Gravity’s Standard Sirens - WebHome < Public · Gravity's Standard Sirens p2 What this talk is about Introduction to Gravitational Waves What are gravitational waves Gravitational

Gravity’s Standard Sirens

B.S. SathyaprakashSchool of Physics and Astronomy

Gravity's Standard Sirens p2

What this talk is aboutIntroduction to Gravitational Waves

What are gravitational wavesGravitational wave detectors: Current status and future plans

Science from Standard SirensSpeed of gravitational waves and mass of the gravitonSeeds of galaxy formation, star formation rateMass function of neutron stars and star formation rateBlack hole “no-hair” theoremCosmological parameters with standard sirensBlack hole spectroscopy


In Newton’s law of gravity the

gravitational potential is given by Poisson’s equation:

2Φ(t, X)= 4πGρ(t,X)In general relativity for weak gravitational fields, for which one can assume that background metric is nearly flat

gαβ

= ηαβ

+ hαβ

where |hαβ

|


Gravitational Wave ObservablesFrequency f = √ρ

Dynamical frequency in the system: twice the orb. freq.

Binary chirp rateMany sources chirp during observation: chirp rate depends only chirp massChirping sources are standard candles

PolarisationIn Einstein’s theory two polarisations -

plus and cross

Luminosity L

= (Asymm.) v10Luminosity is a strong function of velocity: A black hole binary source brightens up a million times during merger

Amplitude h = (Asymm.) (M/R) (M/r)

The amplitude gives strain caused in space as the wave propagates h = dL/LFor binaries the amplitude depends only on chirpmass/distance


Comparison of Gravitational Waves with Electromagnetic Waves

EM waves are transverse waves, with two polarisations, travel at the speed of lightProduction: electronic transitions in atoms and accelerated charges –

what we observe comes from physics of small thingsIncoherent superposition of many, many wavesDetectors sensitive to the intensity of the radiation Normally EM waves cannot be followed in phaseIntensity falls off as inverse square of the distance to sourceDirectional telescopes

GW waves are also transverse waves, with two polarisations, travel at the speed of lightProduction: coherent motion stellar and super-massive black holes, supernovae, big bang, …Often, a single coherent wave, but stochastic background expectedGW detectors are sensitive to the amplitude of the radiationNormally, waves followed in phase, great increase in signal visibilityAmplitude falls off as inverse of the distance to sourceSensitive to wide areas over the sky


Hulse-Taylor Binary: A persistent source of Gravitational Waves

In 1974 Hulse

and Taylor observed the first binary pulsar

Two neutron stars each has mass 1.4 x Sun’s mass Orbital period ~ 7.5 Hrs, eccentricity of 0.62

Einstein’s gravity predicts that the binary should emit gravitational radiation

Causes the two stars to spiral in toward each other leading to a decrease in the orbital periodObserved decrease in period -

about 10 micro seconds per year -

is in agreement

with Einstein’s theory to fraction of a percent


Tayl

or a

nd W

eisb

erg,

200

0, W

ill L

ivin

g Re

view

Accumulated orbital phase shift in PSR 1913+16

Eventually the two stars will coalesce, but that will take another 100 million years


Tidal Gravitational ForcesGravitational effect of a distant source can only be felt through its tidal forcesGravitational waves are traveling, time-

dependent tidal forces.Tidal forces scale with size, typically produce elliptical deformations.


Tidal Action of Gravitational Waves

Cross polarizationPlus polarization


43τ

=t

Interferometric gravitational-wave detectors

0=t 4τ

=t2τ

=t

lhl2

=δ

lδl 22102 −≤=

llh δ

For Typical Astronomical sources


Gravitational Waves Detectors

G070221-00-Z

American LIGO at Hanford

G070221-00-Z

American LIGO at Livingstone

G070221-00-Z

British-German GEO

G070221-00-Z

French Italian VIRGO near PISA

G070221-00-Z

Laser Interferometer Space Antenna

G070221-00-Z

LIGO now at design sensitivity

LLO 4 km – S1 (2002 09 07)LLO 4 km –

S2 (2003 03 01)LHO 4 km –

S3 (2004 01 04)LHO 4 km –

S4 (2005.02.26)LHO 4 km –

S5 (2006.01.02)LIGO SRD Goal, 4 km

h(f)

1/S

qrt(H

z)

Frequency (Hz)

