Alkaline Exospheres of Exoplanet Systems: Evaporative Transmission Spectra

Hydrostatic equilibrium is an excellent approximation for the dense layers of planetary atmospheres where it has been canonically used to interpret transmission spectra of exoplanets. Here we exploit the ability of high-resolution spectrographs to probe tenuous layers of sodium and potassium gas due to their formidable absorption cross-sections. We present an atmosphere-exosphere degeneracy between optically thick and optically thin mediums, raising the question of whether hydrostatic equilibrium is appropriate for Na I lines observed at exoplanets. To this end we simulate three non-hydrostatic, evaporative, density profiles: (i) escaping, (ii) exomoon, and (iii) torus to examine their imprint on an alkaline exosphere in transmission. By analyzing an evaporative curve of growth we find that equivalent widths of $W_{\mathrm{Na D2}} \sim 1- 10$ mA are naturally driven by evaporation rates $\sim 10^3 - 10^5$ kg/s of pure atomic Na. To break the degeneracy between atmospheric and exospheric absorption, we suggest that if the line ratio is $\mathrm{D2/D1} \gtrsim 1.2$ the gas is optically thin on average and roughly indicating a non-hydrostatic structure of the atmosphere/exosphere. We show this is the case for Na I observations at hot Jupiters WASP-49b and HD189733b and also simulate their K I spectra. Lastly, motivated by the slew of metal detections at ultra-hot Jupiters, we suggest a toroidal atmosphere at WASP-76b and WASP-121b is consistent with the Na I data at present.Comment: 23 pages, 21 figures, accepted by MNRA

Linking the evolution of terrestrial interiors and an early outgassed atmosphere to astrophysical observations

A terrestrial planet is molten during formation and may remain so if subject to intense insolation or tidal forces. Observations continue to favour the detection and characterisation of hot planets, potentially with large outgassed atmospheres. We aim to determine the radius of hot Earth-like planets with large outgassed atmospheres and explore differences between molten and solid silicate planets and their influence on the mass-radius relationship and transmission and emission spectra. An interior-atmosphere model, combined with static structure calculations, tracks the evolving radius of a rocky mantle that is outgassing CO$_2$ and H$_2$O. Synthetic emission and transmission spectra are generated for CO$_2$ and H$_2$O dominated atmospheres. Atmospheres dominated by CO$_2$ suppress the outgassing of H$_2$O to a greater extent than previously realised, as previous studies have applied an erroneous relationship between volatile mass and partial pressure. We therefore predict more H$_2$O can be retained by the interior during the later stages of magma ocean crystallisation. Furthermore, formation of a lid at the surface can tie outgassing of H$_2$O to the efficiency of heat transport through the lid, rather than the atmosphere's radiative timescale. Contraction of the mantle as it solidifies gives $\sim5\%$ radius decrease, which can partly be offset by addition of a relatively light species to the atmosphere. We conclude that a molten silicate mantle can increase the radius of a terrestrial planet by around $5\%$ compared to its solid counterpart, or equivalently account for a $13\%$ decrease in bulk density. An outgassing atmosphere can perturb the total radius according to its speciation. Atmospheres of terrestrial planets around M-stars that are dominated by CO$_2$ or H$_2$O can be distinguished by observing facilities with extended wavelength coverage (e.g., JWST).Comment: 19 pages, published in A&A, abstract shortene

Continuous Uniform Finite Time Stabilization of Planar Controllable Systems

Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong $\mathcal{C}^1$ Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances. A finite upper bound on the settling time is also computed. The results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers

Direct observation of 4+ to 2+ gamma transition in 8Be

The low lying states in $^8$Be are believed to have a two-alpha cluster structure and hence a large intrinsic quadrupole deformation. An earlier calculation showed a large collective enhancement in gamma transition probability between the low lying states leading to a 4$^+$ to 2$^+$ gamma branch of $\sim10^{-7}$ and a resonant radiative cross section of 134 nb for the $\alpha+\alpha$ entrance channel. We report here the first experimental evidence for this transition through a $\gamma-\alpha-\alpha$ coincidence measurement in the reaction $^4$He($\alpha,\alpha \gamma$)$^4$He using a gas target. The measured cross sections on and off the 4$^+$ resonance are 165 $\pm$ 41 (stat) $\pm$35 (sys) nb and 39 $\pm$ 25 (stat) $\pm$7 (sys) nb, respectively.Comment: Total 4 pages, 4 figures, in RevTeX format, submitted to PR

