Testing GR with Compact Object Binary Mergers

Transcription

1 Testing GR with Compact Object Binary Mergers Frans Pretorius Princeton University The Seventh Harvard-Smithsonian Conference on Theoretical Astrophysics : Testing GR with Astrophysical Systems May 16, 2012

2 Outline In-principle tests of GR using binary merger GW signals, in the regime where NR is required the promise of unique tests of the dynamical strong-field (SF) regime, yet the curse of templates the late stages of mergers and numerical relativity The case for studying mergers with high eccentricity population estimates more interesting than quasi-circular inspirals in that the SF regime of GR will have a more pronounced effect on the dynamics of the system, and hence waveforms sample eccentric BH/NS merger simulation why these systems could be exquisite laboratories to test GR Conclusions

3 Tests of General Relativity GR predictions are well tested in the weak field regime, including aspects of stationary solutions (gravitational redshift, time dilation, constraints on ppn corrections to the Schwarzschild metric) geodesic dynamics (pericenter precision, lensing, framedragging, constraints ppk parameters) the radiative sector (orbital decay of binary pulsars) Essentially no tests of the strong field regime, stationary or dynamic though NS and candidate-bh systems are consistent with the predictions of GR and it s a profound statement that candidate BH s appear to have event horizons, there is not enough data to disentangle non-gravitational physics, let alone overconstrain the systems, which is essential to being able to test the underlying theory

4 Promise of testing GR using binary mergers Observations of compact object merger GW signals, in particular binary BH systems, is very promising for testing GR in the SF thanks to the no-hair properties of BH s in GR, and similarly that a binary orbit has no hair, the signal, that could be comprised of thousands of cycles, is uniquely determined by a small handful of parameters less clean for systems involving NS s, yet leading order dynamics could probably still be categorized by a single additional equation of state (EOS) parameter will not allow for additional tests of GR without an independent measure of the EOS, though will allow one to constraint the EOS observation of electromagnetic counterparts could provide a wealth of additional information, though again not likely to be useful for precision tests of GR, as many more astrophysical parameters come into play

5 Problem with template-based GW observations Testing GR with GW observations requires several steps beyond detection : crucial to be able characterize the signal with more numbers than the minimum required by GR to fully characterize the signal Using only GR based templates this is impossible with low SNR events, any deviations from GR will simply bias the GR parameters attributed to the event with high SNR events, could notice something is wrong/inconsistent, but what?

6 Problem with template-based GW observations Two main approaches to dealing with these issues (1) study model independent deformations from GR predictions, such as ppe (parameterized post Einstein) (2) provide templates for well-motivated alternative theories well-motivated not only means that there is a good physical reason for the deviation (e.g. can explain dark matter or dark energy), but must be mathematically well posed, as only then is it amenable to numerical solution as far as I am aware, only certain classes of scalar-tensor theories (such as Brans-Dicke) are known to be well posed, yet these are strongly constrained by weak field observations arguments that any theory with higher that second derivatives is (classically) ill posed.

7 The late stages of mergers and numerical relativity To provide template waveforms with the correct SF behavior requires input from numeral solution of the full problem However, no simulations to-date of compact object mergers in alternative theories (with the exception of Healy et al. arxiv: , though this was a BBH system in a scalar tensor theory, where deviations from GR must be induced by hand ), so cannot show examples of strong-field waveform deviations, but the idea of applying future results is as usual any deviation that can modify the evolution of the orbit and subsequent ringdown will result in a dephasing of wave w.r.t the GR prediction is in theory observable, modulo the strength of the dephasing and degeneracy of the effect with modified GR binary parameters will argue that mergers with high eccentricity may be exquisite probes of GR in the very last stages of merger

8 Dynamical capture binaries Recently, a couple of studies have suggested close 2-body encounters in dense cluster environments resulting in a tight binary (via energy loss to GW emission or tidal interaction) could constitute a non-negligible fraction of observable events: For binary BH systems, O Leary et al. [2009MNRAS O] estimate AdLIGO rates of ~ /year from mergers in galactic nuclei alone Lee, Ramirez-Ruiz & Van de Ven [APJ 720, 953 (2010)] claim global event rates of of ~ /yr/gpc 3 The primary difference between dynamical capture binaries and primordial field binaries is a significant fraction of the former will merge with large eccentricity in primordial binaries, due to natal kicks when the compact objects are born, some systems may merge shortly after with larger eccentricity; Kowalska et al. [APJ 527, A70 (2011)] estimate between 0.2% and 2% will have e>0.01, but still less that 0.05

