arXiv subjects

Drake Deming

Publications and source records attributed to Drake Deming.

At least 109 records · Page 6Linked to original sources

arXiv2015

Spectral Eclipse Timing

We utilize multi-dimensional simulations of varying equatorial jet strength to predict wavelength dependent variations in the eclipse times of gas-giant planets. A displaced hot-spot introduces an asymmetry in the secondary eclipse light curve that manifests itself as a measured offset in the timing of the center of eclipse. A multi-wavelength observation of secondary eclipse, one probing the timing of barycentric eclipse at short wavelengths and another probing at longer wavelengths, will reveal the longitudinal displacement of the hot-spot and break the degeneracy between this effect and that associated with the asymmetry due to an eccentric orbit. The effect of time offsets was first explored in the IRAC wavebands by Williams et. al (2006). Here we improve upon their methodology, extend to a broad ranges of wavelengths, and demonstrate our technique on a series of multi-dimensional radiative-hydrodynamical simulations of HD 209458b with varying equatorial jet strength and hot-spot displacement. Simulations with the largest hot-spot displacement result in timing offsets of up to 100 seconds in the infrared. Though we utilize a particular radiative hydrodynamical model to demonstrate this effect, the technique is model independent. This technique should allow a much larger survey of hot-spot displacements with JWST then currently accessible with time-intensive phase curves, hopefully shedding light on the physical mechanisms associated with thermal energy advection in irradiated gas-giants.

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arXiv2015

3.6 and 4.5 $μ$m Phase Curves of the Highly-Irradiated Eccentric Hot Jupiter WASP-14b

We present full-orbit phase curve observations of the eccentric ($e\sim 0.08$) transiting hot Jupiter WASP-14b obtained in the 3.6 and 4.5 $μ$m bands using the \textit{Spitzer Space Telescope}. We use two different methods for removing the intrapixel sensitivity effect and compare their efficacy in decoupling the instrumental noise. Our measured secondary eclipse depths of $0.1882\%\pm 0.0048\%$ and $0.2247\%\pm 0.0086\%$ at 3.6 and 4.5 $μ$m, respectively, are both consistent with a blackbody temperature of $2402\pm 35$ K. We place a $2σ$ upper limit on the nightside flux at 3.6 $μ$m and find it to be $9\%\pm 1\%$ of the dayside flux, corresponding to a brightness temperature of 1079 K. At 4.5 $μ$m, the minimum planet flux is $30\%\pm 5\%$ of the maximum flux, corresponding to a brightness temperature of $1380\pm 65$ K. We compare our measured phase curves to the predictions of one-dimensional radiative transfer and three-dimensional general circulation models. We find that WASP-14b's measured dayside emission is consistent with a model atmosphere with equilibrium chemistry and a moderate temperature inversion. These same models tend to over-predict the nightside emission at 3.6 $μ$m, while under-predicting the nightside emission at 4.5 $μ$m. We propose that this discrepancy might be explained by an enhanced global C/O ratio. In addition, we find that the phase curves of WASP-14b ($7.8 M_{\mathrm{Jup}}$) are consistent with a much lower albedo than those of other Jovian mass planets with thermal phase curve measurements, suggesting that it may be emitting detectable heat from the deep atmosphere or interior processes.

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arXiv2015

Spitzer Secondary Eclipse Observations of Five Cool Gas Giant Planets and Empirical Trends in Cool Planet Emission Spectra

In this work we present Spitzer 3.6 and 4.5 micron secondary eclipse observations of five new cool (<1200 K) transiting gas giant planets: HAT-P-19b, WASP-6b, WASP-10b, WASP-39b, and WASP-67b. We compare our measured eclipse depths to the predictions of a suite of atmosphere models and to eclipse depths for planets with previously published observations in order to constrain the temperature- and mass-dependent properties of gas giant planet atmospheres. We find that the dayside emission spectra of planets less massive than Jupiter require models with efficient circulation of energy to the night side and/or increased albedos, while those with masses greater than that of Jupiter are consistently best-matched by models with inefficient circulation and low albedos. At these relatively low temperatures we expect the atmospheric methane to CO ratio to vary as a function of metallicity, and we therefore use our observations of these planets to constrain their atmospheric metallicities. We find that the most massive planets have dayside emission spectra that are best-matched by solar metallicity atmosphere models, but we are not able to place strong constraints on metallicities of the smaller planets in our sample. Interestingly, we find that the ratio of the 3.6 and 4.5 micron brightness temperatures for these cool transiting planets is independent of planet temperature, and instead exhibits a tentative correlation with planet mass. If this trend can be confirmed, it would suggest that the shape of these planets' emission spectra depends primarily on their masses, consistent with the hypothesis that lower-mass planets are more likely to have metal-rich atmospheres.

