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Oscar Reula

Publications and source records attributed to Oscar Reula.

At least 19 recordsLinked to original sources
arXiv2024

Hyperbolic extensions of constrained PDEs

Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of the well-posedness of the Cauchy problem for these systems. Presently we review the use of hyperbolic reductions, in which the evolution equations are singled out for consideration. We then examine in greater detail the extensions, in which constraints are evolved as auxiliary variables alongside the original variables. Assuming a particular structure of the original system, we give sufficient conditions for strong-hyperbolicity of an extension. This theory is then applied to the examples of electromagnetism and a toy for magnetohydrodynamics.

math.AP↗
arXiv2024

Imaging fermionic dark matter cores at the center of galaxies

Current images of the supermassive black hole (SMBH) candidates at the center of our Galaxy and M87 have opened an unprecedented era for studying strong gravity and the nature of relativistic sources. Very-long-baseline interferometry (VLBI) data show images consistent with a central SMBH within General Relativity (GR). However, it is essential to consider whether other well-motivated dark compact objects within GR could produce similar images. Recent studies have shown that dark matter (DM) halos modeled as self-gravitating systems of neutral fermions can harbor very dense fermionic cores at their centers, which can mimic the spacetime features of a black hole (BH). Such dense, horizonless DM cores can satisfy the observational constraints: they can be supermassive and compact and lack a hard surface. We investigate whether such cores can produce similar observational signatures to those of BHs when illuminated by an accretion disk. We compute images and spectra of the fermion cores with a general-relativistic ray tracing technique, assuming the radiation originates from standard $\alpha$ disks, which are self-consistently solved within the current DM framework. Our simulated images possess a central brightness depression surrounded by a ring-like feature, resembling what is expected in the BH scenario. For Milky Way-like halos, the central brightness depressions have diameters down to $\sim 35\, \mu$as as measured from a distance of approximately $8\,$kpc. Finally, we show that the DM cores do not possess photon rings, a key difference from the BH paradigm, which could help discriminate between the models.

astro-ph.GA↗
arXiv2022

Relativistic force-free models of the thermal X-ray emission in millisecond pulsars observed by NICER

Several important properties of rotation-powered millisecond pulsars (MSPs), such as their mass-radius ratio, equation of state and magnetic field topology, can be inferred from precise observations and modelling of their X-ray light curves. In the present study, we model the thermal X-ray signals originated in MSPs, all the way from numerically solving the surrounding magnetospheres up to the ray tracing of the emitted photons and the final computation of their light curves and spectra. Our modelled X-ray signals are then compared against a set of very accurate NICER observations of four target pulsars: PSR J0437-4715, PSR J1231-1411, PSR J2124-3358 and PSR J0030+0451. We find very good simultaneous fits for the light curve and spectral distribution in all these pulsars. The magnetosphere is solved by performing general relativistic force-free simulations of a rotating neutron star (NS) endowed with a simple centered dipolar magnetic field, for many different stellar compactness and pulsar misalignments. From these solutions, we derive an emissivity map over the surface of the star, which is based on the electric currents in the magnetosphere. In particular, the emission regions (ERs) are determined in this model by spacelike four-currents that reach the NS. We show that this assumption, together with the inclusion of the gravitational curvature on the force-free simulations, lead to non-standard ERs facing the closed-zone of the pulsar, in addition to other ERs within the polar caps. The combined X-ray signals from these two kinds of ERs (both antipodal) allow to approximate the non-trivial interpulses found in all the target MSPs light curves.

astro-ph.HE↗
arXiv2022

Skylight: a new code for general-relativistic ray-tracing and radiative transfer in arbitrary spacetimes

To reproduce the observed spectra and light curves originated in the neighborhood of compact objects requires accurate relativistic ray-tracing codes. In this work, we present Skylight, a new numerical code for general-relativistic ray tracing and radiative transfer in arbitrary space-time geometries and coordinate systems. The code is capable of producing images, spectra, and light curves from astrophysical models of compact objects as seen by distant observers. We incorporate two different schemes, namely Monte Carlo radiative transfer, integrating geodesics from the astrophysical region to distant observers, and camera techniques with backwards integration from the observer to the emission region. The code is validated by successfully passing several test cases, among them: thin accretion disks and neutron star hot spot emission.

astro-ph.HE↗
arXiv2021

Magnetospheres of black hole-neutron star binaries

We perform force-free simulations for a neutron star orbiting a black hole, aiming at clarifying the main magnetosphere properties of such binaries towards their innermost stable circular orbits. Several configurations are explored, varying the orbital separation, the individual spins and misalignment angle among the magnetic and orbital axes. We find significant electromagnetic luminosities, $L\sim 10^{42-46} \, [B_{\rm pole}/ 10^{12}{\rm G}]^2 \, {\rm erg/s}$ (depending on the specific setting), primarily powered by the orbital kinetic energy, being about one order of magnitude higher than those expected from unipolar induction. The systems typically develop current sheets that extend to long distances following a spiral arm structure. The intense curvature of the black hole produces extreme bending on a particular set of magnetic field lines as it moves along the orbit, leading to magnetic reconnections in the vicinity of the horizon. For the most symmetric scenario (aligned cases), these reconnection events can release large-scale plasmoids that carry the majority of the Poynting fluxes. On the other hand, for misaligned cases, a larger fraction of the luminosity is instead carried outwards by large-amplitude Alfv{é}n waves disturbances. We estimate possible precursor electromagnetic emissions based on our numerical solutions, finding radio signals as the most promising candidates to be detectable within distances of $\lesssim 200$\,Mpc by forthcoming facilities like the Square Kilometer Array.

