Optical Spectroscopy of Unbound Asteroid Pairs

The recently discovered unbound asteroid pairs have been suggested to be the result of the decoupling of binary asteroids formed either through collision processes or, more likely, rotational fission of a rubble-pile asteroid after spin-up (Vokrouhlicky et al. 2008, AJ 136, 280; Pravec et al., 2010, Nature, 466, 1085). Much of the evidence for linkage of the asteroids in each pair relies solely on the backwards integrations of their orbits. We report new results from our continuing spectroscopic survey of the unbound asteroid pairs, including the youngest known pair, (6070) Rhineland - (54827) 2001 NQ8. The survey goal is to determine whether the asteroids in each unbound pair have similar spectra and therefore composition, expected if they have formed from a common parent body. Low-resolution spectroscopy covering the range 0.4-0.95 microns was conducted using the 3.6m ESO NTT+EFOSC2 during 2011-2012 and the 4.2m WHT+ACAM. We have attempted to maintain a high level of consistency between the observations of the components in each pair to ensure that differences in the asteroid spectra are not the result of the observing method or data reduction, but purely caused by compositional differences. Our WHT data indicates that the asteroids of unbound pair 17198 - 229056 exhibit different spectra and have been assigned different taxonomies, A and R respectively. Initial analysis of our data from the NTT suggests that the asteroids in unbound pairs 6070 - 54827 and 38707 - 32957 are likely silicate-dominated asteroids. The components of pair 23998 - 205383 are potentially X-type asteroids. We present final taxonomic classifications and the likelihood of spectral similarity in each pair.

Castalia — A Mission to a Main Belt Comet

Main Belt Comets (MBCs) are a newly identified class of solar system object, having asteroid-like orbits but sometimes exhibiting comet-like behavior. We present the case for a mission to an MBC, to be submitted to the European Space Agency.

2P/Encke, the Taurid complex NEOs and the Maribo and Sutter's Mill meteorites

Aims. 2P/Encke is a short period comet that was discovered in 1786 and has been extensively observed and studied for more than 200years. The Taurid meteoroid stream has long been linked with 2P/Encke owing to a good match of their orbital elements, even thoughthe comet’s activity is not strong enough to explain the number of observed meteors. Various small near-Earth objects (NEOs) havebeen discovered with orbits that can be linked to 2P/Encke and the Taurid meteoroid stream. Maribo and Sutter’s Mill are CM typecarbonaceous chondrite that fell in Denmark on January 17, 2009 and April 22, 2012, respectively. Their pre-atmospheric orbits placethem in the middle of the Taurid meteoroid stream, which raises the intriguing possibility that comet 2P/Encke could be the parentbody of CM chondrites.
Methods. To investigate whether a relationship between comet 2P/Encke, the Taurid complex associated NEOs, and CM chondritesexists, we performed photometric and spectroscopic studies of these objects in the visible wavelength range. We observed 2P/Enckeand 10 NEOs on August 2, 2011 with the FORS instrument at the 8.2 m Very Large Telescope on Cerro Paranal (Chile).
Results. Images in the R filter, used to investigate the possible presence of cometary activity around the nucleus of 2P/Encke andthe NEOs, show that no resolved coma is present. None of the FORS spectra show the 700 nm absorption feature due to hydratedminerals that is seen in the CM chondrite meteorites. All objects show featureless spectra with moderate reddening slopes at λ < 800nm. Apart for 2003 QC10 and 1999 VT25, which show a flatter spectrum, the spectral slope of the observed NEOs is compatible withthat of 2P/Encke. However, most of the NEOs show evidence of a silicate absorption in lower S/N data at λ > 800 nm, which is notseen in 2P/Encke, which suggests that they are not related.
Conclusions. Despite similar orbits, we find no spectroscopic evidence for a link between 2P/Encke, the Taurid complex NEOs andthe Maribo and Sutter’s Mill meteorites. However, we cannot rule out a connection to the meteorites either, as the spectral differencesmay be caused by secondary alteration of the surfaces of the NEOs. 

