On the analytic integrability of the cored galactic Hamiltonian

Agraïments: The second author was supported by Portuguese National Funds through FCT - Fundaçâo para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD.We provide a complete characterization of the analytic first integrals of the cored galactic Hamiltonian

On the integrability of a three-dimensional cored galactic Hamiltonian

El títol de la versió pre-print de l'article és: On the complete meromorphic integrability of a three-dimensional cored galactic HamiltonianAgraïments: The first author is partially supported by FEDER-UNAB10-4E-378, and a CAPES grant number 88881.030454/2013-01 from the program CSF-PVE. The second author is supported by Portuguese National Funds through FCT-Fundaçâo para a Ciência e a Tecnologia within the projects PTDC/MAT/117106/2010 and PEst-OE/EEI/LA0009/2013 (CAMGSD).We characterize when the three-dimensional cored galactic Hamiltonian system with Hamiltonian H =1/2(p2x + p2y +p2z/q)+s1 + x2 + y2 +z2/q, is completely meromorphically integrable when q ∈ [√ 0.6, 1]. The key point for this characterization is to transform the non-polynomial cored Hamiltonian System into a polynomial one

The 3-dimensional cored and logarithm potencials: Periodic orits

Agraïments: The first author is partially supported by CNPq grant 201802/2012-0.We study analytically families of periodic orbits for the cored and logarithmic Hamiltonians H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (1+x2 +(y2 +z2)/q2)1/2, and H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (log(1+x2 +(y2 + z2)/q2))/2, with 3 degrees of freedom, which are relevant in the analysis of the galactic dynamics. First, after introducing a scale transformation in the coordinates and momenta with a parameter ε, we show that both systems give essentially the same set of equations of motion up to first order in ε. Then the conditions for finding families of periodic orbits, using the averaging theory up to first order in ε, apply equally to both systems in every energy level H = h > 0. The averaging method used proves the existence of at most three periodic orbits, for ε small enough, and gives an analytic approximation for the initial conditions of these periodic orbits

Dynamical models of dwarf spheroidal galaxies based on distribution functions depending on actions

In this thesis we have addressed the problem of the dynamical modeling of dwarf spheroidal galaxies (dSphs) through the use of distribution functions (DFs) that depend on the action integrals. dSphs are low luminosity, pressure supported, dwarf galaxies that are thought to be extremely dark-matter dominated. In the first part of this thesis, we have introduced a new family of Dfs showing that these DFs are optimal in modeling dSphs. With the aim to constrain their dark-matter distribution and intrinsic stellar velocity distribution, we have presented models of two dSphs: Fornax and Sculptor, comparing the models with state-of-the-art spectroscopic and photometric data sets of these galaxies. We argued that Fornax and Sculptor are dominated by massive dark-matter halos. The dark-matter halo of Fornax has a density distribution with a large core in its central parts, while we were not able to put constraints of the shape on the Sculptor dark-matter density distribution. In the second part of this thesis we have addressed the problem of extending action-based DFs to deal with flattening in a physical way. Since previous flattened models generated via action-based DFs show unphysical behaviors, we have motivated how and shy, in order to make physical and acceptable models, one has to limit the possible functional forms that a DF can assume. We have shown how the models behave when these restrictions are implemented and we have presented the very first flattened, axisymmetric DF-based models with general DFs depending of three independent integrals of motion. We conclude studying the integrability of a few classes of flattened potentials: the complexified Plummer model and flattened potentials generated through flattened DFs depending on actions. We have shown that, in the presented experiments, all the orbits integrated in the flattened DF-based potential remain regular and very few become trapped by resonance

Star Clusters and Dark Matter as Probes of the Spacetime Geometry of Massive Black Holes

This thesis includes two main projects. In the first part, we assess the feasibility of a recently suggested strong-field general relativity test, in which future observations of a hypothetical class of stars orbiting very close to the supermassive black hole at the center of our galaxy, known as Sgr A*, could provide tests of the so-called no-hair theorem of general relativity through the measurement of precessions of their orbital planes. By considering how a distribution of stars and stellar mass black holes in the central cluster would perturb the orbits of those hypothetical stars, we show that for stars within about 0.2 milliparsecs (about 6 light-hours) of the black hole, the relativistic precessions dominate, leaving a potential window for tests of no-hair theorems. Our results are in agreement with N-body simulation results. In the second part, we develop a fully general relativistic phase-space formulation to consider the effects of the Galactic center supermassive black hole Sgr A* on the dark-matter density profile and its applications in the indirect detection of dark matter. We find significant differences from the non-relativistic result of Gondolo and Silk (1999), including a higher density for the spike and a larger degree of central concentration. Having the dark matter profile density in the presence of the massive black hole, we calculate its perturbing effect on the orbital motions of stars in the Galactic center, and find that for the stars of interest, relativistic effects related to the hair on the black hole will dominate the effects of dark matter.Comment: PhD Dissertation, Submitted to the Washington University in St. Louis. arXiv admin note: text overlap with arXiv:astro-ph/0508106, arXiv:0910.3538, arXiv:1208.3931, arXiv:1211.7090, arXiv:hep-ph/0404175 by other author

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity