Parma Workshop on Numerical Relativity and Gravitational Waves 2011


All talks are 20 minutes long, followed by 10 minutes for questions and discussions. Friday afternoon is dedicated to open discussions. The social dinner is scheduled for Thurday evening while on Friday evening a common gateway will be organized for the partecipand leaving on Saturday. The Book of Abstracts is available here

Wed, Sept 7th, 2011
14:00 14:15 Registration
Chair: R. De Pietri
14:15 14:30 R. De Pietri Welcome and introduction
14:30 15:00 B.Giacomazzo
Magnetized Binary Neutron Star Mergers
Binary neutron stars (BNSs) are among the most powerful sources of gravitational waves that will be detected by ground-based interferometers, such as advanced Virgo and LIGO, and they are also thought to be behind the central engine of short gamma-ray bursts. Since BNSs are often magnetized it is necessary to solve the full set of general relativistic magnetohydrodynamic (GRMHD) equations in order to accurately follow the last stages of inspiral, merger and the eventual formation of a black hole surrounded by a torus of magnetized matter. I will report on some recent results obtained using our fully GRMHD code Whisky in simulating the merger of magnetized equal-mass binary neutron star systems. I will in particular describe how magnetic fields can affect the gravitational wave signal emitted by these sources and their possible role in powering short gamma-ray bursts.
15:00 15:30 L.Rezzolla
Jets from merging binaries of compact objects
I will show how the dynamics of a binary of magnetized neutron stars leads to a rapidly-spinning black hole surrounded by a hot and highly-magnetized torus. The development of magnetohydrodynamical instabilities in the torus can amplify by several orders of magnitude the initially turbulent magnetic field, yielding an ordered poloidal field of ~ 1015 G along the black-hole spin-axis, within a half-opening angle of 30 deg, which may naturally launch a relativistic jet. I will also discuss whether jets should be expected during the inspiral and merger of binary supermassive black holes and highlight the difficulties behind their detection.
15:30 16:00 U.Sperhake
Spin alignment and superkick suppression in black-hole binary inspiral
We discuss the alignment/anti-alignment of spins with each other and the orbital angular momentum in the inspiral of black-hole binaries from separations of about 1000M close to the merger stage due to spin-spin and spin-orbit interactions. This phase is modeled using post-Newtonian methods. We discuss implications for the final spin and recoil resulting from the binary merger as predicted by numerical relativity simulations.
16:00 16:30   COFFE BREAK
Chair: S. Bernuzzi
16:30 17:00 I.Hinder
Falloff of the Weyl scalars in NR binary black hole spacetimes
The extraction of gravitational waves from numerical relativity (NR) simulations usually relies crucially on the computation of the Weyl scalar $\Psi_4$. $\Psi_4$ can be interpreted as gravitational radiation in part due to the fact that of all the Weyl curvature scalars $\Psi_0$ to $\Psi_4$, $\Psi_4$ is the only one that has a nonzero flux at infinity due to its 1/r falloff. This is a result of the ``peeling theorem'', according to which the remaining scalars fall off faster than 1/r assuming certain conditions are met. There have recently been questions concerning the extent to which these conditions are met when the Weyl scalars are computed in compact binary NR simulations. We verify that, for a binary black hole simulation, the Weyl scalars obey the peeling theorem to within numerical error
17:00 17:30 G.M.Guidi
The NINJA project
The Numerical INjection Analysis (NINJA) project is a collaboration between numerical relativists and gravitational wave astronomers. The goal is to test gravitational-wave analysis pipelines against the best available waveforms for binary black hole mergers. We present results of the NINJA-1 project and the status of the followup project, NINJA-2, which is currently ongoing. Gianluca M Guidi for the NINJA Collaboration, the LIGO Scientific Collaboration and the Virgo Collaboration.
17:30 18:00 E.Bentivegna
Verifying numerical relativity codes: application-level correctness and runtime tools
As simulations in relativistic astrophysics increase in size and sophistication, verifying code correctness and ensuring consistency in physics and algorithms becomes a daunting task. In this talk, I will discuss strategies to monitor the behavior of a code (from physical modelling to numerical techniques and data operations) in an integrated way. I will, in particular, focus on the use of runtime tools as an ideal probe into the dynamic interaction of the code's components. Finally, I will illustrate the application of these ideas with a few examples from the Cactus framework.
Thu, Sept 8th, 2011
Chair: L. Rezzolla
9:00 9:30 D.Hilditch
Numerical Stability of a conformal decomposition of Z4
I will briefly summarize the motivation for the use of different formulations of GR in numerical relativity. I will then present a conformal decomposition of the Z4 formulation, Z4c, and discuss issues relating to stability in numerical approximation. The discussion will include a presentation of the apples with apples tests, comparing results obtained with BSSNOK and Z4c.