G070221-00-Z

S5 Sensitivity


Future Improvements

Enhanced Detectors (2009-11)2 x increase in sensitivity8 x increase in rate

Advanced Detectors, LIGO and Virgo (2014-

…)12 x increase in sensitivityOver 1000 x increase in rate

3G Detectors: Einstein Telescope

(2018+)10 x increase in sensitivityOver 1000 x increase in rate


Einstein TelescopeET is a conceptual design study supported, for

about 3 years (2008-2011), by the European Commission under the Framework Programme 7 EU financial support ~ 3M€

Aim of the project is the delivery of a conceptual design of a 3rd generation GW observatorySensitivity of the apparatus~10 better than advanced

detectors


Ad LIGO/Virgo NB

Expected Future Sensitivities

1 10 100 1000 1000010 -25

10 -24

10 -23

10 -22

10 -21

10 -20

10 -19

h(f)

[1/s

qrt(H

z)]

F requency [H z ]

(a) 3 rd G eneration (b) LC G T (c) advanced LIG O (d) advanced V irgo (e) L IG O (f) V irgo (g) G E O 600

(a )

(b ) (c )

(d )

(e )

(f)(g )

Credit: M.Punturo

LIGO 2005 AURIGA 2005

Advanced LIGO/Virgo (2014)

Virgo Design

GEO-HF2009

Virgo+ 2008

Einstein GW Telescope

DUAL Mo(Quantum Limit)



ESA-NASA collaboration Intended for launch in 2017

3 space craft, 5 million km apart, in heliocentric orbitTest masses are passive mirrors shielded from solar radiationCrafts orbit out of the ecliptic always retaining their formation


LISA’s

Sensitivity

10-5 10-4 10-3 10-2 10-1 1Hz

105x10

5 M10

6x106 M

Science from Standard Sirens


Burst SourcesGravitational wave bursts

Black hole collisionsSupernovaegamma-ray bursts (GRBs)

Short-hard GRBscould be the result of merger of a neutron star with another NS or a BH

Long-hard GRBscould be triggered by supernovae


Continuous Wave SourcesGravitational wave bursts

Black hole collisionsSupernovaegamma-ray bursts (GRBs)

Continuous waves Rapidly spinning neutron stars or other objects


Stochastic BackgroundsGravitational wave bursts

Black hole collisionsSupernovaegamma-ray bursts

Continuous waves Rapidly spinning neutron stars or other objects

Stochastic backgroundPrimordial backgroundAstrophysical background


Compact Binary Mergers

Compact binary mergersBinary neutron starsBinary black holesNeutron star–black hole binaries

Loss of energy leads to steady inspiral whose waveform has been calculated to order v7

in post-

Newtonian theoryKnowledge of the waveforms allows matched filtering

Why are compact binaries standard sirens?


Compact binaries are standard sirensAmplitude of gravitational waves depends on the combination of Chirp-mass/Distance: Chirp-mass=μ3/5M2/5Gravitational wave observations can independently measure the

amplitude

(this is the strain caused in our

detector) and the chirp-mass

(because the chirp rate depends on the chirp mass)Therefore, binary black hole inspirals are standard sirens: from the apparent luminosity (the strain) we can conclude the luminosity distanceHowever, GW observations alone cannot determine the red-shift to a sourceJoint gravitational-wave and optical observations can facilitate a new cosmological tool

Schutz 86

What do we know about the waveforms from compact binaries?


Compact Binary WaveformsA

mpl

itude

Time

Increasing Spin

Do compact binaries exist in nature?


J0737-3039: Fastest binary pulsar

The fastest Strongly relativistic, Pb =2.5 HrsMildly eccentric, e=0.088Highly inclined (i > 87 deg)

The most relativistic Greatest periastron

advance: dω/dt: 16.8 degrees per year (almost entirely general relativistic effect), compared to relativistic part of Mercury’s perihelion advance of 42 sec per centuryOrbit is shrinking by a few millimeters

each year due to gravitational radiation reaction

Burgay et al Nature 2003

How often do we expect to detect compact binaries?


Expected Annual Coalescence Rates

BNS NS-BH BBH

Initial LIGO(2002-06)

0.015-0.15 0.004-0.13 0.01-1.7

Enhanced LIGO

x2 sensitivity (2009-10)0.15-1.5 0.04-1.4 0.11-18

Advanced LIGOx12 sensitivity (2014+)

20-200 5.7-190 16-2700

Binary Neutron Stars (BNS)Binary Black Boles (BBH)Neutron Star-Black Hole binaries (NS-BH)


Compact binaries in LIGO S5 (5th

science run)

binary neutron star horizon distance

binary black holehorizon distance

S5 data being analyzedHorizon distance (in Mpc) versus total mass (in M ) for binary black holes

Image: R. Powell

Average over run

1 sigma variation

145

120

90

60

30

01 20 40 60 80 100

Do supermassive black hole binaries exist?


