arXiv subjects

Pedro J. Montero

Publications and source records attributed to Pedro J. Montero.

At least 19 recordsLinked to original sources

arXiv2017

Papaloizou-Pringle instability suppression by the magnetorotational instability in relativistic accretion discs

Geometrically thick tori with constant specific angular momentum have been widely used in the last decades to construct numerical models of accretion flows onto black holes. Such discs are prone to a global non-axisymmetric hydrodynamic instability, known as Papaloizou-Pringle instability (PPI), which can redistribute angular momentum and also lead to an emission of gravitational waves. It is, however, not clear yet how the development of the PPI is affected by the presence of a magnetic field and by the concurrent development of the magnetorotational instability (MRI). We present a numerical analysis using three-dimensional GRMHD simulations of the interplay between the PPI and the MRI considering, for the first time, an analytical magnetized equilibrium solution as initial condition. In the purely hydrodynamic case, the PPI selects as expected the large-scale $m=1$ azimuthal mode as the fastest growing and non-linearly dominant mode. However, when the torus is threaded by a weak toroidal magnetic field, the development of the MRI leads to the suppression of large-scale modes and redistributes power across smaller scales. If the system starts with a significantly excited $m=1$ mode, the PPI can be dominant in a transient phase, before being ultimately quenched by the MRI. Such dynamics may well be important in compact star mergers and tidal disruption events.

astro-ph.HE↗

arXiv2016

Dynamical formation of a Reissner-Nordström black hole with scalar hair in a cavity

In a recent letter, we presented numerical relativity simulations, solving the full Einstein--Maxwell--Klein-Gordon equations, of superradiantly unstable Reissner-Nordström black holes (BHs), enclosed in a cavity. Low frequency, spherical perturbations of a charged scalar field, trigger this instability. The system's evolution was followed into the non-linear regime, until it relaxed into an equilibrium configuration, found to be a $\textit{hairy}$ BH: a charged horizon in equilibrium with a scalar field condensate, whose phase is oscillating at the (final) critical frequency. Here, we investigate the impact of adding self-interactions to the scalar field. In particular, we find sufficiently large self-interactions suppress the exponential growth phase, known from linear theory, and promote a non-monotonic behaviour of the scalar field energy. Furthermore, we discuss in detail the influence of the various parameters in this model: the initial BH charge, the initial scalar perturbation, the scalar field charge, mass, and the position of the cavity's boundary (mirror). We also investigate the "explosive" non-linear regime previously reported to be akin to a bosenova. A mode analysis shows that the "explosions" can be interpreted as the decay into the BH of modes that exit the superradiant regime.

gr-qc↗

arXiv2016

On the dynamics of tilted black hole-torus systems

We present results from three-dimensional, numerical relativity simulations of a {\it tilted} black hole-thick accretion disc system. The simulations are analysed using tracer particles in the disc which are advected with the flow. Such tracers, which we employ in these new simulations for the first time, provide a powerful means to analyse in detail the complex dynamics of tilted black hole-torus systems. We show how its use helps to gain insight in the overall dynamics of the system, discussing the origin of the observed black hole precession and the development of a global non-axisymmetric $m=1$ mode in the disc. Our three-dimensional simulations show the presence of quasi-periodic oscillations (QPOs) in the instantaneous accretion rate, with frequencies in a range compatible with those observed in low mass X-ray binaries with either a black hole or a neutron star component. The frequency ratio of the dominant low frequency peak and the first overtone is $o_1/f \sim 1.9$, a frequency ratio not attainable when modelling the QPOs as $p$-mode oscillations in axisymmetric tori.

