arXiv subjects

Guillermo A. González

Publications and source records attributed to Guillermo A. González.

At least 19 recordsLinked to original sources

arXiv2019

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration

We study the effect of the radiation parameter in the location, stability and orbital dynamics in the Lagrange configuration of the restricted four-body problem when one of the primaries is a radiating body. The equations of motion for the test particle are derived by assuming that the primaries revolve in the same plane with uniform angular velocity, and regardless of their mass distribution, they will always lie at the vertices of an equilateral triangle. The insertion of the radiation factor in the restricted four-body problem, let us model more realistically the dynamics of a test particle orbiting an astrophysical system with an active star. The dynamical mechanisms responsible for the smoothening on the basin structures of the configuration space is related to the decrease in the total number of fixed points with increasing values of the radiation parameter. In our model of the Sun-Jupiter-Trojan Asteroid system, it is found that despite the repulsive character of the solar radiation pressure, there exist two stable libration points roughly located at the position of L4 and L5 in the Sun-Jupiter system.

nlin.CD↗

arXiv2019

Orbital dynamics in realistic galaxy models: NGC 3726, NGC 3877 and NGC 4010

In the present paper, using a generalization of the Miyamoto and Nagai potential we adjusted the observed rotation curves of three specific spiral galaxies to the analytical circular velocities. The observational data have been taken from a 21 cm-line synthesis imaging survey using the Westerbork Synthesis Radio Telescope, for three particular galaxies in the Ursa Major cluster: NGC 3726, NGC 3877 and NGC 4010. Accordingly, the dynamics of the system is analyzed in terms of the Poincaré sections method, finding that for larger values of the angular momentum of the test particle or lower values its total energy the dynamics is mainly regular, while on the opposite cases, the dynamics is mainly chaotic. Our toy model opens the possibility to find chaotic bounded orbits for stars in those particular galaxies.

astro-ph.GA↗

arXiv2018

Equilibrium points and basins of convergence in the triangular restricted four-body problem with a radiating body

The dynamics of the four-body problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting-Robertson drag, and solar wind drag. In our setup, three primaries lay at the vertices of an equilateral triangle and move in circular orbits around their common center of mass. Here, one of the primaries is a radiating body and the fourth body (whose mass is negligible) does not affect the motion of the primaries. We show that the existence and the number of equilibrium points of the problem depend on the mass parameters and radiation factor. Consequently, the allowed regions of motion, the regions of the basins of convergence for the equilibrium points, and the basin entropy will also depend on these parameters. The present dynamical model is analyzed for three combinations of mass for the primaries: equal masses, two equal masses, different masses. As the main results, we find that in all cases the libration points are unstable if the radiation factor is larger than 0.01 and hence able to destroy the stability of the libration points in the restricted four-body problem composed by Sun, Jupiter, Trojan asteroid and a test (dust) particle. Also, we conclude that the number of fixed points decreases with the increase of the radiation factor.

nlin.CD↗

arXiv2018

Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system

The dynamics of a test particle in a non-spinning binary black hole system of equal masses is numerically investigated. The binary system is modeled in the context of the pseudo-Newtonian circular restricted three-body problem, such that the primaries are separated by a fixed distance and move in a circular orbit around each other. In particular, the Paczyński-Wiita potential is used for describing the gravitational field of the two non-Newtonian primaries. The orbital properties of the test particle are determined through the classification of the initial conditions of the orbits, using several values of the Jacobi constant, in the Hill's regions of possible motion. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) displaying close encounters. Using the smaller alignment index (SALI) chaos indicator, we further classify bounded orbits into regular, sticky or chaotic. To gain a complete view of the dynamics of the system, we define grids of initial conditions on different types of two-dimensional planes. The orbital structure of the configuration plane, along with the corresponding distributions of the escape and collision/close encounter times, allow us to observe the transition from the classical Newtonian to the pseudo-Newtonian regime. Our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant as well as with the Schwarzschild radius of the black holes.