Indications for an influence of hot Jupiters on the rotation and activity of their host stars

Context. The magnetic activity of planet-hosting stars is an importantfactor for estimating the atmospheric stability of close-in exoplanetsand the age of their host stars. It has long been speculated thatclose-in exoplanets can influence the stellar activity level. However,testing for tidal or magnetic interaction effects in samples ofplanet-hosting stars is difficult because stellar activity hindersexoplanet detection, so that stellar samples with detected exoplanetsshow a bias toward low activity for small exoplanets.

Aims: Weaim to test whether exoplanets in close orbits influence the stellarrotation and magnetic activity of their host stars.

Methods: Wedeveloped a novel approach to test for systematic activity-enhancementsin planet-hosting stars. We use wide (several 100 AU) binary systems inwhich one of the stellar components is known to have an exoplanet, whilethe second stellar component does not have a detected planet andtherefore acts as a negative control. We use the stellar coronal X-rayemission as an observational proxy for magnetic activity and analyzeobservations performed with Chandra and XMM-Newton.

Results: Wefind that in two systems for which strong tidal interaction can beexpected the planet-hosting primary displays a much higher magneticactivity level than the planet-free secondary. In three systems forwhich weaker tidal interaction can be expected the activity levels ofthe two stellar components agree with each other.

Conclusions:Our observations indicate that the presence of Hot Jupiters may inhibitthe spin-down of host stars with thick outer convective layers. Possiblecauses for this effect include a transfer of angular momentum from theplanetary orbit to the stellar rotation through tidal interaction, ordifferences during the early evolution of the system, where the hoststar may decouple from the protoplanetary disk early because of a gapopened by the forming Hot Jupiter.

Distant activity of 67P/Churyumov-Gerasimenko in 2014: Ground-based results during the Rosetta pre-landing phase

As the ESA Rosetta mission approached, orbited, and sent a lander to comet 67P/Churyumov-Gerasimenko in 2014, a large campaign of ground-based observations also followed the comet. We constrain the total activity level of the comet by photometry and spectroscopy to place Rosetta results in context and to understand the large-scale structure of the comet's coma pre-perihelion. We performed observations using a number of telescopes, but concentrate on results from the 8m VLT and Gemini South telescopes in Chile. We use R-band imaging to measure the dust coma contribution to the comet's brightness and UV-visible spectroscopy to search for gas emissions, primarily using VLT/FORS. In addition we imaged the comet in near-infrared wavelengths (JHK) in late 2014 with Gemini-S/Flamingos 2. We find that the comet was already active in early 2014 at heliocentric distances beyond 4 au. The evolution of the total activity (measured by dust) followed previous predictions. No gas emissions were detected despite sensitive searches. The comet maintains a similar level of activity from orbit to orbit, and is in that sense predictable, meaning that Rosetta results correspond to typical behaviour for this comet. The gas production (for CN at least) is highly asymmetric with respect to perihelion, as our upper limits are below the measured production rates for similar distances post-perihelion in previous orbits.

X-ray driven evaporation of exoplanet atmospheres: discovery of a uniquely suited test system

The evaporation of exoplanetary atmospheres is thought to be driven by high-energy irradiation. However, the actual mass loss rates are not well constrained. Co-I Kipping has recently discovered that the star KOI-314, an M1V dwarf at 65 pc distance, is orbited by two earth-sized planets, the inner one of them rocky and the outer one gaseous (P_orb = 14d and 23d). Other recent works have shown an abundance of small rocky planets in very close orbits around their host stars, suggesting that the stellar high-energy irradiation evaporates away gaseous envelopes. KOI-314 is the first nearby system in which earth-sized planets of both types are detected, allowing us to constrain the efficiency of planetary evaporation if the stellar X-ray irradiation is measured. We therefore propose a 10 ks Chandra ACIS-S pointing to determine the stellar X-ray luminosity and hardness ratio. The accuracy of the orbital solution decreases quickly due to Transit-Timing Variations, which is why we ask for DDT.

Diagnóstico de avarias em máquinas rotativas utilizando a análise de órbitas

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica Perfil Manutenção e Produção

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Quotients d'une variété algébrique par un groupe algébrique linéairement réductif et ses sous-groupes maximaux unipotents

La construction d'un quotient, en topologie, est relativement simple; si $G$ est un groupe topologique agissant sur un espace topologique $X$, on peut considérer l'application naturelle de $X$ dans $X/G$, l'espace d'orbites muni de la topologie quotient. En géométrie algébrique, malheureusement, il n'est généralement pas possible de munir l'espace d'orbites d'une structure de variété. Dans le cas de l'action d'un groupe linéairement réductif $G$ sur une variété projective $X$, la théorie géométrique des invariants nous permet toutefois de construire un morphisme de variété d'un ouvert $U$ de $X$ vers une variété projective $X//U$, se rapprochant autant que possible d'une application quotient, au sens topologique du terme. Considérons par exemple $X\subseteq P^{n}$, une $k$-variété projective sur laquelle agit un groupe linéairement réductif $G$ et supposons que cette action soit induite par une action linéaire de $G$ sur $A^{n+1}$. Soit $\widehat{X}\subseteq A^{n+1}$, le cône affine au dessus de $\X$. Par un théorème de la théorie classique des invariants, il existe alors des invariants homogènes $f_{1},...,f_{r}\in C[\widehat{X}]^{G}$ tels que $$C[\widehat{X}]^{G}= C[f_{1},...,f_{r}].$$ On appellera le nilcone, que l'on notera $N$, la sous-variété de $\X$ définie par le locus des invariants $f_{1},...,f_{r}$. Soit $Proj(C[\widehat{X}]^{G})$, le spectre projectif de l'anneau des invariants. L'application rationnelle $$\pi:X\dashrightarrow Proj(C[f_{1},...,f_{r}])$$ induite par l'inclusion de $C[\widehat{X}]^{G}$ dans $C[\widehat{X}]$ est alors surjective, constante sur les orbites et sépare les orbites autant qu'il est possible de le faire; plus précisément, chaque fibre contient exactement une orbite fermée. Pour obtenir une application régulière satisfaisant les mêmes propriétés, il est nécessaire de jeter les points du nilcone. On obtient alors l'application quotient $$\pi:X\backslash N\rightarrow Proj(C[f_{1},...,f_{r}]).$$ Le critère de Hilbert-Mumford, dû à Hilbert et repris par Mumford près d'un demi-siècle plus tard, permet de décrire $N$ sans connaître les $f_{1},...,f_{r}$. Ce critère est d'autant plus utile que les générateurs de l'anneau des invariants ne sont connus que dans certains cas particuliers. Malgré les applications concrètes de ce théorème en géométrie algébrique classique, les démonstrations que l'on en trouve dans la littérature sont généralement données dans le cadre peu accessible des schémas. L'objectif de ce mémoire sera, entre autres, de donner une démonstration de ce critère en utilisant autant que possible les outils de la géométrie algébrique classique et de l'algèbre commutative. La version que nous démontrerons est un peu plus générale que la version originale de Hilbert \cite{hilbert} et se retrouve, par exemple, dans \cite{kempf}. Notre preuve est valide sur $C$ mais pourrait être généralisée à un corps $k$ de caractéristique nulle, pas nécessairement algébriquement clos. Dans la seconde partie de ce mémoire, nous étudierons la relation entre la construction précédente et celle obtenue en incluant les covariants en plus des invariants. Nous démontrerons dans ce cas un critère analogue au critère de Hilbert-Mumford (Théorème 6.3.2). C'est un théorème de Brion pour lequel nous donnerons une version un peu plus générale. Cette version, de même qu'une preuve simplifiée d'un théorème de Grosshans (Théorème 6.1.7), sont les éléments de ce mémoire que l'on ne retrouve pas dans la littérature.

