From prediction to detection: Highlights of the fascinating history of Gravitational Waves

Bala Iyer ICTS-TIFR, Bangalore, India IndIGO Consortium IndIGO Indian Initiative in Gravitational-wave Observations Indian Academy of Science MYM IISc, 1 July 2016 Track One Analytical Relativity Birth of Relativistic Astrophysics

2 General Relativity Einstein’s Relativistic Gravity

Epitome of Mathematical elegance, Conceptual depth, Observational success 25 Nov 2015: Centenary of General Relativity Einstein's view: Gravitation ~ Spacetime Geometry ~ Curvature or Distortion ~ of Spacetime

credit: www.chicagonow.com

Einstein’s Eqns 10 coupled nonlinear PDE Far Reaching Impact • GR can be applied to universe as a whole leading to Modern Cosmology dealing with origin, evolution and end of the universe.. • Extreme warping of space-time: Existence of Neutron stars (3 Msun mass limit) and Black holes. • Prediction of Gravitational waves crowned by the First Detections • Precision Cosmology with observations of CMB • Relativistic Astrophysics: Observations of pulsars, quasars, x-ray sources • Heralds the dawn of a New Transformative Astronomy Gravitational Waves • 1916: Using Linearized gravity Einstein proposed existence of GW as one of General Relativity’s important consequence • 1918: Einstein calculated flux of energy far from source.. Quadrupole Formula.. v2 Gm v2 h Newton = c2 c2 Rc2 c2 • Radiation Reaction ..Radiation Damping. Energy carrying waves vs non-energy carrying wave-like coordinate artefacts.. • 1922: Eddington: Pointed inapplicability of AE's derivation for self gravitating systems. Realized issues of gauge effects subtle :

GW propagate at speed of thought!Complication for a self-gravitating system6 Gravitational Waves do not exist!

• Subtleties continued to vex even Einstein • 1936: Einstein to Born.. • “Together with a young collaborator (Rosen), I arrived at the interesting result that GW do not exist, ...." • Convinced about his erroneous interpretation and retracted in the published paper saying: "fundamental" changes in the paper were required because "consequences" of the Eqns derived in the paper had previously been incorrectly inferred. Complication for a self-gravitating system

7 Post Newtonian Approximation • 1916: To calculate (v/c) relativistic corrections to Newton, Einstein, Droste, De Sitter introduced Post Newtonian (PN) approximation method . • Combines 3 different expansions: weak-field, slow- motion and near-zone expansion • 1PN (v2/c2) corrections to Newtonian Gravity approximation for describing the dynamics of N extended bodies had difficulties in treatments of the internal structures of the bodies. • 1938 Einstein, Infeld and Hoffmann (EIH) – GR N- body problem reached first stage of maturity. Books of Fock, Infeld & Plebanski, Landau & Lifshiftz 8 Self-gravitating system • Complication: For self-gravitating systems orders in velocity are related to orders in non linearity.. By Virial theorem φ =GM/R same order as v2.. • Reaction terms of order (v/c)5 in linear theory will be accompanied by terms (v/c)3 φ/ c2, (v/c)(φ/c2) 2.. for self-gravitating systems • Higher order PN calculation requires dealing dealing with higher order non-linearities of Einstein's Equations. • Landau Lifshiftz (1941) and Fock (1955) extended Quadrupole formula to weakly self-gravitating systems.. Constitute two different approaches to GW generation today.. DIRE vs MPM-PN 9 The Babel

• Many inconsistent results which today we can trace to: Issues related to coordinate vs physical singularities, use of retarded vs advanced potentials or combination, No- incoming BC in a PN scheme… • (Ritz, Tetrode, Infeld, Rosen, Hu, Scheidegger, Goldberg, Havas, Peres, Trautman, Burke-Thorne …..)

