Gravitational Waves Detection And Fourier Methods · PDF file1 Gravitational Waves Detection...

11

Gravitational Waves DetectionAnd Fourier Methods

ISAPP2012Paris, France, July 2012

Patrice Hello

Laboratoire de l’Accélérateur LinéaireOrsay-France

22

1.Gravitational Waves in General Relativity

2.Astrophysical sources

3.Interferometric detection

4.Data Analysis methods

5. The LIGO-Virgo network

Overview

33

Part I

Gravitational wavesin General Relativity

44

What are Gravitational Waves ?

Gravitational Waves (GW) are ripples of space-time

Theory of GW :

1. Einstein equations:

2. Far from sources:

3. Linearization:

4. Gauge TT:

µνµνµνπ

Tc

GRgR

4

8

2

1 =−

hg µνµνµν η +=

0 2 =∇ h

TT

µν

Propagation of some tensor field – h - on flat space-time

02

1 =− RgR µνµν

Prediction in 1916 !

55

Gravitational Wave general properties

• GW propagate at speed of light

• GW have two polarizations “+” and “x”

• GW emission is quadrupolar at lowest order

−=+×

×+

0 0000 00 00 000

hhhhh

TT

µν

Example: plane wave propagating along z axis with 2 polarizationamplitudes h+ and hx:

Corresponding Graviton properties:

• Graviton has null mass

• Graviton has spin 2

77

Gravitational Wave emission(quadrupole formalism)

Tch GTT

µνµνπ

4

2 16 −=∇

( ) [ ]( )cRtGtx QQRc

hTTTTTT / ,2211

4 −−=+&&&&r ( ) [ ]( )cRtGtx Q

Rch

TTTT / 2 , 12

4 −=×&&r

xxxdq νµµν ρ∫∫∫= 3

ρρρρ ~T00/c2 : density of the source

Emission equation in the TT Gauge:

Retarded solution:

) ( 231

3 rxxxdQTTµννµµν δρ −∫∫∫=

Where the reduced quadrupole moment:

Regular quadrupole (inertia) moment:

( ) ( )cRtG

tx QRc

hTTTT

/2

, 4 −= &&r

µνµν

Hence:

88

Gravitational Wave emission:an example

x

y

2 identical point masses in circular orbit around their center of mass

- Orbital plane : xOy- Mass : M- Orbit radius : a- Orbital frequency : f0=2πω0

Q: Compute the 2 amplitudes h+(t) and hx(t) at a distance r on the z axis(without taking into account the radiation reaction !)

O

99

Gravitational Wave emission:an example

( )( )

−+

=000

0)2cos()2sin(

0)2sin()2cos(

0312

02

02

0312

tmatma

tmatma

Q ωωωω

( ) ( )

( ) 0

)/(cos- 224

=

−=

×

+

t

crtmaG

t

hrc

h ωω

t)(s (t)

t)cos( (t)

01

01

ωω

inay

ax

==

t)(s- (t)

t)cos(- (t)

02

02

ωω

inay

ax

==

Positions of the two masses:

So compute the reduced inertia tensor:

After projection on the z direction:

Where ω=2ω0 is TWICE the orbital angular frequency

( ) ( )

( ) ( ))/(sin2

-

)/(cos2

-

224

224

crtmaG

t

crtmaG

t

rch

rch

−=

−=

×

+

ωω

ωω

Note that if we look on the x direction:

Face-on binary => circular polarization

Edge-on binary => linear polarization

1010

Gravitational Wave emission:Orders of magnitude

QQcGP &&&&&& 5

5

µν

µν=Luminosity (Einstein quadrupole formula):

Factor ridiculously « small » !G/5c5 ~10-53 W-1

101050501010--202010 10 MpcMpcCoalescence 2 black holes 10 MCoalescence 2 black holes 10 M

101044441010--212110 10 MpcMpcSupernova 10 MSupernova 10 M

asymmetry 3% asymmetry 3%

1010--111122xx1010--393910 km10 kmH bomb, 1 H bomb, 1 megatonnemegatonne

Asymmetry 10%Asymmetry 10%

1010--292922xx1010--34341 m1 mSteel bar, 500 T, Steel bar, 500 T, ∅∅ = 2 m= 2 m

L = 20 m, 5 cycles/sL = 20 m, 5 cycles/s

PP (W)(W)hhdistancedistancesourcesource

≈

Hertz experiment is impossible for GWs …

1111

Gravitational Wave emissionand compact stars

Pb : G/c5 is very « small ».

Source : mass M, size R, period T, asymmetry a ⇒⇒⇒⇒ 32 / TRMaQ ≈&&&

New parameters• caracteristic speed v•Schwarzchild Radius Rs = 2GM/c2

≈cv

RRa

GcP S

62

2 5

Huge luminosity if• R Rs• v c• a 1

© J. Weber (1974)

TRMa

cGP 6

422

5 ≈Quadrupole formula becomes :

compact stars

c5/G would be much better !!!

1212

Part II

Astrophysical sources of Gravitational waves

1313

Gravitational Wave sources

Compact stars

“High frequency” sources ( f > 1 Hz)

• supernovae (bursts)• binary inspirals (chirps)• black holes ringdowns (damped sine)• isolated neutron stars, pulsars (periodic sources)• stochastic background (stochastic) • …

Amplitudes h(t) on Earth ?Rate of events ?

