What do exotic equations of state have to offer?

We present a short general overview of the main features of exotic models of neutron stars, focusing on the structural and dynamical predictions derived from them. In particular, we discuss the presence of “normal” quark matter and Color-Flavor Locked (CFL) states, including their possible self-bound versions, and mention some different proposals emerging from the study of QCD microphysics. A connection with actual observed data is the main goal to be addressed at this talk and along the meeting. It is demonstrated that exotic equations of state are not soft if the vacuum contributions are large enough, and argued that recent measurements of high pulsar masses (M≥2M _⊙) create problems for hadronic models in which hyperons should be present. The author would like to acknowledge the financial support of CNPq (Brazil).     

Some rotating perfect fluid universes coupled with electromagnetic field interacting with gravitation

Some new interesting solutions, the dynamics, behaviour and phenomena of rotating charged perfect fluid models are investigated, and their physical and geometrical properties are studied in order to substantiate the possibility of the existence of such astrophysical bodies in this Universe. The nature and role of the metric rotation Ω(r,t) as well as that of the matter rotation ω(r,t) are studied for uniform and non-uniform motions. The reactions of the gravitational and charged fields with respect to the rotational motion are studied and possible results are explored for real astrophysical situations, and in some solutions we find the spatial restrictions on the models for realistic conditions. Rotating models which are expanding are obtained in which the rotational motions are decaying with time.     

Bianchi type-VI0 cosmological models in certain theories of gravitation

Exact Bianchi type-VI₀ cosmological solutions to Einstein's equations are presented in vacuum and for stiff-matter in the normal gauge for Lyra's geometry and in scalar-tensor theories developed by Saez and Ballester (1985) and Lau and Prokhovnik (1986). Also cosmological solutions are obtained for pure massive strings (p-strings) and for pure geometric strings. The dynamical behaviour of the models have been discussed.     

A new photometric analysis of the eclipsing binary system ST Carinae

ST Carinae is an eclipsing binary with a period of 0 _. ^d 90165 which is believed to consist of an A0V primary and a secondary of type F5-8IV. About 900 observations inUBV, made by Somerville in 1963 but unreduced at that time, are presented. The Wood model is used to obtain orbital elements, and four different solutions of the light curves are presented. These are also computed with the solutions obtained by previous investigators of this system. The solutions indicate a reasonably consistent geometry, but there is still substantial uncertainty with regard to the mass-ratio and dynamical status of ST Car. The possibility exists that ST Car is in the initial and rapid stage of mass exchange in which the primary component fills its Roche lobe and is losing mass to its companion. The two components of ST Car appear to be of normal dimensions, but additional work is needed to clarify the exact status of this system.     

On quasi-periodic motions around the collinear libration points in the real Earth–Moon system

Due to various perturbations, the collinear libration points of the real Earth–Moon system are not equilibrium points anymore. Under the assumption that the Moon’s motion is quasi-periodic, special quasi-periodic orbits called dynamical substitutes exist. These dynamical substitutes replace the geometrical collinear libration points as time-varying equilibrium points. In the paper, the dynamical substitutes of the three collinear libration points in the real Earth–Moon system are computed. For the points L ₁ and L ₂, linearized motions around the dynamical substitutes are described, and the variational equations of the dynamical substitutes are reduced to a form with a near constant coefficient matrix. Then higher order analytical formulae of the central manifolds are constructed. Using these analytical solutions as initial seeds, Lissajous orbits and halo orbits are computed with numerical algorithms.     

(An)Isotropic models in scalar and scalar-tensor cosmologies

We study how the constants G and Λ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (“quintessence”) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi V, VII₀ and IX, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we arrive at the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function.     

Uranus and Neptune interior models

This paper is concerned with the interior structure of Uranus and Neptune. Our approach is three-fold. First, a set of three-layer models for both Uranus and Neptune are constructed using a method similar to that used in the study of the terrestrial planets. The variations of the mass density (s) and flattening e(s) with fractional mean radius s for two representative models of Uranus and Neptune are calculated. The results are tabulated. A comparison of these models shows that these two planets are probably very similar to each other in their basic dynamical features. Such similarity is very seldom seen in our solar system. Secondly, we check the conformance between the theoretical results and observational data for the two planets. And thirdly, the 6th degree Stokes zonal parameters for Uranus and for Neptune are predicted, based on the interior models put forward in this paper.     

