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High-resolution far-ultraviolet broadband Fourier-transform photoabsorption spectra of ${}^{32}{\rm S}^{16}{\rm O}$, ${}^{33}{\rm S}^{16}{\rm O}$, ${}^{34}{\rm S}^{16}{\rm O}$, and ${}^{36}{\rm S}^{16}{\rm O}$ are recorded in a microwave discharge seeded with SO$_2$ . The $B{}^3{\Sigma}^-(v=4-30) \leftarrow X{}^3{\Sigma}^-(v=0)$ and $C{}^3{\Pi}(v=0-7) \leftarrow X{}^3{\Sigma}^-(v=0)$ bands are observed or inferred in the 43000 to 51000 cm$^{-1}$ (196 to 233 nm) spectral range. This is the first experimental detection of a $C{}^3{\Pi}(v>2)$ level and of any of these observed bands in an S-substituted isotopologue. Additional measurements of $A{}^3{\Pi}(v=1-3) \leftarrow X{}^3{\Sigma}^-(v=0)$ provide a calibration of the SO column density. Measured band profiles are fitted to an effective-Hamiltonian model of coupled excited $B{}^3{\Sigma}^-$ and $C{}^3{\Pi}$ states along with their predissociation linewidths and absorption band strengths. Electronic-state potential-energy curves and transition moments are deduced. The end result is a list of line frequencies, $f$-values, and dissociation widths describing the far-ultraviolet photodissociation spectrum of SO that is accurate enough for computing atmospheric photolytic isotope-fractionation.

The high-resolution B$^1\Sigma^+$ - A$^1\Pi$ (0, 0) and (0, 3) emission bands of the less-abundant $^{13}$C$^{17}$O isotopologue have been investigated by Fourier-transform spectroscopy in the visible region using a Bruker IFS 125HR spectrometer at an accuracy 0.003 cm$^{-1}$. These spectra are combined with high-resolution photoabsorption measurements of the $^{13}$C$^{17}$O B$^1\Sigma^+$ $\leftarrow$ X$^1\Sigma^+$ (0, 0), B$^1\Sigma^+$ $\leftarrow$ X$^1\Sigma^+$ (1, 0) and C$^1\Sigma^+$ $\leftarrow$ X$^1\Sigma^+$ (0, 0) bands recorded with an accuracy of 0.01 cm$^{-1}$ using the vacuum ultraviolet Fourier-transform spectrometer, installed on the DESIRS beamline at the SOLEIL synchrotron. In the studied 17,950 - 22,500 cm$^{-1}$ and 86,800 - 92,100 cm$^{-1}$ regions, 480 transitions have been measured. These new experimental data were combined with data from the C $\to$ A and B $\to$ A systems, previously analyzed in 13C17O. The frequencies of 1003 transitions derived from 12 bands were used to analyze the perturbations between the A$^1\Pi$ ($\nu$ = 0 - 3) levels and rovibrational levels of the d$^3\Delta_i$, e$^3\Sigma^-$, a$'{}^3\Sigma^+$, I$^1\Sigma^-$ and D$^1\Delta$ states as well as to a preliminary investigation of weak irregularities that appear in the B$^1\Sigma^+$ ($\nu$ = 0) level. Deperturbed molecular constants and term values of the A$^1\Pi$ state were obtained. The spin-orbit and L-uncoupling interaction parameters as well as isotopologue-independent spin-orbit and rotation-electronic perturbation parameters were derived., Comment: 37 pages, 8 tables, 7 figures, 91 references

We present an update of the open-source photochemical kinetics code VULCAN (Tsai et al. 2017; https://github.com/exoclime/VULCAN) to include C-H-N-O-S networks and photochemistry. Additional new features are advection transport, condensation, various boundary conditions, and temperature-dependent UV cross-sections. First, we validate our photochemical model for hot Jupiter atmospheres by performing an intercomparison of HD 189733b models between Moses et al. (2011), Venot et al. (2012), and VULCAN, to diagnose possible sources of discrepancy. Second, we set up a model of Jupiter extending from the deep troposphere to upper stratosphere to verify the kinetics for low temperature. Our model reproduces hydrocarbons consistent with observations, and the condensation scheme successfully predicts the locations of water and ammonia ice clouds. We show that vertical advection can regulate the local ammonia distribution in the deep atmosphere. Third, we validate the model for oxidizing atmospheres by simulating Earth and find agreement with observations. Last, VULCAN is applied to four representative cases of extrasolar giant planets: WASP-33b, HD 189733b, GJ 436b, and 51 Eridani b. We look into the effects of the C/O ratio and chemistry of titanium/vanadium species for WASP-33b; we revisit HD 189733b for the effects of sulfur and carbon condensation; the effects of internal heating and vertical mixing ($K_{\textrm{zz}}$) are explored for GJ 436b; we test updated planetary properties for 51 Eridani b with S$_8$ condensates. We find sulfur can couple to carbon or nitrogen and impact other species such as hydrogen, methane, and ammonia. The observable features of the synthetic spectra and trends in the photochemical haze precursors are discussed for each case., Comment: 50 pages, 41 figures, accepted for publication in ApJ

