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Kevin Heng

Publications and source records attributed to Kevin Heng.

At least 109 records · Page 6Linked to original sources
arXiv2018

Analytical Models of Exoplanetary Atmospheres. V. Non-gray Thermal Structure with Coherent Scattering

We apply the picket fence treatment to model the effects brought about by spectral lines on the thermal structure of irradiated atmospheres. The lines may be due to purely absorption processes, purely coherent scattering processes or some combination of absorption and scattering. If the lines arise as a pure absorption process, the surface layers of the atmosphere are cooler whereas this surface cooling is completely absent if the lines are due to pure coherent isotropic scattering. The lines also lead to a warming of the deeper atmosphere. The warming of the deeper layers is, however, independent of the nature of line formation. Accounting for coherent isotropic scattering in the shortwave and longwave continuum results in anti-greenhouse cooling and greenhouse warming on an atmosphere-wide scale. The effects of coherent isotropic scattering in the line and continuum operate in tandem to determine the resulting thermal structure of the irradiated atmosphere.

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arXiv2018

Revisiting the Phase Curves of WASP-43b: Confronting Reanalyzed Spitzer Data with Cloudy Atmospheres

Recently acquired Hubble and Spitzer phase curves of the short-period hot Jupiter WASP-43b make it an ideal target for confronting theory with data. On the observational front, we re-analyze the 3.6 and 4.5 $μ$m Spitzer phase curves and demonstrate that our improved analysis better removes residual red noise due to intra-pixel sensitivity, which leads to greater fluxes emanating from the nightside of WASP-43b, thus reducing the tension between theory and data. On the theoretical front, we construct cloudfree and cloudy atmospheres of WASP-43b using our Global Circulation Model (GCM), THOR, which solves the non-hydrostatic Euler equations (compared to GCMs that typically solve the hydrostatic primitive equations). The cloudfree atmosphere produces a reasonable fit to the dayside emission spectrum. The multi-phase emission spectra constrain the cloud deck to be confined to the nightside and have a finite cloud-top pressure. The multi-wavelength phase curves are naturally consistent with our cloudy atmospheres, except for the 4.5 $μ$m phase curve, which requires the presence of enhanced carbon dioxide in the atmosphere of WASP-43b. Multi-phase emission spectra at higher spectral resolution, as may be obtained using the James Webb Space Telescope, and a reflected-light phase curve at visible wavelengths would further constrain the properties of clouds in WASP-43b.

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arXiv2018

The nature of the TRAPPIST-1 exoplanets

Context. The TRAPPIST-1 system hosts seven Earth-sized, temperate exoplanets orbiting an ultra-cool dwarf star. As such, it represents a remarkable setting to study the formation and evolution of terrestrial planets that formed in the same protoplanetary disk. While the sizes of the TRAPPIST-1 planets are all known to better than 5% precision, their densities have significant uncertainties (between 28% and 95%) because of poor constraints on the planet's masses. Aims.The goal of this paper is to improve our knowledge of the TRAPPIST-1 planetary masses and densities using transit-timing variations (TTV). The complexity of the TTV inversion problem is known to be particularly acute in multi-planetary systems (convergence issues, degeneracies and size of the parameter space), especially for resonant chain systems such as TRAPPIST-1. Methods. To overcome these challenges, we have used a novel method that employs a genetic algorithm coupled to a full N-body integrator that we applied to a set of 284 individual transit timings. This approach enables us to efficiently explore the parameter space and to derive reliable masses and densities from TTVs for all seven planets. Results. Our new masses result in a five- to eight-fold improvement on the planetary density uncertainties, with precisions ranging from 5% to 12%. These updated values provide new insights into the bulk structure of the TRAPPIST-1 planets. We find that TRAPPIST-1\,c and e likely have largely rocky interiors, while planets b, d, f, g, and h require envelopes of volatiles in the form of thick atmospheres, oceans, or ice, in most cases with water mass fractions less than 5%.