Approximate General Solution Of The Two-Dimensional Duffing Dynamical System

This paper presents the approximate general solution of the triple well, double oscillator non-linear dynamical system. This system is non-integrable and the approximate general solution is calculated by application of the Last Geometric Theorem of Poincaré (Birkhoff, 1913, 1925). The original problem, known as the Duffing one, is a 1 degree of freedom system that, besides the conservative force component, includes dumping and external forcing terms (see details in the web site: http://www.uncwil.edu/people/hermanr/chaos/ted/chaos.html). The problem considered here is a 2 degree of freedom, autonomous and conservative one, without dumping, and of axisymmetric potential. The space of permissible motions is scanned for identification of all solutions re-entering after from one to nine oscillations and the precise families of periodic solutions are computed, including their stability parameter, covering all cases with periods T corresponding to 4osc/T. Seven sub-domains of the space of solutions were investigated in detail by zooming, an operation that proved the possibility to advance the accuracy of the approximate general solution to the level permitted by the integration routine. The approximation of the general solution, although impressive, provides clear evidence of the complexity of the problem and the need to proceed to larger period families. Nevertheless, it allows prediction of the areas where chaos and order regions in the Poincaré surfaces of section are to be expected. Examples of such surfaces of sections, as well as of types of closed solutions, are given. Two peculiar points of the space of solutions were identified as crossing, or source points from which infinite families of periodic solutions emanate. The morphology and stability of solutions of the problem are studied and discussed.     

Least squares parameter estimation in chaotic differential equations

A recent least squares algorithm, which is designed to adapt implicit models to given sets of data, especially models given by differential equations or dynamical systems, is reviewed and used to fit the Hénon-Heiles differential equations to chaotic data sets.This numerical approach for estimating parameters in differential equation models, called theboundary value problem approach, is based on discretizing the differential equations like a boundary value problem,e.g. by a multiple shooting or collocation method, and solving the resulting constrained least squares problem with a structure exploiting generalized Gauss-Newton-Method (Bock, 1981).Dynamical systems like the Hénon-Heiles system which can have initial values and parameters that lead to positive Lyapunov exponents or phase space filling Poincaré maps give rise to chaotic time series. Various scenarios representing ideal and noisy data generated from the Hénon-Heiles system in the chaotic region are analyzedw.r.t. initial conditions, parameters and Lyapunov exponents. The original initial conditions and parameters are recovered with a given accuracy. The Lyapunov spectrum is then computed directly from the identified differential equations and compared to the spectrum of the true dynamics.presently at IWR, Universität Heidelberg, Im Neuenheimer Feld 368, D-6900 Heidelberg, Germany     

Formation of planetary systems: A simple synthetical approach

It is shown that by means of elementary assumptions it is possible to obtain models of planetary systems not too different from the observed case. Such assumptions are shown to be the bulk of more detailed models as those by Dole (1970) and Isaacman and Sagan (1977).An accurate fit with the features of the Solar System can be obtained only byad hoc assumptions on various physical quantities and depends also on the possibility of taking into account stochastic processes in the numerical code.We discuss various cases and attempt to derive best fit values for the free parameters of the model. The hypothesis of a moderate mass depletion in the region of outer planets is strongly supported by our results.     

Noether gauge symmetry approach in quintom cosmology

In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether gauge symmetries (NGS). Motivated by this mathematical tool, in this paper, we study the generalized Noether symmetry of quintom model of dark energy, which is a two component fluid model with quintessence and phantom scalar fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potential functions are proposed from the symmetry point of view, but in the quintom models they are used as phenomenological models without clear mathematical justification. From integrability point of view, we found two forms of the scale factor: one is power law and second is de-Sitter. Some cosmological implications of the solutions have been investigated.     

Modified gravity in a viscous and non-isotropic background

We study the dynamical evolution of an f(R) model of gravity in a viscous and anisotropic background which is given by a Bianchi type-I model of the Universe. We find viable forms of f(R) gravity in which one is exactly the Einsteinian model of gravity with a cosmological constant and other two are power law f(R) models. We show that these two power law models are stable with a suitable choice of parameters. We also examine three potentials which exhibit the potential effect of f(R) models in the context of scalar tensor theory. By solving different aspects of the model and finding the physical quantities in the Jordan frame, we show that the equation of state parameter satisfy the dominant energy condition. At last we show that the two power law f(R) models behave like quintessence model at late times and also the shear coefficient viscosity tends to zero at late times.     