Efficient Classification of Satellite Image with Hybrid Approach Using CNN-CA

Today, satellite imagery is being utilized to help repair and restore societal issues caused by habitats for a variety of scientific studies. Water resource search, environmental protection simulations, meteorological analysis, and soil class analysis may all benefit from the satellite images. The categorization algorithms were used generally and the most appropriate strategies are also be used for analyzing the Satellite image. There are several normal classification mechanisms, such as optimum likelihood, parallel piping or minimum distance classification that have presented in some other existing technologies. But the traditional classification algorithm has some disadvantages. Convolutional neural network (CNN) classification based on CA was implemented in this article. Using the gray level Satellite image as the target and CNN image classification by the CA’s selfiteration mechanism and eventually explores the efficacy and viability of the proposed method in long-term satellite remote sensing image water body classification. Our findings indicate that the proposed method not only has rapid convergence speed, reliability but can also efficiently classify satellite remote sensing images with long-term sequence and reasonable applicability. The proposed technique acquires an accuracy of 91% which is maximum than conventional methods

Planetary evolution with atmospheric photoevaporation II: Fitting the slope of the radius valley by combining boil-off and XUV-driven escape

The Kepler satellite has revealed a gap between sub-Neptunes and super-Earths that atmospheric escape models had predicted as an evaporation valley. We seek to contrast results from a simple XUV-driven energy-limited (ELIM) escape model against those from a direct hydrodynamic (HYDRO) model. Besides XUV-driven escape, the latter also includes the boil-off regime. We couple the two models to an internal structure model and follow the planets' temporal evolution over Gyr. To see the population-wide imprint of the two models, we first employ a rectangular grid in initial conditions. We then study the slope of the valley also for initial conditions derived from the Kepler planets. For the rectangular grid, we find that the power-law slope of the valley with respect to orbital period is -0.18 and -0.11 in the ELIM and HYDRO model, respectively. For the initial conditions derived from the Kepler planets, the results are similar (-0.16 and -0.10). While the slope found with the ELIM model is steeper than observed, the one of the HYDRO model is in excellent agreement with observations. The reason for the shallower slope is caused by the two regimes in which the ELIM model fails: First, puffy planets at low stellar irradiation. For them, boil-off dominates mass loss. However, boil-off is absent in the ELIM model, thus it underestimates escape relative to HYDRO. Second, massive compact planets at high XUV irradiation. For them, the ELIM approximation overestimates escape relative to the HYDRO case because of cooling by thermal conduction, neglected in the ELIM model. The two effects act together in concert to yield in the HYDRO model a shallower slope of the valley that agrees very well with observations. We conclude that an escape model that includes boil-off and a more realistic treatment of cooling mechanisms can reproduce one of the most important constraints, the valley slope.Comment: 20 pages, 11 figures, accepted to A&

Continuous second order sliding mode based finite time tracking of a fully actuated biped robot

International audienceA second order sliding mode controller is modified to form a continuous homogeneous controller. Uniform finite time stability is proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piece-wise continuous nonhomogeneous disturbances. The modified controller is then utilised to track reference trajectories for all the joints of a fully actuated biped robot where the joint torque is modeled as the control input. The modified controller ensures the attainment of a finite settling time between two successive impacts. The main contribution of the paper is to provide straightforward and realizable engineering guidelines for reference trajectory generation and for tuning a robust finite time controller in order to achieve stable gait of a biped in the presence of an external force disturbance. Such a disturbance has destabilising effects in both continuous and impact phases. Numerical simulations of a biped robot are shown to support the theoretical results