1414

type II SN = gravitational collapse of the core (Fe) of a massive star (> 10 M

) after having burned all the H fuel neutron star formation

GW Emission ? Depends on asymmetry (poorly known)

Sources of asymmetry • fast rotation (instabilities)• companion star

Modern models :h ~ 10-23 @ 10 Mpcf peaks between 0.3 and 1 kHz1 SN/ 40 yrs / galaxy

Black hole formation:Progenitor too massive collapse black hole

h ~ 10-22 @ 10 Mpcf > 1 kHz + oscillations…

Gravitational Supernovae

1515

Gravitational Supernovae:GW amplitudes

Zwerger & Müller, 1997.

Dimmelmeier et al., 2007.

Complex physics => numerical studies

1616

Main conclusions: + Waveforms not well predicted+ weak amplitudes -> only Galactic Supernova detectable ?

Ott and Burrows, 2006.

+ coupling between the proto-neutron star and the envelope (rotation instabilities induced by turbulence and accretion)

collapse

Gravitational Supernovae:GW amplitudes

Marek et al., 2008.

1717

Gravitational Supernovae:How far can we “see”?

1818

Binary inspirals:GW amplitudes

System of 2 close compact stars

• Varying quadrupole -> GW emission• GW emission -> loss of energy and angular momentum• Loss of (gravitational) energy -> stars become closer• Finally 2 stars merge (or disrupt)

( ) ( )

( ) ( ) )(sin)( cos )(4

)(cos)(2

cos1

)(4

3/2

4

3/5

3/22

4

3/5

ttfiGΜ

t

ttfiGΜ

t

Rch

Rch

TT

TT

ϕπ

ϕπ

=

+=

×

+Spiraling phase(lowest order)

where

csteM

tt

c

Gt

ttc

GMtf

MM

c

c

tot

+

−

−=

−=

=

−

−

8/58/3

5

3/5

8/3

5

3/5

5/25/3

52)(

)()(

5

2561)(

ϕ

π

µ• Chirp mass:

• frequency:

• Phase:

tc : coalescence time

A “chirp”4/1

−

−∝ tt h(t)

c

1919

• « inspiral » : h(t) is a chirp• « merger » : recent numericalprogress

• « ringdown » : black hole quasi normal modes

2 neutron stars @ 10Mpc

hmax ~10-21

fmax (last stable orbit)~ 1 kHz

Binary inspirals: the chirp signal

2020

Baker et al. 2007

Binary inspirals: the merger signal

Simulation of 2 inspiraling Black holesNumerical “tour de force”

2121

NSNS--NS:NS: ((KalogeraKalogera et al et al astroastro--ph/0111452)ph/0111452)

•• 0.001 0.001 –– 1 / 1 / yryr --> > 20 20 MpcMpc

NSNS--BH:BH:

•• 0.001 0.001 –– 1 / 1 / yryr --> > 43 43 MpcMpc

BHBH--BH:BH:

•• 0.0010.001-- 1 / 1 / yryr --> > 100 100 MpcMpc

•• Gain Factor 10Gain Factor 10 on detector on detector sensitivitysensitivity

gain gain factor 1000factor 1000 on the on the eventevent raterate

ΘΘ + MM 4.14.1

Binary inspirals: rate of events(first generation detectors)

ΘΘ + MM 104.1

ΘΘ + MM 1010

2222

GW (indirect) discovery PSR 1913+16

(Hulse & Taylor, Nobel’93)

Gravitational Waves do exist !

PSR 1913+16 : binary pulsar (system of 2 neutron stars, one beinga radio pulsar seen by radiotelescopes) at ~ 7 kpc from Earth.⇒⇒⇒⇒ tests of Gravitation theory in strong field and dynamical regime

Loss of energy by GW emission : orbital period decreases

(merge in 300 billions years)

P (s)P (s) 27906.9807807(9)27906.9807807(9)

dP/dtdP/dt --2.425(10)2.425(10)··1010--1212

ddωω/dt/dt ((ºº/yr)/yr) 4.226628(18)4.226628(18)

MMpp 1.4421.442 ±± 0.003 0.003 MM

MMcc 1.386 1.386 ±± 0.003 0.003 MM

2323

Other sourcesPulsars and rotating Neutron Stars

105 pulsars in the Galaxy, several thousands rapidly rotating.Source of asymmetry ?

- rotation instabilities- magnetic stress- “mountains” on the solid crust …

Radio-astronomy observation of pulsar slowdown sets upper limits on GW emission and neutron star asymmetry (if rate of slowdown totally assigned to GW emission)

⇒Expected amplitudes are weak (h<10-24)

But the signal is periodic ! (“simple” Fourier analysis)

Signal to noise ratio where T is the observation time

)10

()Hz100

)(distance

kpc 10(10~

6226

−− εf

h

T∝S/N

2424

SN (15 kpc)

Vela

Crab

2525

Theoretical predictions (cosmology):

LIGO/Virgo (1 yr integration time) sensitive to

Other sourcesStochastic background

A lot of possible ideas - cosmological backgrounds, phase transitions- cosmic string vibrations- superposition of unresolved sources - …

ln

1

GW fdGW

d (f)

critΩ

ρ

ρ=GW density:

106

GW 20 h

−<Ω 1013

−→rather

107

GW 20 ~ h

−Ω

2626

Which is the physical effect we can detect on Earth ?

