Clouds in the atmospheres of extrasolar planets. IV. On the scattering greenhouse effect of CO2 ice particles: Numerical radiative transfer studies

Owing to their wavelengths dependent absorption and scattering properties, clouds have a strong impact on the climate of planetary atmospheres. Especially, the potential greenhouse effect of CO2 ice clouds in the atmospheres of terrestrial extrasolar planets is of particular interest because it might influence the position and thus the extension of the outer boundary of the classic habitable zone around main sequence stars. We study the radiative effects of CO2 ice particles obtained by different numerical treatments to solve the radiative transfer equation. The comparison between the results of a high-order discrete ordinate method and simpler two-stream approaches reveals large deviations in terms of a potential scattering efficiency of the greenhouse effect. The two-stream methods overestimate the transmitted and reflected radiation, thereby yielding a higher scattering greenhouse effect. For the particular case of a cool M-type dwarf the CO2 ice particles show no strong effective scattering greenhouse effect by using the high-order discrete ordinate method, whereas a positive net greenhouse effect was found in case of the two-stream radiative transfer schemes. As a result, previous studies on the effects of CO2 ice clouds using two-stream approximations overrated the atmospheric warming caused by the scattering greenhouse effect. Consequently, the scattering greenhouse effect of CO2 ice particles seems to be less effective than previously estimated. In general, higher order radiative transfer methods are necessary to describe the effects of CO2 ice clouds accurately as indicated by our numerical radiative transfer studies.Comment: accepted for publication in A&

On the climatic impact of CO2 ice particles in atmospheres of terrestrial exoplanets

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Clouds play a significant role for the energy budget in planetary atmospheres. They can scatter incident stellar radiation back to space, effectively cooling the surface of terrestrial planets. On the other hand, they may contribute to the atmospheric greenhouse effect by trapping outgoing thermal radiation. For exoplanets near the outer boundary of the habitable zone, condensation of CO2 can occur due to the low atmospheric temperatures. These CO2 ice clouds may play an important role for the surface temperature and, therefore, for the question of habitability of those planets. However, the optical properties of CO2 ice crystals differ significantly from those of water droplets or water ice particles. Except for a small number of strong absorption bands, they are almost transparent with respect to absorption. Instead, they are highly effective scatterers at long and short wavelengths. Therefore, the climatic effect of a CO2 ice cloud will depend on how much incident stellar radiation is scattered to space in comparison to the amount of thermal radiation scattered back towards the planetary surface. This contribution aims at the potential greenhouse effect of CO2 ice particles. Their scattering and absorption properties are calculated for assumed particle size distributions with different effective radii and particle densities. An accurate radiative transfer model is used to determine the atmospheric radiation field affected by such CO2 particles. These results are compared to less detailed radiative transfer schemes employed in previous studies

Low-temperature nucleation in a kinetic Ising model under different stochastic dynamics with local energy barriers

Using both analytical and simulational methods, we study low-temperature nucleation rates in kinetic Ising lattice-gas models that evolve under two different Arrhenius dynamics that interpose between the Ising states a transition state representing a local energy barrier. The two dynamics are the transition-state approximation [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)] and the one-step dynamic [H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989)]. Even though they both obey detailed balance and are here applied to a situation that does not conserve the order parameter, we find significant differences between the nucleation rates observed with the two dynamics, and between them and the standard Glauber dynamic [R. J. Glauber, J. Math. Phys. 4, 294 (1963)], which does not contain transition states. Our results show that great care must be exercised when devising kinetic Monte Carlo transition rates for specific physical or chemical systems.Comment: 14 pages RevTex, 6 embedded figures. Minor revisions. J. Chem. Phys., in pres

The extrasolar planet Gliese 581 d: a potentially habitable planet? (Corrigendum to arXiv:1009.5814)

We report here that the equation for H2O Rayleigh scattering was incorrectly stated in the original paper [arXiv:1009.5814]. Instead of a quadratic dependence on refractivity r, we accidentally quoted an r^4 dependence. Since the correct form of the equation was implemented into the model, scientific results are not affected.Comment: accepted to Astronomy&Astrophysic

Low-temperature nucleation in a kinetic Ising model with soft stochastic dynamics

We study low-temperature nucleation in kinetic Ising models by analytical and simulational methods, confirming the general result for the average metastable lifetime, = A*exp(beta*Gamma) (beta = 1/kT) [E. Jordao Neves and R.H. Schonmann, Commun. Math. Phys. 137, 209 (1991)]. Contrary to common belief, we find that both A and Gamma depend significantly on the stochastic dynamic. In particular, for a ``soft'' dynamic, in which the effects of the interactions and the applied field factorize in the transition rates, Gamma does NOT simply equal the energy barrier against nucleation, as it does for the standard Glauber dynamic, which does not have this factorization property.Comment: 4 pages RevTex4, 2 figures. Phys. Rev. Lett., in pres