10 Chandrasekhar and GW • 1960's: Chandrasekhar - Radiation Reaction problem.. How does emission of GW affect the emitting system when its self-gravitating? • First to show conceptually that radiation reaction problem could be solved. Assembled together the essential ingredients: Landau-Lifshiftz pseudo- tensor to include the non-linearities of the Grav field, Retarded potentials and near-zone expansion to implement outgoing BC following Trautman. • Gave astrophysicists confidence that GR was physically reasonable and well behaved. Energy and AM radiated as GW was correctly balanced by

the loss of mechanical energy and AM. 11 • ) GW GR Centenary August Black Holes • 1916: First Exact Soln of EE: Schwarzschild • 1939: Oppenheimer and Snyder showed Sph. Symm collapse of dust due to gravitational self-attraction leads to Ap. BH. BH not considered physical due to idealizations of SS and dust • 1960s: Nature of Schwarzschild singularity at R=2GM/c2 understood by the work of Finkelstein, Kruskal. Global methods of Penrose, Hawking, • Notion of Event horizon. Schwarzschild Black hole. • 1963: Kerr Solution. Rotating Black hole

12 Schwarzschild Oppenheimer Snyder Volkov

Penrose Hawking Kerr Black Holes

• BH Perturbations (Regge, Wheeler, Teukolsky)

• 1970 - Vishveshwara • Linear Stability, Quasi normal modes of BH • Innermost stable circular orbit R= 6 G M/c2; • Light Ring: R=3 G M/c2

14 Track Two Physical effect of GW And how we can measure them Felix Pirani Hermann Bondi

16 GR1 - Chapel Hill - 1957 • 1957: Conference on role of Gravitation in Physics Chapel Hill - GR1 • GW problem was solved and Quest for GW detection born • Pirani: Focus on and Analyse effect of GW rather than generation of GW. • Effect of GW determined by Eqn of Geodesic deviation. In presence of GW a set of FF masses would experience genuine motion relative to each other. Thus GW were real.

17 GR1 - Chapel Hill - 1957 • Bondi asks: Can U connect two masses with a dashpot thus absorbing energy from the wave. • Pirani replies: I have not put an absorption term but put in a spring. U can invent a system with such a term quickly.. • Bondi credited with sticky bead argument. • Tidal motion of particles due to GW generates heat by the rubbing of particles against the rod! GW could in principle heat a suitably contrived mechanical system!

18 GW are Physical • GW can be made to do all sorts of strange things by choice of coordinates, but the way they interact with matter must always make sense physically. A ring of particles would be tidally stretched and squeezed in a oscillatory time dependent manner if GW incident normally on it

• 1962: Far from the source, using null coordinates and the Weyl tensor, "Bondi News" (derivative of shear) is related to mass loss providing a coordinate invariant characterization of GW.. (Pirani, Bondi, Metzner, Sachs, Goldberg, Newman..). 19 Joe Weber: Tragic Pioneer

• Weber and Wheeler were at Chapel Hill • 1960 Weber Bar idea • Confidence in physicality of GW. Weber began GW detection when theory of the subject was in disarray, disabling! • 1969 Weber's first claim of GW detection; coincident excitations of bars at Aragone Natl Lab and Univ of Maryland coming from galactic centre. • 1972+:Other groups failed to replicate Weber's results (Braginsky, Tyson, 20 Drever, Garwin and Levine,..) Laser Interferometers for GW detection • 1963 Gerstenstein and Pustovit: Laser interferometry to detect GW • 1964: Rai Weiss (MIT) - While teaching GR asked: What is measurable in GR? Found the answer in Pirani, who had not put spring or dashpot but said: It is assumed that an observer by use of light signals or otherwise determines the coordinates of a neighbouring particle in his local cartesian coordinate system. • 1972: Rai Weiss's instruction book.. HW problem.. Rai envisions LIGO