2727

Detectable effect of GW

GW ⇒ perturbation of the metric⇒ measurements of distances (*) are affected

A B

xdthd

dtxd 2

2

2

2

2

1

νµ

µν−=

GW Geodesic deviation equation(weak field):

L

hLδL 21≈⇒ Variation of measured distance between A and B

Amplitude h(t) rate of deformation of space-time !

(*) modern measurement e.g. by time of flight of photons

2828

Effect of GW on a set of test masses

One cycle

Effect of h+

Effect of hx

2929

Ideas for detecting a GW ?

• GW modifies light travels• Effect is differentiel• Effect is tiny (needs sensitive measurement)

must be sensitive to h ~10-21

⇒ Michelson interferometer !

3030

Part III

Interferometric detectionof Gravitational Waves

3131

History

1960 1st detector (Weber)1963 1st idea interferometric detection (Gersenshtein&Pustovoit, Weber)1969 Wrong claim (Weber)197X Weber detectors all over the world1972 Itf feasibility study (Weiss) and 1st prototype (Forward)1974 PSR1913+16 (Hulse&Taylor)End 70s cryogenic bars, itf prototypes (Glasgow, Garching, Caltech)1986 birth of collaboration VIRGO (France+Italy, Nikhef joined in 2006 )1989 VIRGO proposal, LIGO proposal (USA)1992 LIGO funded1993 VIRGO funded1996 start construction VIRGO et LIGO2005 LIGO in operation2007 VIRGO in operation2007-2011 LIGO-VIRGO joint data takings2011-12 Start upgrades -> Advanced LIGO and Advanced VIRGO2015 First science runs for aLIGO and AdVIrgo…

3232

Resonant detectors(Weber’s bars)

From Weber (60’s) …

… to Auriga (2000s)

3333

Itf detection principle

[ ] )cos( 1 2

0det φ∆+= CPP

Suspended mirrors Test masses

GW optical paths are modified detected power is modified

3434

The optical signal is proportional to h(t) !

[ ] )cos( 1 2

0det φ∆+= CPP λ

πλ

πδφφφ hLL 4

4 GWOP +∆=+∆=∆where

Static dephasing(itf tuning)

Effect of the GW

[ ] )sin( )cos( 1 2

GWOPOP0

detδφφφ ×∆−∆+≈ PP

1 ≈C

The signal !

It remains to show that δφGW is prop. to h …

3535

The optical phase is proportional to h(t)(exercise)

−=

+

+

0 000

0 00

0 0 0

0 000

h

hh

TT

µνAssume itf arms along x and y directions and GW with normal incidenceand polarized along itf arms (only h+)

x

y

Start from space-time interval ds2 = 0 for photons

Integrate along the x axis (back and forth) – assume long wavelength approximation

Derive the round trip travel time for photons in the x arm

Do the same for the other arm

Deduce the round trip time difference between the two arms

Finally give the OPD or equivalently the dephasing due to GW:

( ) νµµνµν

νµµν η dxdxhdxdxgds 02 +===

λπδφ Lh+= 4

GW

Phase shift is proportional to h(t) !

3636

−=+×

×+

0 0000 00 00 000

hhhhh

TT

µν

And if the GW has any incidence and any polarization ?(could be an exercise!)

in the wave frame

Euler angles (Θ, Φ, Ψ)-> itf frame(arms along x and y axis)

Φ

ΘΨ

x

y

z

h+(t) of previous page has to be replaced by:

ΨΦΘ+ΨΦΘ+=ΨΦΘ

ΨΦΘ−ΨΦΘ+=ΨΦΘ

×

+

2cos2sincos2sin2cos)cos1(2

1) ,,(

2sin2sincos2cos2cos)cos1(2

1) ,,(

2

2

F

F

where we define the “beam patterns” as

(t)) ,,((t)) ,,()t( ××++ ΨΦΘ+ΨΦΘ= hFhFh

3737

The interferometric detector is not directional

Antenna patterns

Response if not directional => impossible to reconstruct completely h(t) with a single itf

but not uniform either => detector can be blind (null response along bisectors)

=> 2 (very good) reasons to operate more than one detector !

3838

Noises in interferometric detectors

• optical readout noise (photon counting noise + radiation pressure noise)

• seismic noise (and filtering)

• thermal noise

• laser noises

• others

⇒ General design of itf detectors

3939

Optical readout noise

2 aspects: photon counting noise (or shot noise) and radiation pressure noise

x

y

Pdet

Counting statistics (Poisson): • Let’s note n = rate of arrival on PD (Hz)• Average number of photons incident on thePD during time τ is then• Standard deviation

• Detected power in average

• Detected power fluctuation (RMS) :

Photons detected by photodiode (PD) at the output

NN =στnN =

τωω /det hh NnP ==

τωδ /det hNP =

4040

NOISE SIGNAL

Signal :

Noise:

2

cos

)( OPdet

0φ

τω

δ ∆=hP

P

GWOPOP

0S )( )(2

cos2

sin δφφφ ×∆∆= PP

Signal to noise ratio :GW

OP0

det

s 2

sin )( δφφωτ

δ×∆==

h

P

P

P

N

S

Phase sensitivity :0

~

P

ωφδ h≈ sensitivity :0

shot 4

~

PLh

ωπλ h≈

~ 10-10 rad/Hz1/2 for P0 = 20 W and @ 1.06 µm

πφ OP

=∆

Dark fringe

Shot noise

[ ] )sin( )cos( 1 2

GWOPOP0

det δφφφ ×∆−∆+≈ PP

==

τωτωδ

/

/

det

det

h

h

NP

NP

[ ]

