Gravitational Wave Detection
Overview of Why and How
Dan Burbank and Tony Young
AST5022
Introduction
Background Physics
Sources
Detectors and Detector Implications
Questions
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 g  ( x)    h ( x) , SR plus
small addition (considering 1-D propagation)
• Define
0

0
h (t , z )  
0

0

0 0 0

1 0 0
f (t  z )

0 1 0

0 0 0 
where
f (t  z)  1
• Define spacetime element
ds 2  dt 2  [1  f (t  z )]dx 2  [1  f (t  z )]dy 2  dz 2
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
L*
1
L(t )   dx[1  hxx (t ,0)]1 / 2  L* [1  hxx (t ,0)] as h is very small
0
2
– Simplified this gives the change in L* as
dL* 1
 hxx (t ,0)
L*
2
dL* 1
– Suppose f (t  z )  a sin[ w(t  z )   ] then
 a sin( wt   )
L*
2
and the fractional change in distance along the x-axis oscillates
periodically with half the amplitude of the gravitational wave
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
0

0
h (t , z )  
0

0

0 0 0

0 1 0
f (t  z )
1 0 0

0 0 0 
– The most general metric is the superposition
0
0
0
0


f  (t  z ) 0 
 0 f  (t  z )
h (t , z )  
0 f  (t  z )  f  (t  z ) 0 


0
0
0
0 

Giving the two transverse polarizations + and x (as mentioned in class).
Background Physics
Power 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
da
64 G 3 m1 m2 (m1  m2 )  73 2 37 4 

1 e  e 
5
3
2 7/2 
dt
5 c a (1  e )
96 
 24
– 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)
ao4
 circ (ao ) 
4
where
64 G 3

m1 m2 (m1  m2 )
5
5 c
-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

h(t )  ho cos( 2ft   f t 2   o )
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 ringdown 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
Laser Interferometer
– 10-4< f < 104
– When DLx , DLy 
DLy
DLx
*“Relativity,
Gravitation and Cosmology”, TP Cheng, 2nd Ed, p337 ff
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
1 𝑇
𝑛
𝑇→∞ 2𝑇 −𝑇
• Time average of noise2, 𝑛(𝑡)2 = lim
𝑡 𝑛∗ 𝑡 𝑑𝑡
• Power Spectral Density, PSD = Sn(f), has units 1/f and relates to noise2
∞
by 𝑛(𝑡)2 = 0 𝑑𝑓 𝑆𝑛 (f).
• When lower integration limit = 0 this is called “one sided PSD”
• Root PSD = 𝑃𝑆𝐷 has units 1/𝑓, 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
∞
h
• SNR = −∞ 𝑑 log 𝑓 [ c ]2
hn
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
Signal
detection
uses QND
technique
Laser is modulated to create RF
sidebands for cavity length
control. AS_RF takes that signal
to control system.
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
𝑆𝑄𝐿ℎ
[𝐻𝑧 −0.5 ]
=
8ℏ
𝑀𝐿2 Ω2
M
Mass of each identical test mass
W
GW angular frequency
ℏPlanck’s constant/2
L
Length of the interferometer’s arms
DL
Time evolving difference in arm lengths
h(t)=DL/L Dimensionless gravitational wave signal
• “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
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
VIRGO
isolation
stack
LIGO
http://www.egogw.it/virgodescription
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”
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 + s22 )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
• 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
LISA: a mission to detect and observe gravitational waves, O Jennrich, in Gravitational Wave and Particle
Astrophysics, Proc SPIE v5500
References
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•
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•
•
•
•
•
•
•
•
•
•
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