For accurate modelling of observations of exoplanet atmospheres, quantification of the pressure broadening of infrared absorption lines for and by a variety of gases at elevated temperatures is needed. High-resolution high-temperature H2-pressure-broadened spectra are recorded for the CH4 v3-band P-branch. Measured linewidths for 116 transitions between 2840 and 3000 cm^{-1} with temperature and pressures ranging between 300 and 700 K, and 10 and 933 Torr, respectively, were used to find rotation- and tetrahedral-symmetry-dependent coefficients for pressure and temperature broadening and pressure-induced lineshifts. The new pressure-broadening data will be useful in radiative-transfer models for retrieving the properties of observed expolanet atmospheres., Comment: 23 pages, 10 figures, 7 tables, Resubmitted for 2nd round of revisions to JQSRT (Journal of Quantitative Spectroscopy & Radiative Transfer). Comments welcome!

Motivated by the work of Cooper & Showman, we revisit the chemical relaxation method, which seeks to enhance the computational efficiency of chemical-kinetics calculations by replacing the chemical network with a handful of independent source/sink terms. Chemical relaxation solves the evolution of the system and can treat disequilibrium chemistry, as the source/sink terms are driven towards chemical equilibrium on a prescribed chemical timescale, but it has surprisingly never been validated. First, we generalize the treatment by forgoing the use of a single chemical timescale, instead developing a pathway analysis tool that allows us to identify the rate-limiting reaction as a function of temperature and pressure. For the interconversion between methane and carbon monoxide and between ammonia, and molecular nitrogen, we identify the key rate-limiting reactions for conditions relevant to currently characterizable exo-atmospheres (500-3000 K, 0.1 mbar to 1 kbar). Second, we extend chemical relaxation to include carbon dioxide and water. Third, we examine the role of metallicity and carbon-to-oxygen ratio in chemical relaxation. Fourth, we apply our pathway analysis tool to diagnose the differences between our chemical network and that of Moses and Venot. Finally, we validate the chemical relaxation method against full chemical kinetics calculations in one dimension. For WASP-18b-, HD 189733b- and GJ 1214-b-like atmospheres, we show that chemical relaxation is mostly accurate to within an order of magnitude, a factor of 2 and $\sim 10\%$, respectively. The level of accuracy attained allows for the chemical relaxation method to be included in three-dimensional general circulation models., Comment: Accepted by ApJ. 19 pages, 14 figures

We present an open-source and validated chemical kinetics code for studying hot exoplanetary atmospheres, which we name VULCAN. It is constructed for gaseous chemistry from 500 to 2500 K using a reduced C-H-O chemical network with about 300 reactions. It uses eddy diffusion to mimic atmospheric dynamics and excludes photochemistry. We have provided a full description of the rate coefficients and thermodynamic data used. We validate VULCAN by reproducing chemical equilibrium and by comparing its output versus the disequilibrium-chemistry calculations of Moses et al. and Rimmer & Helling. It reproduces the models of HD 189733b and HD 209458b by Moses et al., which employ a network with nearly 1600 reactions. We also use VULCAN to examine the theoretical trends produced when the temperature-pressure profile and carbon-to-oxygen ratio are varied. Assisted by a sensitivity test designed to identify the key reactions responsible for producing a specific molecule, we revisit the quenching approximation and find that it is accurate for methane but breaks down for acetylene, because the disequilibrium abundance of acetylene is not directly determined by transport-induced quenching, but is rather indirectly controlled by the disequilibrium abundance of methane. Therefore, we suggest that the quenching approximation should be used with caution and must always be checked against a chemical kinetics calculation. A one-dimensional model atmosphere with 100 layers, computed using VULCAN, typically takes several minutes to complete. VULCAN is part of the Exoclimes Simulation Platform (ESP; http://www.exoclime.net/) and publicly available at http://github.com/exoclime/VULCAN ., Comment: Accepted for publication in ApJS http://www.exoclime.net/

