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## Strong-field Gravity

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**Strong-field Gravity**Frans Pretorius Princeton University Gravitational Wave Tests of Alternative Theories of Gravity in the Advanced Detector Era MSU, April 6 2013**Outline**• Motivation • understanding strong-field GR through observation of gravitational wave sources in the universe • Focus : binary compact object mergers • observing/constraining systematic deviations from expected models of GW emission • whether deviations from GR, or in the case of neutron stars poorly understood physics of matter at nuclear density • rare events : eccentric mergers • electromagnetic counterparts • Questions**The strong-field regime of GR**• No characteristic scales in the field equations • Define the dynamical strong field regime as that governed by solutions to the field equations • that exhibit highly non-linear spacetime kinematics/dynamics • where the radiative degrees of freedom are strongly excited**The strong-field regime of GR**• Non-linear regime: introduce a length scale R containing a total mass M, expect strong non-linearity when**The strong-field regime of GR**• In the radiative regime, to leading order the power emitted in gravitational waves isfor a source with quadrupole moment Q: with T a characteristic time scale on which the source varies. • If T=R/c, the light crossing time of the system, and it is in the non-linear regime where GM/Rc2 ~ 1, then the characteristic power approaches the Planck luminosity:**The strong-field regime of GR**• Observations of neutron stars and candidate black holes show that there are places in the universe where strong field gravity is relevant • Binary pulsar observations show that the leading order radiative dynamics of gravity is as described by GR • However, no direct observations of dynamical strong field physics, nor are existing observations of NS and candidate BHs detailed enough to test or constrain GR in this regime • Why is it important to test GR in this regime, given it has passed all weak-field tests? • The predictions of GR are rather profound : the nature of the non-linearity is about as extreme as it can be in a classical field theory in that singularities generically form • The mystery of dark energy : on scales of order the Hubble radius the global dynamics of spacetime is fully within the non-linear regime of GR.**Compact Object Mergers**• Mergers of binary BH, and the inspiral phase of binary NS and BH/NS binaries are excellent systems to test strong-field GR • from binary pulsar observations we have good evidence that the early stages of inspiral is as governed by GR GR based templates should be adequate for detecting a large subset of systems • late stages of inspiral approach the dynamical strong-field regime • Mergers involving NSs, in particular the later stages where disruption and EM emission may occur, could reveal much about the inner structure of NSs, which is uncertain due to poorly understood properties of matter at such extreme densities and pressures • In the simplest hydrodynamic model of a NS, this uncertainty is quantified in the equation of state (EOS) of the fluid, which determines two important properties of a binary that could have observable consequences : • the mass-radius relationship of individual NSs before merger • the dynamics of matter during and after collision for NS/NS mergers, and the details of tidal disruption in BH/NS systems**Proposed Gravitational Wave tests of GR**• classify as intrinsic (self-consistency checks with GR), e.g. • mapping the multipole structure of Kerr [Ryan, PRD 56 (1997); Collins and Hughes, PRD 69 (2004)] • black hole “spectroscopy” [Dreyer et al., CQG 787 (2004); Berti et al. PRD 73 (2006)] • the modified PN framework [Arun et al., CQG 23 (2006)] • various “unparameterized” tests, such as jacknife, coherent residuals, etc. • vs. extrinsic (deviations from GR) • alternative theories, e.g. Brans-Dicke, Chern-Simons, massive graviton, etc. • any parameterized intrinsic test can be “inverted” to give information about a particular deviation, filtered through the assumptions of the particular test • the parameterized post-Einsteinian (ppE) approach is largely in this category, though makes no specific assumptions on a particular alternative theory, model deviation, etc.