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Numerical Relativity of Strongly Gravitating Systems L Numerical Relativity of strongly gravitating systems L. Lehner Perimeter Institute/CIFAR NR goal: understand ‘strongly gravitating’ regimes “Instead of: If we think hard enough, we don’t need a computer, With the right resources we can simulate situations we can't even begin to think through, and thereby provide us with completely new and unexpected things to think about” [M. Choptuik] • (M/L) ~ 1 ; (v/c) ~ 1 ; no `restrictive’ symmetries solve Einstein equations in full generality • Overarching questions: – Gravitational waves & connection with behaviour of source: gravitational wave astronomy – Understanding of spacetime structure in relevant/interest scenarios – Explore conjectures – Provide intuition for `analytical modeling’, mathematical analysis – uncover surprises… What’s involved – express EEs in terms of an initial boundary value problem (formulation) – ensure a well posed problem is defined (eqns & BCs) adopt or rewrite eqns to ensure symmetric/strong hyperbolicity of evolution equations – discretize equations (to obtain an algebraic problem) which introduces a discrete length h (as h 0 one recovers continuum problem) adopt particular approximation methods/algorithms/discretization strategies – recognize discrete equations do not necessarily behave well (in continuum terms, eqns & data off the constraint surface and physical conditions) modify continuum eqns so that constraint surface is an attractor – Avoid singular region (through excision or slicing) – Implement eqns on sufficiently powerful computational infrastructure (software & hardware) • Arguably < 1990s : head-on collision of black holes (Smarr’80) critical phenomena in GR (Choptuik 86-93). Things changed rapidly after that, especially from 2005 onwards • In particular: BBH problem has largely moved into the ``precision-physics’’ realm (i.e. ‘new-physics’/effort 0, but crucial for grav wave astronomy!) – Challenges in pamaterization of waveforms (and complete wavetrain), which method (EOB/Hybrid/EFT, anything else)?, ‘smart’ runs (ROM,SVD) – Connection with larger astrophysical context (effects on surrounding material/gas/plasma?) – Ultimately, is there a much smarter way to revisit the problem? (2-time scale approach?) • Non-vacuum binaries: ‘global understanding of the problem’ OK, but much physics still to be explored and many opportunities to tie with already existing observations, analytic approaches and conjectures [TBD] • What is General Relativity isn’t correct? Few well defined options here! Use those as guidance for schemes like PPE and/or illustrate what new calculations to do in PN-based approaches [TBD] ? (sufficiently thorough? unlikely…) • But there is a much life beyond the 2-body problem! – Cosmology: (bubble collisions in multiverse, ekpyrotic scenarios, inhomogeneous cosmologies to ‘explain’ away the dark sector [BHs in lattices] – Core-collapse supernovae – AdS/CFT applications, or motivations for gravity studies [TBD] ; – higher dimensional gravity – Ellusive critical phenomena beyond spherical symmetry – BH evaporation qns, – etc…. Dirty-2-body problem in GR (NS/BH) • Cauchy formulation of EEs: (generalized) Harmonic or: BSSN (ADM-augmented eqns for well posedness). [Note: both employing a rather rigid set of gauge conditions] . • NS physics involves: Resistive, Relativistic Magneto Hydrodynamics; generalized equation of state; microphysics. • Several scales: star size, micro-scales associated with magnetized matter dynamics, different local/global phenomena (neutrino production, neutrino difusssion, instabilities, turbulence, etc.). – Not all are equally relevant on the bulk dynamics for ‘short’ times, but can impact both observations and long-term behavior of the system 49 – Crucially, energy released from the system is ~ 10 ergs (MT/Msun ) ~ SN (M T/Msun ); temporarily a ‘ms magnetar pulsar’ is formed; a BH might form – (related interesting systems involving BHs and WDs, main seqn stars, etc: TDEs! But far harder to track numerically in full GR) • PROMISELAND: gravity waves, EM waves, neutrinos: ‘multimessenger astronomy’ Ideally, we would like to have as much info as possible, and even better if it is during the cleanest stages. – GWs are clean! (at least prior to merger depending on the system). But our available detectors only go so far in freqn. Especially relevant for NS-NS – EM radiation is the complete opposite, but its existence in some systems will be key. [arxiv:1055.01607] Also, they can potentially provide crucial clues to help remove GW degeneracies after merger. Ie: possible magnetization levels? Provide evidence of possible deviations from General Relativity which might not be ‘observable’ through current grav. wave opportunities. [arxiv:1410.0638] Connecting theory with