We present a comprehensive study of the abundance of carbon dioxide in exoplanetary atmospheres in hot, hydrogen-dominated atmospheres. We construct novel 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, 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 may wish 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., Comment: Accepted by ApJ. 12 pages, 8 figures, 2 tables

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. 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 address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate 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. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen and oxygen. 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., Comment: Accepted by ApJ. 9 pages, 4 figures

We consider the formation of solar infrared (2-6 micron) rovibrational bands of carbon monoxide (CO) in CO5BOLD 3D convection models, with the aim to refine abundances of the heavy isotopes of carbon (13C) and oxygen (18O,17O), to compare with direct capture measurements of solar wind light ions by the Genesis Discovery Mission. We find that previous, mainly 1D, analyses were systematically biased toward lower isotopic ratios (e.g., R23= 12C/13C), suggesting an isotopically "heavy" Sun contrary to accepted fractionation processes thought to have operated in the primitive solar nebula. The new 3D ratios for 13C and 18O are: R23= 91.4 +/- 1.3 (Rsun= 89.2); and R68= 511 +/- 10 (Rsun= 499), where the uncertainties are 1 sigma and "optimistic." We also obtained R67= 2738 +/- 118 (Rsun= 2632), but we caution that the observed 12C17O features are extremely weak. The new solar ratios for the oxygen isotopes fall between the terrestrial values and those reported by Genesis (R68= 530, R6= 2798), although including both within 2 sigma error flags, and go in the direction favoring recent theories for the oxygen isotope composition of Ca-Al inclusions (CAI) in primitive meteorites. While not a major focus of this work, we derive an oxygen abundance of 603 +/- 9 ppm (relative to hydrogen; 8.78 on the logarithmic H= 12 scale). That the Sun likely is lighter than the Earth, isotopically speaking, removes the necessity to invoke exotic fractionation processes during the early construction of the inner solar system.

We present results from a model of oxygen isotopic anomaly production through selective photodissociation of CO within the collapsing proto-Solar cloud. Our model produces a proto-Sun with a wide range of Delta_17O values depending on the intensity of the ultraviolet radiation field. Dramatically different results from two recent Solar wind oxygen isotope measurements indicate that a variety of compositions remain possible for the solar oxygen isotope composition. However, constrained by other measurements from comets and meteorites, our models imply the birth of the Sun in a stellar cluster with an enhanced radiation field and are therefore consistent with a supernova source for 60Fe in meteorites., Comment: 27 pages, 10 figures. Accepted for publication in M&PS, typos corrected

We present an approximate analytic model that has been developed for examining hydrodynamic flow near the surface of a fiber optic sensor. An analysis of the conservation of momentum, the continuity equation and the Navier-Stokes equation for compressible flow was used to develop expressions for the velocity and the density as a function of the distance along the flow and above a two dimensional flat surface. When examining the flow near the surface, these expressions can be used to estimate the sensitivity required to perform direct optical measurements and to parameterize the shear force for indirect optical measurements. The use of these results allows for direct modeling of sensors using the optical properties of the flow field. Future work includes analyzing the optical parametric design of fiber optic sensors, modeling sensors to utilize those parameters for optimal measurements involving different mixtures of fluid flow.

This paper identifies the bases and rationale for the concept of cooperative learning; describes the dynamics of the cooperative learning approach; and proposes methods that college faculty can use to enhance student motivation and learning. Cooperative learning is defined and is reported to have positive effects on student achievement, human relations skills, trust among students, and emotional involvement in and commitment to learning. Disadvantages, such as the lack of short-term extrinsic rewards for students who rely on such reinforcement, are also noted. Three types of cooperative learning are then detailed with examples: (1) group investigation--in which students in small groups work through six steps in researching a topic and preparing a report; (2) reiterative problem-based learning--in which student groups identify a problem, engage in independent study, assess their inquiry strategy, and iterate the process; and (3) co-op/co-op--in which students work through 10 steps involving both individual and group learning and presentations. Includes seven references. (DB)