9:30 10:00 A.Weyhausen
Constraint damping for the Z4 formulation of general relativity
The Z4 formulation of general relativity provides a build in damping scheme which promises to damp away constraint violations during free evolutions. In this talk I present the results of a numerical study of the damping system in Z4c, a conformal decomposition of Z4. I will dicuss the effect of the damping on low-frequency and on high-amplitude perturbations of flat space-time as well and on the long-term dynamics of puncture and compact star initial data in the context of spherical symmetry.
10:00 10:30 P. Cerdá-Durán
Gravitational waves in the Fully Constrained Formulation
The Fully Constrained Formulation (FCF) of General Relativity is a novel framework introduced as an alternative to the hyperbolic formulations traditionally used in numerical relativity. The FCF equations form a hybrid elliptic-hyperbolic system of equations including explicitly the constraints. We present an implicit-explicit numerical algorithm to solve the hyperbolic part, whereas the elliptic sector shares the form and properties with the well known Conformally Flat Condition (CFC) approximation. We show the stability and convergence properties of the numerical scheme with numerical simulations of vacuum solutions. We have performed the first numerical evolutions of the coupled system of hydrodynamics and Einstein equations within FCF. We apply this formalism to extract gravitational waves from compact objects.
10:30 11:00   COFFE BREAK
Chair: U. Sperhake
11:00 11:30 A.Nerozzi
A new approach to the Newman-Penrose formalism
The Newman-Penrose formalism is widely used in the areas of numerical relativity and perturbation theory as the quantities introduced by the formalism are coordinate independent and therefore give a gauge invariant description of the physical properties of the space-time under study, among which its gravitational wave content. Perturbation theory for a rotating black hole is introduced within this formalism, through the Teukolsky equation. However, the full set of equations introduced by the formalism is not yet fully understood, and even the mechanism that allows the decoupling of the Teukolsky equation is not yet fully clear. Understanding better the nature of these equations would turn out to be very helpful in several areas, as for example attempts to obtain a higher dimensional version of the Teukolsky equation have failed up to date. We present a new approach to the Newman-Penrose formalism that aims to simplify considerably the whole formalism, giving a better understanding of the known features, and suggesting procedures to extend such features to more general scenarios of interest.
11:00 11:30 S.Hergt
Canonical Treatment of Noncanonical pN Potentials for Spinning Compact Binaries
Essentially there are two different ways to derive EOMs for spinning compact binaries in post-Newtonian (pN) approximation. One method is called the Effective Field Theory approach that aims to calculate an effective potential for the interaction with the disadvantage to depend on noncanonical coordinates in nonreduced phase space, i.e the spin supplementary condition specifying the frame of reference is not yet eliminated. A more elaborate method is to directly derive a Hamiltonian within the ADM approach. Starting from a fourdimensional covariant action functional the general procedure and formulae to compare the corresponding potentials and Hamiltonians are derived, clarifying the short notice on this procedure in arXiv:1002.2093.
12:00 12:30 R.Sturani
Complete phenomenological waveforms from spinning coalescing binaries
An accurate knowledge of the coalescing binary gravitational waveform is crucial for experimental searches as the ones performed by the LIGO-Virgo collaboration. We present the construction of analytical phenomenological waveforms describing the signal sourced by generically spinning binary systems. The gap between the initial inspiral part of the waveform, described by spin-Taylor approximants, and its final ring-down part, described by damped exponentials, is bridged by a phenomenological phase calibrated by comparison with the dominant spherical harmonic mode of a set of waveforms including both numerical and phenomenological waveforms of different type. The Advanced LIGO noise-weighted overlap integral between the numerical and phenomenological waveforms presented here ranges between 0.95 and 0.99 for a wide span of mass values.
12:30 13:00 S.Foffa
The energy of a binary system at 3PN and beyond
I will show how the effective field theory methods for the gravitationally bound two-body system proposed by Goldberger and Rothstein can be employed to efficiently compute the conservative dynamics of a binary system. In particular, I will show how this method successfully reproduce the already known effective action at 3PN order, and I will sketch the steps to extend the computation to the yet-unknown 4PN order.
13:00 14:30   LUNCH BREAK
Chair: S. Foffa
14:30 15:00 L.Gualtieri
Tidal interaction in compact binaries: a post-Newtonian affine framework
Semi-analytical approaches can be very useful in describing compact star coalescing binaries. In our approach, based on the post-Newtonian expansion and on the affine approximation, we model the tidal deformation of neutron stars in the coalescence of compact binary systems. We apply our approach to study black hole-neutron star coalescences up to the onset of neutron star tidal disruption, comparing our results with the outcome of numerical relativity simulations.