**The ppE framework**• Strategy [Yunes & FP, PRD 80 (2009)] • akin to the parameterized post-Newtonian (ppN) framework [Schiff, Nordtvedt, Will, 60’s & 70’s] to test for deviations from the Schwarzschild metric in the solar system, or the parameterized post-Keplarian (ppK) framework[Damour & Taylor, 1992], to test GR in binary pulsar systems) • begin with a pure GR template bank for a given event, or class of events, where one expects deviations from GR to not be so drastic as to miss all detections with GR templates • introduce parameterized deformations of the templates, where each new parameter is ostensibly “well motivated”, for .e.g. one or more of • consistent will all existing tests, yet can produce observable deviations in the dynamical, strong field regime • predicted by a reasonable alternative theory • characterizes a plausible strong-field correction, e.g. more rapid late time inspiral due to excitation of a new degree of freedom (scalar waves, different polarizations, etc). • use the ppE templates post-detection of an event with a GR template bank • i.e., start to probe directions in template space “orthogonal” to GR**The minimal ppEinspiral template**• hIGR(f) is the GR inspiral component, e.g. to leading order • u=pMf, with M the chirp mass • a,b,a,b are ppE parameters • extended to include non-GR polarizations in Chatziioannou, Yunes and Cornish, PRD 86 2012 GR: a=0, b=0 Brans-Dicke: a=0, b=-7/3Massive graviton: a=0, b=-1 Chern-Simons like parity-violation: a=1, b=0 Dynamical Chern-Simons gravity: a=3, b=4/3varying G: a=-8/3, b=-13/3 certain extra dimensions: a=0, b=-13/3 quadratic curvature: a=0, b=-1/3 modified PN: a=0, b≠0, b=(k-5)/3, k I**Scenarios that can be explored with ppE**templates GR ppE Quantify the likelihood of GR being the underlying theory describing the event, within the class modeled by ppE GR Business as usual Theory See Sampson, Cornish & Yunes [arXiv:1303.1185],& Cornish, Sampson, Yunes & FP. [PRD 84 (2011)] for explicit examples Understand the bias that could be introduced filtering non-GR events with a GR template Measure deviations from GR characterized by non-GR ppE parameters GR**Limitations of current ppE waveforms**• Models small deviations that smoothly approach the GR limit • Only one concrete example to date [Barausse, Palenzuela, Ponce, Lehner, 2013] to guide how the late stages of merger and inspiral could change in a viable alternative theory, in this case binary NS mergers in the Damour, Esposito-Farese spontaneous scalarization scalar-tensor theory • Some aspects of dipole radiation incorporated in ppE for inspiral of scalarized stars, though late time behavior can be drastically different from GR depending on the NS masses ; e.g. scalarization can rapidly be induced in an uncharged NS by a charged companion close to merger • would effectively need step functions in parameter and frequency space to model in a ppE like manner**Rare (?) Events : dynamical capture binaries**• Recently, a couple of studies have suggested close 2-body encounters in dense cluster environments resulting in a tight binary could constitute a non-negligible fraction of observable events: • For binary BH systems, O’Leary et al. [2009MNRAS.395.2127O] estimate AdLIGO rates of ~ 1-103/year from mergers in galactic nuclei alone • “optimistic” assumption is a large dispersion in the average black hole density from galaxy to galaxy • Lee, Ramirez-Ruiz & Van de Ven [APJ 720, 953 (2010)] claim global event rates of NS/NS and BH/NS systems in globular clusters of ~1-102/yr/Gpc3 • BH/NS and/or NS/NS systems possible SGRB progenitors; estimated rate of ~ 8-30/yr/Gpc3 for isotropic emission SGRBs [Guetta & Piran, A&A, 453, 823 (2006)], several times larger if beamed; these systems could thus constitute a significant fraction of sGRB events • “optimistic” assumptions