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arXiv2018

SUPERSHARP - Segmented Unfolding Primary for Exoplanet Research via Spectroscopic High Angular Resolution Photography

We propose to search for biosignatures in the spectra of reflected light from about 100 Earth-sized planets that are already known to be orbiting in their habitable zones (HZ). For a sample of G and K type hosts, most of these planets will be between 25 and 50 milli-arcsec (mas) from their host star and 1 billion to 10 billion times fainter. To separate the planet's image from that of its host star at the wavelength (763nm) of the oxygen biosignature we need a telescope with an aperture of 16 metres. Furthermore, the intensity of the light from the host star at the position in the image of the exoplanet must be suppressed otherwise the exoplanet will be lost in the glare. This presents huge technical challenges. The Earth's atmosphere is turbulent which makes it impossible to achieve the required contrast from the ground at 763nm. The telescope therefore needs to be in space and to fit the telescope in the rocket fairing it must be a factor of 4 or more times smaller when folded than when operational. To obtain spectroscopy of the planet's biosignature at 763nm we need to use an integral field spectrometer (IFS) with a field of view (FOV) of 1000 x 1000 milli-arcsec (mas) and a spectral resolution of 100. This is a device that simultaneously takes many pictures of the exoplanet each at a slightly different wavelength which are then recorded as a data cube with two spatial dimensions and one wavelength dimension. In every data cube wavelength slice, the background light from the host star at the location of the planet image must be minimised. This is achieved via a coronagraph which blocks the light from the host star and active/adaptive optics techniques which continuously maintain very high accuracy optical alignment to make the images as sharp as possible. These are the technical challenges to be addressed in a design study.

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arXiv2017

Orbital misalignment of the Neptune-mass exoplanet GJ 436b with the spin of its cool star

The angle between the spin of a star and its planets' orbital planes traces the history of the planetary system. Exoplanets orbiting close to cool stars are expected to be on circular, aligned orbits because of strong tidal interactions with the stellar convective envelope. Spin-orbit alignment can be measured when the planet transits its star, but such ground-based spectroscopic measurements are challenging for cool, slowly-rotating stars. Here we report the characterization of a planet three-dimensional trajectory around an M dwarf star, derived by mapping the spectrum of the stellar photosphere along the chord transited by the planet. We find that the eccentric orbit of the Neptune-mass exoplanet GJ 436b is nearly perpendicular to the stellar equator. Both eccentricity and misalignment, surprising around a cool star, can result from dynamical interactions (via Kozai migration) with a yet-undetected outer companion. This inward migration of GJ 436b could have triggered the atmospheric escape that now sustains its giant exosphere. Eccentric, misaligned exoplanets orbiting close to cool stars might thus hint at the presence of unseen perturbers and illustrate the diversity of orbital architectures seen in exoplanetary systems.

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arXiv2017

Optical properties of potential condensates in exoplanetary atmospheres

The prevalence of clouds in currently observable exoplanetary atmospheres motivates the compilation and calculation of their optical properties. First, we present a new open-source Mie scattering code known as LX-MIE, which is able to consider large size parameters ($\sim 10^7$) using a single computational treatment. We validate LX-MIE against the classical MIEV0 code as well as previous studies. Second, we embark on an expanded survey of the published literature for both the real and imaginary components of the refractive indices of 32 condensate species. As much as possible, we rely on experimental measurements of the refractive indices and resort to obtaining the real from the imaginary component (or vice versa), via the Kramers-Kronig relation, only in the absence of data. We use these refractive indices as input for LX-MIE to compute the absorption, scattering and extinction efficiencies of all 32 condensate species. Finally, we use a three-parameter function to provide convenient fits to the shape of the extinction efficiency curve. We show that the errors associated with these simple fits in the Wide Field Camera 3 (WFC3), J, H and K wavebands are $\sim 10\%$. These fits allow for the extinction cross section or opacity of the condensate species to be easily included in retrieval analyses of transmission spectra. We discuss prospects for future experimental work. The compilation of the optical constants and LX-MIE are publicly available as part of the open-source Exoclime Simulation Platform (http://www.exoclime.org).

