Keith Riles

U. Michigan

Physics Dept.

Jackson Science Café

Hudson Grill – December 8, 2011

Looking for Ripples in the Fabric of Space-Time:

LIGO- the Laser Interferometer Gravitational-Wave Observatory

Presentation supported by the Michigan Space Grant Consortium and Jackson Community College

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What are Gravitational Waves?

Recall that a wave is a disturbance that propagates:

Before we discuss wave propagation, we need to understand how space can be disturbed by anything!

Space itself!

What exactly is disturbed by a gravitational wave?

Courtesy: Prof. Andrew Davidhazy -

Rochester Institute of Technology

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Space deformationEinstein’s Field Equation:

Gμν = 8 π Tμν

And numerical solutions are tough too!

Except for handful of highly symmetric problems (e.g., spheres!), these equations must be solved numerically, not algebraically

Mathematically, this equation represents ten different coupled, partial differential equations relating the curvature of space (embodied in Gμν) to energy and momentum (embodied in Tμν)

“Matter tells spacetime how to curve, and curved space tells matter how to move"

But the essence of these equations is summed up nicely by general relativity pioneer John Wheeler:

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Courtesy: LIGO Laboratory

Space deformation“Rubber-sheet model” of space:

Heavy mass warps the “surface”, creating a depression

Another mass rolls toward the depression

And deepens it!

Highly “non-linear” equations

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Making wavesNow imagine two very compact stars (neutron stars or black holes) in a tight binary orbiting system:

Space is “swirled” by the orbiting stars, creating a ripple that propagates to distant regions of the universe (to us we hope!)

Courtesy Jet Propulsion Laboratory

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Making wavesAre there really such star systems out there?

YES!

In 1974 Joseph Taylor and Russell Hulse discovered a binary system with two neutron stars, one of which is a pulsar

Observed 17-Hz pulsar

PSR 1913+16 Unseen companion (neutron star)

Orbital Period (“year”) is 7.75 hours

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Making wavesThe Taylor-Hulse binary system’s orbit shrinks about 3 mm every revolution

Coalescence in about 300 million years

So why is the orbit decaying?

Gravitational wave emission Energy loss!

Present orbital extent

Orbit slowly shrinking

Weisberg et al, 1981

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Making waves

Why are we so sure we understand the decay of this binary system?

By measuring the precise timing of pulsar signals, one can infer the present orbital parameters

Einstein’s Theory of General Relativity then predicts the rate of decay from gravitational radiation energy loss

Did Einstein get it right?

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Making waves

YES!

Graph at right shows the change in orbital period (seconds) over 25 years of observations

Smooth curve is absolute prediction from General Relativity (no free parameters!)

Dots are measured data

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Making waves

Can we detect this orbital system’s waves here on Earth?

NO

On Earth we can hope to see only waves with frequencies greater than ~10 Hz

The characteristic frequency for this system is ~1/(4 hours) ~ 70 μHz

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Making waves

Well, what if we waited around for 300 million years?

What might we “see”?

A Chirp!

Graphs show waveform for 4 different 1-second intervals near the end of the inspiral, a.k.a., “death spiral”

(in arbitrary but consistent units)

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Last nine secondsof inspiral

Making waves

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Nature of Gravitational Waves

How is the strength of a gravitational wave described?

By fractional change in distance, i.e., strain

Denote time-dependent dimensionless strain displacement (tiny!) by h(t):

ΔL(t) ~ h(t) x LL

ΔL

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Gravitational Waves from “Out There”

Imagine two neutron stars: Each with mass equal to 1.4 solar masses In circular orbit of radius 20 km (imminent coalescence) Resulting orbital frequency is 400 Hz (!) Resulting GW frequency is 800 Hz

Courtesy: Dr. Peter Shawhan - Caltech

Einstein predicts:

h ≈10−21

(distance/ 50 million light years)

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How small is 10-21 ?

0.000000000000000000001

million x million x million x thousand

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or

diameter of an atom

distance from Earth to Sun

or

Experimental challenge! Well suited to high-precision interferometry

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Interference

Waves are characterized by their interference

– with other waves or with themselves

Courtesy: Prof. Andrew Davidhazy - Rochester Institute of Technology

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Interference

Constructive DestructivePartial

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Audio Interference Demonstration

Speaker 1

Speaker 2

With two audio speakers driven at same frequency (coherently), an interference pattern is set up in the room

Try plugging one ear and moving the other ear to sample the minima and maxima of the pattern

Courtesy: Wiley & Sons: Halliday/Resnick/Walker text

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Suspended Interferometers

What is an interferometer?