astro-ph.HE↗

arXiv2016

Quasistationary solutions of scalar fields around accreting black holes

Massive scalar fields can form long-lived configurations around black holes. These configurations, dubbed quasi-bound states, have been studied both in the linear and nonlinear regimes. In this paper we show that quasi-bound states can form in a dynamical scenario in which the mass of the black hole grows significantly due to the capture of infalling matter. We solve the Klein-Gordon equation numerically in spherical symmetry, mimicking the evolution of the spacetime through a sequence of analytic Schwarzschild black hole solutions of increasing mass. It is found that the frequency of oscillation of the quasi-bound states decreases as the mass of the black hole increases. In addition, accretion leads to a significative increase of the exponential decay of the scalar field energy due to the presence of terms of order higher than linear in the exponent. We compare the black hole mass growth rates used in our study with estimates from observational surveys and extrapolate our results to values of the scalar field masses consistent with models that propose scalar fields as dark matter in the universe. We show that even for unrealistically large mass accretion rates, quasi-bound states around accreting black holes can survive for cosmological timescales. Our results provide further support to the intriguing possibility of the existence of dark matter halos based on (ultra-light) scalar fields surrounding supermassive black holes in galactic centers.

gr-qc↗

arXiv2016

Explosion and final state of an unstable Reissner-Nordstrom black hole

A Reissner-Nordström black hole (BH) is superradiantly unstable against spherical perturbations of a charged scalar field, enclosed in a cavity, with frequency lower than a critical value. We use numerical relativity techniques to follow the development of this unstable system -- dubbed a charged BH bomb -- into the non-linear regime, solving the full Einstein--Maxwell--Klein-Gordon equations, in spherical symmetry. We show that: $i)$ the process stops before all the charge is extracted from the BH; $ii)$ the system settles down into a hairy BH: a charged horizon in equilibrium with a scalar field condensate, whose phase is oscillating at the (final) critical frequency. For low scalar field charge, $q$, the final state is approached smoothly and monotonically. For large $q$, however, the energy extraction overshoots and an explosive phenomenon, akin to a $bosenova$, pushes some energy back into the BH. The charge extraction, by contrast, does not reverse.

gr-qc↗

arXiv2016

Numerical relativity simulations of thick accretion disks around tilted Kerr black holes

In this work we present 3D numerical relativity simulations of thick accretion disks around tilted Kerr BH. We investigate the evolution of three different initial disk models with a range of initial black hole spin magnitudes and tilt angles. For all the disk-to-black hole mass ratios considered (0.044-0.16) we observe significant black hole precession and nutation during the evolution. This indicates that for such mass ratios, neglecting the self-gravity of the disks by evolving them in a fixed background black hole spacetime is not justified. We find that the two more massive models are unstable against the Papaloizou-Pringle (PP) instability and that those PP-unstable models remain unstable for all initial spins and tilt angles considered, showing that the development of the instability is a very robust feature of such PP-unstable disks. Our lightest model, which is the most astrophysically favorable outcome of mergers of binary compact objects, is stable. The tilt between the black hole spin and the disk is strongly modulated during the growth of the PP instability, causing a partial global realignment of black hole spin and disk angular momentum in the most massive model with constant specific angular momentum l. For the model with non-constant l-profile we observe a long-lived m=1 non-axisymmetric structure which shows strong oscillations of the tilt angle in the inner regions of the disk. This effect might be connected to the development of Kozai-Lidov oscillations. Our simulations also confirm earlier findings that the development of the PP instability causes the long-term emission of large amplitude gravitational waves, predominantly for the l=m=2 multipole mode. The imprint of the BH precession on the gravitational waves from tilted BH-torus systems remains an interesting open issue that would require significantly longer simulations than those presented in this work.

gr-qc↗

arXiv2016

Critical phenomena in the aspherical gravitational collapse of radiation fluids

We study critical phenomena in the gravitational collapse of a radiation fluid. We perform numerical simulations in both spherical symmetry and axisymmetry, and observe critical scaling in both supercritical evolutions, which lead to the formation of a black hole, and subcritical evolutions, in which case the fluid disperses to infinity and leaves behind flat space. We identify the critical solution in spherically symmetric collapse, find evidence for its universality, and study the approach to this critical solution in the absence of spherical symmetry. For the cases that we consider, aspherical deviations from the spherically symmetric critical solution decay in damped oscillations in a manner that is consistent with the behavior found by Gundlach in perturbative calculations. Our simulations are performed with an unconstrained evolution code, implemented in spherical polar coordinates, and adopting "moving-puncture" coordinates.