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arXiv2017

Secondary atmospheres on HD 219134 b and c

We analyze the interiors of HD~219134~b and c, which are among the coolest super Earths detected thus far. Without using spectroscopic measurements, we aim at constraining if the possible atmospheres are hydrogen-rich or hydrogen-poor. In a first step, we employ a full probabilistic Bayesian inference analysis in order to rigorously quantify the degeneracy of interior parameters given the data of mass, radius, refractory element abundances, semi-major axes, and stellar irradiation. We obtain constraints on structure and composition for core, mantle, ice layer, and atmosphere. In a second step, we aim to draw conclusions on the nature of possible atmospheres by considering atmospheric escape. Specifically, we compare the actual possible atmospheres to a threshold thickness above which a primordial (H$_2$-dominated) atmosphere can be retained against evaporation over the planet's lifetime. The best constrained parameters are the individual layer thicknesses. The maximum radius fraction of possible atmospheres are 0.18 and 0.13 $R$ (radius), for planets b and c, respectively. These values are significantly smaller than the threshold thicknesses of primordial atmospheres: 0.28 and 0.19 $R$, respectively. Thus, the possible atmospheres of planets b and c are unlikely to be H$_2$-dominated. However, whether possible volatile layers are made of gas or liquid/solid water cannot be uniquely determined. Our main conclusions are: (1) the possible atmospheres for planets b and c are enriched and thus possibly secondary in nature, and (2) both planets may contain a gas layer, whereas the layer of HD 219134 b must be larger. HD 219134 c can be rocky.

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arXiv2017

Retrieval Analysis of the Emission Spectrum of WASP-12b: Sensitivity of Outcomes to Prior Assumptions and Implications for Formation History

We analyze the emission spectrum of the hot Jupiter WASP-12b using our HELIOS-R retrieval code and HELIOS-K opacity calculator. When interpreting Hubble and Spitzer data, the retrieval outcomes are found to be prior-dominated. When the prior distributions of the molecular abundances are assumed to be log-uniform, the volume mixing ratio of HCN is found to be implausibly high. A VULCAN chemical kinetics model of WASP-12b suggests that chemical equilibrium is a reasonable assumption even when atmospheric mixing is implausibly rigorous. Guided by (exo)planet formation theory, we set Gaussian priors on the elemental abundances of carbon, oxygen and nitrogen with the Gaussian peaks being centered on the measured C/H, O/H and N/H values of the star. By enforcing chemical equilibrium, we find substellar O/H and stellar to slightly superstellar C/H for the dayside atmosphere of WASP-12b. The superstellar carbon-to-oxygen ratio is just above unity, regardless of whether clouds are included in the retrieval analysis, consistent with Madhusudhan et al. (2011). Furthermore, whether a temperature inversion exists in the atmosphere depends on one's assumption for the Gaussian width of the priors. Our retrieved posterior distributions are consistent with the formation of WASP-12b in a solar-composition protoplanetary disk, beyond the water iceline, via gravitational instability or pebble accretion (without core erosion) and migration inwards to its present orbital location via a disk-free mechanism, and are inconsistent with both in-situ formation and core accretion with disk migration, as predicted by Madhusudhan et al. (2017). We predict that the interpretation of James Webb Space Telescope WASP-12b data will not be prior-dominated.

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arXiv2017

Analytical Models of Exoplanetary Atmospheres. IV. Improved Two-stream Radiative Transfer for the Treatment of Aerosols