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arXiv2015

Spitzer Secondary Eclipses of the Dense, Modestly-irradiated, Giant Exoplanet HAT-P-20b Using Pixel-Level Decorrelation

HAT-P-20b is a giant exoplanet that orbits a metal-rich star. The planet itself has a high total density, suggesting that it may also have a high metallicity in its atmosphere. We analyze two eclipses of the planet in each of the 3.6- and 4.5 micron bands of Warm Spitzer. These data exhibit intra-pixel detector sensitivity fluctuations that were resistant to traditional decorrelation methods. We have developed a simple, powerful, and radically different method to correct the intra-pixel effect for Warm Spitzer data, which we call pixel-level decorrelation (PLD). PLD corrects the intra-pixel effect very effectively, but without explicitly using - or even measuring - the fluctuations in the apparent position of the stellar image. We illustrate and validate PLD using synthetic and real data, and comparing the results to previous analyses. PLD can significantly reduce or eliminate red noise in Spitzer secondary eclipse photometry, even for eclipses that have proven to be intractable using other methods. Our successful PLD analysis of four HAT-P-20b eclipses shows a best-fit blackbody temperature of 1134 +/-29K, indicating inefficient longitudinal transfer of heat, but lacking evidence for strong molecular absorption. We find sufficient evidence for variability in the 4.5 micron band that the eclipses should be monitored at that wavelength by Spitzer, and this planet should be a high priority for JWST spectroscopy. All four eclipses occur about 35 minutes after orbital phase 0.5, indicating a slightly eccentric orbit. A joint fit of the eclipse and transit times with extant RV data yields e(cos{omega}) = 0.01352 (+0.00054, -0.00057), and establishes the small eccentricity of the orbit to high statistical confidence. Given the existence of a bound stellar companion, HAT-P-20b is another excellent candidate for orbital evolution via Kozai migration or other three-body mechanism.

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arXiv2015

Spectroscopic Evidence for a Temperature Inversion in the Dayside Atmosphere of the Hot Jupiter WASP-33b

We present observations of two occultations of the extrasolar planet WASP-33b using the Wide Field Camera 3 (WFC3) on the HST, which allow us to constrain the temperature structure and composition of its dayside atmosphere. WASP-33b is the most highly irradiated hot Jupiter discovered to date, and the only exoplanet known to orbit a delta-Scuti star. We observed in spatial scan mode to decrease instrument systematic effects in the data, and removed fluctuations in the data due to stellar pulsations. The RMS for our final, binned spectrum is approximately 1.05 times the photon noise. We compare our final spectrum, along with previously published photometric data, to atmospheric models of WASP-33b spanning a wide range in temperature profiles and chemical compositions. We find that the data require models with an oxygen-rich chemical composition and a temperature profile that increases at high altitude. We also find that our spectrum displays an excess in the measured flux towards short wavelengths that is best explained as emission from TiO. If confirmed by additional measurements at shorter wavelengths, this planet would become the first hot Jupiter with a temperature inversion that can be definitively attributed to the presence of TiO in its dayside atmosphere.

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arXiv2015

Low False-Positive Rate of Kepler Candidates Estimated From A Combination Of Spitzer And Follow-Up Observations