gr-qc↗

arXiv2015

Quasistationary solutions of self-gravitating scalar fields around collapsing stars

Recent work has shown that scalar fields around black holes can form long-lived, quasistationary configurations surviving for cosmological timescales. With this requirement, scalar fields cannot be discarded as viable candidates for dark matter halo models in galaxies around central supermassive black holes (SMBH). One hypothesis for the formation of most SMBHs at high redshift is the gravitational collapse of supermassive stars (SMS) with masses of $\sim10^5 \rm {M_{\odot}}$. Therefore, a constraint for the existence of quasi-bound states of scalar fields is their survival to such dynamic events. To answer this question we present in this paper the results of a series of numerical relativity simulations of gravitationally collapsing, spherically symmetric stars surrounded by self-gravitating scalar fields. We use an ideal fluid equation of state with adiabatic index $Γ=4/3$ which is adequate to simulate radiation-dominated isentropic SMSs. Our results confirm the existence of oscillating, long-lived, self-gravitating scalar field configurations around non-rotating black holes after the collapse of the stars.

gr-qc↗

arXiv2015

Quasi-stationary solutions of self-gravitating scalar fields around black holes

Recent perturbative studies have shown the existence of long-lived, quasi-stationary configurations of scalar fields around black holes. In particular, such configurations have been found to survive for cosmological timescales, which is a requirement for viable dark matter halo models in galaxies based on such type of structures. In this paper we perform a series of numerical relativity simulations of dynamical non-rotating black holes surrounded by self-gravitating scalar fields. We solve numerically the coupled system of equations formed by the Einstein and the Klein-Gordon equations under the assumption of spherical symmetry using spherical coordinates. Our results confirm the existence of oscillating, long-lived, self-gravitating scalar fields configurations around non-rotating black holes in highly dynamical spacetimes with a rich scalar field environment. Our numerical simulations are long-term stable and allow for the extraction of the resonant frequencies to make a direct comparison with results obtained in the linearized regime. A byproduct of our simulations is the existence of a degeneracy in plausible long-lived solutions of Einstein equations that would induce the same motion of test particles, either with or without the existence of quasi-bound states.

gr-qc↗

arXiv2015

Numerical Relativity in Spherical Polar Coordinates: Off-center Simulations

We have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN equations, a factoring of all tensor components, as well as a partially implicit Runge-Kutta method, and does not rely on a regularization of the equations, nor does it make any assumptions about the symmetry across the origin. In order to demonstrate this feature we present here several off-centered simulations, including simulations of single black holes and neutron stars whose center is placed away from the origin of the coordinate system, as well as the asymmetric head-on collision of two black holes. We also revisit our implementation of relativistic hydrodynamics and demonstrate that a reference-metric formulation of hydrodynamics together with a factoring of all tensor components avoids problems related to the coordinate singularities at the origin and on the axes. As a particularly demanding test we present results for a shock wave propagating through the origin of the spherical polar coordinate system.

gr-qc↗

arXiv2015

Measuring the black hole spin direction in 3D Cartesian numerical relativity simulations

We show that the so-called flat-space rotational Killing vector method for measuring the Cartesian components of a black hole spin can be derived from the surface integral of Weinberg's pseudotensor over the apparent horizon surface when using Gaussian normal coordinates in the integration. Moreover, the integration of the pseudotensor in this gauge yields the Komar angular momentum integral in a foliation adapted to the axisymmetry of the spacetime. As a result, the method does not explicitly depend on the evolved lapse $α$ and shift $β^i$ on the respective timeslice, as they are fixed to Gaussian normal coordinates, while leaving the coordinate labels of the spatial metric $γ_{ij}$ and the extrinsic curvature $K_{ij}$ unchanged. Such gauge fixing endows the method with coordinate invariance, which is not present in integral expressions using Weinberg's pseudotensor, as they normally rely on the explicit use of Cartesian coordinates.

