Why we analyze data Lee Samuel Finn Center for Gravitational Wave Physics

The Special Province of Experiment Theory conjectures; experiment ascertains Data do not “speak for themselves” –Interpreted through prism of conjecture, statistical analysis Statistical analysis –Posing fair questions, getting honest answers

Why we analyze data What are gravity’s characteristics? –Are “black holes” black holes? What characterizes grav. wave sources and their environments? –Stellar cluster evolution Number, distribution compact binaries –How are black holes made? Are there intermediate mass black holes?

Why now? Four “regimes” of data analysis –“Upper limits” –Detection of rare, single events –Detection of large event samples –Confusion limited detection LIGO upper limits and rare event detections are interesting –Event rate upper limits or detections will challenge binary evolution models –Detection of, e.g., ~ M  BH

Where can we observe the effects of a massive graviton? –Solar system: Planetary orbits don’t satisfy Kepler law scaling with semi-major axis –Galaxy clusters: size bounded by compton wavelength Bounding The Graviton Mass With P. Sutton, Phys. Rev. D 65, (2002) For weak fields h  of general relativity behaves as a massless spin-2 field –For static fields: h tt ~ 1/r For weak fields h  of general relativity behaves as a massless spin-2 field –For static fields: h tt ~ 1/r Suppose that field is actually massive –Static fields have Yukawa potential

Dynamical Fields A graviton mass affects the dynamical theory as well –Massless theory Two polarization modes Speed of light propagation Where are these effects manifest? –Systems radiating with periods P ~ h/mc 2 –h/mc 2 = 1h (1.15x10 –18 eV/m) –Massive theory Additional polarization modes Non-trivial dispersion relation

Gravitational Wave Driven Binary Evolution Orbital decay rate set by grav. wave luminosity –How to observe evolution? Binary pulsar systems –Pulsars Rotating, magnetized neutron stars Extremely regular electromagnetic beacons –Clock in orbit Observed pulse rate variations determine binary system parameters –Measure orbital decay, compare to prediction, measure/bound m 2

Relativistic Binary Pulsar Systems PSR , –Period: 27907s –Eccentricity: –  : 0.25% +/– 0.22% –m 90% < 8.3x10 –20 eV/c –Period: 36352s –Eccentricity: –  : -12.0%+/–7.8% –m 90% < 6.4x10 –20 eV/c 2 Bound depends on period, decay rate, eccentricity –order unity  determined by confidence level p Joint bound: m 90% < 7.6x10 –20 eV/c 2

What is the “Graviton” Spin? CW Sources: –Bars, IFOs are sensitive to polarizations other than h +,x –Diurnal signal modulation differentiates polarizations Spherical resonant detectors –Distinguish polarization modes directly –Cf. Lobo PRD 52, 591 (1995), Bianchi et al. CQG 13, 2865 (1996), Coccia et al. PRD 57, 2051 (1998), Fairhurst et al. (in prep.) Theoretical constructs –Additional fields (e.g., Brans- Dicke-Jordan scalar field)

Three stages of compact binary coalescence Observing Black Holes With O. Dreyer, D. Garrison, B. Kelly, B. Krishnan, R. Lopez –Inspiral Very sensitive to initial conditions –Ringdown Discrete quasi-normal mode spectrum –Merger Black hole formation Waveform unknown, very possibly unknowable

Flanagan & Hughes Phys. Rev. D57 (1998) Massive Black Hole Coalescence Ringdown –Discrete quasi-normal mode spectrum –High S/N: for LISA S/N ~ 100 at rate 10/y, 10 at rate 100/y No-hair theorem: –( f, t ) fixed by M, J, “quant.” #s (n, l, m) Are the observed modes consistent with a single (M, a) pair?

Estimate (f,  pairs –Each pair suggests set of (M,a,n,l,m) n-tuples BH Normal Mode Spectrum Definitive black hole existence proof? –Can non-BH mimic QNM n- tuple relationship? Observe ringdown – s(t)~  exp(-t/  k ) sin 2  f k t –Resolve into damped sinusoids

 - and Gravitational Wave Bursts: What may we learn? Progenitor mass, angular momentum –Radiated power peaks at frequency related to black hole M, J Differentiate among progenitors –SN, binary coalescence have different gw intensity, spectra Internal vs. external shocks –Elapsed time between gw, g- ray burst depends on whether shocks are internal or external Analysts describe an analysis that brings science into contrast –Spectra, elapsed time between , gw bursts, etc. Hypernovae; collapsars; NS/BH, He/BH, WD/BH mergers; AIC; … Black hole + debris torus  -rays generated by internal or external shocks Relativistic fireball

Polarized gravitational waves from  -ray bursts  -ray bursts are beamed –Angular momentum axis Observational selection effect: –Observed sources seen down rotation axis Gravitational waves? –Polarized grav. waves observed with  -ray bursts –Polarization correlated with Photon luminosity, delay between grav,  -ray bursts Kobayashi & Meszaros, Ap. J. 585:L89-L92 (2003)

Why we analyze data… I must study Politicks and War that my sons may have liberty to study Mathematicks and Philosophy. My sons ought to study Mathematicks and Philosophy, Geography, natural History, Naval Architecture, navigation, Commerce and Agriculture, in order to give their Children a right to study Painting, Poetry, Musick, Architecture, Statuary, Tapestry and Porcelaine. John Adams, to Abigail, 12 May 1780