15:00 15:30 A.Nagar
The effective one body description of tidal effects in compact binaries and its comparison with numerical relativity simulations
The late part of the gravitational wave signal of binary neutron star inspirals can in principle yield crucial information on the nuclear equation of state via its dependence on relativistic tidal parameters. In the hope of describing analytically the late part of the gravitational wave signal, I will briefly introduce an extension of the effective-one-body formalism that includes the tidal interaction. The analytical predictions are then compared/constrasted with two numerical relativity simulations of inspiralling and coalescing neutron star binaries. By calibrating one single flexibility parameter accounting for higher-order tidal effects, one finds that the EOB model can reproduce, within the numerical error, the two waveforms essentially up to merger.
15:30 16:00 J.Steinhoff
The PN Approximation Beyond Point-Masses
Compact objects like black holes or neutron stars can approximately be described by point masses very well. However, very interesting astronomical information might be contained in effects to gravitational waves arising from the object's higher multipoles (or their finite size). Some of these effects can be modeled by an extension of the point mass action. Based on such an action, contributions of dipole (i.e., spin) and quadrupole to the post-Newtonian (PN) approximation can be obtained. The potential relevance of recent results (such as arXiv:1104.3079 and arXiv:1002.2093) for gravitational wave astronomy is briefly discussed.
16:00 16:30   COFFE BREAK
Chair: A. Nagar
16:30 17:00 S.Dolan
Self-force calculations for black hole inspirals
Advances in numerical relativity (NR) since 2005 have led to rapid progress in the modelling of black hole inspirals. Yet an important frontier awaits: the large mass-ratio regime. For example, in the final year before merger, an Extreme Mass-Ratio Inspiral (EMRI) will undergo $~ 10^5$ orbits in the strong-field regime. EMRIs may be analysed via black hole perturbation theory, by assuming the small body follows a trajectory on the background spacetime of the large black hole, and that the trajectory is perturbed away from a geodesic of the background by a `self-force'. Practical methods for computing self-force effects at first order in the mass ratio are now well-established. In this short review, I will focus on four emerging themes in the self-force programme: (i) comparison of gauge-invariant results from gravitational self-force (GSF) calculations with other methodologies (e.g. Post-Newtonian, EOB and NR in arXiv:1106.3278); (ii) ongoing development of numerical schemes for highly accurate calculations of GSF on Kerr spacetime; (iii) aspirations to achieve accurate, self-consistent long-term orbital evolutions of EMRIs using GSF calculations; (iv) understanding of new qualitatively new phenomena, such as resonances [arXiv:1009.4923], which have practical implications for data analysis strategies.
17:00 17:30 K.Takami
A quasi-radial stability criterion for rotating relativistic stars
The stability properties of relativistic stars against gravitational collapse to black holes is a classical problem in general relativity. In 1988, a sufficient criterion for secular instability was established by Friedman, Ipser \& Sorkin, who proved that a sequence of uniformly rotating barotropic stars are secularly unstable on one side of a turning point and then argued that a stronger result should hold: that the sequence should be stable on the opposite side, with the turning point marking the onset of secular instability. We show here that this expectation is not met. By computing in full general relativity the F-mode frequency for a large number of rotating stars, we show that the neutral-stability point, that is, where the frequency becomes zero, differs from the turning point for rotating stars. Using numerical simulations, we validate that the new criterion can be used to assess the dynamical stability of relativistic rotating stars. (This work is appeared in MNRAL(2011).)
17:30 18:00 L.Villain
Properties of stationary differentially rotating relativistic cold stars
Stationary configurations of differentially rotating relativistic polytrops are studied using a multidomain pseudo-spectral code based on the method developed in Jena (Ansorg, Kleinwächter, Meinel, 2003). Results concerning the solution space, the maximal masses, and the maximal values of rotation parameters such as the ratio between kinetic and gravitational energies will be presented and analyzed for several cold equations of states. Implications for the emission of gravitational waves from binary neutron star mergers will be discussed.
20:30 ---
Social Dinner
At the "Trattoria ai Corriere" with a menu of the tipical Parmesan food.
A vegeterian option will available on advanced request.
(web page) [DIRECTION]
Fri, Sept 9th, 2011
Chair: B. Giacomazzo
9:30 10:00 R.Ciolfi
Instability of Purely Poloidal Magnetic Fields in Neutron Stars
We consider the nonlinear evolution of a nonrotating neutron star with a purely poloidal magnetic field, in general relativity. We find that an instability develops in the region of the closed magnetic field lines and over an Alfven timescale, as predicted by perturbation theory. After the initial unstable growth, our evolutions show that a toroidal magnetic field component is generated, which increases until it is locally comparable in strength with the poloidal one. On longer timescales the system relaxes to a new non-axisymmetric configuration with a reorganization of the stellar structure and large-amplitude oscillations, mostly in the fundamental mode. We discuss the energies involved in the instability and the impact they may have on the phenomenology of magnetar flares and on their detectability through gravitational-wave emission.
