Gravitational Wave DetectionOverview of Why and How

Dan Burbank and Tony YoungAST5022

Introduction

Background PhysicsSourcesDetectors and Detector ImplicationsQuestions

Gravitational Waves

• Speed-of-light wave propagation solution of Einstein’s Field Equations– In general, accelerating mass results in rippled spacetime. GW is the

propagation of these ripples.– Weakness of gravitational interaction compared to other forces means

GW are hard to detect, small amplitudes.– Carry energy

Background Physics• Simplest example is a linearized plane wave• Metric is near flat and can be written as , SR plus

small addition (considering 1-D propagation)• Define

where

• Define spacetime element

)(

0000

0100

0010

0000

),( ztfzth

22222 )](1[)](1[ dzdyztfdxztfdtds

)()( xhxg

1)( ztf

Gravity: Intro into GR, Hartle. 2003.

Background Physics• Measuring a change in distance between two test masses in a plane

orthogonal to the direction of propagation– Consider a wave traveling in z-direction and two test masses, one at

the origin and on the x axis a coordinate distance L* (in the unperturbed flat spacetime).

– As the GW passes the length will change as a function of time given by

as h is very small

– Simplified this gives the change in L* as

– Suppose then and the fractional change in distance along the x-axis oscillates periodically with half the amplitude of the gravitational wave

)]0,(2

11[)]0,(1[)( *0

2/1*

thLthdxtL xx

L

xx )0,(

2

1

*

* thL

dLxx

])(sin[)( ztwaztf )sin(2

1

*

* wtaL

dL

Background Physics• Given this linearized gravitational wave propagating in the z direction

– Leads to no change in separation between two test masses lying along the z-axis

– Only x-y separations change as the gravitational wave travels by.– There is stretching of the x and y distances with different phases from

the given metric giving the + polarization but a different metric could have been written as

– The most general metric is the superposition

Giving the two transverse polarizations + and x (as mentioned in class).

)(

0000

0010

0100

0000

),( ztfzth

0000

0)()(0

0)()(0

0000

),(ztfztf

ztfztfzth

Background PhysicsPower radiated in 2 body system.– Through some crazy math done in 1963/1964 you can show that the

change in distance between two orbiting bodies is

– The distance between the objects changes because the system is emitting gravitational waves that carry energy and angular momentum.

– Given the relationship above, you can calculate the lifetime of an orbit of two bodies (assumes circular orbits)

where

422/7232121

5

3

96

37

24

731

)1(

)(

5

64ee

ea

mmmm

c

G

dt

da

4)(

4o

ocirc

aa )(

5

6421215

3

mmmmc

G

-Gravitational radiation from the motion of two point masses, P. C. Peters, Phys. Rev. ,136, 1224 [1964]-Gravitational radiation from point masses in a Keplerian orbit, P. C. Peters and J. Mathews, Phys. Rev., 131, 435 [1963]

Background Physics• As the orbit decays the

frequency of the gravitational waves change and can create noticeable profiles such as

• The frequency will increase as the orbital frequency increases and the amplitude will increase

• Knowing the exact parameters of this “chirp” frequency can also be used to give a luminosity distance

)2cos()( 2oo tffthth

http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf

Primordial GW (GW background)

• GW observed in the CMB and are a result of inflation• Current efforts to detect CMB polarization which is the imprint of

primordial GWs at the time of CMB production

Compact Binary White Dwarfs

• Close binary WDs will likely serve as calibration standards– Well modeled– Numerous and relatively nearby– Frequency range ( >10mHz) is within spectral range of Earth-based

interferometers– Observations will improve understanding of formation on Type 1a

supernovae

White dwarf binary background

Massive Black Hole Binaries

• GW from higher redshift massive black hole binaries, MBHB, are likely to provide some understanding of the early evolution of galaxies

• Massive Population 3 stars are thought to have seeded the formation of galactic massive black holes

• Space-based eLISA will likely be able to observe inspiral, merger, and ring-down phases

Extreme mass ratio in-spirals, EMRI

• The Sag A* black hole provides a relatively nearby potential GW generation associated with stellar masses spiraling into the massive black hole

• Space-based eLISA should make it possible to study this type of events in other galaxies

Other Sources

• Supernova• Pulsars

C. D. Ott, Class. Quantum Grav. 26 (2009) 06300

How do we detect gravitational waves?