Viscous ΛCDM universe models

We explore flat ΛCDM models with bulk viscosity, and study the role of the bulk viscosity in the evolution of these universe models. The dynamical equations for these models are obtained and solved for some cases of bulk viscosity. We obtain differential equations for the Hubble parameter H and the energy density of dark matter ρ _m , for which we give analytical solutions for some cases and for the general case we give a numerical solution. Also we calculate the statefinder parameters for these models and display them in the s–r-plane.     

Slowly rotating perfect-fluid universes coupled with zero-mass scalar field

Certain new analytic solutions for rotating perfect-fluid spheres in the Robertson-Walker universe are found out to substantiate the possibility of the existence of rotating cosmological objects coupled with zero-mass scalar field. Exact solutions for the metric rotation (r, t) and the matter rotation (r, t) under different conditions are obtained and their nature and role are investigated. Except for perfect dragging the scalar field is found to have a damping effect on the rotation of matter. In some solutions we find out the restrictions on the radii of the models for realistic astrophysical situations. Rotating models which can also be expanding are also obtained, in which case the rotational velocities are found to decay with the time; and these models may be taken as examples of real astrophysical objects in the Universe.     

Stability of fictitious Trojan planets in extrasolar systems

Our work deals with the dynamical possibility that in extrasolar planetary systems a terrestrial planet may have stable orbits in a 1:1 mean motion resonance with a Jovian like planet. We studied the motion of fictitious Trojans around the Lagrangian points L₄/L₅ and checked the stability and/or chaoticity of their motion with the aid of the Lyapunov Indicators and the maximum eccentricity. The computations were carried out using the dynamical model of the elliptic restricted three‐body problem that consists of a central star, a gas giant moving in the habitable zone, and a massless terrestrial planet. We found 3 new systems where the gas giant lies in the habitable zone, namely HD99109, HD101930, and HD33564. Additionally we investigated all known extrasolar planetary systems where the giant planet lies partly or fully in the habitable zone. The results show that the orbits around the Lagrangian points L₄/L₅ of all investigated systems are stable for long times (10⁷ revolutions). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G

The dynamics of the circular restricted three-body Earth-Moon-particle problem predicts the existence of the retrograde periodic orbits around the Lagrangian equilibrium point L1. Such orbits belong to the so-called family G (Broucke, Periodic orbits in the restricted three-body problem with Earth-Moon masses, JPL Technical Report 32–1168, 1968) and starting from them it is possible to define a set of trajectories that form round trip links between the Earth and the Moon. These links occur even with more complex dynamical systems as the complete Sun-Earth-Moon-particle problem. One of the most remarkable properties of these trajectories, observed for the four-body problem, is a meaningful inclination gain when they penetrate into the lunar sphere of influence and accomplish a swing-by with the Moon. This way, when one of these trajectories returns to the proximities of the Earth, it will be in a different orbital plane from its initial Earth orbit. In this work, we present studies that show the possibility of using this property mainly to accomplish transfer maneuvers between two Earth orbits with different altitudes and inclinations, with low cost, taking into account the dynamics of the four-body problem and of the swing-by as well. The results show that it is possible to design a set of nominal transfer trajectories that require ΔV _Total less than conventional methods like Hohmann, bi-elliptic and bi-parabolic transfer with plane change.     