We present a novel generalization of the two-stream method of radiative transfer, which allows for the accurate treatment of radiative transfer in the presence of strong infrared scattering by aerosols. We prove that this generalization involves only a simple modification of the coupling coefficients and transmission functions in the hemispheric two-stream method. This modification originates from allowing the ratio of the first Eddington coefficients to depart from unity. At the heart of the method is the fact that this ratio may be computed once and for all over the entire range of values of the single-scattering albedo and scattering asymmetry factor. We benchmark our improved two-stream method by calculating the fraction of flux reflected by a single atmospheric layer (the reflectivity) and comparing these calculations to those performed using a 32-stream discrete-ordinates method. We further compare our improved two-stream method to the two-stream source function (16 streams) and delta-Eddington methods, demonstrating that it is often more accurate at the order-of-magnitude level. Finally, we illustrate its accuracy using a toy model of the early Martian atmosphere hosting a cloud layer composed of carbon-dioxide ice particles. The simplicity of implementation and accuracy of our improved two-stream method renders it suitable for implementation in three-dimensional general circulation models. In other words, our improved two-stream method has the ease of implementation of a standard two-stream method, but the accuracy of a 32-stream method.

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arXiv2017

Balmer-dominated shocks in Tycho's SNR: omnipresence of CRs

We present wide-field, spatially and highly resolved spectroscopic observations of Balmer filaments in the northeastern rim of Tycho's supernova remnant in order to investigate the signal of cosmic-ray (CR) acceleration. The spectra of Balmer-dominated shocks (BDSs) have characteristic narrow (FWHM $\sim$ 10 kms$^{-1}$) and broad (FWHM $\sim$ 1000 kms$^{-1}$) H$α$ components. CRs affect the H$α$-line parameters: heating the cold neutrals in the interstellar medium results in broadening of the narrow H$α$-line width beyond 20 kms$^{-1}$, but also in reduction of the broad H$α$-line width due to energy being removed from the protons in the post-shock region. For the first time we show that the width of the narrow H$α$ line, much larger than 20 kms$^{-1}$, is not a resolution or geometric effect nor a spurious result of a neglected intermediate (FWHM $\sim$ 100 kms$^{-1}$) component resulting from hydrogen atoms undergoing charge exchange with warm protons in the broad-neutral precursor. Moreover, we show that a narrow line width $\gg$ 20 kms$^{-1}$ extends across the entire NE rim, implying CR acceleration is ubiquitous, and making it possible to relate its strength to locally varying shock conditions. Finally, we find several locations along the rim, where spectra are significantly better explained (based on Bayesian evidence) by inclusion of the intermediate component, with a width of 180 kms$^{-1}$ on average.

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arXiv2017

Balmer filaments in Tycho's supernova remnant: an interplay between cosmic-ray and broad-neutral precursors

We present H$α$ spectroscopic observations and detailed modelling of the Balmer filaments in the supernova remnant Tycho. We used Galaxy H$α$ Fabry-Pérot Spectrometer on the William Herschel Telescope with a 3.4'$\times$3.4' field-of-view, 0.2" pixel scale and $σ_\rm{instr}=8.1$ km/s resolution at 1" seeing for $\sim10$ hours, resulting in 82 spatial-spectral bins that resolve the narrow H$α$ line in the entire Tycho's northeastern rim. For the first time, we can mitigate artificial line broadening from unresolved differential motion, and probe H$α$ emission parameters in varying shock and ambient medium conditions. Broad H$α$ line remains unresolved within spectral coverage of 392 km/s. We employed Bayesian inference to obtain reliable parameter confidence intervals, and quantify the evidence for models with multiple line components. The median H$α$ narrow-line full-width at half-maximum of all bins and models is $W_\rm{NL}=(54.8\pm1.8)$ km/s at the $95\%$ confidence level, varying within [35, 72] km/s between bins and clearly broadened compared to the intrinsic (thermal) $\approx20$ km/s. Possible line splits are accounted for, significant in $\approx18\%$ of the filament, and presumably due to remaining projection effects. We also find wide-spread evidence for intermediate-line emission of a broad-neutral precursor, with median $W_\rm{IL}=(180\pm14)$ km/s ($95\%$ confidence). Finally, we present a measurement of the remnant's systemic velocity, $V_\rm{LSR}=-34$ km/s, and map differential line-of-sight motions. Our results confirm the existence and interplay of shock precursors in Tycho's remnant. In particular, we show that suprathermal narrow-line emission is near-universal in Tycho and that, in absence of an alternative explanation, collisionless supernova remnant shocks constitute a viable acceleration source for Galactic TeV Cosmic-Ray protons.