21 Laser Interferometers for GW detection

• As a GW from a NS-NS binary in Virgo cluster passes, the arm lengths of km scale IFO change (10 -18m) tidally causing the interference pattern to change at the photodiode. • GW detection is about seeing the biggest things that ever happen by measuring the smallest changes that have ever been measured - Harry Collins. 22 Reference Documents Slide Credit Stan Whitcomb

Three documents central to the technical history of LIGO • “Rai’s RLE paper” » “Electromagnetically Coupled Broadband Gravitational Antenna” » R. Weiss, Quarterly Reports of the Research Laboratory of Electronics MIT 105, p. 54 (1973). » Paper “… grew out of an undergraduate seminar that I ran at M.I.T. several years ago…” • The “Blue Book” » “A Study of a Long Baseline Gravitational Wave Antenna System” » Authors: Paul Linsay, Peter Saulson, Rai Weiss » Dated October 1983, but not really published • NSF Proposal for LIGO Construction (’89 proposal) » Proposal team: Robbie Vogt, Ron Drever, Rai Weiss, Kip Thorne, Fred Raab, but with contributions from many others

23 RLE Paper Slide credit: Stan Whitcomb

First detailed noise/ sensitivity analysis » Shot noise/ radiation pressure » Thermal noise » Seismic noise » Gravity gradient » …

24 Gerstenstein & Pustovoit; Forward, Billing and Winkler, Meers..

Ray Weiss Ray Weiss Ron Drever

Adalberto Kip Thorne Kip Thorne Alain Brillet 25 Giazotto Track Three Discovery of the Binary Pulsar

High quality data ≈ Proof that GW exist

26 Binary Pulsar B1913+16 • 1974 Hulse and Taylor Discovered the Binary Pulsar 1913+16

• If General relativity is right the system must emit GW and inspiral inwards Orbital period slowly decreasing at just the rate predicted by GR for emission of GW!!! Indeed, Orbit shrinks by 3

mm/orbit.. 27 Quadrupole Formula controversy to Mark II Approximation methods • Prospects of testing PN theory against Hulse- Taylor system once again revived more critical questions regarding existing treatment of GW. Forced a revisit to approximation methods in GR to remedy mathematical shortcomings in the existing approaches. Led to MPM-PN • Mandated improved approaches to the 2-body problem: Modern versions of EIH to obtain: a = aNewton + a1PN + a2PN + a2:5PN • (1980's,early 90's Ohta, Okamura, Kimura, Hiida; Bel et al, Damour- Deruelle, Damour; Futamase and Schutz; Walker-Will; Grischuk Kopeijkin, Haridass & Soni. Kip Thorne's 1980 Rev. Mod. Phys. State of the art in techniques involved and results then available) 28 Insights into GR and GW from Binary Pulsars • Binary pulsars like 1913+16 provide direct observational proof that gravity propagates at velocity of light and has a quadrupolar structure • GR valid beyond quasi-stationary weak-field regime. Probed for first time in regimes involving radiative effects and strong fields. GR passed all binary pulsar tests with flying colors • Existence of binary neutron stars emitting GW for hundreds of million years before coalescing spectacularly in sensitivity BW of detectors like LIGO/Virgo • Binary Pulsar population underlay the estimated number of GW events for Laser Interferometric GW detectors.

29 Track Four Towards Direct Detection of Gravitational Waves

30 The Last three minutes.. Coalescing Compact Binaries

Late Inspiral and Merger Epochs of compact binaries of neutron stars or black holes provide us possible strong sources of GW for LIGO and Virgo in the `high' frequency range 10 Hz - 10 kHz Note …. v/c ~ .4 ..Highly Relativistic.. We have guaranteed sources for the GW detectors if there are enough of them. The waveform is a CHIRP : Amplitude and Frequency increasing with Time 31 Matched Filtering, Source Modelling

