The generalized non-conservative model of a 1-planet system - revisited

We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular momentum and the spin vectors of the bodies. Thus, we analyze full, spatial model of the planetary system. Both objects are assumed to be deformed due to their own rotations, as well as due to the mutual tidal interactions. The general relativity corrections are considered in terms of the post-Newtonian approximation. Besides the conservative contributions to the perturbing forces, there are also taken into account non-conservative effects, i.e., the dissipation of the mechanical energy. This dissipation is a result of the tidal perturbation on the velocity field in the internal zones with non-zero turbulent viscosity (convective zones). Our main goal is to derive the equations of the orbital motion as well as the equations governing time-evolution of the spin vectors (angular velocities). We derive the Lagrangian equations of the second kind for systems which do not conserve the mechanical energy. Next, the equations of motion are averaged out over all fast angles with respect to time-scales characteristic for conservative perturbations. The final equations of motion are then used to study the dynamics of the non-conservative model over time scales of the order of the age of the star. We analyze the final state of the system as a function of the initial conditions. Equilibria states of the averaged system are finally discussed.Comment: 37 pages, 13 figures, accepted to Celestial Mechanics and Dynamical Astronom

The Uncertainty in Newton's Constant and Precision Predictions of the Primordial Helium Abundance

The current uncertainty in Newton's constant, G_N, is of the order of 0.15%. For values of the baryon to photon ratio consistent with both cosmic microwave background observations and the primordial deuterium abundance, this uncertainty in G_N corresponds to an uncertainty in the primordial 4He mass fraction, Y_P, of +-1.3 x 10^{-4}. This uncertainty in Y_P is comparable to the effect from the current uncertainty in the neutron lifetime, which is often treated as the dominant uncertainty in calculations of Y_P. Recent measurements of G_N seem to be converging within a smaller range; a reduction in the estimated error on G_N by a factor of 10 would essentially eliminate it as a source of uncertainty in the calculation of the primordial 4He abundance.Comment: 3 pages, no figures, fixed typos, to appear in Phys. Rev.

Physics of rotation in stellar models

In these lecture notes, we present the equations presently used in stellar interior models in order to compute the effects of axial rotation. We discuss the hypotheses made. We suggest that the effects of rotation might play a key role at low metallicity.Comment: 32 pages, 7 figures, lectures, CNRS school, will be published by Springe

Tidal friction in close-in satellites and exoplanets. The Darwin theory re-visited

This report is a review of Darwin's classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) the capture into a 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.Comment: 30 pages, 7 figures, corrected typo

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

YREC: The Yale Rotating Stellar Evolution Code

The stellar evolution code YREC is outlined with emphasis on its applications to helio- and asteroseismology. The procedure for calculating calibrated solar and stellar models is described. Other features of the code such as a non-local treatment of convective core overshoot, and the implementation of a parametrized description of turbulence in stellar models, are considered in some detail. The code has been extensively used for other astrophysical applications, some of which are briefly mentioned at the end of the paper.Comment: 10 pages, 2 figures, ApSS accepte

Space Vehicle Terrestrial Environment Design Requirements Guidelines

The terrestrial environment is an important driver of space vehicle structural, control, and thermal system design. NASA is currently in the process of producing an update to an earlier Terrestrial Environment Guidelines for Aerospace Vehicle Design and Development Handbook. This paper addresses the contents of this updated handbook, with special emphasis on new material being included in the areas of atmospheric thermodynamic models, wind dynamics, atmospheric composition, atmospheric electricity, cloud phenomena, atmospheric extremes, and sea state. In addition, the respective engineering design elements are discussed relative to terrestrial environment inputs that require consideration. Specific lessons learned that have contributed to the advancements made in the application and awareness of terrestrial environment inputs for aerospace engineering applications are presented