include CO density in globular cluster core • more pessimistic assumptions could lower rates by up to several orders of magnitude**Dynamical capture binaries**• The primary difference between “primordial” vs dynamical capture binaries is a significant fraction of the latter will merge with large eccentricity • note that there are other mechanisms that can potentially lead to high eccentricity mergers not considered in the preceeding studies, including Kozai resonance in a hiearchical triple, and a close encounter of a CO binary with a star • some order of magnitude relations • maximum pericenter passage for capture via GW emission:rp,m (31h)2/7v-4/7 M ; velocity at infinity v (in geometric units) total mass M=m1+m2, symmetric mass ratio h = m1m2/M2 • globular cluster v~10km/s galactic nuclear cluster v~1000km/s ; e.g. rp,mranges from around 600M to 40M for 4:1 mass ratio mergers**Dynamical capture binaries**• some order of magnitude relations • gravitational focusing rp b2v2/2Mwith impact parameter b ; i.e. capture cross section is linear in terms of the initial pericenter passage • characteristic frequency of GW emission fgw rp-1(rp/2M)-1/2 • frequency at capture ranges from 1 Hz /M10for q=0.1 in a globular cluster to 100Hz /M10for q=1 in a nuclear cluster • decay of orbital eccentricity due to GW emission rp,i 0.57 rp,f(1+ef )ef-12/19 (ei=1) • E.g. in a nuclear cluster, 20-40% (q=1 – 0.1) of encounters will have e<0.1 by the time rp reaches 10M (close to merger); this range is 94-96% in globular clusters**Merging with large eccentricity**• GW signal more a sequence of bursts than a chirp • quasi-circular templates not a good match[Brown & Huerta, arXiv:1301.1895 ], present burst searches do not add signals from multiple correlated bursts, and burst stacking strategies [Kalmus et al., PRD80 (2009) 042001]not yet adapted for these sources • Kocsis & Levin [arXiv:1109.417 (2011)] estimate the early (till separations of ~10M) repeated burst phase could be seen with AdLIGO out to 200-300Mpc for BH/NS mergers (300-600 Mpc for BBHs mergers) • Using Lee et al. event rates, this suggests AdLIGO detection rates of 0.3 – 10/yr for BH/NS systems; including the last stages of the merger should increase these rates, in particular for the more massive systems • due to the larger angular momentum more time spent in the strong field regime • could see some zoom-whirl dynamics in waveform near merger**Sample BH/BH eccentric mergers**• top from Healy, Levin & Shoemaker, PRL 103, 131101 (2009); m1/m2=1/3, a1 =a2=0.3 anti-aligned with orbital angular momentum (L=4.10) • bottom from Gold & Bruegmann[arXiv:1209.4085]; equal mass, non-spinning, initial e~.7 “usual” passage through pericenter whirl phase; how much present sensitive to initial conditions**BH/NS merges with eccentricity**• An interesting coincidence for astrophysically relevant NS/BH masses : a 1.5 M๏ neutron star will reach it’s Roche-limit within the range of unstable circular orbits for black holes with masses ~ 5-15 M๏ • how a BH tears a NS apart could reveal much about the EOS, not only via GW emission but consequent electromagnetic and neutrino emission • unstable binary orbits are a distinct feature of GR, and probe the strongest field regions visible outside the horizon • A quasi-circular inspiral will only spend a fraction of an orbit within this regime • not much time to see interesting tidal effects, nor leave a marked imprint on the GW signal • On the other hand, dynamical capture binaries on high eccentricity orbits could have multiple close encounters near this regime • much richer phenomenology of outcomes, and in many cases more GW power will be radiated at slightly lower frequencies, improving detectability with AdLIGO[Kocsis and Levin, arXiv:1109.4170]**Sample BH/NS merger**B.Stephens, W. East, & FP ApJ 737 (2011) L5 Newtonian e~1, rp= 7.0 M MNS0=1.35 M๏ (R=15.2km,M/R=0.13); MBH0=5.40 M๏ disk mass ~ 0.41 M๏ unbound material ~ 0.20 M๏ ~ 0.0043M energy emitted in GW’s initially non-spinning BH, final BH spin a~0.33 2H EOS (Mmax=2.83 M๏) (geometric time units, duration ~ 20 ms) rest mass