Brisure de symétrie par la réduction des groupes de Lie simples à leurs sous-groupes de Lie réductifs maximaux

Dans ce travail, nous exploitons des propriétés déjà connues pour les systèmes de poids des représentations afin de les définir pour les orbites des groupes de Weyl des algèbres de Lie simples, traitées individuellement, et nous étendons certaines de ces propriétés aux orbites des groupes de Coxeter non cristallographiques. D'abord, nous considérons les points d'une orbite d'un groupe de Coxeter fini G comme les sommets d'un polytope (G-polytope) centré à l'origine d'un espace euclidien réel à n dimensions. Nous introduisons les produits et les puissances symétrisées de G-polytopes et nous en décrivons la décomposition en des sommes de G-polytopes. Plusieurs invariants des G-polytopes sont présentés. Ensuite, les orbites des groupes de Weyl des algèbres de Lie simples de tous types sont réduites en l'union d'orbites des groupes de Weyl des sous-algèbres réductives maximales de l'algèbre. Nous listons les matrices qui transforment les points des orbites de l'algèbre en des points des orbites des sous-algèbres pour tous les cas n<=8 ainsi que pour plusieurs séries infinies des paires d'algèbre-sous-algèbre. De nombreux exemples de règles de branchement sont présentés. Finalement, nous fournissons une nouvelle description, uniforme et complète, des centralisateurs des sous-groupes réguliers maximaux des groupes de Lie simples de tous types et de tous rangs. Nous présentons des formules explicites pour l'action de tels centralisateurs sur les représentations irréductibles des algèbres de Lie simples et montrons qu'elles peuvent être utilisées dans le calcul des règles de branchement impliquant ces sous-algèbres.

Les actions de groupes en géométrie symplectique et l'application moment

Ce mémoire porte sur quelques notions appropriées d'actions de groupe sur les variétés symplectiques, à savoir en ordre décroissant de généralité : les actions symplectiques, les actions faiblement hamiltoniennes et les actions hamiltoniennes. Une connaissance des actions de groupes et de la géométrie symplectique étant prérequise, deux chapitres sont consacrés à des présentations élémentaires de ces sujets. Le cas des actions hamiltoniennes est étudié en détail au quatrième chapitre : l'importante application moment y est définie et plusieurs résultats concernant les orbites de la représentation coadjointe, tels que les théorèmes de Kirillov et de Kostant-Souriau, y sont démontrés. Le dernier chapitre se concentre sur les actions hamiltoniennes des tores, l'objectif étant de démontrer le théorème de convexité d'Atiyha-Guillemin-Sternberg. Une discussion d'un théorème de classification de Delzant-Laudenbach est aussi donnée. La présentation se voulant une introduction assez exhaustive à la théorie des actions hamiltoniennes, presque tous les résultats énoncés sont accompagnés de preuves complètes. Divers exemples sont étudiés afin d'aider à bien comprendre les aspects plus subtils qui sont considérés. Plusieurs sujets connexes sont abordés, dont la préquantification géométrique et la réduction de Marsden-Weinstein.

L'astronomie nouvelle de Kepler et la logique de la découverte

Cette thèse propose une étude des raisons théoriques et empiriques impliquées dans l’élaboration d’une nouvelle astronomie par Johannes Kepler (1571-1630) tel qu’exposé dans son ouvrage Astronomia nova (1619). Cette thèse se déroule en deux temps : la première partie touche de près aux textes mêmes de Kepler, tandis que la seconde partie utilise la notion d’abduction pour interpréter logiquement ce processus de découverte et de justification. La première partie débute avec une analyse du projet de Kepler et de ses fondements philosophiques, métaphysiques et théologiques tels qu’exposés dans son premier ouvrage, le Mysterium cosmographicum. Ensuite, une étude des propos explicites de Kepler quant à la nature et au statut des hypothèses astronomiques est proposée via une étude de son traité intitulé Apologia pro Tychone contra Ursum. Une étude attentive des sources philosophiques, mathématiques et scientifiques ayant influencé Kepler pour sa nouvelle astronomie est ensuite proposée avant l’analyse détaillée des arguments scientifiques et des différentes étapes démonstratives qui sont présentés dans l’Astronomia nova. La deuxième partie vise à éclairer le débat sur l’abduction en se penchant d’abord sur trois approches traditionnelles (Platon, Aristote et Épicure) quant à la connaissance scientifique des phénomènes célestes permettant d’obtenir un discours vraisemblable ou une multiplicité d’explications concordantes avec les phénomènes. Enfin, quatre interprétations contemporaines et abductives du processus de découverte suivi par Kepler dans l’Astronomia nova sont présentées, reformulées et critiquées afin de proposer une nouvelle interprétation abductive laissant une plus grande place au projet même de construire une astronomie nouvelle fondée sur les causes. Cela nous donne des outils pour mieux saisir le sens et la portée de ce qui peut être désigné comme étant la « révolution képlérienne », soit le passage d’un système géocentrique à un système non pas simplement héliocentrique mais héliodynamique, ayant permis aux astronomes de s’affranchir du paradigme des orbites circulaires.

