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

Why we analyze data

Lee Samuel FinnCenter for Gravitational Wave

Physics

The Special Province of Experiment

• Theory conjectures; experiment ascertains

QuickTime™ and aCinepak decompressorare needed to see this picture.

• 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., ~100-1000 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 MassWith P. Sutton, Phys. Rev. D 65, 044022 (2002)

• For weak fields h of general relativity behaves as a massless spin-2 field– For static fields: htt ~ 1/r

−∂t2 +∇2

( )h μν =−16πTμν

h μν =hμν −12

ημνh⎡ ⎣ ⎢

⎤ ⎦ ⎥

∇2h tt =−16πρ⇒ h tt ≈M / r

• For weak fields h of general relativity behaves as a massless spin-2 field– For static fields: htt ~ 1/r

∇2 −m2( )h tt =−16πρ

⇒ h tt ≅e−rm

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

−∂t2 +∇2

( )h μν =−16πTμν

ω2 −k2 =0

• Where are these effects manifest?– Systems radiating with

periods P ~ h/mc2

– h/mc2 = 1h (1.15x10–18 eV/m)

−∂t2 +∇2 −m2

( )h μν =−16πTμν

ω2 −k2 −m2 =0

– 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 m2

Relativistic Binary Pulsar Systems PSR 1913+16,

1534+12

• 1913+16– Period: 27907s– Eccentricity: 0.61713– : 0.25% +/– 0.22%

– m90% < 8.3x10–20 eV/c2

• 1534+12– Period: 36352s– Eccentricity: 0.27368– : -12.0%+/–7.8%

– m90% < 6.4x10–20 eV/c2

• Bound depends on period, decay rate, eccentricity– order unity

determined by confidence level p

m2 <mp2 =κ

245

F e( )2πhc2Pb

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2

Δ

Δ ≡˙ P b − ˙ P GR

˙ P GR

, F e( ) =1+

7324

e2 +3796

e4

1−e2( )3

Joint bound: m90% < 7.6x10–20 eV/c2

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 HolesWith 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 2fkt

– 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