gr-qc↗

arXiv2015

Trumpet Slices in Kerr Spacetimes

We introduce a new time-independent family of analytical coordinate systems for the Kerr spacetime representing rotating black holes. We also propose a (2+1)+1 formalism for the characterization of trumpet geometries. Applying this formalism to our new family of coordinate systems we identify, for the first time, analytical and stationary trumpet slices for general rotating black holes, even for charged black holes in the presence of a cosmological constant. We present results for metric functions in this slicing and analyze the geometry of the rotating trumpet surface.

gr-qc↗

arXiv2014

General relativistic hydrodynamics in curvilinear coordinates

In this paper we report on what we believe is the first successful implementation of relativistic hydrodynamics, coupled to dynamical spacetimes, in spherical polar coordinates without symmetry assumptions. We employ a high-resolution shock-capturing scheme, which requires that the equations be cast in flux-conservative form. One example of such a form is the :Valencia" formulation, which has been adopted in numerous applications, in particular in Cartesian coordinates. Here we generalize this formulation to allow for a reference-metric approach, which provides a natural framework for calculations in curvilinear coordinates. In spherical polar coordinates, for example, it allows for an analytical treatment of the singular r and sin(θ) terms that appear in the equations. We experiment with different versions of our generalized Valencia formulation in numerical implementations of relativistic hydrodynamics for both fixed and dynamical spacetimes. We consider a number of different tests -- non-rotating and rotating relativistic stars, as well as gravitational collapse to a black hole -- to demonstrate that our formulation provides a promising approach to performing fully relativistic astrophysics simulations in spherical polar coordinates.

gr-qc↗

arXiv2014

Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: comparison with the BSSN formulation in spherical symmetry

We adopt a reference-metric approach to generalize a covariant and conformal version of the Z4 system of the Einstein equations. We refer to the resulting system as ``fully covariant and conformal", or fCCZ4 for short, since it is well suited for curvilinear as well as Cartesian coordinates. We implement this fCCZ4 formalism in spherical polar coordinates under the assumption of spherical symmetry using a partially-implicit Runge-Kutta (PIRK) method and show that our code can evolve both vacuum and non-vacuum spacetimes without encountering instabilities. Our method does not require regularization of the equations to handle coordinate singularities, nor does it depend on constraint-preserving outer boundary conditions, nor does it need any modifications of the equations for evolutions of black holes. We perform several tests and compare the performance of the fCCZ4 system, for different choices of certain free parameters, with that of BSSN. Confirming earlier results we find that, for an optimal choice of these parameters, and for neutron-star spacetimes, the violations of the Hamiltonian constraint can be between 1 and 3 orders of magnitude smaller in the fCCZ4 system than in the BSSN formulation. For black-hole spacetimes, on the other hand, any advantages of fCCZ4 over BSSN are less evident.

gr-qc↗

arXiv2013

Collapse of Nonlinear Gravitational Waves in Moving-Puncture Coordinates

We study numerical evolutions of nonlinear gravitational waves in moving-puncture coordinates. We adopt two different types of initial data -- Brill and Teukolsky waves -- and evolve them with two independent codes producing consistent results. We find that Brill data fail to produce long-term evolutions for common choices of coordinates and parameters, unless the initial amplitude is small, while Teukolsky wave initial data lead to stable evolutions, at least for amplitudes sufficiently far from criticality. The critical amplitude separates initial data whose evolutions leave behind flat space from those that lead to a black hole. For the latter we follow the interaction of the wave, the formation of a horizon, and the settling down into a time-independent trumpet geometry. We explore the differences between Brill and Teukolsky data and show that for less common choices of the parameters -- in particular negative amplitudes -- Brill data can be evolved with moving-puncture coordinates, and behave similarly to Teukolsky waves.