10:00 10:30 B.Zink
GPU Computing and Magnetar Instabilities
Graphics Processing Units (GPUs) have made a significant impact on high-performance computing in recent years. I will explain why that is the case, and why GPU computing is particularly interesting for numerical relativity simulations. As an application, I will discuss general relativistic magnetohydrodynamics simulations of global magnetic field instabilities in magnetars using the GPU-accelerated HORIZON code.
10:30 11:00 L.Del Zanna
The ECHO code: from classical MHD to GRMHD in dynamical spacetimes
In this talk I will review the basic features of ECHO, the Eulerian Conservative High Order code developed in Florence, and I will discuss selected applications from classical MHD for Heliospheric physics, to relativistic MHD for high-energy Astrophysics, and the most recent upgrade: the full GR version coupled to an Einstein solver in the Conformally Flatness Condition for the physics of compact objects in axisymmetric spacetimes.
11:00 11:30   COFFE BREAK
Chair: D. Hilditch
11:30 12:00 D.Radice
Discontinuous-Galerkin methods for general-relativistic hydrodynamics
I will present my work on discontinuous-Galerkin methods for general-relativistic hydrodynamics. I will explain the key ideas behind these methods and show some of the results that we obtained while testing them for general-relativistic hydrodynamics in spherical symmetry.
12:00 12:30 K.Dionysopoulou
General Relativistic Resistive Magnetohydrodynamics with Whisky
We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (GR-RRMHD) equations within the Whisky code. The numerical method adopted exploits the properties of IMEX Runge-Kutta numerical schemes in order to treat the stiff terms of the equations. We have performed 1D, 2D and 3D numerical tests and we show that our method is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing physical setups in all ranges of conductivities. Finally, we present some preliminary results of a magnetized spherical star in the high-conductivity regime and compare with the corresponding ideal-MHD solution.
12:30 13:00 A.Mignone
Harten-Lax-van Leer Riemann Solvers for Relativistic MHD
Modern shock-capturing schemes heavily rely on the solution of the Riemann problem, describing the decay of a discontinuity separating two adjacent constant states. Here I review the Harten-Lax-van Leer family of Riemann solvers (HLL, HLLC and HLLD) where an initial guess to the characteristic wave speeds is given without any knowledge a priori of the solution. It is shown that the accuracy of the solution depends on the number of waves included in the approximation. In particular, a 5-wave HLLD scheme is proposed by approximating the solution with a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than its classical counterpart since the normal velocity is no longer constant across the rotational modes. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten-Lax-van Leer solver and the HLLC schemes.
13:00 14:30   LUNCH BREAK
Chair: P. Cerdá-Durán
14:30 15:00 O.Zanotti
General relativistic radiation hydrodynamics of accretion flows
I present a new code for performing general-relativistic radiation-hydrodynamics simulations of accretion flows onto black holes. The radiation field is treated in the optically-thick approximation, with the opacity contributed by Thomson scattering and thermal bremsstrahlung. The analysis is concentrated on a detailed numerical investigation of hot two-dimensional, Bondi-Hoyle accretion flows with various Mach numbers. I report significant differences with respect to purely hydrodynamical evolutions. In particular, once the system relaxes to a radiation-pressure dominated regime, the accretion rates become about two orders of magnitude smaller than in the purely hydrodynamical case, remaining however super-Eddington as are the luminosities. Overall, this approach provides the first self-consistent calculation of the Bondi-Hoyle luminosity, most of which is emitted within r~100 M from the black hole, with typical values $L/L_{Edd} \sim 1-7$, and corresponding energy efficiencies ~0.09-0.5. The possibility of computing luminosities self-consistently allows to compare with the bremsstrahlung luminosity often used in modeling the electromagnetic counterparts to supermassive black-hole binaries, to find that in the optically-thick regime these more crude estimates are about 20 times larger than the radiation-hydrodynamics results.
15:00 15:30 N.Bucciantini
Strong magnetic fields in neutron stars: GRBs and other high energy phenomena
High energy phenomena in astrophysics often involve compact objects and strong magnetic fields. It is the presence of a magnetic field that allow one to extract the large amount of energy, available either in rotation or accretion, and convert it into relativistic outflows, which are the primary responsible for the EM signal we detect. In particular I will discuss the case of Magnetars, GRBs and Pulsars. I will present our code XNS for NS equilibria, and some results on vibrating modes in the presence of a strong magnetic field.
15:30 15:45 Conclusion
15:45 16:30   COFFE BREAK
16:30 19:00 Open discussion
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