∆=∆+=2

cos )cos( 1 2

OP20OP

0det

φφ PP

P

White spectral density

4141

Radiation pressure noise

Decreasing the shot noise => increasing the power !Power fluctuations => radiation pressure (RP) force fluctuations=> Mirror position fluctuations !

c

PF =rpRP force on a mirror where P is the incident power on a mirror (=P0/2)

cP

F

σσ =The force fluctuation is then

τωτωσ

2/ 0

P

hh

PN ==Where (as derived in previous slide)

The RP force spectral density is then (white).c

PP

cfF

λπω2

2

2

1)(

~ 00RP

hh ==

The mirror response to this force is then:c

P

mffF

fmfx

λππ 30

2RP2 4

1)(

~)2(

1)(~ h==

In term of GW amplitude sensitivity:c

P

mLffx

Lfh

λπ 30

2RP 2

1)(~2

)(~ h==

4242

Optical readout noise as quadratic sum of shot and RP noises

2RP

2shotreadout )(

~)(

~)(

~fhfhfh +=

L=3000; % arm length (meters)lambda=1.06e-6; % wavelength (meters)P0=20; % laser power (Watts)mass=10; % mirror mass (kg)

Shot noise

RP noise

RP noise only relevant at low frequencies => Non relevant for first generation itfs

4343

Standard quantum limit

00

2RP

2shot

2readout )(

~)(

~)(

~

P

BAPfhfhfh +=+= is minimum for 2

min ,0 cfMB

AP λπ==

To each frequency corresponds one optimum and the envelope of all the optima for the readout noise defines the standard quantum limit:

min ,0P

222sql 4)(

~

fmLfh

πh=

The SQL is a 1/f noise

The SQL depends only on the mirror masses (and arm length)

The SQL is not a real limit. It can be beat in some frequency band(other optical configurations, squeezed states of light ….)

4444

How to improve the detection scheme ?

00shot 2

2

1

4

~

P

c

LPLh

πλω

πλ hh ==

We can play only on the arm length L and the power P0

Shot noise limited itf :

Increase the (optical) length:+ kilometric arm length (not more than a few km: cost and … Earth curvature !!!)

+ fold the light in the arms => Fabry-Perot (FP) cavitiesFP cavity of length 3 km and finesse 50 => optical length ~ 100 km

Increase the circulating power:+ itf tuned at a dark fringe => all the light is reflected back to the laser.The itf can be seen as a (almost) perfectly reflecting optical device.The idea is to add an extra mirror between the laser and the beamsplitter(“recycling mirror”)⇒ New FP cavity with power gain if at resonance for the laser wavelength(“recycling cavity”)

4545

→ kilometric arm length : 1 m → 3 km→ add Fabry-Perot cavities (Finesse = 50 ⇒ Gain ~ 30)→→ add « recycling » mirror (P = 1 kW on the beamsplitter)

sensitivitysensitivity :: h ~ Hz /Photodiode

Laser

Gain :Gain : 3000 × 30 50 × ~ 106

10-173 10-2110-2310-22

bright

fringe

LASER power : Pin = 20 Wsensitivity in P / 1 h ∝

(shot noise)

Optical design is completed

4646

Laser Nd:YAG

P=20 W

Input Mode CleanerLength = 144 m

Recycling

Output Mode CleanerLength = 4 cm

L=3kmFinesse=50

L=3kmFinesse=50P=1kW

Virgo optical design

+ Clean the Gaussian mode of the laser beam+ filter HF laser fluctuations

Filter spurious beams(increase the contrast)

1.06 µm (IR)

4747

Seismic noise

Mesure on site : Hz / m 2 10 ) (~

6

ffx

−

≈ ⇒⇒⇒⇒ Must be attenuated

5 dampers with fundamental freq. ~ 0.6 Hz :

Simple spring : 0 )( 2

2

=−+ sxxkdt

xdm

Transfer function : 220

20

)(~)(~

)(~

ωωω

ωωω −==

sxxH

Above resonance :2

0 |)(~

|

≈ ωωωH

N dampers :N

H2

0 |)(~

|

≈ ωωω

Hz10 Hz107x ~ @

22

≈−

sismh

4848

Virgo « superattenuator »

L ~ 7 m; M ~ 1 ton+ inverted pendulum

Seismic attenuation:~ 1014 @ 10 Hz

(measured)

⇒ fres ~ 30 mHz

lg m

k 2π1 f res −= -

4949

Thermal noise

Fluctuation dissipation theorem (Callen et al., 1951 …)

⇒ dissipation is source of noise in any mechanical system

))(( 4)(~

B2

therm fZTkfF ℜ=Fluctuating force power spectral density

(where Z is the mechanical impedance)

Gives rise to fluctuating motion (position noise) ))(( )(~22

B2therm fY

f

Tkfx ℜ=

π(where Y=1/Z is the mechanical admittance)

Exemple of gas-damped spring or pendulum

From the equation of motion mFxxQ

x /20

0 =++ ωω&&&

( ) 2220

2220

0B2therm

/

1

4)(~

QmQ

Tkx

ωωωωωω

+−=

show that the position

Where is the angular frequency (more simple) fπω 2=

(thermal) noise is

5050

Thermal noise

Mirrors+suspensions:a lot of mechanical oscillators under vacuumInternal friction is the relevant dissipation source.