Sagittarius A: A Galactic SMBH


Super-massive black hole mergers


SMBH binary in NGC 6240

X-ray observations have revealed that the nucleus of NGC 6240 contains an SMBH binary that will coalesce within the Hubble timeThe high visibility of the signal means we can see SMBH binaries anywhere in the UniverseWe can catch the signal at early times to predict the precise time and position of the coalescence event, allowing the event to be observed simultaneously by other telescopes.

NGC6240, Kamossa et al


Visibility of SMBH binary mergers

Cutler and Vecchio

What can we expect to learn by observing compact binaries?


Capture of Small Black Holes by Super- massive Black Holes


Do gravitational waves travel at the speed of light

Coincident observation of a supernova and the associated gravitational radiation can be used to constrain the speed of gravitational waves to a fantastic degree:If Δt is the time difference in the arrival times of GW and optical radiation and D is the distance to the source then the fractional difference in the speeds is

Should also be possible with coincident observation of inspirals and gamma-ray bursts


Counting the Polarization States

Cross polarizationPlus polarization

Only two states in GR: h+

and hx


Polarization States in a Scalar-Tensor Theory

Will


Stellar mass functions, star formation rate

Accurate parameter measurement can be used via population synthesis models to obtain, using ground-

based observations,Neutron star mass functionStellar mass functionsStar formation rate

One can identify the seeds of galaxy formation

(an open problem in cosmology) and mass-function of black hole seeds

with LISA observations of massive black hole

binaries


Testing the No-Hair TheoremRyan


Gravitational Capture and Testing Uniqueness of Black Hole Spacetimes

Ryan; Finn and Thorne

Glampedakis and Babak


Concordant Cosmological Model

The early universe went through a hot initial phaseHubble expansion, cosmic microwave background, nucleosynthesis,

Most of the universe is darkGalaxy rotation curves, gravitational lensing, cluster dispersion velocities, …

The universe has undergone an accelerated expansionMeasurement of luminosity distance Vs red-shift relation using type-Ia

supernovae as standard candlesMany steps involved in setting up the cosmic distance ladder which is necessary to calibrate standard candles

Current paradigm needs independent verifications and cross-checksGravitational wave astronomy can provide a calibration of the distance scale without the need for multiple stepsBlack hole binaries are ideal standard sirens


How can we measure cosmological parameters?

Luminosity distance Vs. red shift has cosmological parameters H0

, ΩM

, Ωb

, ΩΛ

, w, etc.

Einstein Telescope will detect 1000’s of compact binary mergers for which the source can be identified (e.g. GRB) and red-shift measured.A fit to such observations can determine the cosmological parameters to better than a few percent.

∫ +Λ +Ω++Ω

+= 2/1)1(33

0 ])1()1([)1(

wM

Lzz

dzH

zcD


Solving the Enigma of Dark Energy

Although binary black holes are standard sirens, LISA’s angular resolution might not be good enough to locate the

host galaxy and hence might not be possible to measure red-shiftWeak gravitational lensing

could limit the LISA’s

ability to

measure the dark energy equation of state parameter w

Higher Harmonics will enable better point of sourcesShould measure, masses, luminosity distance and sky position more accurately

LISA should be able to measure w to within a few percent

Hughes and Holz

Arun Et Al


Spectrum of the signal

Arun et al (2007a)


