8 June 2004Summer School on Gravitational Wave Astronomy 1 Gravitational Wave Detection #1: Gravity...

8 June 2004 Summer School on Gravitational Wave Astronomy

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Gravitational Wave Detection #1:

Gravity waves and test masses

Peter SaulsonSyracuse University


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Plan for the week

1. Overview2. How detectors work3. Precision of interferometric measurement4. Time series analysis, linear system

characterization5. Seismic noise and vibration isolation6. Thermal noise7. Fabry-Perot cavities and their

applications8. Servomechanisms9. LIGO 10.LISA


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A set of freely-falling test particles


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Electromagnetic wave moves charged test

bodies


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Gravity wave: distorts set of test masses in transverse directions


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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


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Transmitters of gravitational waves:

solar mass objects changing their quadrupole moments on msec time

scales


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Gravitational waveform lets you read out source

dynamicsThe evolution of the mass distribution can be read out from the gravitational waveform:

Coherent relativistic motion of large masses can be directly observed.

)(21

)(4

tIc

G

rth &&=

( ) ( )I dV x x r rμν μ ν μνδ ρ≡ −∫ 2 3/ .


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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

kg m2s-2.

At distance of 1 km, h = 9 x10-39.

Not very strong.

&& .I = ×16 111


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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.

Hence, expect h ~ 10-21

(on msec time scales!)


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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.


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Resonant detector (or “Weber bar”)

Cooled by liquid He, rms sensitivity at/below 10-18.

A massive (aluminum) cylinder. Vibrating in its gravest longitudinal mode, its two ends are like two test masses connected by a spring.


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An alternative detection strategy

Tidal character of wave argues for test masses as far apart as practicable. Perhaps masses hung as pendulums, kilometers apart.


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Sensing relative motions of distant free masses

Michelsoninterferometer


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A length-difference-to-brightnesstransducer

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.


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Laser Interferometer Gravitational Wave

Observatory4-km Michelson interferometers, with mirrors on pendulum suspensions, at Livingston LA and Hanford WA.Site at Hanford WA has both 4-km and 2-km.Design sensitivity:hrms = 10-21.


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Other large interferometers

• TAMA (Japan), 300 mnow operational

• GEO (Germany, Britain), 600 mcoming into operation

• VIRGO (Italy, France) 3 kmconstruction complete, commissioning has begun


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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.


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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!


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Why Einstein should have worried about g.w.

detectionHe knew about binary stars, but not about neutron stars or black holes.

His paradigm of measuring instruments: – interferometer (xrms~/20, hrms~10-9)

– galvanometer (rms~10-6 rad.)

Gap between experimental sensitivity and any conceivable wave amplitude was huge!


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Gravitational wave detection is almost

impossibleWhat 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.


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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.


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Strain sensitivity of 10-

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Why it is “impossible”:

Natural “tick mark” on interferometric ruler is one wavelength.

Michelson could read a fringe to /20, yielding hrms of a few times 10-9.

.arms oflength

lengths arm comparecan which wetoprecision ~rmsh


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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.


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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.


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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.


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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


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Freely-falling masses


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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 clockEinstein’s train gedanken experiment


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The space-time interval in special relativity

Special relativity says that the interval

between two events is invariant (and thus worth paying attention to.)

In shorthand, we write it aswith the Minkowski metric given as

222222 dzdydxdtcds +++−=

ννη dxdxds =2

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛−

=

1000

0100

0010

0001

μνη


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Generalize a little

General relativity says almost the same thing, except the metric can be different.

The trick is to find a metric that describes a particular physical situation.

The metric carries the information on the space-time curvature that, in GR, embodies gravitational effects.

νν dxdxgds =2

νg


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Gravitational waves

Gravitational waves propagating through flat space are described by

with a wave propagating in the z-direction described by

Two parameters = two polarizations

ννν η hg +=

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

−=

0000

00

00

0000

ab

bahμν


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Plus polarization

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

−=+

0000

0100

0010

0000

h


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Cross polarization

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=×

0000

0010

0100

0000

h


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Solving for variation in light travel time

( )ds c dt h dx2 2 211

21 0= − + + =

⇒dt

ch dx= +

⎛⎝⎜

⎞⎠⎟∫∫

11

12 11

⇒( )Δτ =h t

NL

c

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8 June 2004Summer School on Gravitational Wave Astronomy 1 Gravitational Wave Detection #1: Gravity...

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