Suspension wire vibrations

substrate vibrations

Pendulum mode

Internal friction modeled by a generalizationof Hooke’s Law:

xfikF ))(1(spring φ+−=

φ = “loss angle” (related to spring anelasticity)

From the new equation of motion and assuming φ =cste =1/Q, show that the thermal noise power spectrum in case of internal friction is

( ) 240

2220

00B2therm

/

1

4)(~

QmQ

Tkx

ωωωωωωω

+−=

Note that both models (gas-damped and internal friction) give thesame noise at resonance (ω=ω0) but differ considerably off resonance• LF: gas-damp noise -> cst

internal noise -> cst/ω1/2

• HF: gas-damp noise -> cst/ω2

internla noise -> cst/ω5/2

5151

Thermal noise

Internal friction

Gas-damped spring

Q=106

f0=1 kHzM=30 kgT=300 K

1/f2

1/f5/2

1/f1/2

indep. of f

5252

Frequency fluctuations + length asymmetry ⇒ phase noise

νδπφδ ~ 2 ~

cd=

If optical path difference d=0 : no constraintBut asymmetry unavoidable: d = ∆∆∆∆(FL) = L ∆∆∆∆F+F ∆∆∆∆L

Recall shot noise limited phase sensitivity : hFLc

~

2

~ πνφδ ≈

So laser frequency noise induces new noise: ( ) ννδ ~

~ ×∆+∆≈

FF

LLhOG

• target sensitivy :• asymmetry ~10-3

• freq. ν ≈ 2.8 x 1014 Hz

Hz10 x3 ~ 23

≈−

h

⇒⇒⇒⇒ spec. HzHz 10 ~ 5< −νδ

Active laser frequency stabilization + « mode-cleaner » cavity(Fabry-Perot = low pass filter !)

LASER frequency noise

5353

Laser servoed to reference cavityRigid cavity (ULE) => etalon

Under vacuum

Under the input bench

LASER frequency stabilization

5454

Solution for Virgo:• Steel tubes ∅∅∅∅ ~1.2 m, e ~ 4 mm.• 200 modules (15 m long) in each arm• bake out 400°C after production,

150 °C (H2O) on site • 10 pumping stations / arm

Residual gas index fluctuations ⇒⇒⇒⇒ phase noise Ultra high Vacuum is needed

Requirement : residual pressure < 10-7 mbar

Vacuum volume in VIRGO : 2x3kmx1.2m ~ 7000 m3 !

Ultra High Vacuum

5555

LIGO (itf center : beamsplitter and input FP mirrors)

5656

Virgo (itf center)

5757

Mirrors

•• Spec: total losses Spec: total losses < 2%< 2% (guarantee 1kW on (guarantee 1kW on beamsplitterbeamsplitter): ):

«« coatingcoating »» absorption absorption (< 1 (< 1 ppmppm)) and substrate absorption and substrate absorption (<2 (<2 ppmppm/cm)/cm)

Diffusion losses < 5 Diffusion losses < 5 ppmppm

Geometrical Aberrations (Geometrical Aberrations (δδzz < < λλ/100)/100)

Curvature asymmetry < 3%Curvature asymmetry < 3%

Finesse asymmetry < few % (laser noises)Finesse asymmetry < few % (laser noises)

Solution : pure Silica mirrors (SiOSolution : pure Silica mirrors (SiO22) with special design) with special design

from manufacturerfrom manufacturer

Virgo mirrors : Virgo mirrors : ØØ = 35 cm and = 35 cm and widthwidth = 10 or 20 cm= 10 or 20 cm

35 cm

10 cm

5858

Virgo beamsplitter installation

5959

Residual mirror rugosity ⇒⇒⇒⇒ scattered light + seismic motion of tubes

⇒⇒⇒⇒ phase noise !

solution:• very good mirrors OK.• Baffles (80 in each bras)

• steel baffles in the tubes• black glass in towers (close to mirrors)

Scattered light

Random phase

6060

Glass baffles

6161

Sensitivity curve(Virgo design example)

6262

6.26 MHz8.35 MHz

BS

CoE

DiE

BMS

WIcamera

NI

camera

PR

Interferometer control

Virgo control system

+ 4 “lengths” to control+ Angular motion

6363

Interferometer control

Coil+magnet

6464

Virgo sensitivity evolution

Not an easy task to reach the design sensitivity !

6565

Towards advanced detectors

Virgo site:Beginning of 2012

6666

Advanced Virgo setup

Changes in optical configuration:

• Laser power increase• Higher finesse cavities• Signal recycling

Plus• Improved thermal compensation• Suspended external benches• Diffused light mitigation• Fused Silica suspension wires• …

6767

Advanced Virgo sensitivity

Goal: gain of a factor 10 in sensitivity (events rate x 1000 !!!)

Signal recycling : sensitivity can be tunable

6868

Part IV

GW Data Analysis

6969

The problem

Search for a temporal signal s(t) in a noise n(t) with complex structure.

What is recorded is h(t) = n(t)+s(t) … so how to extract s(t) ?

The noise is characterised by its spectral density (see next slide)

Well known problem of Signal Processing (radar, telecommunications …)

Solution is easy if the signal is known a priori => matched filtering

Binary systems : chirp signal is approximately known - up to 3PN order, ie (v/c)6

⇒ Matched filtering can be applied

Supernovae : signal is poorly known (not a robust prediction)⇒ Other methods

Rotating neutron stars : (quasi) periodic signal⇒ Fourier analysis (nothing but matched filtering for sinusoidal signals)

Nota Bene: In practice the noise is not Gaussian and not stationary !