0 1000 20000

1

2x 10

−3

SNR−6 −4 −20

0.5

1

log10 ΔΩN

/ srad−5 0 50

0.5

1

log10 ΔΩL / srad

−3 −2 −1 0 10

1

2

log10 Δ DL / D

L

−2 −1 00

1

2

log10 Δβ−1.5 −1 −0.5 0 0.5

0

1

2

log10 Δσ

−0.5 0 0.5 1 1.50

0.5

1

1.5

log10 Δ tc / sec

−5 −4 −30

1

2

log10 Δ cm / cm−5 −4 −3 −2 −1

0

1

2

log10 Δ μ / μ

(0.1, 0.1) 106

M Trias and Sintes


0 500 10000

2

4x 10

−3

SNR−5 −4 −3 −2 −1

0

0.5

1

log10 ΔΩN

/ srad−5 0 50

0.5

1

log10 ΔΩL / srad

−2 0 20

0.5

1

1.5

log10 Δ DL / D

L

−1.5 −1 −0.5 0 0.50

1

2

3

log10 Δβ−1.5 −1 −0.5 0 0.50

1

2

3

log10 Δσ

1 20

1

2

3

log10 Δ tc / sec

−4.5 −4 −3.5 −3 −2.50

1

2

log10 Δ cm / cm−3 −2 −1 00

1

2

log10 Δ μ / μ

(0.1, 1) 106

M Trias and Sintes


0 100 2000

0.005

0.01

0.015

SNR−4 −3 −2 −10

0.5

1

log10 ΔΩN

/ srad−3 −2 −1 0 10

1

2

3

log10 ΔΩL / srad

−2 −1 00

1

2

3

log10 Δ DL / D

L

−1 0 1 20

1

2

log10 Δβ0 1 2

0

2

4

log10 Δσ

3 4 50

1

2

3

log10 Δ tc / sec

−3 −2 −10

1

2

3

log10 Δ cm / cm−2 −1 0 10

1

2

log10 Δ μ / μ

(0.1, 10) 106

M Trias and Sintes


Fractional error in w, the parameter characterizing the dark energy equation of state

(105, 106) M

∆w/|w| 0.050 0.033 0.0096 0.011 0.0062 0.014 0.025

(106, 107) M

∆w/|w| 0.13 0.068 0.016 0.029 0.010 0.025 0.073

Arun et al 2008

Measuring the Dark Energy with LISA


What can gravitational waves reveal about the Universe?

Was Einstein right?Is the nature of gravitational radiation

as predicted by Einstein?Are black holes hairless and are there naked singularities?

Unsolved problems in astrophysicsWhat is the origin of gamma ray bursts?What is the structure of neutron stars

and other compact objects?

CosmologyWhat is dark energy?How did massive

black holes at galactic nuclei

form?

Fundamental questionsWhat were the physical conditions

at the big bang?Are there really ten spatial dimensions?

�Gravity’s Standard SirensWhat this talk is aboutWhat are Gravitational Waves? Gravitational Wave ObservablesComparison of Gravitational Waves with Electromagnetic WavesHulse-Taylor Binary: A persistent source of Gravitational WavesAccumulated orbital phase shift in PSR 1913+16Tidal Gravitational ForcesTidal Action of Gravitational WavesInterferometric gravitational-wave detectors Gravitational Waves DetectorsSlide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16LIGO now at design sensitivityS5 SensitivityFuture ImprovementsEinstein TelescopeSlide Number 21Expected Future SensitivitiesSlide Number 23Laser Interferometer Space AntennaSlide Number 25Slide Number 26LISA’s SensitivityScience from Standard SirensBurst SourcesContinuous Wave SourcesStochastic BackgroundsCompact Binary MergersWhy are compact binaries standard sirens?Compact binaries are standard sirensWhat do we know about the waveforms from compact binaries?Compact Binary WaveformsDo compact binaries exist in nature?J0737-3039: Fastest binary pulsarHow often do we expect to detect compact binaries?Expected Annual Coalescence RatesCompact binaries in LIGO S5 �(5th science run)Do supermassive black hole binaries exist?Sagittarius A: A Galactic SMBHSuper-massive black hole mergersSMBH binary in NGC 6240Visibility of SMBH binary mergersWhat can we expect to learn by observing compact binaries?Capture of Small Black Holes by Super-massive Black HolesDo gravitational waves travel at the speed of lightCounting the Polarization StatesPolarization States in a �Scalar-Tensor TheoryStellar mass functions, star formation rateTesting the No-Hair TheoremGravitational Capture and Testing Uniqueness of Black Hole SpacetimesConcordant Cosmological ModelHow can we measure cosmological parameters?Solving the Enigma of Dark EnergySpectrum of the signal(0.1, 0.1) 106 M(0.1, 1) 106 M(0.1, 10) 106 MFractional error in w, the parameter characterizing the dark energy equation of stateWhat can gravitational waves reveal about the Universe?

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Gravity’s Standard Sirens - WebHome < Public · Gravity's Standard Sirens p2 What this talk is about Introduction to Gravitational Waves What are gravitational waves Gravitational