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arXiv2017

HELIOS-Retrieval: An Open-source, Nested Sampling Atmospheric Retrieval Code, Application to the HR 8799 Exoplanets and Inferred Constraints for Planet Formation

We present an open-source retrieval code named HELIOS-Retrieval (hereafter HELIOS-R), designed to obtain chemical abundances and temperature-pressure profiles from inverting the measured spectra of exoplanetary atmospheres. In the current implementation, we use an exact solution of the radiative transfer equation, in the pure absorption limit, in our forward model, which allows us to analytically integrate over all of the outgoing rays (instead of performing Gaussian quadrature). Two chemistry models are considered: unconstrained chemistry (where the mixing ratios are treated as free parameters) and equilibrium chemistry (enforced via analytical formulae, where only the elemental abundances are free parameters). The nested sampling algorithm allows us to formally implement Occam's Razor based on a comparison of the Bayesian evidence between models. We perform a retrieval analysis on the measured spectra of the HR 8799b, c, d and e directly imaged exoplanets. Chemical equilibrium is disfavored by the Bayesian evidence for HR 8799b, c and d. We find supersolar C/O, C/H and O/H values for the outer HR 8799b and c exoplanets, while the inner HR 8799d and e exoplanets have substellar C/O, substellar C/H and superstellar O/H values. If these retrieved properties are representative of the bulk compositions of the exoplanets, then they are inconsistent with formation via gravitational instability (without late-time accretion) and consistent with a core accretion scenario in which late-time accretion of ices occurred differently for the inner and outer exoplanets. For HR 8799e, we find that spectroscopy in the K band is crucial for constraining C/O and C/H. HELIOS-R is publicly available as part of the Exoclimes Simulation Platform (ESP; www.exoclime.org).

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arXiv2017

How does the shape of the stellar spectrum affect the Raman scattering features in the albedo of exoplanets?

Diagnostic potential of the spectral signatures of Raman scattering imprinted in planetary albedo spectra at short optical wavelengths has been demonstrated in research on Solar System planets and has recently been proposed as a probe of exoplanet atmospheres, complementary to albedo studies at longer wavelengths. Spectral features caused by Raman scattering offer insight into the properties of planetary atmospheres, such as the atmospheric depth, composition, and temperature, as well as the possibility of detecting and spectroscopically identifying spectrally inactive species, such as H$_2$ and N$_2$, in the visible wavelength range. Raman albedo features, however, depend on both the properties of the atmosphere and the shape of the incident stellar spectrum. Identical planetary atmospheres can produce very different albedo spectra depending on the spectral properties of the host star. Here we present a set of geometric albedo spectra calculated for atmospheres with H$_2$/He, N$_2$, and CO$_2$ composition, irradiated by different stellar types ranging from late A to late K stars. Prominent albedo features caused by Raman scattering appear at different wavelengths for different types of host stars. We investigate how absorption due to alkali elements, sodium and potassium, may affect the intensity of Raman features, and discuss the preferred observing strategies for detecting Raman features in future observations.

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arXiv2017

Habitable Moist Atmospheres On Terrestrial Planets Near the Inner Edge Of the Habitable Zone Around M-dwarfs