Dimensionless cosmology

Although it is well known that any consideration of the variations of fundamental constants should be restricted to their dimensionless combinations, the literature on variations of the gravitational constant $G$ is entirely dimensionful. To illustrate applications of this to cosmology, we explicitly give a dimensionless version of the parameters of the standard cosmological model, and describe the physics of Big Bang Neucleosynthesis and recombination in a dimensionless manner. The issue that appears to have been missed in many studies is that in cosmology the strength of gravity is bound up in the cosmological equations, and the epoch at which we live is a crucial part of the model. We argue that it is useful to consider the hypothetical situation of communicating with another civilization (with entirely different units), comparing only dimensionless constants, in order to decide if we live in a Universe governed by precisely the same physical laws. In this thought experiment, we would also have to compare epochs, which can be defined by giving the value of any {\it one} of the evolving cosmological parameters. By setting things up carefully in this way one can avoid inconsistent results when considering variable constants, caused by effectively fixing more than one parameter today. We show examples of this effect by considering microwave background anisotropies, being careful to maintain dimensionlessness throughout. We present Fisher matrix calculations to estimate how well the fine structure constants for electromagnetism and gravity can be determined with future microwave background experiments. We highlight how one can be misled by simply adding $G$ to the usual cosmological parameter set

Asteroseismology of Eclipsing Binary Stars in the Kepler Era

Eclipsing binary stars have long served as benchmark systems to measure fundamental stellar properties. In the past few decades, asteroseismology - the study of stellar pulsations - has emerged as a new powerful tool to study the structure and evolution of stars across the HR diagram. Pulsating stars in eclipsing binary systems are particularly valuable since fundamental properties (such as radii and masses) can determined using two independent techniques. Furthermore, independently measured properties from binary orbits can be used to improve asteroseismic modeling for pulsating stars in which mode identifications are not straightforward. This contribution provides a review of asteroseismic detections in eclipsing binary stars, with a focus on space-based missions such as CoRoT and Kepler, and empirical tests of asteroseismic scaling relations for stochastic ("solar-like") oscillations.Comment: 28 pages, 12 figures, 2 tables; Proceedings of the AAS topical conference "Giants of Eclipse" (AASTCS-3), July 28 - August 2 2013, Monterey, C

Airborne observations of peroxy radicals during the EMeRGe campaign in Europe

In this study, airborne measurements of the sum of hydroperoxyl (HO2) and organic peroxy (RO2) radicals that react with nitrogen monoxide (NO) to produce nitrogen dioxide (NO2), coupled with actinometry and other key trace gases measurements, have been used to test the current understanding of the fast photochemistry in the outflow of major population centres. The measurements were made during the airborne campaign of the EMeRGe (Effect of Megacities on the transport and transformation of pollutants on the Regional to Global scales) project in Europe on board the High Altitude and Long Range Research Aircraft (HALO). The measurements of RO on HALO were made using the in situ instrument Peroxy Radical Chemical Enhancement and Absorption Spectrometer (PeRCEAS). RO is to a good approximation the sum of peroxy radicals reacting with NO to produce NO2. RO mixing ratios up to 120 pptv were observed in air masses of different origins and composition under different local actinometric conditions during seven HALO research flights in July 2017 over Europe. Radical production rates were estimated using knowledge of the photolysis frequencies and the precursor concentrations measured on board, as well as the relevant rate coefficients. Generally, high concentrations were measured in air masses with high production rates. In the air masses investigated, is primarily produced by the reaction of O1D with water vapour and the photolysis of nitrous acid (HONO) and of the oxygenated volatile organic compounds (OVOCs, e.g. formaldehyde (HCHO) and glyoxal (CHOCHO)). Due to their short lifetime in most environments, the RO concentrations are expected to be in a photostationary steady state (PSS), i.e. a balance between production and loss rates is assumed. The production and loss rates and the suitability of PSS assumptions to estimate the mixing ratios and variability during the airborne observations are discussed. The PSS assumption for is considered robust enough to calculate mixing ratios for most conditions encountered in the air masses measured. The similarities and discrepancies between measured and PSS calculated mixing ratios are discussed. The dominant terminating processes for in the pollution plumes measured up to 2000 m are the formation of nitrous acid, nitric acid, and organic nitrates. Above 2000 m, HO2–HO2 and HO2–RO2 reactions dominate the removal. calculations by the PSS analytical expression inside the pollution plumes probed often underestimated the measurements. The underestimation is attributed to the limitations of the PSS equation used for the analysis. In particular, this expression does not account for the yields of from the oxidation and photolysis of volatile organic compounds, VOCs, and OVOCs other than those measured during the EMeRGe research flights in Europe. In air masses with NO mixing ratios ≤50 pptv and low ratios, the measured is overestimated by the analytical expression. This may be caused by the formation of H2O and O2 from OH and HO2, being about 4 times faster than the rate of the OH oxidation reaction of the dominant OVOCs considered