Modeling the Local Interstellar Medium

The state of our observational and theoretical knowledge of the localinterstellar medium (LISM) is reviewed. The LISM stretches out from thelocal Cloud, surrounding the solar system to the boundary of the LocalBubble, which is a region of distinct anticorrelation between HI (N _H< 10²⁰ cm^-2) and 1/4 keV diffuse soft X-rays. After discussingsome key observations in soft X-rays, obtained by ROSAT and DXS, and inthe EUV by the EUVE satellite and the EURD instrument onboard Minisat, Iwill critically review models of the LISM. Since we cannot determine theplasma state (temperature, density, etc.) directly, the best plasmadiagnostic tool is high resolution spectroscopy. The interpretationof the data then has to rely heavily on plasma emission models. I willpoint out several caveats in the standard procedure. Preference is givento dynamical models of the Local Bubble in general and to non-equilibriumplasma emission models in particular, which have to be calculatedself-consistently. Such a model can explain (i) the deficiency of EUVlines as observed by EUVE, (ii) the dispersion measure and scintillationproperties of a nearby pulsar, (iii) the existence of local neutral HIclouds, and (iv) OVI absorption line widths. New model spectra of theLISM will be presented and briefly compared with DXS, EUVE and preliminaryEURD results.     

Diffusion of stars in a harmonic potential

In a simple approximation, the evolution of a stellar system can be described in terms of the solutions to a diffusion equation for motion in a harmonic potential. This paper presents a discussion and characterization of the normal modes for this equation. These solutions are of particular interest in that they provide a simple example of the interplay between dynamical and relaxation phenomena. For the case of a large system, in which the relaxation timet _r is much greater than the dynamical timet _d,there exists a well-defined sense in which the effects of relaxation may be viewed as a perturbation of motion in the fixed field: the dynamical effects give rise to a purely oscillatory behavior, whereas collisions among stars provide a dissipative mechanism that drives the system towards the unique isothermal equilibrium. Alternatively, the presence of the fixed potential serves to alter the e-folding time for the various modes. In the limit thatt _r t _d , all characteristic relaxation times are essentially doubled. This suggests a danger in the use of velocity space equations to model the effects of evaporation.     

On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem

This paper focuses on some aspects of the motion of a small particle moving near the Lagrangian points of the Earth–Moon system. The model for the motion of the particle is the so-called bicircular problem (BCP), that includes the effect of Earth and Moon as in the spatial restricted three body problem (RTBP), plus the effect of the Sun as a periodic time-dependent perturbation of the RTBP. Due to this periodic forcing coming from the Sun, the Lagrangian points are no longer equilibrium solutions for the BCP. On the other hand, the BCP has three periodic orbits (with the same period as the forcing) that can be seen as the dynamical equivalent of the Lagrangian points. In this work, we first discuss some numerical methods for the accurate computation of quasi-periodic solutions, and then we apply them to the BCP to obtain families of 2-D tori in an extended neighbourhood of the Lagrangian points. These families start on the three periodic orbits mentioned above and they are continued in the vertical (z and ż) direction up to a high distance. These (Cantor) families can be seen as the continuation, into the BCP, of the Lyapunov family of periodic orbits of the Lagrangian points that goes in the (z, ż) direction. These results are used in a forthcoming work [9] to find regions where trajectories remain confined for a very long time. It is remarkable that these regions seem to persist in the real system. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling Total Solar Irradiance Variations Using Automated Classification Software on Mount Wilson Data

We present the results using the AutoClass analysis application available at NASA/Ames Intelligent Systems Div. (2002) which is a Bayesian, finite mixture model classification system developed by Cheeseman and Stutz (1996). We apply this system to Mount Wilson Solar Observatory (MWO) intensity and magnetogram images and classify individual pixels on the solar surface to calculate daily indices that are then correlated with total solar irradiance (TSI) to yield a set of regression coefficients. This approach allows us to model the TSI with a correlation of better than 0.96 for the period 1996 to 2007. These regression coefficients applied to classified pixels on the observed solar surface allow the construction of images of the Sun as it would be seen by TSI measuring instruments like the Solar Bolometric Imager recently flown by Foukal et al. (Astrophys. J. 611, L57, 2004). As a consequence of the very high correlation we achieve in reproducing the TSI record, our approach holds out the possibility of creating an on-going, accurate, independent estimate of TSI variations from ground-based observations which could be used to compare, and identify the sources of disagreement among, TSI observations from the various satellite instruments and to fill in gaps in the satellite record. Further, our spatially-resolved images should assist in characterizing the particular solar surface regions associated with TSI variations. Also, since the particular set of MWO data on which this analysis is based is available on a daily basis back to at least 1985, and on an intermittent basis before then, it will be possible to estimate the TSI emission due to identified solar surface features at several solar minima to constrain the role surface magnetic effects have on long-term trends in solar energy output.