(Abridged) NASA's Kepler mission has provided several thousand transiting planet candidates, yet only a small subset have been confirmed as true planets. Therefore, the most fundamental question about these candidates is the fraction of bona fide planets. Estimating the rate of false positives of the overall Kepler sample is necessary to derive the planet occurrence rate. We present the results from two large observational campaigns that were conducted with the Spitzer telescope during the the Kepler mission. These observations are dedicated to estimating the false positive rate (FPR) amongst the Kepler candidates. We select a sub-sample of 51 candidates, spanning wide ranges in stellar, orbital and planetary parameter space, and we observe their transits with Spitzer at 4.5 microns. We use these observations to measures the candidate's transit depths and infrared magnitudes. A bandpass-dependent depth alerts us to the potential presence of a blending star that could be the source of the observed eclipse: a false-positive scenario. For most of the candidates (85%), the transit depths measured with Kepler are consistent with the depths measured with Spitzer as expected for planetary objects, while we find that the most discrepant measurements are due to the presence of unresolved stars that dilute the photometry. The Spitzer constraints on their own yield FPRs between 5-40%, depending on the KOIs. By considering the population of the Kepler field stars, and by combining follow-up observations (imaging) when available, we find that the overall FPR of our sample is low. The measured upper limit on the FPR of our sample is 8.8% at a confidence level of 3 sigma. This observational result, which uses the achromatic property of planetary transit signals that is not investigated by the Kepler observations, provides an independent indication that Kepler's false positive rate is low.

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arXiv2014

Observations of Transiting Exoplanets with the James Webb Space Telescope (JWST), Publications of the Astronomical Society of the Pacific (PASP), December 2014

This article summarizes a workshop held on March, 2014, on the potential of the James Webb Space Telescope (JWST) to revolutionize our knowledge of the physical properties of exoplanets through transit observations. JWST's unique combination of high sensitivity and broad wavelength coverage will enable the accurate measurement of transits with high signal-to-noise. Most importantly, JWST spectroscopy will investigate planetary atmospheres to determine atomic and molecular compositions, to probe vertical and horizontal structure, and to follow dynamical evolution, i.e. exoplanet weather. JWST will sample a diverse population of planets of varying masses and densities in a wide variety of environments characterized by a range of host star masses and metallicities, orbital semi-major axes and eccentricities. A broad program of exoplanet science could use a substantial fraction of the overall JWST mission.

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arXiv2014

The Transiting Exoplanet Survey Satellite

The Transiting Exoplanet Survey Satellite (TESS) will search for planets transiting bright and nearby stars. TESS has been selected by NASA for launch in 2017 as an Astrophysics Explorer mission. The spacecraft will be placed into a highly elliptical 13.7-day orbit around the Earth. During its two-year mission, TESS will employ four wide-field optical CCD cameras to monitor at least 200,000 main-sequence dwarf stars with I = 4-13 for temporary drops in brightness caused by planetary transits. Each star will be observed for an interval ranging from one month to one year, depending mainly on the star's ecliptic latitude. The longest observing intervals will be for stars near the ecliptic poles, which are the optimal locations for follow-up observations with the James Webb Space Telescope. Brightness measurements of preselected target stars will be recorded every 2 min, and full frame images will be recorded every 30 min. TESS stars will be 10-100 times brighter than those surveyed by the pioneering Kepler mission. This will make TESS planets easier to characterize with follow-up observations. TESS is expected to find more than a thousand planets smaller than Neptune, including dozens that are comparable in size to the Earth. Public data releases will occur every four months, inviting immediate community-wide efforts to study the new planets. The TESS legacy will be a catalog of the nearest and brightest stars hosting transiting planets, which will endure as highly favorable targets for detailed investigations.

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arXiv2014

Updated Spitzer Emission Spectroscopy of Bright Transiting Hot Jupiter HD189733b

We analyze all existing secondary eclipse time series spectroscopy of hot Jupiter HD189733b acquired with the now defunct Spitzer/IRS instrument. We describe the novel approaches we develop to remove the systematic effects and extract accurate secondary eclipse depths as a function of wavelength in order to construct the emission spectrum of the exoplanet. We compare our results to a previous study by Grillmair et al. that did not examine all data sets available to us. We are able to confirm the detection of a water feature near 6μm claimed by Grillmair et al. We compare the planetary emission spectrum to three model families -- based on isothermal atmosphere, gray atmosphere, and two realizations of the complex radiative transfer model by Burrows et al., adopted in Grillmair et al.'s study. While we are able to reject the simple isothermal and gray models based on the data at the 97% level just from the IRS data, these rejections hinge on eclipses measured within relatively narrow wavelength range, between 5.5 and 7μm. This underscores the need for observational studies with broad wavelength coverage and high spectral resolution, in order to obtain robust information on exoplanet atmospheres.

