The Nature of Scientific Proof in the Age of Simulations

Is numerical mimicry a third way of establishing truth?Comment: Published in American Scientist: Volume 102, Number 3, Pages 174 to 177 (http://www.americanscientist.org/issues/pub/2014/3/the-nature-of-scientific-proof-in-the-age-of-simulations

A Cloudiness Index for Transiting Exoplanets Based on the Sodium and Potassium Lines: Tentative Evidence for Hotter Atmospheres Being Less Cloudy at Visible Wavelengths

We present a dimensionless index that quantifies the degree of cloudiness of the atmosphere of a transiting exoplanet. Our cloudiness index is based on measuring the transit radii associated with the line center and wing of the sodium or potassium line. In deriving this index, we revisited the algebraic formulae for inferring the isothermal pressure scale height from transit measurements. We demonstrate that the formulae of Lecavelier et al. and Benneke & Seager are identical: the former is inferring the temperature while assuming a value for the mean molecular mass and the latter is inferring the mean molecular mass while assuming a value for the temperature. More importantly, these formulae cannot be used to distinguish between cloudy and cloudfree atmospheres. We derive values of our cloudiness index for a small sample of 7 hot Saturns/Jupiters taken from Sing et al. We show that WASP-17b, WASP-31b and HAT-P-1b are nearly cloudfree at visible wavelengths. We find the tentative trend that more irradiated atmospheres tend to have less clouds consisting of sub-micron-sized particles. We also derive absolute sodium and/or potassium abundances $\sim 10^2$ cm$^{-3}$ for WASP-17b, WASP-31b and HAT-P-1b (and upper limits for the other objects). Higher-resolution measurements of both the sodium and potassium lines, for a larger sample of exoplanetary atmospheres, are needed to confirm or refute this trend.Comment: Accepted by ApJL. 6 pages, 1 figure, 2 table

On the Existence of Shocks in Irradiated Exoplanetary Atmospheres

Supersonic flows are expected to exist in the atmospheres of irradiated exoplanets, but the question of whether shocks develop lingers. Specifically, it reduces to whether continuous flow in a closed loop may become supersonic and if some portions of the supersonic flow steepen into shocks. We first demonstrate that continuous, supersonic flow may exist in two flavors: isentropic and non-isentropic, with shocks being included in the latter class of solutions. Supersonic flow is a necessary but insufficient condition for shocks to develop. The development of a shock requires the characteristics of neighboring points in a flow to intersect. We demonstrate that the intersection of characteristics may be quantified via knowledge of the Mach number. Finally, we examine 3D simulations of hot Jovian atmospheres and demonstrate that shock formation is expected to occur mostly on the dayside hemisphere, upstream of the substellar point, because the enhanced temperatures near the substellar point provide a natural pressure barrier for the returning flow. Understanding the role of shocks in irradiated exoplanetary atmospheres is relevant to correctly modeling observables such as the peak offsets of infrared phase curves.Comment: Accepted by ApJ Letters. 5 pages, 4 figure

The Next Great Exoplanet Hunt

What strange new worlds will our next-generation telescopes find?Comment: Published in American Scientist: Volume 103, Number 3, Pages 196 to 203 (http://www.americanscientist.org/issues/feature/2015/3/the-next-great-exoplanet-hunt). Error concerning liquid helium correcte

Analytical Models of Exoplanetary Atmospheres. I. Atmospheric Dynamics via the Shallow Water System

Within the context of exoplanetary atmospheres, we present a comprehensive linear analysis of forced, damped, magnetized shallow water systems, exploring the effects of dimensionality, geometry (Cartesian, pseudo-spherical and spherical), rotation, magnetic tension and hydrodynamic and magnetic sources of friction. Across a broad range of conditions, we find that the key governing equation for atmospheres and quantum harmonic oscillators are identical, even when forcing (stellar irradiation), sources of friction (molecular viscosity, Rayleigh drag and magnetic drag) and magnetic tension are included. The global atmospheric structure is largely controlled by a single, key parameter that involves the Rossby and Prandtl numbers. This near-universality breaks down when either molecular viscosity or magnetic drag acts non-uniformly across latitude or a poloidal magnetic field is present, suggesting that these effects will introduce qualitative changes to the familiar chevron-shaped feature witnessed in simulations of atmospheric circulation. We also find that hydrodynamic and magnetic sources of friction have dissimilar phase signatures and affect the flow in fundamentally different ways, implying that using Rayleigh drag to mimic magnetic drag is inaccurate. We exhaustively lay down the theoretical formalism (dispersion relations, governing equations and time-dependent wave solutions) for a broad suite of models. In all situations, we derive the steady state of an atmosphere, which is relevant to interpreting infrared phase and eclipse maps of exoplanetary atmospheres. We elucidate a pinching effect that confines the atmospheric structure to be near the equator. Our suite of analytical models may be used to decisively develop physical intuition and as a reference point for three-dimensional, magnetohydrodynamic (MHD) simulations of atmospheric circulation.Comment: Accepted by ApJS, 36 pages, 6 figures, 3 tables, 273 equation