Analytical Studies on Diffusion and lntermittency in Chaotic Maps

The study of simple chaotic maps for non-equilibrium processes in statistical physics has been one of the central themes in the theory of chaotic dynamical systems. Recently, many works have been carried out on deterministic diffusion in spatially extended one-dimensional maps This can be related to real physical systems such as Josephson junctions in the presence of microwave radiation and parametrically driven oscillators. Transport due to chaos is an important problem in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion coefficient in terms of the periodic orbits of the system in the form of cycle expansions. But the fact is that the chaotic motion in such spatially extended maps has two complementary aspects- - diffusion and interrnittency. These are related to the time evolution of the probability density function which is approximately Gaussian by central limit theorem. It is noticed that the characteristic function method introduced by Fujisaka and his co-workers is a very powerful tool for analysing both these aspects of chaotic motion. The theory based on characteristic function actually provides a thermodynamic formalism for chaotic systems It can be applied to other types of chaos-induced diffusion also, such as the one arising in statistics of trajectory separation. It was noted that there is a close connection between cycle expansion technique and characteristic function method. It was found that this connection can be exploited to enhance the applicability of the cycle expansion technique. In this way, we found that cycle expansion can be used to analyse the probability density function in chaotic maps. In our research studies we have successfully applied the characteristic function method and cycle expansion technique for analysing some chaotic maps. We introduced in this connection, two classes of chaotic maps with variable shape by generalizing two types of maps well known in literature.

Modelling of Ultraviolet and Vissible Emissions in Comets

Comets are the spectacular objects in the night sky since the dawn of mankind. Due to their giant apparitions and enigmatic behavior, followed by coincidental calamities, they were termed as notorious and called as `bad omens'. With a systematic study of these objects modern scienti c community understood that these objects are part of our solar system. Comets are believed to be remnant bodies of at the end of evolution of solar system and possess the material of solar nebula. Hence, these are considered as most pristine objects which can provide the information about the conditions of solar nebula. These are small bodies of our solar system, with a typical size of about a kilometer to a few tens of kilometers orbiting the Sun in highly elliptical orbits. The solid body of a comet is nucleus which is a conglomerated mixture of water ice, dust and some other gases. When the cometary nucleus advances towards the Sun in its orbit the ices sublimates and produces the gaseous envelope around the nucleus which is called coma. The gravity of cometary nucleus is very small and hence can not in uence the motion of gases in the cometary coma. Though the cometary nucleus is a few kilometers in size they can produce a transient, extensive, and expanding atmosphere with size several orders of magnitude larger in space. By ejecting gas and dust into space comets became the most active members of the solar system. The solar radiation and the solar wind in uences the motion of dust and ions and produces dust and ion tails, respectively. Comets have been observed in di erent spectral regions from rocket, ground and space borne optical instruments. The observed emission intensities are used to quantify the chemical abundances of di erent species in the comets. The study of various physical and chemical processes that govern these emissions is essential before estimating chemical abundances in the coma. Cameron band emission of CO molecule has been used to derive CO2 abundance in the comets based on the assumption that photodissociation of CO2 mainly produces these emissions. Similarly, the atomic oxygen visible emissions have been used to probe H2O in the cometary coma. The observed green ([OI] 5577 A) to red-doublet emission ([OI] 6300 and 6364 A) ratio has been used to con rm H2O as the parent species of these emissions. In this thesis a model is developed to understand the photochemistry of these emissions and applied to several comets. The model calculated emission intensities are compared with the observations done by space borne instruments like International Ultraviolet Explorer (IUE) and Hubble Space Telescope (HST) and also by various ground based telescopes.

Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.