Terrestrial planets in the habitable zones (HZs) of low-mass stars and cool dwarfs have received significant scrutiny recently because their shorter orbital periods increase their chances of detection and characterization compared to planets around G-dwarfs. As these planets are likely tidal-locked, improved 3D numerical simulations of such planetary atmospheres are needed to guide target selection. Here we use a 3-D climate system model, updated with new water-vapor absorption coefficients derived from the HITRAN 2012 database, to study ocean covered planets at the inner edge of the HZ around late-M to mid-K stars ($2600$ K <= Teff <= 4500K). Our results indicate that these updated water-vapor coefficients result in significant warming compared to previous studies, so the inner HZ around M-dwarfs is not as close as suggested by earlier work. Assuming synchronously rotating planets with background 1 bar N2 atmospheres, we find that planets at the inner HZ of stars with Teff > 3000K undergo the classical "moist-greenhouse" (H2O mixing ratio > 10-3 in the stratosphere) at significantly lower surface temperature (~ 280K) in our 3-D model compared with 1-D climate models (~ 340K). This implies that some planets around low mass stars can simultaneously undergo water-loss and remain habitable. However, for star with Teff <= 3000K, planets at the inner HZ may directly transition to a runaway state, while bypassing the moist greenhouse water-loss entirely. We analyze transmission spectra of planets in a moist green-house regime, and find that there are several prominent H2O features within JWST instruments range. Thus, relying only upon standard Earth-analog spectra with 24-hour rotation period around M-dwarfs for habitability studies will miss the strong H2O features that one would expect to see on synchronously rotating planets around M-dwarf stars, with JWST.

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arXiv2017

Radiative Transfer for Exoplanet Atmospheres

Remote sensing of the atmospheres of distant worlds motivates a firm understanding of radiative transfer. In this review, we provide a pedagogical cookbook that describes the principal ingredients needed to perform a radiative transfer calculation and predict the spectrum of an exoplanet atmosphere, including solving the radiative transfer equation, calculating opacities (and chemistry), iterating for radiative equilibrium (or not), and adapting the output of the calculations to the astronomical observations. A review of the state of the art is performed, focusing on selected milestone papers. Outstanding issues, including the need to understand aerosols or clouds and elucidating the assumptions and caveats behind inversion methods, are discussed. A checklist is provided to assist referees/reviewers in their scrutiny of works involving radiative transfer. A table summarizing the methodology employed by past studies is provided.

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arXiv2017

The theory of transmission spectra revisited: a semi-analytical method for interpreting WFC3 data and an unresolved challenge

The computation of transmission spectra is a central ingredient in the study of exoplanetary atmospheres. First, we revisit the theory of transmission spectra, unifying ideas from several workers in the literature. Transmission spectra lack an absolute normalization due to the a priori unknown value of a reference transit radius, which is tied to an unknown reference pressure. We show that there is a degeneracy between the uncertainty in the transit radius, the assumed value of the reference pressure (typically set to 10 bar) and the inferred value of the water abundance when interpreting a WFC3 transmission spectrum. Second, we show that the transmission spectra of isothermal atmospheres are nearly isobaric. We validate the isothermal, isobaric analytical formula for the transmission spectrum against full numerical calculations and show that the typical errors are ~0.1% (~10 ppm) within the WFC3 range of wavelengths for temperatures of 1500 K (or higher). Third, we generalize the previous expression for the transit radius to include a small temperature gradient. Finally, we analyze the measured WFC3 transmission spectrum of WASP-12b and demonstrate that we obtain consistent results with the retrieval approach of Kreidberg et al. (2015) if the reference transit radius and reference pressure are fixed to assumed values. The unknown functional relationship between the reference transit radius and reference pressure implies that it is the product of the water abundance and reference pressure that is being retrieved from the data, and not just the water abundance alone. This degeneracy leads to a limitation on how accurately we may extract molecular abundances from transmission spectra using WFC3 data alone. Finally, we compare our study to that of Griffith (2014) and discuss why the degeneracy was missed in previous retrieval studies. [abridged]

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arXiv2017

A seven-planet resonant chain in TRAPPIST-1

The TRAPPIST-1 system is the first transiting planet system found orbiting an ultra-cool dwarf star. At least seven planets similar to Earth in radius and in mass were previously found to transit this host star. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 d orbital period for the outermost planet, TRAPPIST-1h, which was unconstrained until now. This value matches our theoretical expectations based on Laplace relations and places TRAPPIST-1h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1h has a radius of 0.727 Earth radii and an equilibrium temperature of 173 K. We have also measured the rotational period of the star at 3.3 d and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf.

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