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Noise spectral density

Autocorrelation of process x(t) : ∫−

+=∞→

2/

2/

)()( 1 ) ( lim T

Tx txtxdt

TTA ττ

Power Spectral Density (PSD) : Sx( f ) = Fourier Transform of Ax(t)

Dimension ofSx( f ) = (dimension of x)2 / frequency

Amplitude Spectral Density : ) ( ) (~ ffx S x=

If x(t) corresponds to a stochastic process (noise), its DSA gives thecontribution of each frequency to the total noise

∫∞

=0

2 ) ( dffS xσ Link between PSD and RMS :

22/

2/

2)( 1

) ( lim ∫−

−

∞→=

T

T

fti

xetxdt

TTfS π

In practice, we use the estimator:

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Matched filtering principle(Wiener, 1949)

Usable if the signal is known a priori (and optimal if Gaussian

noise)

Principle: correlate the data with a template (a copy of the expectedsignal)

Signal to noise ratio ρρρρ : ∫∞+ ×=

0

~~2

) (

*) ( ) ( 4 dffS

ftfhh

ρ

h : detector output t : templateSh : detector noise (one-sided) spectral density

ρ ρ ρ ρ 2222 = <h|t>

Signal to noise ratio (squared) ρρρρ2222 can be seen as a scalar product :

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Matched filtering principle

∫∞+ ×=

0

~~2

) (

*) ( ) ( 4 dffS

ftfhh

ρ

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Signal and template : identical shapesTemplate : w = 1 ms. Signal : w = 1 msTemplate : normalized <t|t> =1 Signal : Intrinsic SNR = <h|h> = 10Filter max output : ρρρρ = <h|t> = 10

Signal and template : mismatched shapesTemplate : w = 1 ms. Signal : w = 5 msTemplate : normalized <t|t> =1 Signal : Intrinsic SNR = <h|h> = 10Filter max output : ρρρρ = <h|t> = 7

Matched filtering : example

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Matched filtering for binary inspirals

( ) ( )

( ) ( ) )(sin)( cos )(4

)(cos)(2

cos1

)(4

3/2

4

3/5

3/22

4

3/5

ttfiGΜ

t

ttfiGΜ

t

Rch

Rch

TT

TT

ϕπ

ϕπ

=

+=

×

+

The phase ϕ(t) depends primarily on star masses

⇒ 2 unknown (intrinsic) parameters+ extrinsinc parameters (angles) that play no role in thedetection process apart a scaling of the amplitude.

General scheme:

• Define the ambiguity function:

• And expand up to second order:

• Set a minimal match between nearby templates:

• criteria to locate templates

⟩+⟨=Γ )(|)(),( λλλλλrrrrr

dttd

νµµν λλλλ ddgd

2

11),( −≈Γ

rr defines a metric inparameter space!!!

MM),( ≥Γ λλrr

d

MM12

1 −≤νµµν λλ ddg

Parameter space (M1, M2) must be tiled with templates

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M1 and M2 = [1;30] M

, MM=0.95, f=[40;2000]HzPN order =2, template number = 11369

2D parameter space => condition defines ellipses in the plane !MM12

1 −≤νµµν λλ ddg

.)(sec0τ

.)(sec5.1τPhysical boundaries


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Chirp phase known today up to 3 PN order (3.5 PN being computed)

- spins correction (-> 4 intrinsic parameters)- template frequency cut-off, last stable orbit ?

2PN proved to be robust for detection purposes but not for parameterestimation (extraction of masses)

Current (theoretical) issues

Current (technical) issues

Data to be processed with high number of templates

- cluster of machines- memory access etc …

Worse with network analysis => hierarchical searches

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The problem of burst data analysis

Supernova waveforms prediction

Not robust predictions => matchedfiltering can not be robust !

⇒Robust detections methods needed(but necessarily suboptimal)

However matched filter can be used for catching some part of the signal

For example Gaussian peak templatescan be used for detecting main peakappearing in some burst waveforms(of course part of the signal SNR is lost)

Some other burst signals are also well known, e.g. black hole oscillations <-> ringdown signals with 2 parameters (frequency and damping time)

related to BH mass and angular momentum => matched filtering mustbe used. (but marginal signals in term of detectability)

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Burst data analysisExamples of suboptimal methods

Signal in white noise

Moving averageEnergy excessIn moving window

Slope changedetector

Offset detector

Combination of SF and OF(quadratic filter)

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Burst data analysisTime-frequency methods

Wavelet methods

S-transform

Q- pipeline

∫+∞

∞−

−−= dteQftwthQfX ftiπττ 2),,()(),,(

∫+∞

∞−

−−−

= dteethfS ftift

πτ

τ 22

)( 22

)(),(

Signal only

Signal + noise

More versatile methods

Etc…

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Burst data analysisTime-frequency methods

Whatever the details of the method : search some excess powerin a time-frequency map

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The necessity of network analysis

Events are very rare

Output of one detector is mainly (non Gaussian) noise !

