Molecular-Kinetic Simulations of Escape from the Ex-planet and Exoplanets: Criterion for Transonic Flow

The equations of gas dynamics are extensively used to describe atmospheric loss from solar system bodies and exoplanets even though the boundary conditions at infinity are not uniquely defined. Using molecular-kinetic simulations that correctly treat the transition from the continuum to the rarefied region, we confirm that the energy-limited escape approximation is valid when adiabatic expansion is the dominant cooling process. However, this does not imply that the outflow goes sonic. In fact in the sonic regime, the energy limited approximation can significantly under estimate the escape rate. Rather large escape rates and concomitant adiabatic cooling can produce atmospheres with subsonic flow that are highly extended. Since this affects the heating rate of the upper atmosphere and the interaction with external fields and plasmas, we give a criterion for estimating when the outflow goes transonic in the continuum region. This is applied to early terrestrial atmospheres, exoplanet atmospheres, and the atmosphere of the ex-planet, Pluto, all of which have large escape rates. The paper and its erratum, combined here, are published: ApJL 768, L4 (2013); ApJ, 779, L30 (2013).Comment: 11 pages, 3 figure

Scaling and universality in coupled driven diffusive models

Inspired by the physics of magnetohydrodynamics (MHD) a simplified coupled Burgers-like model in one dimension (1d), a generalization of the Burgers model to coupled degrees of freedom, is proposed to describe 1dMHD. In addition to MHD, this model serves as a 1d reduced model for driven binary fluid mixtures. Here we have performed a comprehensive study of the universal properties of the generalized d-dimensional version of the reduced model. We employ both analytical and numerical approaches. In particular, we determine the scaling exponents and the amplitude-ratios of the relevant two-point time-dependent correlation functions in the model. We demonstrate that these quantities vary continuously with the amplitude of the noise cross-correlation. Further our numerical studies corroborate the continuous dependence of long wavelength and long time-scale physics of the model on the amplitude of the noise cross-correlations, as found in our analytical studies. We construct and simulate lattice-gas models of coupled degrees of freedom in 1d, belonging to the universality class of our coupled Burgers-like model, which display similar behavior. We use a variety of numerical (Monte-Carlo and Pseudospectral methods) and analytical (Dynamic Renormalization Group, Self-Consistent Mode-Coupling Theory and Functional Renormalization Group) approaches for our work. The results from our different approaches complement one another. Possible realizations of our results in various nonequilibrium models are discussed.Comment: To appear in JSTAT (2009); 52 pages in JSTAT format. Some figure files have been replace

Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation

A systematic analysis of the Burgers--Kardar--Parisi--Zhang equation in $d+1$ dimensions by dynamic renormalization group theory is described. The fixed points and exponents are calculated to two--loop order. We use the dimensional regularization scheme, carefully keeping the full $d$ dependence originating from the angular parts of the loop integrals. For dimensions less than $d_c=2$ we find a strong--coupling fixed point, which diverges at $d=2$, indicating that there is non--perturbative strong--coupling behavior for all $d \geq 2$. At $d=1$ our method yields the identical fixed point as in the one--loop approximation, and the two--loop contributions to the scaling functions are non--singular. For $d>2$ dimensions, there is no finite strong--coupling fixed point. In the framework of a $2+\epsilon$ expansion, we find the dynamic exponent corresponding to the unstable fixed point, which describes the non--equilibrium roughening transition, to be $z = 2 + {\cal O} (\epsilon^3)$, in agreement with a recent scaling argument by Doty and Kosterlitz. Similarly, our result for the correlation length exponent at the transition is $1/\nu = \epsilon + {\cal O} (\epsilon^3)$. For the smooth phase, some aspects of the crossover from Gaussian to critical behavior are discussed.Comment: 24 pages, written in LaTeX, 8 figures appended as postscript, EF/UCT--94/3, to be published in Phys. Rev. E

Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.Comment: 90 pages, 16 figure