astro-ph.HE↗
arXiv2021

New Numerical Interface Scheme for the Kurganov-Tadmor second-order Method

In this paper, we develop a numerical scheme to handle interfaces across computational domains in multi-block schemes for the approximation of systems of conservation laws. We are interested in transmitting shock discontinuities without lowering the overall precision of the method. We want to accomplish this without using information from interior points of adjacent grids, that is, sharing only information from boundary points of those grids. To achieve this, we choose to work with the second-order Kurganov-Tadmor (KT) method at interior points, relaxing it to first order at interfaces. This allows us to keep second-order overall accuracy (in the relevant norm) and at the same time preserve the TVD property of the original scheme. After developing the method we performed several standard one and two-dimensional tests. Among them, we used the one-dimensional advection and Burgers equations to verify the second-order convergence of the method. We also tested the two-dimensional Euler equations with an implosion and a Gresho vortex\cite{liska2003}. In particular, in the two-dimensional implosion test we can see that regardless of the orientation of shocks with respect to the interface, they travel across them without appreciable deformation both in amplitude and front direction.

math.NA↗
arXiv2019

On necessary and sufficient conditions for strong hyperbolicity

In this work we study constant-coefficient first order systems of partial differential equations and give necessary and sufficient conditions for those systems to have a well posed Cauchy Problem. In many physical applications, due to the presence of constraints, the number of equations in the PDE system is larger than the number of unknowns, thus the standard Kreiss conditions can not be directly applied to check whether the system admits a well posed initial value formulation. In this work we find necessary and sufficient conditions such that there exists a reduced set of equations, of the same dimensionality as the set of unknowns, which satisfy Kreiss conditions and so are well defined and properly behaved evolution equations. We do that by studying the systems using the Kronecker decomposition of matrix pencils and, once the conditions are meet, finding specific families of reductions which render the system strongly hyperbolic. We show the power of the theory in some examples: Klein Gordon, the ADM, and the BSSN equations by writing them as first order systems, and studying their Kronecker decomposition and general reductions.

gr-qc↗
arXiv2019

Astrophysical jets from boosted compact objects

We perform full 3D numerical simulations of compact objects, such as black holes or neutron stars, boosted through an ambient force-free plasma that posses a uniform magnetization. We study jet formation and energy extraction from the resulting stationary late time solutions.The implementation of appropriate boundary conditions has allowed us to explore a wide range of boost velocities, finding the jet power scales as $γv^2$ (being $γ$ the Lorentz factor). We also explore other parameters of the problem like the orientation of the motion respect to the asymptotic magnetic field or the inclusion of black hole spin. Additionally, by comparing a black hole with a perfectly conducting sphere in flat spacetime, we manage to disentangle curvature effects from those produced by the perfect conducting surface. It is shown that when the stellar compactness is increased these two effects act in combination, further enhancing the luminosity produced by the neutron star.

astro-ph.HE↗
arXiv2018

Pulsar magnetospheres in General Relativity

The main contribution to the pulsar power can be calculated by assuming a rotating magnetically-dominated magnetosphere described by the force-free approximation. Although this simple model has been used thoroughly to study pulsar magnetospheres in the flat spacetime regime, only few works have considered the relativistic corrections introduced by the curvature and frame-dragging effects induced by a rotating neutron star. Here we revisit the problem and describe pulsar magnetospheres within full General Relativity, quantifying the corrections as a function of the angular velocity, the compactness of the star and the misalignment angle between the spin and the magnetic dipole. We provide analytical expressions for the pulsar luminosity by fitting our numerical results. Finally, we also analyze the effect of the relativistic corrections on the braking index, which indicates a slight increment in its value.

astro-ph.HE↗
arXiv2017

A novel scheme for simulating the force-free equations: boundary conditions and the evolution of solutions towards stationarity

Force-Free Electrodynamics (FFE) describes a particular regime of magnetically dominated relativistic plasmas, which arises on several astrophysical scenarios of interest such as pulsars or active galactic nuclei. In this article, we present a full 3D numerical implementation of the FFE evolution around a Kerr black hole. The novelty of our approach is three-folded: i) We use the "multi-block" technique to represent a domain with $S^2 \times \mathbb{R}^{+}$ topology within a stable finite-differences scheme. ii) We employ as evolution equations those arising from a covariant hyperbolization of the FFE system. iii) We implement stable and constraint-preserving boundary conditions to represent an outer region given by a uniform magnetic field aligned or misaligned respect to the symmetry axis. We find stationary jet solutions which reach equilibrium --through boundary conditions-- with the outer numerical surface. This is so, even when the outer boundary is located very close to the central region (i.e. $r_{out}\sim 10M $). These numerical solutions reproduce most of the known results for analogue astrophysical settings.