possible observations: simulations What’s under the hood? • Einstein equations (gravity), also some alternative gravity theories • Resistive MHD ([possibly magnetized] matter [and magnetosphere] behavior) • Tabulated equations of state • Neutrino treatment (leakage scheme, moment formulations, accounting for cooling & emission, timescales are OK) NS-NS: anatomy of merger • Early on PN is enough • tidal effects visible ~ 10 5 (v/c) R kL, • nonlinear effects • then ‘bar’ structure. Strongly dependent on masses/EOS and more • How long does it last? So…. • Similarly, BH-NS is being tracked (with about the same amount of physics) • Quasi-circular and eccentric binaries • Gravitational waves & template encoding ongoing Much fun to be had • Electromagnetic counterparts! (also neutrino detection if close) – Tremendous ‘fixation’ on GRBs: BH & disk canonical idea • Interesting connection with dynamics and NS-NS vs BH-NS option • But, there can be EM counterparts even without a sGRB – However, slowly, complementary options are being identified as well as alternatives. The problem is however *very* dirty • Baryon `poisoning’ of the system • Opacities of different processes involved • Uncertainties on what and how radiates • We can take guidance on some systems we do know and measure: Pulsars and Supernovae Discriminating options • Concentrate on premerger stage: Emission Induced by magnetosphere’s dynamics as binary tightens. Pulsar guidance emission across many bands. High frequency ‘best’ understood (and sidesteps optical depth issues) • Also, ‘kilonovae’ related to radiactive decay of r-processes. Distribution is tied to how neutron rich the material that powers the process is. Standard suspect: supernovae… but simulations point to ejecta not sufficiently neutron rich Also, one association with GRB 130603B [Tanvir etal Nature ‘13, Berger etal Astrophys J. Letters ‘13] ). infrared signal implies high neutron richness Pulsar guidance • NS isn’t in vacuum. [Goldreich- Julian] Magnetosphere induced by pair creation • Charges shorts out E.B ‘force free’ condition L ~ B 2 Ω4 R6 [1+ sin(x) 2 ] [Spitkovsky 2006 ] • Gaps, current sheet : zones where particle acceleration can take place • Plasma arguments are ‘generic’ enough that should be applicable to compact binaries Pre -merger: PULSAR ON STEROIDS • As with pulsars, magnetosphere interactions with binaries can induce a strong Poynting flux scaling as L ~ B2 (1/a) 5 • Similar structure to pulsar magnetosphere: current sheet, gaps, closed/``open’’ field lines, polarity changes, etc. • In pulsar, radio emission poorly understood, but better handle on gamma/x-ray side [e.g. Bai- Spitkovski] • Could be seen to at least 10Mpc • Furthermore, collapse of merged will generate a burst of order sGRB’s energies What and how to see them? [Spitkovsky-Bai] Gravity waves to guide the observation. Coincident signal and fairly non-collimated [Green,Ortiz,Westernacher-Schneider ++, in prep] Aside: what if GR is not correct? GWs might tell us so, but we might need also EM waves • Scalar-tensor theories [Fierz-Jordan-Brans-Dicke,Damour- Esposito-Farese,…] – Gravity mediated by usual tensor degrees of freedom + a non- minimally coupled scalar field – New phenomenology : • Dipole radiation • Spontaneous scalarization provides a non-trivial ‘scalar charge’ to compact stars • While significantly constrained by solar and pulsar tests, interesting parameter space remains • Non-linear interactions were largely unexplored more ‘generic’ scalarization possible [dynamics and/or induced scalarization] • Dipole radiation modifies dynamical behavior. • Important deviations from GR behavior (eg separation and grav wave signals) • Furthermore, non-monotonic behavior of corrections (implications for, e.g. PPE) - Interaction between differently scalarized stars induces a dynamical readjustment of charges to become equal - ALIGO will have a hard time digging this out for moderate and low mass binaries - EM signals can potentially save the day [Barausse,Palenzuela,Ponce,LL 2013; Sampson etal 2014, also Shibata,Taniguichi, Okawa, Buonanno ‘14] Fast -forward and outwards… Ejecta & properties • Also, other ejecta from winds driven by the eventual accretion disk is possible, though this is less neutron rich [Fernandez etal ‘15] and expected signal would be in the optical. Summarizing multiple results & larger view • Amount & characteristics of ejecta quite tied to EoS. – Very little < 0.001 M o for stiff EoS, velocity of ejecta ~ similar [0.1 – 0.4c] & Y e quite peaked at ~ 0.25 – On the other hand, enough [0.001-0.01 M o] for soft EoS [collision takes place deeper in the potential]. Y e peaked at ~ 0.2 with significant amounts in [0.1-0.2] – Ye values? Y e in [0.25 – 0.4] optical signal [Fernandez,Kasen,Quataert ‘15], lower values, peaked
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