astro-ph.GA↗

arXiv2018

General Relativistic Razor-Thin Disks with Magnetically Polarized Matter

The origin of magnetic fields in the universe still remains unknown and constitutes one of the most intriguing questions in astronomy and astrophysics. Their significance is enormous since they have a strong influence on many astrophysical phenomena. In regards of this motivation, theoretical models of galactic disks with sources of magnetic field may contribute to understand the physics behind them. Inspired by this, we present a new family of analytical models for thin disks composed by magnetized material. The solutions are axially symmetric, conformastatic and are obtained by solving the Einstein-Maxwell Field Equations for continuum media without the test field approximation, and assuming that the sources are razor-thin disk of magnetically polarized matter. We find analytical expressions for the surface energy density, the pressure, the polarization vector, the electromagnetic fields, the mass and the rotational velocity for circular orbits, for two particular solutions. In each case, the energy-momentum tensor agrees with the energy conditions and also the convergence of the mass for all the solutions is proved. Since the solutions are well-behaved, they may be used to model astrophysical thin disks, and also may contribute as initial data in numerical simulations. In addition, the process to obtain the solutions is described in detail, which may be used as a guide to find solutions with magnetized material in General Relativity.

gr-qc↗

arXiv2018

Numerical general relativistic MHD with magnetically polarized matter

The magnetically polarized matter in astrophysical systems may be relevant in some magnetically dominated regions. For instance, the funnel that is generated in some highly magnetized disks configurations whereby relativistic jets are thought to spread, or in pulsars where the fluids are subject to very intense magnetic fields. With the aim of dealing with magnetic media in the astrophysical context, we present for the first time the conservative form of the GRMHD equations with a non-zero magnetic polarization vector $m^μ$. Then, we follow the Anile method to compute the eigenvalue structure in the case where the magnetic polarization is parallel to the magnetic field, and it is parametrized by the magnetic susceptibility $χ_m$. This approximation allows us to describe diamagnetic fluids, for which $χ_m<0$, and paramagnetic fluids where $χ_m>0$. The theoretical results were implemented in the CAFE code to study the role of the magnetic polarization in some 1D Riemann problems. We found that independently of the initial condition, the first waves that appear in the numerical solutions are faster in diamagnetic materials than in paramagnetic ones. Moreover, the constant states between the waves change notably for different magnetic susceptibilities. All these effects are more appreciable if the magnetic pressure is much bigger than the fluid pressure. Additionally, with the aim of analysing a magnetic media in a strong gravitational field, we carry out for the first time the magnetized Michel accretion of a magnetically polarized fluid. With this test, we found that the numerical solution is effectively maintained over time ($t>4000$), and that the global convergence of the code is $\gtrsim$ 2 for $χ_{m}\lesssim 0.005$, for all the magnetic field strength $β$ we considered.

astro-ph.HE↗

arXiv2017

MAGNUS: A new resistive MHD code with heat flow terms

We present a new magnetohydrodynamic (MHD) code for the simulation of wave propagation in the solar atmosphere, under the effects of electrical resistivity, but not dominant, and heat transference in a uniform 3D grid. The code is based on the finite volume method combined with the HLLE and HLLC approximate Riemann solvers, which use different slope limiters like MINMOD, MC, and WENO5. In order to control the growth of the divergence of the magnetic field, due to numerical errors, we apply the Flux Constrained Transport method, which is described in detail to understand how the resistive terms are included in the algorithm. In our results, it is verified that this method preserves the divergence of the magnetic fields within the machine round-off error. For the validation of the accuracy and efficiency of the schemes implemented in the code, we present some numerical tests in 1D and 2D for the ideal MHD. Later, we show one test for the resistivity in a magnetic reconnection process and one for the thermal conduction, where the temperature is advected by the magnetic field lines. Moreover, we display two numerical problems associated with the MHD wave propagation. The first one corresponds to a 3D evolution of a vertical velocity pulse at the photosphere-transition-corona region, while the second one consists in a 2D simulation of a transverse velocity pulse in a coronal loop.

astro-ph.SR↗

arXiv2017

Relativistic Static Thin Disks of Polarized Matter

An infinite family of exact solutions of the electrovacuum Einstein-Maxwell equations is presented. The family is static, axially symmetric and describe thin disks composed by electrically polarized material in a conformastatic spacetime. The form of the conformastatic metric allows us to write down the metric functions and the electromagnetic potentials in terms of a solution of the Laplace equation. We find a general expression for the surface energy density of the disk, the pressure, the polarization vector, the electromagnetic fields and the velocity rotation for circular orbits. As an example, we present the first model of the family and show the behavior of the different physical variables.