Atmospheric Escape Processes and Planetary Atmospheric Evolution

The habitability of the surface of any planet is determined by a complex evolution of its interior, surface, and atmosphere. The electromagnetic and particle radiation of stars drive thermal, chemical and physical alteration of planetary atmospheres, including escape. Many known extrasolar planets experience vastly different stellar environments than those in our Solar system: it is crucial to understand the broad range of processes that lead to atmospheric escape and evolution under a wide range of conditions if we are to assess the habitability of worlds around other stars. One problem encountered between the planetary and the astrophysics communities is a lack of common language for describing escape processes. Each community has customary approximations that may be questioned by the other, such as the hypothesis of H-dominated thermosphere for astrophysicists, or the Sun-like nature of the stars for planetary scientists. Since exoplanets are becoming one of the main targets for the detection of life, a common set of definitions and hypotheses are required. We review the different escape mechanisms proposed for the evolution of planetary and exoplanetary atmospheres. We propose a common definition for the different escape mechanisms, and we show the important parameters to take into account when evaluating the escape at a planet in time. We show that the paradigm of the magnetic field as an atmospheric shield should be changed and that recent work on the history of Xenon in Earth's atmosphere gives an elegant explanation to its enrichment in heavier isotopes: the so-called Xenon paradox

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

nIFTy galaxy cluster simulations – I. Dark matter and non-radiative models

We have simulated the formation of a galaxy cluster in a Ʌ cold dark matter universe using 13 different codes modelling only gravity and non-radiative hydrodynamics (RAMSES, ART, AREPO, HYDRA and nine incarnations of GADGET). This range of codes includes particle-based, moving and fixed mesh codes as well as both Eulerian and Lagrangian fluid schemes. The various GADGET implementations span classic and modern smoothed particle hydrodynamics (SPH) schemes. The goal of this comparison is to assess the reliability of cosmological hydrodynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be non-radiative. We compare images of the cluster at z = 0, global properties such as mass and radial profiles of various dynamical and thermodynamical quantities. The underlying gravitational framework can be aligned very accurately for all the codes allowing a detailed investigation of the differences that develop due to the various gas physics implementations employed. As expected, the mesh-based codes RAMSES, ART and AREPO form extended entropy cores in the gas with rising central gas temperatures. Those codes employing classic SPH schemes show falling entropy profiles all the way into the very centre with correspondingly rising density profiles and central temperature inversions. We show that methods with modern SPH schemes that allow entropy mixing span the range between these two extremes and the latest SPH variants produce gas entropy profiles that are essentially indistinguishable from those obtained with grid-based methods

Martian atmospheric temperature and density profiles during the 1st year of NOMAD/TGO solar occultation measurements

We present vertical profiles of temperature and density from solar occultation (SO) observations by the “Nadir and Occultation for Mars Discovery” (NOMAD) spectrometer on board the Trace Gas Orbiter (TGO) during its first operational year, which covered the second half of Mars Year 34. We used calibrated transmittance spectra in 380 scans, and apply an in-house pre-processing to clean data systematics. Temperature and CO2 profiles up to about 90 km, with consistent hydrostatic adjustment, are obtained, after adapting an Earth-tested retrieval scheme to Mars conditions. Both pre-processing and retrieval are discussed to illustrate their performance and robustness. Our results reveal the large impact of the MY34 Global Dust Storm (GDS), which warmed the atmosphere at all altitudes. The large GDS aerosols opacity limited the sounding of tropospheric layers. The retrieved temperatures agree well with global climate models (GCM) at tropospheric altitudes, but NOMAD mesospheric temperatures are wavier and globally colder by 10 K in the perihelion season, particularly during the GDS and its decay phase. We observe a warm layer around 80 km during the Southern Spring, especially in the Northern Hemisphere morning terminator, associated to large thermal tides, significantly stronger than in the GCM. Cold mesospheric pockets, close to CO2 condensation temperatures, are more frequently observed than in the GCM. NOMAD CO2 densities show oscillations upon a seasonal trend that track well the latitudinal variations expected. Results uncertainties and suggestions to improve future data re-analysis are briefly discussed

Transient HCl in the atmosphere of Mars

A major quest in Mars’ exploration has been the hunt for atmospheric gases, potentially unveiling ongoing activity of geophysical or biological origin. Here, we report the first detection of a halogen gas, HCl, which could, in theory, originate from contemporary volcanic degassing or chlorine released from gas-solid reactions. Our detections made at ~3.2 to 3.8 μm with the Atmospheric Chemistry Suite and confirmed with Nadir and Occultation for Mars Discovery instruments onboard the ExoMars Trace Gas Orbiter, reveal widely distributed HCl in the 1- to 4-ppbv range, 20 times greater than previously reported upper limits. HCl increased during the 2018 global dust storm and declined soon after its end, pointing to the exchange between the dust and the atmosphere. Understanding the origin and variability of HCl shall constitute a major advance in our appraisal of martian geo- and photochemistry