observe up to 1,000,000 stars and detect and characterize hundreds of small planets, and thousands of planets in the Neptune to gas giant regime out to the HZ. It will therefore provide the first large-scale catalogue of bulk characterized planets with accurate radii, masses, mean densities and ages. This catalogue will include Earth-like planets at intermediate orbital distances, where surface temperatures are moderate. Coverage of this parameter range with statistical numbers of bulk characterized planets is unique to PLATO 2.0. ...
    Full-text · Article · Oct 2014 · Experimental Astronomy
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    ABSTRACT: We present high resolution transmission spectra of giant planet atmospheres from a coupled 3-D atmospheric dynamics and transmission spectrum model that includes Doppler shifts which arise from winds and planetary motion. We model jovian planets covering more than two orders of magnitude in incident flux, corresponding to planets with 0.9 to 55 day orbital periods around solar-type stars. The results of our 3-D dynamical models reveal certain aspects of high resolution transmission spectra that are not present in simple 1-D models. We find that the hottest planets experience strong substellar to anti-stellar (SSAS) winds, resulting in transmission spectra with net blue shifts of up to 3 km s$^{-1}$, whereas less irradiated planets show almost no net Doppler shifts. Compared to 1-D models, peak line strengths are significantly reduced for the hottest atmospheres owing to Doppler broadening from a combination of rotation (which is faster for close-in planets under the assumption of tidal locking) and atmospheric winds. Finally, high resolution transmission spectra may be useful in studying the atmospheres of exoplanets with optically thick clouds since line cores for very strong transitions should remain optically thick to very high altitude. High resolution transmission spectra are an excellent observational test for the validity of 3-D atmospheric dynamics models, because they provide a direct probe of wind structures and heat circulation. Ground-based exoplanet spectroscopy is currently on the verge of being able to verify some of our modeling predictions, most notably the dependence of SSAS winds on insolation. We caution that interpretation of high resolution transmission spectra based on 1-D atmospheric models may be inadequate, as 3-D atmospheric motions can produce a noticeable effect on the absorption signatures.
    Preview · Article · Sep 2014 · The Astrophysical Journal
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    Kevin Heng · Adam P. Showman
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    ABSTRACT: The characterization of exoplanetary atmospheres has come of age in the last decade, as astronomical techniques now allow for albedos, chemical abundances, temperature profiles and maps, rotation periods and even wind speeds to be measured. Atmospheric dynamics sets the background state of density, temperature and velocity that determines or influences the spectral and temporal appearance of an exoplanetary atmosphere. Hot exoplanets are most amenable to these characterization techniques; in the present review, we focus on highly-irradiated, large exoplanets (the "hot Jupiters"), as astronomical data begin to confront theoretical questions. We summarize the basic atmospheric quantities inferred from the astronomical observations. We review the state of the art by addressing a series of current questions and look towards the future by considering a separate set of exploratory questions. Attaining the next level of understanding will require a concerted effort of constructing multi-faceted, multi-wavelength datasets for benchmark objects. Understanding clouds presents a formidable obstacle, as they introduce degeneracies into the interpretation of spectra, yet their properties and existence are directly influenced by atmospheric dynamics. Confronting general circulation models with these multi-faceted, multi-wavelength datasets will help us understand these and other degeneracies. The coming decade will witness a decisive confrontation of theory and simulation by the next generation of astronomical data.
    Preview · Article · Jul 2014 · Annual Review of Earth and Planetary Sciences
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    ABSTRACT: The current instrumentation plan for the E-ELT foresees a High Resolution Spectrograph conventionally indicated as HIRES. Shaped on the study of extra-solar planet atmospheres, Pop-III stars and fundamental physical constants, HIRES is intended to embed observing modes at high-resolution (up to R=150000) and large spectral range (from the blue limit to the K band) useful for a large suite of science cases that can exclusively be tackled by the E-ELT. We present in this paper the solution for HIRES envisaged by the "HIRES initiative", the international collaboration established in 2013 to pursue a HIRES on E-ELT.
    Full-text · Conference Paper · Jun 2014
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    Kevin Heng · João M. Mendonça · Jaemin Lee
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    ABSTRACT: We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We further demonstrate that traditional non-isothermal treatments of each atmospheric layer lead to unphysical contributions to the fluxes. We concoct recipes for implementing two-stream radiative transfer in stand-alone calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat and the properties of scattering both in optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing and incoming fluxes in the convective regime.
    Preview · Article · Apr 2014 · The Astrophysical Journal Supplement Series

Publication Stats

999 Citations
378.52 Total Impact Points

Institutions

  • 2015
    • University of Notre Dame
      • Department of Physics
      South Bend, Indiana, United States
    • Columbia University
      New York, New York, United States
  • 2013-2015
    • Universität Bern
      • • Physics Institute
      • • Center for Space and Habitability
      Berna, Bern, Switzerland
    • European Southern Observatory
      Arching, Bavaria, Germany
  • 2010-2012
    • ETH Zurich
      • Institute for Astronomy
      Zürich, Zurich, Switzerland
    • Hochschule für Technik Zürich
      Zürich, Zurich, Switzerland
  • 2008-2009
    • Institute for Advanced Study
      Princeton Junction, New Jersey, United States
  • 2007-2008
    • Max Planck Institute for Extraterrestrial Physics
      Arching, Bavaria, Germany
    • Max Planck Institute for Astrophysics
      Arching, Bavaria, Germany
  • 2004-2008
    • University of Colorado at Boulder
      • • Center for Astrophysics and Space Astronomy
      • • Department of Astrophysical and Planetary Sciences
      Boulder, Colorado, United States