density r**Sample BH/NS merger**• Gravitational wave emission from previous example**The lever arm of eccentricity**• Because of the small capture cross section due to GW energy loss, each close encounter of the repeated burst phase occurs deep in the strong-field regime (within a few to tens of M) • can think of the evolving orbit as a sequence of ellipses, with the parameters of the ellipse changing quite abruptly during each pericenter passage • for high eccentricity, a relatively small deviation in the change of the parameters of the ellipse would result in a largedephasing of the signal at the next close; e.g.dT is the change in arrival time of the next burst corresponding to a change dE in the energy at previous burst, which resulted in an orbit with effective eccentricity e**Sample NS/NS merger**W. East, B.Stephens and FP, ApJ 760 (2012) L4 Newtonian e~1, rp= 10.0 M MNS0=1.35 M๏ each (R=11.6km,M/R=0.17)HB EOS, shown (Mmax=2.12 M๏) ~ 0.00147M energy emitted in GW’s during first periaps passage Estimated period of subsequent orbit T~65ms For the B EOS (R=10.9km,M/R=0.18, Mmax=2.00 M๏), ~19% more energy emitted during first passage, with estimated T~50ms (energy lost to GW dominates compared to excitation of f-mode) The 2H EOS (R=15.2km,M/R=0.13, Mmax=2.83 M๏) NSs touch on the first encounter and consequently merge rest mass density r**The promise and problem of detecting/identifying eccentric**mergers • The lever arm of eccentricity, coincidence of tidal radius with ISO in BH/NS systems, and potential for multiple encounters in the most dynamical, strong field regime that is likely possible for astrophysical encounters, suggests these systems could be ideal laboratories for testing GR and constraining matter at extreme densities. • However, these same properties will make it challenging to construct waveforms accurate enough for optimal (template) detection • same order of magnitude energy loss to merger compared to quasi-circular inspiral, however here all of it is occurring when v/c is large • lengthy times between bursts relative to burst timescale; would need calculation of the change of orbit in this large v/c regime accurate enough to maintain phase coherence over the longer inter-burst timescale**Stacking excess power**• Propose instead to use incoherent (power) stacking of the bursts in a time-frequency analysis, similar to the method proposed by Kalmus et al. [Phys.Rev. D80 (2009)], for searches of GWs with sGRB repeaters Spectrum of rp=9M, M=10 M๏ BH-BH encounter, using model waveform from S. McWilliams et al., Phys. Rev. D 87, 043004 (2013)**Stacking excess power**• Roughly, for an N burst event, expect to accumulate SNR via N1/4 vs. optimal N1/2 of matched filtering • Results of Kalmus et al. suggest method is robust to uncertainties in the placement of the time-frequency tiles as long as each tile overlaps the majority of the power • less stringent accuracy required … need time between bursts to within roughly a GW cycle, vs. a fraction of a cycle for coherent detection • currently working with Kai Sheng Tai, S. McWilliams & N. Yunes to see if this bares out**Characterizing the GR event**• Decompose the GR waveforms as a discrete sequence of bursts in time • Adequate for a power stacking search, characterize this by a sequence of times ti and time-window width ti containing a given fraction of the energy • to leading order the corresponding central frequency and frequency-width of the tile will be 1/ti • Given the orbital parameters qi(masses, spins, eccentricity, pericenter distance, etc.) preceding the ithburst, can compute tiand the evolution of the orbital parameters to give qi+1 and hence ti+1 ti+1 f ti t ti ti+1**ppE deformations**Ongoing work with N. Loutrel, S. McWilliams, K.S. Tai &N. Yunes • To motivate the form of the ppE modified sequence, we begin with a GR model using a sequence of Keplarian orbits, evolving under leading order (Peters & Matthews) GW emission, then modify the conservative and dissipative dynamics via:where e =M/rp • Note : the coefficients are not all independent in that we assume the usual forms for