gr-qc↗

arXiv2017

Ideal Magnetohydrodynamics with Radiative Terms: Energy Conditions

Nowadays, the magnetic and radiation fields are very important to understand the matter accretion into compact objects, the dynamics of binary systems, the equilibrium configurations of neutron stars, the photon diffusion, etc. The energy and the momentum associated to these fields, along with the matter one, need to satisfy some conditions that guarantee an appropriate physical behavior of the source and its gravitational field. Based on this fact, we present the energy conditions for a perfect fluid with magnetic and radiation field, in which the radiation part of the energy-momentum tensor is assumed to be approximately isotropic, in accordance with the optically thick regime. In order to find these conditions, the stress tensor of the system is written in an orthonormal basis in which it becomes diagonal, and the energy conditions are computed through contractions of the energy-momentum tensor with the four velocity vector of an arbitrary observer. Finally, the conditions for a magnetized fluid are presented as a particular case in which the radiation contribution is zero.

gr-qc↗

arXiv2017

On the conservation of the Jacobi integral in the post-Newtonian circular restricted three-body problem

In the present paper, using the first-order approximation of the $n$-body Lagrangian (derived on the basis of the post-Newtonian gravitational theory of Einstein, Infeld, and Hoffman), we explicitly write down the equations of motion for the planar circular restricted three-body problem. Additionally, with some simplified assumptions, we obtain two formulas for estimating the values of the mass/distance and velocity/speed of light ratios appropriate for a given post-Newtonian approximation. We show that the formulas derived in the present study, lead to a good numerical conservation of the Jacobi constant and allow for an approximate equivalence between the Lagrangian and Hamiltonian approaches at the same post-Newtonian order. Accordingly, the dynamics of the system is analyzed in terms of the Poincaré sections method and Lyapunov exponents, finding that for specific values of the Jacobi constant the dynamics can be either chaotic or regular. Our results suggest that the chaoticity of the post-Newtonian system is slightly in- creased in comparison with its Newtonian counterpart.

astro-ph.EP↗

arXiv2017

On the Influence of the Mass Definition in the Stability of Axisymmetric Relativistic Thin Disks

The study on the stability of relativistic disks is one of the most important criteria for the characterization of astrophysically relevant galactic or accretion disks models. In this paper, we perform an analysis of the stability of static axisymmetric relativistic thin disks, by introducing a first-order perturbation into the energy-momentum tensor of the fluid. The formalism is applied to three particular models built with the aid of the displace-cut-reflect (DCR) method, and previously considered in literature (Ujevic and Letelier, 2004), but modifying the mass criteria, i.e., using the Komar mass instead of the total surface mass. Under this conditions, it is found that the total mass values are independent of the parameters of the DCR-method, which let us choose the boundary condition for the cutoff radius, such that it takes the maximum value that allows an appreciable and well-behaved perturbation on the disk. As a general result, we found that the Komar mass is more appropriate to define the cutoff radius.

gr-qc↗

arXiv2016

Pseudo-Newtonian planar circular restricted 3-body problem

We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor-Hoenselaers-Perjés procedure, we perform an expansion in the mass potential of a static massive spherical source up to the first non-Newtonian term, giving place to a gravitational potential that includes first-order general relativistic effects. With this result, we model a system composed by two pseudo-Newtonian primaries describing circular orbits around their common center of mass, and a test particle orbiting the system in the equatorial plane. The dynamics of the new system of equations is studied in terms of the Poincaré section method and the Lyapunov exponents, where the introduction of a new parameter $ε$, allows us to observe the transition from the Newtonian to the pseudo-Newtonian regime. We show that when the Jacobian constant is fixed, a chaotic orbit in the Newtonian regime can be either chaotic or regular in the pseudo-Newtonian approach. As a general result, we find that most of the pseudo-Newtonian configurations are less stable than their Newtonian equivalent.

gr-qc↗

arXiv2016

The Energy-Momentum Tensor for a Dissipative Fluid in General Relativity

Considering the growing interest of the astrophysicist community in the study of dissipative fluids with the aim of getting a more realistic description of the universe, we present in this paper a physical analysis of the energy-momentum tensor of a viscous fluid with heat flux. We introduce the general form of this tensor and, using the approximation of small velocity gradients, we relate the stresses of the fluid with the viscosity coefficients, the shear tensor and the expansion factor. Exploiting these relations, we can write the stresses in terms of the extrinsic curvature of the normal surface to the 4-velocity vector of the fluid, and we can also establish a connection between the perfect fluid and the symmetries of the spacetime. On the other hand, we calculate the energy conditions for a dissipative fluid through contractions of the energy-momentum tensor with the 4-velocity vector of an arbitrary observer. This method is interesting because it allows us to compute the conditions in a reasonable easy way and without considering any approximation or restriction on the energy-momentum tensor.