Quantum approach to nucleation times of kinetic Ising ferromagnets

Low temperature dynamics of Ising ferromagnets under finite magnetic fields are studied in terms of quantum spin representations of stochastic evolution operators. These are constructed for the Glauber dynamic as well as for a modification of this latter, introduced by K. Park {\it et al.} in Phys. Rev. Lett. {\bf 92}, 015701 (2004). In both cases the relaxation time after a field quench is evaluated both numerically and analytically using the spectrum gap of the corresponding operators. The numerical work employs standard recursive techniques following a symmetrization of the evolution operator accomplished by a non-unitary spin rotation. The analytical approach uses low temperature limits to identify dominant terms in the eigenvalue problem. It is argued that the relaxation times already provide a measure of actual nucleation lifetimes under finite fields. The approach is applied to square, triangular and honeycomb lattices.Comment: 14 pages, 6 figure

Clouds in the atmospheres of extrasolar planets. II. Thermal emission spectra of Earth-like planets influenced by low and high-level clouds

We study the impact of multi-layered clouds (low-level water and high-level ice clouds) on the thermal emission spectra of Earth-like planets orbiting different types of stars. Clouds have an important influence on such planetary emission spectra due to their wavelength dependent absorption and scattering properties. We also investigate the influence of clouds on the ability to derive information about planetary surface temperatures from low-resolution spectra.Comment: accepted for publication in A&

A spectral survey of an ultra-hot Jupiter: Detection of metals in the transmission spectrum of KELT-9 b

Context: KELT-9 b exemplifies a newly emerging class of short-period gaseous exoplanets that tend to orbit hot, early type stars - termed ultra-hot Jupiters. The severe stellar irradiation heats their atmospheres to temperatures of $\sim 4,000$ K, similar to the photospheres of dwarf stars. Due to the absence of aerosols and complex molecular chemistry at such temperatures, these planets offer the potential of detailed chemical characterisation through transit and day-side spectroscopy. Studies of their chemical inventories may provide crucial constraints on their formation process and evolution history. Aims: To search the optical transmission spectrum of KELT-9 b for absorption lines by metals using the cross-correlation technique. Methods: We analyse 2 transits observed with the HARPS-N spectrograph. We use an isothermal equilibrium chemistry model to predict the transmission spectrum for each of the neutral and singly-ionized atoms with atomic numbers between 3 and 78. Of these, we identify the elements that are expected to have spectral lines in the visible wavelength range and use those as cross-correlation templates. Results: We detect absorption of Na I, Cr II, Sc II and Y II, and confirm previous detections of Mg I, Fe I, Fe II and Ti II. In addition, we find evidence of Ca I, Cr I, Co I, and Sr II that will require further observations to verify. The detected absorption lines are significantly deeper than model predictions, suggesting that material is transported to higher altitudes where the density is enhanced compared to a hydrostatic profile. There appears to be no significant blue-shift of the absorption spectrum due to a net day-to-night side wind. In particular, the strong Fe II feature is shifted by $0.18 \pm 0.27$ km~s$^{-1}$, consistent with zero. Using the orbital velocity of the planet we revise the steller and planetary masses and radii.Comment: Submitted to Astronomy and Astrophysics on January 18, 2019. Accepted on May 3, 2019. 26 pages, 11 figure

Class Attendance and Students’ Evaluations of Teaching: Do No-Shows Bias Course Ratings and Rankings?

Background: Many university departments use students’ evaluations of teaching (SET) to compare and rank courses. However, absenteeism from class is often nonrandom and, therefore, SET for different courses might not be comparable. Objective: The present study aims to answer two questions. Are SET positively biased due to absenteeism? Do procedures, which adjust for absenteeism, change course rankings? Research Design: The author discusses the problem from a missing data perspective and present empirical results from regression models to determine which factors are simultaneously associated with students’ class attendance and course ratings. In order to determine the extent of these biases, the author then corrects average ratings for students’ absenteeism and inspect changes in course rankings resulting from this adjustment. Subjects: The author analyzes SET data on the individual level. One or more course ratings are available for each student. Measures: Individual course ratings and absenteeism served as the key outcomes. Results: Absenteeism decreases with rising teaching quality. Furthermore, both factors are systematically related to student and course attributes. Weighting students’ ratings by actual absenteeism leads to mostly small changes in ranks, which follow a power law. Only a few, average courses are disproportionally influenced by the adjustment. Weighting by predicted absenteeism leads to very small changes in ranks. Again, average courses are more strongly affected than courses of very high or low in quality. Conclusions: No-shows bias course ratings and rankings. SET are more appropriate to identify high- and low-quality courses than to determine the exact ranks of average courses