gr-qc↗

arXiv2012

Numerical Relativity in Spherical Polar Coordinates: Evolution Calculations with the BSSN Formulation

In the absence of symmetry assumptions most numerical relativity simulations adopt Cartesian coordinates. While Cartesian coordinates have some desirable properties, spherical polar coordinates appear better suited for certain applications, including gravitational collapse and supernova simulations. Development of numerical relativity codes in spherical polar coordinates has been hampered by the need to handle the coordinate singularities at the origin and on the axis, for example by careful regularization of the appropriate variables. Assuming spherical symmetry and adopting a covariant version of the BSSN equations, Montero and Cordero-Carrión recently demonstrated that such a regularization is not necessary when a partially implicit Runge-Kutta (PIRK) method is used for the time evolution of the gravitational fields. Here we report on an implementation of the BSSN equations in spherical polar coordinates without any symmetry assumptions. Using a PIRK method we obtain stable simulations in three spatial dimensions without the need to regularize the origin or the axis. We perform and discuss a number of tests to assess the stability, accuracy and convergence of the code, namely weak gravitational waves, "hydro-without-hydro" evolutions of spherical and rotating relativistic stars in equilibrium, and single black holes.

gr-qc↗

arXiv2012

BSSN equations in spherical coordinates without regularization: vacuum and non-vacuum spherically symmetric spacetimes

Brown has recently introduced a covariant formulation of the BSSN equations which is well suited for curvilinear coordinate systems. This is particularly desirable as many astrophysical phenomena are symmetric with respect to the rotation axis or are such that curvilinear coordinates adapt better to their geometry. However, the singularities associated with such coordinate systems are known to lead to numerical instabilities unless special care is taken (e.g., regularization at the origin). Cordero-Carrion will present a rigorous derivation of partially implicit Runge-Kutta methods in forthcoming papers, with the aim of treating numerically the stiff source terms in wave-like equations that may appear as a result of the choice of the coordinate system. We have developed a numerical code solving the BSSN equations in spherical symmetry and the general relativistic hydrodynamic equations written in flux-conservative form. A key feature of the code is that it uses a second-order partially implicit Runge-Kutta method to integrate the evolution equations. We perform and discuss a number of tests to assess the accuracy and expected convergence of the code, namely a pure gauge wave, the evolution of a single black hole, the evolution of a spherical relativistic star in equilibrium, and the gravitational collapse of a spherical relativistic star leading to the formation of a black hole. We obtain stable evolutions of regular spacetimes without the need for any regularization algorithm at the origin.

gr-qc↗

arXiv2012

Relativistic collapse and explosion of rotating supermassive stars with thermonuclear effects

We present results of general relativistic simulations of collapsing supermassive stars with and without rotation using the two-dimensional general relativistic numerical code Nada, which solves the Einstein equations written in the BSSN formalism and the general relativistic hydrodynamics equations with high resolution shock capturing schemes. These numerical simulations use an equation of state which includes effects of gas pressure, and in a tabulated form those associated with radiation and the electron-positron pairs. We also take into account the effect of thermonuclear energy released by hydrogen and helium burning. We find that objects with a mass of 5x10^{5} solar mass and an initial metallicity greater than Z_{CNO}~0.007 do explode if non-rotating, while the threshold metallicity for an explosion is reduced to Z_{CNO}~0.001 for objects uniformly rotating. The critical initial metallicity for a thermonuclear explosion increases for stars with mass ~10^{6} solar mass. For those stars that do not explode we follow the evolution beyond the phase of black hole formation. We compute the neutrino energy loss rates due to several processes that may be relevant during the gravitational collapse of these objects. The peak luminosities of neutrinos and antineutrinos of all flavors for models collapsing to a BH are ~10^{55} erg/s. The total radiated energy in neutrinos varies between ~10^{56} ergs for models collapsing to a BH, and ~10^{45}-10^{46} ergs for models exploding.

astro-ph.CO↗