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arXiv2014

Constraints on the Atmospheric Circulation and Variability of the Eccentric Hot Jupiter XO-3b

We report secondary eclipse photometry of the hot Jupiter XO-3b in the 4.5~$μ$m band taken with the Infrared Array Camera (IRAC) on the Spitzer Space Telescope. We measure individual eclipse depths and center of eclipse times for a total of twelve secondary eclipses. We fit these data simultaneously with two transits observed in the same band in order to obtain a global best-fit secondary eclipse depth of $0.1580\pm 0.0036\%$ and a center of eclipse phase of $0.67004\pm 0.00013 $. We assess the relative magnitude of variations in the dayside brightness of the planet by measuring the size of the residuals during ingress and egress from fitting the combined eclipse light curve with a uniform disk model and place an upper limit of 0.05$\%$. The new secondary eclipse observations extend the total baseline from one and a half years to nearly three years, allowing us to place an upper limit on the periastron precession rate of $2.9\times 10^{-3}$ degrees/day the tightest constraint to date on the periastron precession rate of a hot Jupiter. We use the new transit observations to calculate improved estimates for the system properties, including an updated orbital ephemeris. We also use the large number of secondary eclipses to obtain the most stringent limits to date on the orbit-to-orbit variability of an eccentric hot Jupiter and demonstrate the consistency of multiple-epoch Spitzer observations.

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arXiv2014

Water Vapour Absorption in the Clear Atmosphere of an exo-Neptune

Transmission spectroscopy to date has detected atomic and molecular absorption in Jupiter-sized exoplanets, but intense efforts to measure molecular absorption in the atmospheres of smaller (Neptune-sized) planets during transits have revealed only featureless spectra. From this it was concluded that the majority of small, warm planets evolve to sustain high mean molecular weights, opaque clouds, or scattering hazes in their atmospheres, obscuring our ability to observe the composition of these atmospheres. Here we report observations of the transmission spectrum of HAT-P-11b (~4 Earth radii) from the optical to the infrared. We detected water vapour absorption at 1.4 micrometre wavelength. The amplitude of the water absorption (approximately 250 parts-per- million) indicates that the planetary atmosphere is predominantly clear down to ~1 mbar, and sufficiently hydrogen-rich to exhibit a large scale height. The spectrum is indicative of a planetary atmosphere with an upper limit of ~700 times the abundance of heavy elements relative to solar. This is in good agreement with the core accretion theory of planet formation, in which gas giant planets acquire their atmospheres by directly accreting hydrogen-rich gas from the protoplanetary nebulae onto a large rocky or icy core.

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arXiv2014

The 4.5 $μ$m full-orbit phase curve of the hot Jupiter HD 209458b

The hot Jupiter HD 209458b is particularly amenable to detailed study as it is among the brightest transiting exoplanet systems currently known (V-mag = 7.65; K-mag = 6.308) and has a large planet-to-star contrast ratio. HD 209458b is predicted to be in synchronous rotation about its host star with a hot spot that is shifted eastward of the substellar point by superrotating equatorial winds. Here we present the first full-orbit observations of HD 209458b, in which its 4.5 $μ$m emission was recorded with $Spitzer$/IRAC. Our study revises the previous 4.5 $μ$m measurement of HD 209458b's secondary eclipse emission downward by $\sim$35% to $0.1391%^{+0.0072%}_{-0.0069%}$, changing our interpretation of the properties of its dayside atmosphere. We find that the hot spot on the planet's dayside is shifted eastward of the substellar point by $40.9^{\circ}\pm{6.0^{\circ}}$, in agreement with circulation models predicting equatorial superrotation. HD 209458b's dayside (T$_{bright}$ = 1499 $\pm$ 15 K) and nightside (T$_{bright}$ = 972 $\pm$ 44 K) emission indicates a day-to-night brightness temperature contrast smaller than that observed for more highly irradiated exoplanets, suggesting that the day-to-night temperature contrast may be partially a function of the incident stellar radiation. The observed phase curve shape deviates modestly from global circulation model predictions potentially due to disequilibrium chemistry or deficiencies in the current hot CH$_{4}$ line lists used in these models. Observations of the phase curve at additional wavelengths are needed in order to determine the possible presence and spatial extent of a dayside temperature inversion, as well as to improve our overall understanding of this planet's atmospheric circulation.

