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
QuickTime™ and a Cinepak decompressor are needed to see this picture.
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., ~1001000 M8 BH
Bounding The Graviton Mass
With 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
• Suppose that field is actually
massive
– Static fields have Yukawa
potential
• 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
2
2



 t
h  16T
1


h

h


h


 


2

 2 htt  16  htt  M / r
2
2


m

htt  16
e rm
 htt 
r
Dynamical Fields
•
A graviton mass affects the
dynamical theory as well
– Massless theory
• Two polarization modes
• Speed of light propagation
– Massive theory
• Additional polarization
modes
• Non-trivial dispersion
relation
• Where are these effects
manifest?
– Systems radiating with
periods P ~ h/mc2
– h/mc2 = 1h (1.15x10–18 eV/m)

2
t
 2 h  16T
2  k2  0

2
t
 2  m2 h  16T
2  k2  m 2  0
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
• Bound depends
on period, decay
rate, eccentricity
2
 2 
24
m  m k
F e  2  D
5
c Pb 
2
2
p
Ý
PÝ
b  PGR
D
, Fe 
Ý
PGR
1
• 1913+16
–
–
–
–
73 2 37 4
e 
e
24
96
2 3
1

e
 
– order unity k
determined by
confidence level p
• 1534+12
Period: 27907s
Eccentricity: 0.61713
D: 0.25% +/– 0.22%
m90% < 8.3x10–20 eV/c2
–
–
–
–
Period: 36352s
Eccentricity: 0.27368
D: -12.0%+/–7.8%
m90% < 6.4x10–20 eV/c2
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., BransDicke-Jordan scalar field)
Observing Black Holes
With O. Dreyer, D. Garrison, B. Kelly, B. Krishnan, R. Lopez
• Three stages of compact
binary coalescence
– Inspiral
• Very sensitive to initial
conditions
– Merger
• Black hole formation
• Waveform unknown, very
possibly unknowable
– Ringdown
• Discrete quasi-normal
mode spectrum
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?
Flanagan & Hughes
Phys. Rev. D57 (1998)
BH Normal Mode Spectrum
• Observe ringdown
– s(t)~S exp(-t/tk) sin 2fkt
– Resolve into damped sinusoids
• Estimate (f,t pairs
– Each pair suggests set of
(M,a,n,l,m) n-tuples
• Definitive black hole existence
proof?
– Can non-BH mimic QNM ntuple relationship?
g- and Gravitational Wave Bursts:
What may we learn?
Hypernovae;
collapsars; NS/BH,
He/BH, WD/BH
mergers; AIC; …
Black hole +
debris torus
•
– Radiated power peaks at
frequency related to black hole
M, J
•
g-rays generated
•
by internal or
external shocks
Relativistic
fireball
Progenitor mass, angular
momentum
•
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
g, gw bursts, etc.
Polarized gravitational waves
from g-ray bursts
• g-ray bursts are beamed
– Angular momentum axis
• Observational selection
effect:
– Observed sources seen
down rotation axis
• Gravitational waves?
– Polarized grav. waves
observed with g-ray bursts
– Polarization correlated with
• Photon luminosity, delay
between grav, g-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