9 Merging with large eccentricity GW signal more a sequence of bursts than a chirp Kocsis & Levin [arxiv: (2011)] estimate the early (till separations of ~10M) repeated burst phase could be seen with AdLIGO out to Mpc for BH/NS mergers ( Mpc for BBHs mergers) Using Lee et al. event rates, this suggests AdLIGO detection rates of /yr for BH/NS systems (a few times this for BH/BH 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 close to the regime of unstable orbits, which (at least compared to Newtonian dynamics) is a distinct feature of strong-field GR could have multiple close encounters, and begin to see the imprint of zoomwhirl dynamics in waveform for BH/NS systems, an interesting coincidence for astrophysically relevant masses is a 1.5 M neutron star will reach it s Roche-limit within the range of unstable orbits for black holes with masses ~ 5-15 M the SF regime of GR will thus have significant effect on how the NS is disrupted and the amount of material ejected, which is of significance to EM counterparts and R-process element production

10 Simulations of BH/NS dynamical capture binaries Exampe from a study of (marginally) hyperbolic encounters [B.Stephens, W. East, FP, arxiv: ; arxiv: ] 4:1 mass ratio Velocity at w ~ 1000km/s (critical impact parameter for capture ~3000M) [and one initially bound system with e=0.75] Consider a range of impact parameters; parameterize by r p, Newtonian estimate of initial pericenter separation (capture threshold ~ r p ~42M ) Look at 3 values of initial BH spin, a=0, and a= 0.5 aligned with the orbital angular momentum GR (generalized harmonic formulation) + ideal hydrodynamics NS has one of 3 piecewise polytropic EOS (plus a thermal component) designed to mimic current realistic EOS models, going from soft (B), to intermediate (HB) to stiff (2H) [Read et al. PRD 79 (2009)]

11 Early Results As a function of input parameters see significant variability in : amount of material left in accretion disk larger disk masses expected to be important for powering SGRBs estimated amount of unbound material could be relevant for explaining late time Xray afterglows observed in some SGRBs, or be sources of other EM transients amount of zoom-whirl behavior in orbit and GW signal Two primary factors influencing the variability radius of NS function of EOS pericenter distance relative to location of the innermost stable orbit (ISO) function of BH spin, orbital eccentricity and impact parameter the closer to the ISO the longer the NS lingers in the strong field regime; if within the Roche radius more tidal stripping if the pericenter is within the ISO radius then a plunge will occur, other wise a second (or perhaps more) close encounters possible

12 Sample BH/NS merger r p = 6.95M M NS0 =1.35 M M BH0 =5.40 M disk mass ~ M unbound material ~ M ~ 0.017M energy emitted in GW s initially non-spinning BH, final BH spin a~0.47 HB EOS (time unit in movie is wrong) rest mass density

13 Sample BH/NS merger Gravitational wave emission from previous example

14 Close-up of NS density and velocity field in the NS center of mass frame, following initial tidal perturbation by the BH velocity field is consistent with an f-mode oscillation Sample BH/NS merger

15 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 SF 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 large dephasing of the signal at the next close encounter (thanks to Chris Thompson for emphasizing this); e.g. T 1 e is the change in arrival time of the next burst corresponding to a change in the energy at previous burst, which resulted in an orbit with eccentricity e E 5 2

16 Conclusions Rich promise to use direct detection of GW from inspiralling compact object binaries to test/constrain GR Presented an argument why eccentric mergers may be an exceptional laboratory to do this (in addition to learning about the nuclear EOS, compact object populations, etc.), however then the challenge is to realize an effective data analysis strategy to take advantage of the lever arm of eccentricity (i.e., perhaps not the best good idea to simply apply bruteforce matched filtering with eccentricity-enhanced inspiral template) and of course nature has to be kind and provide a large enough population of these events that some will be observed