One single detector can not reliably distinguish a real event from a fake one(unless you perfectly know your detector …)

Coincidences with other detector(s) may allow such a selection(or at least eliminate a number of candidates)

Coincidences with other GW detectorsAt least 3 detectors needed to reconstruct the GW signal(GW timing => triangulation to determine the sky position box)

Coincidences with other messengersGRBs (collapses or mergers)Neutrinos (collapses)…

The golden way to validate a first direct detection: detection by the GWnetwork and prediction of the source direction and confirmation of aHE event by GRB satellites or ν detectors …

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VIRGO HANFORD LIVINGSTON

The LIGO-VIRGO Network :

Times delays set the Source Reconstruction Accuracy: Minimal angular resolution ~ 1o

(could be much worse)

Beam patternsVirgo LIGO-Hanford LIGO-Livingston

Network data analysis

Light time of flight : HL ~ 10 msec., VL ~ 26 msec. and VH ~ 27 msec.

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Network data analysisSource location reconstruction

2 itfs : source localized on a Great Circle of the celestial sphere3 itfs : intersection of 2 Great Circles : 2 points (true location + mirror image wrt plane of 3 itfs)4 itfs : no degeneracy

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Network data analysisCoincident approach

Trigger lists in one day of simulated data. Simulated burst events with varying h from constant direction (Galactic center).

Coincidences efficiencies :

Efficiency Efficiency ((%)%)

False alarm False alarm rate (rate (HzHz))

BurstsBursts

~ 3.10~ 3.10--661010--661010--660.10.1

2222

LVLV

6060222241411919555560606363

HL HL υυ HV HV υυ LVLVHVHVHLHLHLVHLVVVLLHH

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Network data analysisCoherent approach

Coincidences with 3 GW detectors: the easiest way to proceed.

Another way is to combine all 3 GW data streams into a single one⇒ Coherent approach

Single data stream that keeps all the information (even the onewhich would be “under threshold” in a single detector)

But very heavy method (need to test every cell in the sky)⇒ in practice coincidence method with coherent follow-up on candidates

Possibility to build “null streams”, i.e. data stream combinationsthat kill the GW event, to veto events of instrumental origine.

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Real data analysisData Quality Studies

One single itf: non Gaussian and non stationary noise with many “glitches”Many glitches look like GW events !

First step is to clean the data stream from identified artifacts or suspicious events.

Help of many probes (acoustic, seismic, magnetic …) whose signals are recorded in auxiliary channels.

If an event in main (GW) channel is coincident with an event in some aux. channel : suspicious event which must be flagged !

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Exemple of glitches in the Virgo main channel (and origines)

LIGO&Virgo coll., Class. Quantum Grav. 29 (2012) 155002

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Hierarchy of Data Quality Flags (typically 3 categories):

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Effect of DQ flags on single itf triggers

Search for NS-NS binariesDouble coincident eventsFull VSR2 period

LIGO&Virgo coll., Class. Quantum Grav. 29 (2012) 155002

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Real data analysisBackground estimation and significance

Data Quality studies help to reduce the number of artefacts but are notsufficient to estimate the background of a search for a certain signal.

Lot of (high) SNR events remain : we don’t fully understand itf’s noise andwe can’t predict the background distribution

Hopefully we have a powerfull method to estimate background in a coincidence experiment (e.g. GW events in 2 itfs)

time

Data stream itf 1

Data stream itf 2

t0

Data stream itf 2

t’0

By time-shifting 2 data streams we have a new coincidence experiment

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Real data analysisBackground estimation and significance

With many time shifts we obtain many coincident triggers and constructour analysis background

Time shifts must be larger than time delays between itfs larger then signal durations but not too large to avoid long period coherence (day-night …)

Finally distribution of time shifted events -> estimation of the analysis background

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Real data analysisSensitivity estimation

The sensitivity is estimated by injecting known signals in the dataRecovery (or not) of injected signals => efficiency curves

Detection effiency Vs. signal strain for SineGaussian signals(235Hz and 1304Hz central frequencies) with linear or elliptical polarisations.

∫+∞

∞−

= dtthhrss )(2

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Real data analysisTuning

Exemple of a toy analysis : looking for coincident events between 2 itfs

• Blue : background (time shifted events)• Pink : injections• Green : zero-lag events

Cuts on individual SNRs and on combined (SNR1*SNR2) in orderto have a small remaining false alarm rate (e.g. 1 ev event every 10 yrs)and to keep a good sensitivity.

Once you are happy, you look finally at the true (“zero-lag”) coincidences

REAL BLIND ANALYSIS!

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Network data analysisThe use of other messengers

External triggers ease the search !⇒ Have to look for events only in a restricted time windowaround the event and for a known location in the sky

Lot of studies for instance with - GRBs (Swift, Fermi …)- Soft Gamma Repeaters- High Energy Neutrinos (ICECUBE, Antares)- Low Energy Neutrinos (SuperK)

⇒ Main outcome is upper-limit on possible GW emission

In general GAIN of a FACTOR 2-3 wrt all sky blind analysis(“see” ~one order of magnitude further)

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An exemple

Coincidences with neutrinos in case of gravitational collapse

GW emission ~ coincident with the bounce

Neutrino flash delayed by ∆t νflash-GW ~ 3.5 +/- 0.5 ms

+ delay due to propagation of massive neutrino:

.E

MeV 10

eV 1kpc 10 ms 2.5

222

GW-e

×

×

×≈ ∆

v

cmdt νν

⇒ GW and neutrinos detected within 10ms (add safety factor and detectorsystematic errors)

• Neutrino detection can validate a GW flash detection in case of Galactic supernova

• Coincident detection can set constraint on neutrino massesUpper-limit (current detectors)eV 7.0≤νm

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Another exemple

Short GRB <-> NS-NS coalescenceLong GRB <-> Gravitational collapse (hypernova)

GWs and GRBs

Analysis window~10 minutesfits astrophys. scenario

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The LIGO-Virgo network

(Today and tomorrow)

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The GW detectors (near-future) world

LIGOGEO600 Virgo

KAGRA

AIGO ?