kinetic energy and angular momentum, and that to leading order the frequency and width of the burst is 1/t**ppE deformations**• (preliminary) carrying through the calculation suggests the following for a minimal ppE modified burst sequence where c,x, f and g are the ppE parameters, and can explicitly (though non-trivially) be related to the parameters introduced on the previous slide • as with the original ppE can “generalize” to an arbitrarily accurate GR computation for tGR and dtGR, though then the interpretation of the ppE parameters will not be as straight-forward • we have ignored the amplitude of each burst – with templates and inspiralppE the amplitude is less important than the phase, and here we similarly expect the difference in power in each burst to be less important, but plan to explore this in the future (e.g. using the expected power to accordingly weight each tile in the stack)**Compact object mergers and EM counterparts**• There are numerous suggestions on possible counterparts to merger events involving NS • precursors • EM interaction, unipolar induction [Lipunov-Pachenko 96, Vietri 96, Hansen-Lyutikov 00, McWilliams & Levin ‘11, Piro ‘12, Lai ’12, Palenzuela et al ’12,’13] • tidal/resonances induced ``crust cracking’’ [Tsang et.al. ’12, East & FP ‘12] • poynting-flux driven bubbles and shocks [Medvedev-Loeb ‘12] • prompt to post-merger • short gamma ray burts (seconds) • optical to UV “kilonova” powered by radioactive decay of ejecta (a day to a week) [Metzger & Berger ‘12, Piran, Nakar & Rosswog ‘12, Kasen ‘12] • radio emission from interaction of outflow with surrounding matter (weeks to years) [Nakar & Piran ‘11] • radio to X-ray emission (seconds to days) from strong shocks in NS/NS mergers [Kyutoku, Ioka & Shibata, ‘12], from turbulence [Zrake & MacFadyen, ‘13], hypermassive NS collapse to a BH [Lehner et al, ’11 • Too early to say how this could test GR, in particular given that many of the above are poorly understood even with the framework of conventional physics • will show a couple of examples illustrating potential EM sources from simulations of Luis’ group**BH jets & the membrane paradigm**BH: (poor) conductor Battery: Black hole’s rotation Plasma to close the circuit Far load: to dissipate energy L ~ B2 a2 [this is *not* a Penrose-type process] However, this is just a picture, does it hold ? Need full solution to compare against - - - - - - + + + [Narayan-McClintock 2011]**The binary case: “braided jets”**• Orbit Black holes move through B. Hall effect analogue. • ‘circuit’ can be established due to charge separation • Thus, expect Poynting flux through orbiting stages, and get a contribution from standard BZ effect: L ~ B2 (v2 + k a2 ) emissions from z ~ 1 could be detected Poynting flux [Palenzuela,Lehner,Liebling, Science 2010, Neilsen et al ‘11, Garret et al ‘11]**NS-NS : PRECURSORS to merger event**Energetics: (initial B = 1011 G. two 1.4 MO NS) • Basic arguments: • Unipolar induction: • L ~ B2 (R/a)6 v2 ~ W14/3 • Aligned (dipole) rotator • L ~ (BsRs3)2 W4 ~ W4 • ‘Effective’ quadrupole • L ~ (BeRe4)2 W6 ~ W2/3 • EM details encode orbital behavior • ‘pulsar revival’! • [Palenzuela,Lehner,Ponce,Liebling, et.al ‘12.]**Questions**• Can the Advanced generation of LIGO/VIRGO/GEO/LCGT/KAGRA discover anything beyond the expected, whether new classes of sources, or unexpected properties of anticipated sources? • Gave two examples related to compact object mergers (particular) sequences of correlated bursts for mergers with large eccentricity "mildy" deformed inspiral chirps via ppEthough successful discovery (or constraints against) would require these be moved to the “expected” class for purposes of analysis • Can EM counterpart observations help? Perhaps even before the first GW detections? • What about other classes of source/waveform model? • stochastic, burst, quasi-periodic • how tied are the strategies to expectations of the underlying physics/astrophysics? e.g., NS mountains, QPOs, shape of the GW spectrum from the early universe, cosmic ray dynamics, etc.

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