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arXiv2014

Water vapor in the spectrum of the extrasolar planet HD 189733b: 2. The eclipse

Spectroscopic observations of exoplanets are crucial to infer the composition and properties of their atmospheres. HD 189733b is one of the most extensively studied exoplanets and is a corner stone for hot Jupiter models. In this paper, we report the day-side emission spectrum of HD 189733b in the wavelength range 1.1 to 1.7 $μ$m obtained with the Hubble Space Telescope Wide Field Camera 3 in spatial scan mode. The quality of the data is such that even a straightforward analysis yields a high precision Poisson noise limited spectrum: the median 1-$σ$ uncertainty is 57 ppm per 0.02 $μ$m bin. We also build a white-light curve correcting for systematic effects and derive an absolute eclipse depth of 96$\pm$39 ppm. The resulting spectrum shows marginal evidence for water vapor absorption, but can also be well explained by a blackbody spectrum. However, the combination of these WFC3 data with previous Spitzer photometric observations is best explained by a day-side atmosphere of HD 189733b with no thermal inversion and a nearly solar or sub-solar H$_2$O abundance in a cloud-free atmosphere. Alternatively, this apparent sub-solar abundance may be the result of clouds or hazes which future studies need to investigate.

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arXiv2014

Statistical Eclipses of Close-in Kepler Sub-Saturns

We present a method to detect small atmospheric signals in Kepler's planet candidate light curves by averaging light curves for multiple candidates with similar orbital and physical characteristics. Our statistical method allows us to measure unbiased physical properties of Kepler's planet candidates, even for candidates whose individual signal-to-noise precludes the detection of their secondary eclipse. We detect a secondary eclipse depth of 3.83 +1.10/-1.11 ppm for a group of 31 sub-Saturn (R < 6 Earth radii) planet candidates with the greatest potential for a reflected light signature ((R_p/a)^2 > 10 ppm). Including Kepler-10b in this group increases the depth to 5.08 +0.71/-0.72 ppm. For a control group with (R_p/a)^2 < 1 ppm, we find a depth of 0.36 +/- 0.37 ppm, consistent with no detection. We also analyze the light curve of Kepler-10b and find an eclipse depth of 7.08 +/- 1.06 ppm. If the eclipses are due solely to reflected light, this corresponds to a geometric albedo of 0.22 +/- 0.06 for our group of close-in sub-Saturns, 0.37 +/- 0.05 if including Kepler-10b in the group, and 0.60 +/- 0.09 for Kepler-10b alone. Including a thermal emission model does not change the geometric albedo appreciably, assuming the Bond albedo is 2/3 the geometric albedo. Our result for Kepler-10b is consistent with previous works. Our result for close-in sub-Saturns shows that Kepler-10b is unusually reflective, but our analysis is consistent with the results of Demory (2014) for super-Earths. Our results also indicate that hot Neptunes are typically more reflective than hot Jupiters.

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arXiv2014

H2O abundances in the atmospheres of three hot Jupiters

The core accretion theory for giant planet formation predicts enrichment of elemental abundances in planetary envelopes caused by runaway accretion of planetesimals, which is consistent with measured super-solar abundances of C, N, P, S, Xe, and Ar in Jupiter's atmosphere. However, the abundance of O which is expected to be the most dominant constituent of planetesimals is unknown for solar system giant planets, owing to the condensation of water in their ultra-cold atmospheres, thereby posing a key unknown in solar system formation. On the other hand, hundreds of extrasolar hot Jupiters are known with very high temperatures (>~1000 K) making them excellent targets to measure H2O abundances and, hence, oxygen in their atmospheres. We constrain the atmospheric H2O abundances in three hot Jupiters (HD 189733b, HD 209458b, and WASP-12b), spanning a wide temperature range (1200-2500 K), using their near-infrared transmission spectra obtained using the HST WFC3 instrument. We report conclusive measurements of H2O in HD 189733b and HD 209458b, while that in WASP-12b is not well constrained by present data. The data allow nearly solar as well as significantly sub-solar abundances in HD 189733b and WASP-12b. However, for HD 209458b, we report the most precise H2O measurement in an exoplanet to date that suggests a ~20-135 sub-solar H2O abundance. We discuss the implications of our results on the formation conditions of hot Jupiters and on the likelihood of clouds in their atmospheres. Our results highlight the critical importance of high-precision spectra of hot Jupiters for deriving their H2O abundances.