• Gravitational waves cannot be detected at a single point. • By Equivalence Principle, gravity can be transformed away at a single

point by an appropriate coordinate system*

• GW fluctuations, DL, in baseline distance, L, between test mass pairs, have all these observable properties– DL /L GW propagation – DL /L<10-21 – 10-4< f < 104

– When DLx , DLy

*“Relativity, Gravitation and Cosmology”, TP Cheng, 2nd Ed, p337 ff

DLx

DLy

Laser Interferometer

Current Gravitational Wave Detection Initiatives• Earth based

– LIGO, aLIGO• 4km baseline interferometers near Hanford, WA and Livingston, LA• aLIGO is LIGO with upgraded capability (fully operational in 2015)

– VIRGO• 3km baseline interferometer near Pisa, Italy

– GEO600• 0.6km baseline interferometer near Sarstadt (by Hanover), Germany

– KAGRA• 2 sets of 3km baseline interferometers underground in Kamioka mine, Japan• Cryogenic cooling of detector components

• Space based– eLISA

• ESA rescoped LISA after NASA dropped out in 2011 due to lack of funding• eLISA technology demonstration satellite to be launched in 2015• 10e6 km baseline interferometer in solar orbit near Earth

Signal and Noise for GW Detectors - Conventions

• Strain is the dimensionless amplitude of a GW, DL /L, or “h”• Signal , s(t) = n(t) + h(t), where n(t) is noise, also dimensionless• Time average of noise2, = • Power Spectral Density, PSD = Sn(f), has units 1/f and relates to noise2

by(f). • When lower integration limit = 0 this is called “one sided PSD”• Root PSD = has units , and is the most commonly graphed • Characteristic Strain hcis dimensionless

• This is useful in SNR calculation. hc(f) 2=4f2|h(f)|2, hn(f)2 =fSn(f) and• SNR = 2

Gravitational wave sensitivity curves, CJ Moore, RH Cole, CPL Berry, arXiv:1408.0740v1 [gr-qc] 4 Aug 2014

Noise Sources affecting GW Detectors

• Quantum noise– Shot noise scales with sqrt(laser power), whereas signal scales linearly– Power level within the cavity is enhanced by setting the cavity length

precisely (via a phase locked loop) to a multiple of the illumination wavelength, leading to a high power density resonance, improving S/N ratio.

– Shot noise is also reduced by using a “squeezed light” source• Seismic gravitational gradients

– Going underground or into space helps• Thermal noise in test masses and suspensions

– Cryogenic cooling helps

Actual Implementation – complex source and detector

• Ground-based interferometers are similar to the Japanese KAGRA design• Laser frequency is selected to resonate in X and Y arm Fabry-Perot etalons• Power recycling used on input and signal recycling used on output

3km arms in vacuum, test masses cooled to 20K

Laser is modulated to create RF sidebands for cavity length control. AS_RF takes that signal to control system.