gr-qc↗
arXiv2016

Covariant Hyperbolization of Force-free Electrodynamics

Force-Free Flectrodynamics (FFE) is a non-linear system of equations modeling the evolution of the electromagnetic field, in the presence of a magnetically dominated relativistic plasma. This configuration arises on several astrophysical scenarios, which represent exciting laboratories to understand physics in extreme regimes. We show that this system, when restricted to the correct constraint submanifold, is symmetric hyperbolic. In numerical applications is not feasible to keep the system in that submanifold, and so, it is necessary to analyze its structure first in the tangent space of that submanifold and then in a whole neighborhood of it. As already shown by Pfeiffer, a direct (or naive) formulation of this system (in the whole tangent space) results in a weakly hyperbolic system of evolution equations for which well-possednes for the initial value formulation does not follows. Using the generalized symmetric hyperbolic formalism due to Geroch, we introduce here a covariant hyperbolization for the FFE system. In fact, in analogy to the usual Maxwell case, a complete family of hyperbolizers is found, both for the restricted system on the constraint submanifold as well as for a suitably extended system defined in a whole neighborhood of it. A particular symmetrizer among the family is then used to write down the pertaining evolution equations, in a generic ($3+1$)-decomposition on a background spacetime. Interestingly, it turns out that for a particular choice of the lapse and shift functions of the foliation, our symmetrized system reduces to the one found by Pfeiffer. Finally we analyze the characteristic structure of the resulting evolution system.

gr-qc↗
arXiv2015

Nonlinear electrodynamics as a symmetric hyperbolic system

Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the point-wise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that, the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a non-empty intersection. Namely that there exist families of symmetrizers in the sense of Geroch which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well-posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg.

gr-qc↗
arXiv2013

Multi-solitons with vector mesons on the two-sphere

Recent studies have suggested a strong connection between the static solutions of the 3D Skyrme model and those corresponding to its low-dimensional analog (baby-Skyrme model) on a two-sphere. We have found almost identical solutions considering an alternative two-dimensional model in which a vector meson field is introduced and coupled to the system, instead of the usual Skyrme term. It has been known that including this vector meson field in three dimensions stabilizes the non-linear sigma model without the need of a term quartic on derivatives of the pion fields (Skyrme term). In the present work, we have numerically searched for static multi-solitonic solutions of this alternative stabilization, for the case in which the base-space is a two-sphere. Moreover, we analyze the stability of these solutions under small perturbations in a fully dynamical setting. We have also considered the inclusion of a particular potential term into the Lagrangian, and explored the low/high-density phases of solitons for different ranges of the parameter space, achieving solitons localized enough that allow us to compare with planar (two-dimensional) studies.

hep-th↗
arXiv2012

Turbulent flows for relativistic conformal fluids in 2+1 dimensions

We demonstrate that relativistic conformal hydrodynamics in 2+1 dimensions displays a turbulent behaviour which cascades energy to longer wavelengths on both flat and spherical manifolds. Our motivation for this study is to understand the implications for gravitational solutions through the AdS/CFT correspondence. The observed behaviour implies gravitational perturbations of the corresponding black brane/black hole spacetimes (for sufficiently large scales/temperatures) will display a similar cascade towards longer wavelengths.

hep-th↗
arXiv2011

Robustness of the Blandford-Znajek mechanism

The Blandford-Znajek mechanism has long been regarded as a key ingredient in models attempting to explain powerful jets in AGNs, quasars, blazzars etc. In such mechanism, energy is extracted from a rotating black hole and dissipated at a load at far distances. In the current work we examine the behaviour of the BZ mechanism with respect to different boundary conditions, revealing the mechanism robustness upon variation of these conditions. Consequently, this work closes a gap in our understanding of this important scenario.

astro-ph.HE↗
arXiv2008

Beyond ideal MHD: towards a more realistic modeling of relativistic astrophysical plasmas

Many astrophysical processes involving magnetic fields and quasi-stationary processes are well described when assuming the fluid as a perfect conductor. For these systems, the ideal-magnetohydrodynamics (MHD) description captures the dynamics effectively and a number of well-tested techniques exist for its numerical solution. Yet, there are several astrophysical processes involving magnetic fields which are highly dynamical and for which resistive effects can play an important role. The numerical modeling of such non-ideal MHD flows is significantly more challenging as the resistivity is expected to change of several orders of magnitude across the flow and the equations are then either of hyperbolic-parabolic nature or hyperbolic with stiff terms. We here present a novel approach for the solution of these relativistic resistive MHD equations exploiting the properties of implicit-explicit (IMEX) Runge Kutta methods. By examining a number of tests we illustrate the accuracy of our approach under a variety of conditions and highlight its robustness when compared with alternative methods, such as the Strang-splitting. Most importantly, we show that our approach allows one to treat, within a unified framework, both those regions of the flow which are fluid-pressure dominated (such as in the interior of compact objects) and those which are instead magnetic-pressure dominated (such as in their magnetospheres)

astro-ph↗