Transcript Gravitational Wave Detection #1: Gravity waves and test masses

Gravitational Wave Detection #1:
Gravity waves and test masses
Peter Saulson
Syracuse University
Plan for the week
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Overview
How detectors work
Precision of interferometric measurement
Time series analysis, linear system characterization
Seismic noise and vibration isolation
Thermal noise
Fabry-Perot cavities and their applications
Servomechanisms
LIGO
LISA
A set of freely-falling
test particles
Electromagnetic wave moves
charged test bodies
Gravity wave: distorts set of test
masses in transverse directions
Comparison table, EM vs GW
charge
mass
E and B fields
h = shear strain
c
c
Maxwell 1867 Einstein 1916
Hertz 1886-91
?
pretty strong
very weak
Transmitters of gravitational waves:
solar mass objects changing their quadrupole
moments on msec time scales
Gravitational waveform lets you
read out source dynamics
The evolution of the mass distribution can be
read out from the gravitational waveform:
1 2G 
h(t ) 
I (t )
4
r c
Coherent relativistic motion of large masses can
be directly observed.


I    dV x x   r 2 / 3  r .
Why not a Hertz experiment?
Hertz set up transmitter, receiver on opposite
sides of room.
Two 1-ton masses, separated by 2 meters, spun
at 1 kHz, has
11 kg m2s-2.

I  16
.  10
At distance of 1 l  300 km,
h = 9 x10-39.
Not very strong.
Binary signal strength estimate
For a binary star,
h = r/R,
where
R = distance to source, and
r = rS1rS2/a, with
rS1,2 Schwarzschild radii of the stars,
and a is their separation.
Often, r ~ 1 km (neutron star binary).
At Virgo Cluster, R ~ 1021 km.
-21
Hence, expect h ~ 10
(on msec time scales!)
Gravity wave detectors
Need:
– A set of test masses,
– Instrumentation sufficient to see tiny motions,
– Isolation from other causes of motions.
Challenge:
Best astrophysical estimates predict fractional
separation changes of only 1 part in 1021, or less.
Resonant detector
(or “Weber bar”)
A massive (aluminum) cylinder. Vibrating in its
gravest longitudinal mode, its two ends are like
two test masses connected by a spring.
Cooled by liquid He, rms sensitivity at/below 10-18.
An alternative detection strategy
Tidal character of wave argues for test masses
as far apart as practicable. Perhaps masses
hung as pendulums, kilometers apart.
Sensing relative motions of
distant free masses
Michelson
interferometer
A length-difference-to-brightness
transducer
Wave from x arm.
Wave from y arm.
Light exiting from
beam splitter.
As relative arm
lengths change,
interference causes
change in
brightness at
output.
Laser Interferometer
Gravitational Wave Observatory
4-km Michelson
interferometers, with
mirrors on pendulum
suspensions, at
Livingston LA and
Hanford WA.
Site at Hanford WA
has both 4-km and 2km.
Design sensitivity:
hrms = 10-21.
Other large interferometers
• TAMA (Japan), 300 m
now operational
• GEO (Germany, Britain), 600 m
coming into operation
• VIRGO (Italy, France) 3 km
construction complete, commissioning has begun
Gravity wave detection:
challenge and promise
Challenges of gravity wave detection appear so
great as to make success seem almost
impossible.
from Einstein on ...
The challenges are real, but are being overcome.
Einstein and tests of G.R.
• Classic tests:
– Precession of Mercury’s orbit: already seen
– Deflection of starlight: ~1 arcsec, O.K.
– Gravitational redshift in a star: ~10-6, doable.
• Possible future test:
– dragging of inertial frames, 42 marcsec/yr,
Einstein considered possibly feasible in future
• Gravitational waves: no comment!
Why Einstein should have
worried about g.w. detection
He knew about binary stars, but not about
neutron stars or black holes.
His paradigm of measuring instruments:
– interferometer (xrms~ l /20, hrms~10-9)
– galvanometer (qrms~10-6 rad.)
Gap between experimental sensitivity and any
conceivable wave amplitude was huge!
Gravitational wave detection is
almost impossible
What is required for LIGO to succeed:
• interferometry with free masses,
• with strain sensitivity of 10-21 (or better!),
• equivalent to ultra-subnuclear position
sensitivity,
• in the presence of much larger noise.
Interferometry with free masses
What’s “impossible”: everything!
Mirrors need to be very accurately aligned (so
that beams overlap and interfere) and held
very close to an operating point (so that
output is a linear function of input.)
Otherwise, interferometer is dead or swinging
through fringes.
Michelson bolted everything down.
Strain sensitivity of 10-21
Why it is “impossible”:
precisionto which we can comparearm lengths
hrms ~
.
lengthof arms
Natural “tick mark” on interferometric ruler is
one wavelength.
Michelson could read a fringe to l/20, yielding
hrms of a few times 10-9.
Ultra-subnuclear position
sensitivity
Why people thought it was impossible:
• Mirrors made of atoms, 10-10 m.
• Mirror surfaces rough on atomic scale.
• Atoms jitter by large amounts.
Large mechanical noise
How large?
Seismic: xrms ~ 1 m.
Thermal
– mirror’s CM: ~ 3 x 10-12 m.
– mirror’s surface: ~ 3 x 10-16 m.
Finding small signals
in large noise
Why it is “impossible”:
Everyone knows you need a signal-to-noise
ratio much larger than unity to detect a
signal.
Science Goals
• Physics
– Direct verification of the most “relativistic” prediction of
general relativity
– Detailed tests of properties of grav waves: speed, strength,
polarization, …
– Probe of strong-field gravity – black holes
– Early universe physics
• Astronomy and astrophysics
– Abundance & properties of supernovae, neutron star
binaries, black holes
– Tests of gamma-ray burst models
– Neutron star equation of state
– A new window on the universe
Freely-falling masses
Distance measurement
in relativity…
… is done most straightforwardly by
measuring the light travel time along a
round-trip path from one point to another.
Because the speed of light is the same for all
observers.
Examples:
light clock
Einstein’s train gedanken experiment
The space-time interval
in special relativity
Special relativity says that the interval
ds2  c 2dt2  dx2  dy2  dz2
between two events is invariant (and thus
worth paying attention to.)
In shorthand, we write it as ds2   dx dx
with the Minkowski metric given as
 
 1

0

0

0

0
1
0
0
0
0
1
0
0

0
0

1 
Generalize a little
General relativity says almost the same thing,
except the metric can be different.
ds2  g dx dx
The trick is to find a metric g  that describes a
particular physical situation.
The metric carries the information on the spacetime curvature that, in GR, embodies
gravitational effects.
Gravitational waves
Gravitational waves propagating through flat
space are described by
g    h
with a wave propagating in the z-direction
described by  0 0 0 0 
h


 0 a b 0

0 b  a 0


 0 0 0 0


Two parameters = two polarizations
Plus polarization
0

ˆh   0

0

0

0 0
1 0
0 1
0 0
0

0
0

0 
Cross polarization
0

ˆh   0

0

0

0
0
1
0
0
1
0
0
0

0
0

0 
Solving for variation in light
travel time


ds 2  c 2 dt 2  1  h11 dx 2  0
1 
1 
 dt  c  1  2 h11  dx
2 NL
  ht 
c