Signal detection uses QND technique

Interferometer design of the KAGRA gravitational wave detector, Y Aso, et al, arxiv.org ,1306.6747v1

Quantum limits on interferometer detection

• For a test mass position measurement that generates “back action” results the “standard quantum limit” of uncertainty

• SQL for an interferometer is

• “Quantum Non Demolition” or QND techniques can evade SQL

Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors, A Buonanno and Y Chen, PHY REV D, 64, 042006

M Mass of each identical test massW GW angular frequencyPlanck’s constant/2pL Length of the interferometer’s arms

DL Time evolving difference in arm lengthsh(t)=DL/L Dimensionless gravitational wave signal

𝑆𝑄𝐿h [𝐻𝑧−0.5]=√ 8ℏ

𝑀 𝐿2Ω2

Beating back seismic noise in Earth-based detectors

• Seismic waves passing a GW detector induce density and local gravity fluctuations that mimic the differential GW signal

Seismic gravity-gradient noise in interferometric gravitational-wave detectors, S Hughes, K Thorne, PHYS REV D, 58, 122002

• Detector components are mechanically isolated by “stacks”

http://www.ego-gw.it/virgodescription

LIGO

VIRGO isolation stack

Example: KAGRA Noise Analysis

Interferometer design of the KAGRA gravitational wave detector, Y Aso, et al, arxiv.org ,1306.6747v1

Expected Source Signal and Noise

http://rhcole.com/apps/GWplotter/

Use of “Null Stream” to Minimize False Positives

• Co-locating and co-aligning two identical GW detectors facilitates synthesis of a null data stream*

• Example– Detector 1 outputs signal S1 = N1 + h(t)– Detector 2 outputs signal S2= N2 + h(t)– N1 and N2 are uncorrelated noise deviations around the signal h(t), have standard

deviations s1 and s2

– S1-S2 = h(t)-h(t) + (s1 2 + s2

2 )0.5 = root sum squared of the detector noise st dev

• If a candidate “signal” appears in the null stream, if can be immediately rejected

• Seismic gravity gradient noise would not be eliminated, as both detectors would see this externally-sourced noise as a real signal

• Null streams can be created for non co-located detectors, canceling signal emanating from a specific direction in the sky… basis for locating sources

*Near optimal solution to the inverse problem for gravitational-wave bursts”, Y Gursel, M Tinto, Phys Rev D 40, 3884

eLISA Space Based GW Detector

LISA: a mission to detect and observe gravitational waves, O Jennrich, in Gravitational Wave and Particle Astrophysics, Proc SPIE v5500

• Laser Interferometer in Space Antenna, LISA, provides unique capabilities – Immune to seismic noise– Long baseline provides 0.001 - 1Hz GW spectrum sensitivity needed for observing

massive black hole mergers

• Multiple identical or similar detectors to improve detection confidence

References• Relativity, Gravitation and Cosmology, TP Cheng, 2010, p337 ff• Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors, A

Buonanno and Y Chen, PHY REV D, 64, 042006• Seismic gravity-gradient noise in interferometric gravitational-wave detectors, S Hughes, K Thorne, PHYS

REV D, 58, 122002• http://www.ego-gw.it/virgodescription• Near optimal solution to the inverse problem for gravitational-wave bursts”, Y Gursel, M Tinto, Phys Rev D

40, 3884• LISA: a mission to detect and observe gravitational waves, O Jennrich, in Gravitational Wave and Particle

Astrophysics, Proc SPIE v5500 • Interferometer design of the KAGRA gravitational wave detector, Y Aso, et al, arxiv.org ,1306.6747v1• Gravitational wave sensitivity curves, CJ Moore, RH Cole, CPL Berry, arXiv:1408.0740v1 [gr-qc] 4 Aug 2014• Gravitational radiation from the motion of two point masses. P. C. Peters, Phys. Rev. ,136, 1224 [1964]• Gravitational radiation from point masses in a Keplerian orbit, P. C. Peters and J. Mathews, Phys. Rev., 131,

435 [1963]• http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf• Gravity: Introduction to Einstein’s General Relativity, Hartle. 2003.• C. D. Ott, Classical and Quantum Grav. 26 (2009) 06300• A model for Gravitational Wave Emission from Neutrino-Driven Core-Collapse Supernova. Murphy, J. W.,

Ott, C. D., & Burrows, A. 2009, arXiv:0907.4762