GW are WEAK SIGNALS buried in LARGE NOISE of detector Require Matched Filtering (MF) both for their Detection or Extraction and Parameter Estimation or Characterisation Success of MF requires Accurate model of signal using GR. Favours sources like Coalescing Compact Binaries (CCB) [NS-NS, BH-BH, NS-BH] over unmodelled sources like supernovae. Expt Needed and Led to Progress in 2-body problem in GR much beyond Binary Pulsar case … 1990+: Indian Legacy in GW research in groups at IUCAA on Data Analyses (Dhurandhar) and RRI on Source modelling (BI) 32 Last three minutes – Cutler et al • When LIGO was funded in early nineties, and efforts to construct accurate CCB waveforms for NS-NS, BH-BH started, it was soon realised that far higher order PN accurate waveforms would be needed to accurately describe GW in the final stages of inspiral and merger ( v/c ~ .2, GM/(R c2) ~.2) than the 2.5PN adequate for Binary Psr work ( v/c ~ 10- 3, GM/ (R c2) ~ 10-6). CCB were highly relativistic at these late epochs • Physical insights were essential to simplify the goals and achieve the required accuracy for waveforms to construct template banks.. They include: Quasi-circular motion near merger, Priority to modelling Phase rather than amplitude, Adiabatic approximation modelling inspiral as motion from a circular orbit to next, Modelling binaries as point particles

using Delta functions. Self field Regularization 33 • Multipolar Post Minkowskian - Post Newtonian Method Figure Credit: Thorne Effective-One-Body (EOB) Buonanno, Damour (1999, 2000) • Starting point: High order PN and perturbation theory results guided by the insight that non-perturbative effects can be captured analytically if key ingredients that enter the two body dynamics and GW emission are properly resummed about the exact test particle results • Basic idea is to first construct an auxiliary effective description of real conservative dynamics in which an effective particle of mass M and effective spin S moves in a deformed Kerr-like geometry g(M;S) s.t. conservative dynamics is equivalent (when expanded in powers of 1/c2) to original, relative PN-expanded dynamics. Supplement by Radiation reaction force computed from a inspiral-merger waveform and attach to a Ringdown QNM around merger time.

38 (Buonanno, Damour 2000)

39 Pretorius & Numerical Relativity Breakthrough • Pre 2005: Instead of BBH crashes there used to be only code crashes! Dramatic advances in NR allow stable, robust BH merger simulations.. • Pretorius (2005) produced the first simulation with large number of orbits through merger using Modified harmonic coords, compactification of Num Dom at spatial infinity, singularity excision and damping of constraints. • 2006: Campanelli et al, Baker et al • With this amazing breakthrough in NR, one has reliable waveforms for the late inspiral and merger parts of the binary evolution which can be used for constructing

templates. 40 Baker et al (2006)

41 EXQUISITE THEORY

Post Newtonian - Effective One Body/Phenomenological (Ajith et al + ) Numerical Relativity 42 The Data Analysis Infrastructure • Using Best Waveform models construct Template Banks and efficiently cover the parameter space to be explored ( masses, spins) for detection first and parameter estimation later. • Group around Sanjeev Dhurandhar at Inter University Centre for Astronomy and Astrophysics (IUCAA) contributed significantly to GW Data Analysis since 1990 • SPA, template placement, hierarchical strategy, parameter estimation, radiometer search methods, detector characterization, CW search strategies 43 The unforgiving experiment

Pre-stabilized Laser Active Seismic Isolation

Output Mode Cleaner ‘Test Mass’ Mirror

‘TransMon’ Telescope

Credit: D. Reitze 44 And at last … • With Advanced LIGO, we achieved the technology to make a direct detection of gravitational waves 100 years after Einstein predicted them. • We also have corresponding progress in the two body problem in general relativity to detect GW, characterize them and begin to test general relativity • From the NS binaries justifying our proposal (known-knowns), to the discovery of the BH binaries at our first detection (known- unknowns), one is now left speculating about the possibilities GW astronomy may reveal (unknown unknowns) 45 Feb 11 2016

Was the 1919 of our generation. What more would Einstein want at the centenary of GR, GW, BH?? 46