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arXiv2014

Atmospheric Characterization of 5 Hot Jupiters with Wide Field Camera 3 on the Hubble Space Telescope

We probe the structure and composition of the atmospheres of 5 hot Jupiter exoplanets using the Hubble Space Telescope Wide Field Camera 3 (WFC3) instrument. We use the G141 grism (1.1-1.7 $μ$m) to study TrES-2b, TrES-4b, and CoRoT-1b in transit, TrES-3b in secondary eclipse, and WASP-4b in both. This wavelength region includes a predicted absorption feature from water at 1.4 $μ$m, which we expect to be nondegenerate with the other molecules that are likely to be abundant for hydrocarbon-poor (e.g. solar composition) hot Jupiter atmospheres. We divide our wavelength regions into 10 bins. For each bin we produce a spectrophotometric light curve spanning the time of transit and/or eclipse. We correct these light curves for instrumental systematics without reference to an instrument model. For our transmission spectra, our mean $1-σ$ precision per bin corresponds to variations of 2.1, 2.8, and 3.0 atmospheric scale heights for TrES-2b, TrES-4b, and CoRoT-1b, respectively. We find featureless spectra for these three planets. We are unable to extract a robust transmission spectrum for WASP-4b. For our dayside emission spectra, our mean $1-σ$ precision per bin corresponds to a planet-to-star flux ratio of $1.5\times10^{-4}$ and $2.1\times10^{-4}$ for WASP-4b and TrES-3b, respectively. We combine these estimates with previous broadband measurements and conclude that for both planets isothermal atmospheres are disfavored. We find no signs of features due to water. We confirm that WFC3 is suitable for studies of transiting exoplanets, but in staring mode multi-visit campaigns are necessary to place strong constraints on water abundance.

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arXiv2014

The Emergent 1.1-1.7 Micron Spectrum of the Exoplanet CoRoT-2b as Measured Using the Hubble Space Telescope

We have used Hubble/WFC3 and the G141 grism to measure the secondary eclipse of the transiting very hot Jupiter CoRoT-2b in the 1.1-1.7$μ$m spectral region. We find an eclipse depth averaged over this band equal to $395^{+69}_{-45}$ parts per million, equivalent to a blackbody temperature of $1788\pm18$K. We study and characterize several WFC3 instrumental effects, especially the "hook" phenomenon described by Deming et al. (2013). We use data from several transiting exoplanet systems to find a quantitative relation between the amplitude of the hook and the exposure level of a given pixel. Although the uncertainties in this relation are too large to allow us to develop an empirical correction for our data, our study provides a useful guide for optimizing exposure levels in future WFC3 observations. We derive the planet's spectrum using a differential method. The planet-to-star contrast increases to longer wavelength within the WFC3 bandpass, but without water absorption or emission to a $3σ$ limit of 85 ppm. The slope of the WFC3 spectrum is significantly less than the slope of the best-fit blackbody. We compare all existing eclipse data for this planet to a blackbody spectrum, and to spectra from both solar abundance and carbon-rich (C/O=1) models. A blackbody spectrum is an acceptable fit to the full dataset. Extra continuous opacity due to clouds or haze, and flattened temperature profiles, are strong candidates to produce quasi-blackbody spectra, and to account for the amplitude of the optical eclipses. Our results show ambiguous evidence for a temperature inversion in this planet.

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arXiv2014

A featureless transmission spectrum for the Neptune-mass exoplanet GJ 436b

GJ 436b is a warm-- approximately 800 K--extrasolar planet that periodically eclipses its low-mass (half the mass of the Sun) host star, and is one of the few Neptune-mass planets that is amenable to detailed characterization. Previous observations have indicated that its atmosphere has a methane-to-CO ratio that is 100,000 times smaller than predicted by models for hydrogen-dominated atmospheres at these temperatures. A recent study proposed that this unusual chemistry could be explained if the planet's atmosphere is significantly enhanced in elements heavier than H and He. In this study we present complementary observations of GJ 436b's atmosphere obtained during transit. Our observations indicate that the planet's transmission spectrum is effectively featureless, ruling out cloud-free, hydrogen-dominated atmosphere models with an extremely high significance of 48 sigma. The measured spectrum is consistent with either a high cloud or haze layer located at a pressure of approximately 1 mbar or with a relatively hydrogen-poor (three percent hydrogen and helium mass fraction) atmospheric composition.

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