Courtesy: Wikipedia

Interference at detector depends on difference in lengths of two armsMichelson

Interferometer Demonstration

Gravitational waves cause length differences!

ΔL(t) ~ h(t) x L

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LIGO Observatories

Livingston

Hanford

Observation of nearly simultaneous signals 3000 km apart rules out terrestrial artifacts

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LIGO Detector Facilities

Vacuum System

• Stainless-steel tubes

(1.24 m diameter, ~10-8 torr)

• Protected by concrete enclosure

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LIGO Detector Facilities

LASER Infrared (1064 nm, 10-W) Nd-YAG laser from Lightwave (now commercial product!) Elaborate intensity & frequency stabilization system, including feedback from main

interferometer

Optics High-quality fused silica (25-cm diameter) Suspended by single steel wire Actuation of alignment / position via magnets & coils

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LIGO Detector Facilities

Seismic Isolation Multi-stage (mass & springs) optical table support gives 106 suppression Pendulum suspension gives additional 1 / f 2 suppression above ~1 Hz

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The road to design sensitivity at Hanford…

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Harder road at Livingston…

Livingston Observatory located in pine forest popular with pulp wood cutters

Spiky noise (e.g. falling trees) in 1-3 Hz band creates dynamic range problem for arm cavity control

40% livetime

Solution:Retrofit with active feed-forward isolation system (using technology developed for Advanced LIGO)

Fixed

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What Limits the Sensitivityof the Interferometers?

• Seismic noise & vibration limit at low frequencies

• Atomic vibrations (Thermal Noise) inside components limit at mid frequencies

• Quantum nature of light (Shot Noise) limits at high frequencies

• Myriad details of the lasers, electronics, etc., can make problems above these levels

Best design sensitivity:

~ 3 x 10-23 Hz-1/2 @ 150 Hz

achieved

< 2 x 10-23

Status of the Search

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No discoveries yet, but

• Still examining data we have taken

• Major upgrade of LIGO under way now Advanced LIGO

Will increase volume of “visible universe” by factor of 1000 Guaranteed discovery – but not until ~2015

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What will the sky look like?

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What will the sky look like?

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What will the sky look like?

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What will the sky look like?

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What will the sky look like?

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What will the sky look like?

Stay Tuned!

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Before looking at gravitational waves,

let’s first review wave motion itself

Waves

Loosely speaking, waves are oscillating disturbances that propagate:

Courtesy: Prof. Andrew Davidhazy - Rochester Institute of Technology

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Examples of Waves

Easily visible:

• Surface water waves

• Plucked guitar string

• Jerked rope

Harder to see, but intuitively plausible:

• Seismic waves (ground vibration)

• Sound waves (in air, liquid and solids)

More abstract (but measurable!):

• Electromagnetic waves = Light (oscillating electric & magnetic fields)

• Gravitational waves (oscillation of space itself!)

Courtesy: Wiley & Sons – Halliday/Resnick/Walker text

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Wavelength, Frequency, etc.

Sinusoidal waves are characterized by well defined:

• Wavelength – distance between adjacent “crests” in “snapshot”:

• Period – Time between successive crests at fixed location

• Frequency – Number of crests per second passing fixed location

• Speed = Wavelength / Period ( = Wavelength × Frequency )

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Wavelength, Frequency, etc.

Audible sound waves have frequencies in the range 20 Hz – 20,000 Hz

- depending on the listener’s age

At room temperature, sound speed in air is about 340 m/s (~760 mph)

- and cumulative exposure to heavy metal, rap, etc

Sound demonstrations:

440 Hz (middle A -- λ = 2.5 feet)

1,000 Hz ( λ = 13 inches )

4,000 Hz ( λ = 3.3 inches )

20,000 Hz ( λ = 0.7 inch )

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Electromagnetic Spectrum

Human Eye Sensitivity

Courtesy: Wiley & Sons – Halliday/Resnick/Walker text

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Wavelength, Frequency, etc.

Most waves are NOT pure sinusoids!

Human speech, automobile engines, bird chirps, even instrumental notes contain rich spectra of frequencies

Sample piano note spectrum

440 Hz

Sample pipe organ note spectrum

440 Hz

Piano middle A note (“440 Hz”) Pipe organ middle A note (“440 Hz”)

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Wavelength, Frequency, etc.

Samples of human speech with spectra

Sample 1

(middle-aged man)

Courtesy: Lizzie & Katie Riles

(6-year-old girls)

Sample 2