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I. Cordero-Carrión

Publications and source records attributed to I. Cordero-Carrión.

8 recordsLinked to original sources
arXiv2024

A Black-Hole Excision Scheme for General Relativistic Core-Collapse Supernova Simulations

Fallback supernovae and the collapsar scenario for long-gamma ray burst and hypernovae have received considerable interest as pathways to black-hole formation and extreme transient events. Consistent simulations of these scenarios require a general relativistic treatment and need to deal appropriately with the formation of a singularity. Free evolution schemes for the Einstein equations can handle the formation of black holes by means of excision or puncture schemes. However, in constrained schemes, which offer distinct advantages in long-term numerical stability in stellar collapse simulations over well above $10^{4}$ light-crossing time scales, the dynamical treatment of black-hole spacetimes is more challenging. Building on previous work on excision in conformally flat spacetimes, we here present the implementation of a black-hole excision scheme for supernova simulations with the CoCoNuT-FMT neutrino transport code. We describe in detail a choice of boundary conditions that ensures long-time numerical stability, and also address upgrades to the hydrodynamics solver that are required to stably evolve the relativistic accretion flow onto the black hole. The scheme is currently limited to a spherically symmetric metric, but the hydrodynamics can be treated multi-dimensionally. For demonstration, we present a spherically symmetric simulation of black-hole formation in an $85 M_\odot$ star, as well as a two-dimensional simulation of the fallback explosion of the same progenitor. These extend past 9s and 0.3s after black-hole formation, respectively.

astro-ph.HE↗
arXiv2019

A standard siren measurement of the Hubble constant from GW170817 without the electromagnetic counterpart

We perform a statistical standard siren analysis of GW170817. Our analysis does not utilize knowledge of NGC 4993 as the unique host galaxy of the optical counterpart to GW170817. Instead, we consider each galaxy within the GW170817 localization region as a potential host; combining the redshift from each galaxy with the distance estimate from GW170817 provides an estimate of the Hubble constant, $H_0$. We then combine the $H_0$ values from all the galaxies to provide a final measurement of $H_0$. We explore the dependence of our results on the thresholds by which galaxies are included in our sample, as well as the impact of weighting the galaxies by stellar mass and star-formation rate. Considering all galaxies brighter than $0.01 L^\star_B$ as equally likely to host a BNS merger, we find $H_0= 76^{+48}_{-23}$ km s$^{-1}$ Mpc$^{-1}$ (maximum a posteriori and 68.3% highest density posterior interval; assuming a flat $H_0$ prior in the range $\left[ 10, 220 \right]$ km s$^{-1}$ Mpc$^{-1}$). Restricting only to galaxies brighter than $0.626 L^\star_B$ tightens the measurement to $H_0= 77^{+37}_{-18}$ km s$^{-1}$ Mpc$^{-1}$. We show that weighting the host galaxies by stellar mass or star-formation rate provides entirely consistent results with potentially tighter constraints. While these statistical estimates are inferior to the value from the counterpart standard siren measurement utilizing NGC 4993 as the unique host, $H_0=76^{+19}_{-13}$ km s$^{-1}$ Mpc$^{-1}$ (determined from the same publicly available data), our analysis is a proof-of-principle demonstration of the statistical approach first proposed by Bernard Schutz over 30 years ago.

astro-ph.CO↗
arXiv2018

Calibration of Advanced Virgo and Reconstruction of the Gravitational Wave Signal h(t) during the Observing Run O2

In August 2017, Advanced Virgo joined Advanced LIGO for the end of the O2 run, leading to the first gravitational waves detections with the three-detector network. This paper describes the Advanced Virgo calibration and the gravitational wave strain h(t) reconstruction during O2. The methods are the same as the ones developed for the initial Virgo detector and have already been described in previous publications, this paper summarizes the differences and emphasis is put on estimating systematic uncertainties. Three versions of the h(t) signal have been computed for the Virgo O2 run, an online version and two post-run reprocessed versions with improved detector calibration and reconstruction algorithm. A photon calibrator has been used to establish the sign of h(t) and to make an independent partial cross-check of the systematic uncertainties. The uncertainties reached for the latest h(t) version are 5.1% in amplitude, 40 mrad in phase and 20 microseconds in timing.

gr-qc↗
arXiv2016

On the equivalence between the Scheduled Relaxation Jacobi method and Richardson's non-stationary method

The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of $P$ relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of $M$ consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method. Our method to estimate the weights has the advantage that the explicit computation of the maximum and minimum eigenvalues of the matrix $A$ is replaced by the (much easier) calculation of the maximum and minimum frequencies derived from a von Neumann analysis. This set of weights is also optimal for the general problem, resulting in the fastest convergence of all possible SRJ schemes for a given grid structure. We also show that with the set of weights computed for the optimal SRJ scheme for a fixed cycle size it is possible to estimate numerically the optimal value of the parameter $ω$ in the Successive Overtaxation (SOR) method in some cases. Finally, we demonstrate with practical examples that our method also works very well for Poisson-like problems in which a high-order discretization of the Laplacian operator is employed. This is of interest since the former discretizations do not yield consistently ordered $A$ matrices. Furthermore, the optimal SRJ schemes here deduced, are advantageous over existing SOR implementations for high-order discretizations of the Laplacian operator in as much as they do not need to resort to multi-coloring schemes for their parallel implementation. (abridged)

math.NA↗
arXiv2015

Scheduled Relaxation Jacobi method: improvements and applications

Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ schemes, as the mixed (non-linear) algebraic-differential equations from which they result become notably stiff. Here we present a new methodology for obtaining the parameters of SRJ schemes that overcomes the limitations of the original algorithm and provide parameters for SRJ schemes with up to 15 levels and resolutions of up to $2^{15}$ points per dimension, allowing for acceleration factors larger than several hundreds with respect to the Jacobi method for typical resolutions and, in some high resolution cases, close to 1000. Furthermore, we extend the original algorithm to apply it to certain systems of non-linear ePDEs.

math.NA↗
arXiv2012

On numerical relativistic hydrodynamics and barotropic equations of state

The characteristic formulation of the relativistic hydrodynamic equations (Donat et al 1998 J. Comput. Phys. 146 58), which has been implemented in many relativistic hydro-codes that make use of Godunov-type methods, has to be slightly modified in the case of evolving barotropic flows. For a barotropic equation of state, a removable singularity appears in one of the eigenvectors. The singularity can be avoided by means of a simple renormalization which makes the system of eigenvectors well defined and complete. An alternative strategy for the particular case of barotropic flows is discussed.

astro-ph.SR↗
arXiv2008

Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations

Bonazzola, Gourgoulhon, Grandclément, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic system. We have carried out a preliminary analysis of the mathematical structure of that system, in particular focusing on the equations governing the evolution for the deviation of a conformal metric from a flat fiducial one. The choice of a Dirac's gauge for the spatial coordinates guarantees the mathematical characterization of that system as a (strongly) hyperbolic system of conservation laws. In the presence of boundaries, this characterization also depends on the boundary conditions for the shift vector in the elliptic subsystem. This interplay between the hyperbolic and elliptic parts of the complete evolution system is used to assess the prescription of inner boundary conditions for the hyperbolic part when using an excision approach to black hole spacetime evolutions.

gr-qc↗