On the Stability of Super-Earth Atmospheres

We investigate the stability of super Earth atmospheres around M stars using a 7-parameter, analytical framework. We construct stability diagrams in the parameter space of exoplanetary radius versus semi-major axis and elucidate the regions in which the atmospheres are stable against the condensation of their major constituents, out of the gas phase, on their permanent nightside hemispheres. We find that super Earth atmospheres which are nitrogen-dominated ("Earth-like") occupy a smaller region of allowed parameter space, compared to hydrogen-dominated atmospheres, because of the dual effects of diminished advection and enhanced radiative cooling. Furthermore, some super Earths which reside within the habitable zones of M stars may not possess stable atmospheres, depending on the mean molecular weight and infrared photospheric pressure of their atmospheres. We apply our stability diagrams to GJ 436b and GJ 1214b, and demonstrate that atmospheric compositions with high mean molecular weights are disfavoured if these exoplanets possess solid surfaces and shallow atmospheres. Finally, we construct stability diagrams tailored to the Kepler dataset, for G and K stars, and predict that about half of the exoplanet candidates are expected to habour stable atmospheres if Earth-like conditions are assumed. We include 55 Cancri e and CoRoT-7b in our stability diagram for G stars.Comment: Accepted by ApJ. 10 pages, 6 figures. No changes from previous version, except for added hypen in titl

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).Comment: accepted version; 15 pages, 5 figures, 3 table

Retrieval analysis of 38 WFC3 transmission spectra and resolution of the normalisation degeneracy

A comprehensive analysis of 38 previously published Wide Field Camera 3 (WFC3) transmission spectra is performed using a hierarchy of nested-sampling retrievals: with versus without clouds, grey versus non-grey clouds, isothermal versus non-isothermal transit chords and with water, hydrogen cyanide and/or ammonia. We revisit the "normalisation degeneracy": the relative abundances of molecules are degenerate at the order-of-magnitude level with the absolute normalisation of the transmission spectrum. Using a suite of mock retrievals, we demonstrate that the normalisation degeneracy may be partially broken using WFC3 data alone, even in the absence of optical/visible data and without appealing to the presence of patchy clouds, although lower limits to the mixing ratios may be prior-dominated depending on the measurement uncertainties. With James Webb Space Telescope-like spectral resolutions, the normalisation degeneracy may be completely broken from infrared spectra alone. We find no trend in the retrieved water abundances across nearly two orders of magnitude in exoplanet mass and a factor of 5 in retrieved temperature (about 500 to 2500 K). We further show that there is a general lack of strong Bayesian evidence to support interpretations of non-grey over grey clouds (only for WASP-69b and WASP-76b) and non-isothermal over isothermal atmospheres (no objects). 35 out of 38 WFC3 transmission spectra are well-fitted by an isothermal transit chord with grey clouds and water only, while 8 are adequately explained by flat lines. Generally, the cloud composition is unconstrained.Comment: Accepted by MNRAS. 33 pages, 29 figures, 3 table

Debris discs around M stars: non-existence versus non-detection

Motivated by the reported dearth of debris discs around M stars, we use survival models to study the occurrence of planetesimal discs around them. These survival models describe a planetesimal disc with a small number of parameters, determine if it may survive a series of dynamical processes and compute the associated infrared excess. For the WISE satellite, we demonstrate that the dearth of debris discs around M stars may be attributed to the small semi-major axes generally probed if either: 1. the dust grains behave like blackbodies emitting at a peak wavelength coincident with the observed one; 2. or the grains are hotter than predicted by their blackbody temperatures and emit at peak wavelengths that are shorter than the observed one. At these small distances from the M star, planetesimals are unlikely to survive or persist for time scales of 300 Myr or longer if the disc is too massive. Conversely, our survival models allow for the existence of a large population of low-mass debris discs that are too faint to be detected with current instruments. However, our interpretation becomes less clear and large infrared excesses are allowed if only one of these scenarios holds: 3. the dust grains are hotter than blackbody and predominantly emit at the observed wavelength; 4. or are blackbody in nature and emit at peak wavelengths longer than the observed one. Both scenarios imply that the parent planetesimals reside at larger distances from the star than inferred if the dust grains behaved like blackbodies. In all scenarios, we show that the infrared excesses detected at 22 and 70 microns from AU Mic are easily reconciled with its young age. We elucidate the conditions under which stellar wind drag may be neglected when considering dust populations around M stars. The WISE satellite should be capable of detecting debris discs around young M stars with ages on the order of 10 Myr.Comment: Accepted by MNRAS. 11 pages, 9 figure