LIGO-India

(Advanced)(Advanced)

9999

The worldwide collaboration

LIGO + LIGO Science Community (aggregate GEO600)and Virgo

have joined their forces in 2007

• joint data takings• full data sharing• 4 joint search groups with co-chairs from each collaboration

- bursts- compact binary coalescences- continuous waves (pulsars)- stochastic GWs

• Joint run and planning committee

Agreement renewed last year (2011) -> cover the Advanceddetectors area (data taking to re-start end of 2014)

+ Ongoing discussions with Japan (KAGRA collaboration)

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LIGO

’05 ’06 ’07 ’08 ’09 ’10 ’11 ’12 ’13 ’14 ’15 ’16

S4 S5

VSR1 VSR2 VSR3

S6 GEO-HF

VSR5 VSR6

S7 S8

Now

GEO

Virgo

Advanced LIGO →→→→

Advanced Virgo →→→→

AstroWatch

VSR4???

LIGO-Virgo joint data takings

Virgo duty cycle ~90%

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The LIGO-Virgo networkCompared sensitivities

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The LIGO-Virgo networkA selection of scientific results

Search for compact binary coalescences:No detection (yet)−−−−>>>> upper limits on event rates

Best UL’s

Range of astrophysicalpredictions

The gap is less than 1 order of magnitude!(important for advanced detectors)

LIGO&Virgo coll., Phys.Rev.D 85:082002 (2012)

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Search for bursts: upper limits on event rates Vs signal strength(here generic SineGaussian signals)

Limit due to finite observation time

Search sensitivity at thesefrequencies

LIGO&Virgo coll., arXiv1202.2788 [gr-qc] (2012)

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Short GRB detected in direction of M31

Search for binary coalescences in theGRB error box

No GW event found-> GRB occurred in a further galaxybehind M31 (if it is a real GRB)

SGR scenario not excluded by GWSearch.

Astrophys.J.681:1419-1428 (2008)

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Search for continuous GWs (pulsars)

Spin-down limit for known pulsars (1 yr integration time)

Virgo sensitivity

Advanced-

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Results for the Crab pulsar(30Hz): h0~3.4x10-25

(4xbelow the spin-down limit)

Results for Vela (11Hz): h0~2x10-24 (1.7x below the spin-down limit)

Excluded by e.m. observations

Excluded by GW searches

(LIGO&Virgo coll., Astrophys.J.737:93 (2011))

LIGO coll., Astrophys.J.683:L45-L50 (2011)

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Search for cosmological background(s)

LIGO&Virgo coll., Nature 460-994 (2009)

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The itf detectors are sensitive to amplitude h(t) so increasing thesensitivity by a factor 2 increase the detection range also by 2 andthe volume of observable universe by 23 !- Advanced detectors (improvement of sensitivity by factor 10)⇒ Detection of binary inspirals guaranteed ! (event rate > 1/yr)

The LIGO-Virgo (and others) networkThe Future

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The next decade

Advanced LIGO and Advanced VIRGO : first data in 2015?+ LIGO India+ KAGRA in Japan

+ LISA (now eLISA/NGO) Space mission (date ?)

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KAGRA (prev.”LCGT”) itf in JapanLocated in the Kamioka siteUnderground (less seismic noise)Cryogenic (less thermal noise)

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And after!!!(The 3rd generation)

Cryogenic interferometric detectors

Underground detectors

All reflective optics (gratings as beamsplitters etc …)

Triangular detectors

Capacitive drivers for mirror control

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Conclusions

A new experimental field !

(astro)physics is not yet there … but be patient

Binary inspirals detection likely to be routine in the next decade

GW detectors matched for Galactic Supernovae (likely to be the case forever…)

GW astronomy soon full partner of multi-messenger HE astrophysics

Some science prospects:• Tests of gravitation (GW celerity and polarization …)• First direct Black Hole observations• Collapse dynamics• Equation of state of compact stars• Cosmology (compact binaries as standard candles)• …

New messenger … new vision of the Universe ?

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Some references

http://wwwcascina.virgo.infn.it/

http://www.ligo.caltech.edu/

http://lisa.nasa.gov/

Peter Saulson, “Fundamentals of interferometric gravitational wave detectors”, World Scientific, 1994.

J.D.E. Creighton, W.G. Anderson, “Gravitational-Wave Physics and Astronomy”,Wiley series in Cosmology, 2011.

http://www.einsteinathome.org/ Help the GW community in pulsar detection !

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Signal recycling configuration(Advanced LIGO and Advanced Virgo)

Advantages:• Beat the SQL in some band• Can tailor the frequency response

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Burst data analysisHow to compare methods

Many methods that can be compared in terms of

• efficiency• time resolution• frequency resolution if adapted to method

Source @ 14.6 kpc

Signal: DFM a1b2g1

Universal method does not exist

⇒ Necessary to use different Methods to be sure to cover the“parameter space”

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