gr-qc↗

arXiv2016

Distribution functions for a family of axially symmetric galaxy models

We present the derivation of distribution functions for the first four members of a family of disks, previously obtained in (MNRAS, 371, 1873, 2006), which represent a family of axially symmetric galaxy models with finite radius and well behaved surface mass density. In order to do this we employ several approaches that have been developed starting from the potential-density pair and, essentially using the method introduced by Kalnajs (Ap. J., 205, 751, 1976) we obtain some distribution functions that depend on the Jacobi integral. Now, as this method demands that the mass density can be properly expressed as a function of the gravitational potential, we can do this only for the first four discs of the family. We also find another kind of distribution functions by starting with the even part of the previous distribution functions and using the maximum entropy principle in order to find the odd part and so a new distribution function, as it was pointed out by Dejonghe (Phys. Rep., 133, 217, 1986). The result is a wide variety of equilibrium states corresponding to several self-consistent finite flat galaxy models.

astro-ph↗

arXiv2015

Static Thin Disks with Haloes as Sources of Conformastatic Spacetimes

Two new families of exact solutions to the Einstein equations for a conformastatic spacetime with axial symmetry are presented which describe thin disks of dust immersed in a spheroidal halo. The solutions are obtained by expressing the metric function in terms of an auxiliary function which satisfies the Laplace equation, a characteristic property of the conformastatic spacetimes. The first family of solutions is obtained from the displacement, cut and reflexion method, which introduces a discontinuity in the first $z$-derivate of the metric tensor across the plane of the disk. The second family of solutions is obtained by using the oblate spheroidal coordinates because they adapt to the shape of the source and introduce naturally a cutting radius for the disk. The energy densities of the disk and the halo are everywhere positive and well behaved and their energy-momentum tensor agrees with all the energy conditions. Some particular solutions for the energy density of the disk and the halo are presented and the rotational curves are obtained by solving the geodesic equation for a particle that moves in circular orbits in the plane of the disk.

gr-qc↗

arXiv2015

Cracking in charged relativistic spheres

Using the concept of cracking, we have explored the influence of density fluctuations on isotropic and anisotropic charged matter configurations in General Relativity with "barotropic" equations of state, $P = P(ρ)$ and $P_{\perp}= P_{\perp}(ρ)$ and a mass-charge relation $Q=Q(ρ)$. We have refined the idea that density fluctuations affect physical variables and their gradients, i.e. the radial pressure and charge density gradients. It is found that not only anisotropic charged models could present cracking (or overturning), but also isotropic charged matter configurations could be affected by density fluctuations.

gr-qc↗

arXiv2013

Exact relativistic models of thin disks around static black holes in a magnetic field

The exact superposition of a central static black hole with surrounding thin disk in presence of a magnetic field is investigated. We consider two models of disk, one of infinite extension based on a Kuzmin-Chazy-Curzon metric and other finite based on the first Morgan-Morgan disk. We also analyze a simple model of active galactic nuclei consisting of black hole, a Kuzmin-Chazy-Curzon disk and two rods representing jets, in presence of magnetic field. To explain the stability of the disks we consider the matter of the disk made of two pressureless streams of counterrotating charged particles (counterrotating model) moving along electrogeodesic. Using the Rayleigh criterion we derivate for circular orbits the stability conditions of the particles of the streams. The influence of the magnetic field on the matter properties of the disk and on its stability are also analyzed.

gr-qc↗

arXiv2013

Conformastatic disk-haloes in Einstein-Maxwell gravity

We present a relativistic model describing a thin disk surrounded by a halo in presence of an electromagnetic field. The model is obtained by solving the Einstein-Maxwell equations on a particular conformastatic spacetime background and by using the distributional approach for the energy-momentum tensor. A class of solutions is obtained in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. A particular solution is given that is asymptotically flat and singularity-free, and satisfies all the energy conditions.

gr-qc↗