Gravity’s Standard Sirens

B.S. Sathyaprakash School of Physics and Astronomy What this talk is about

Introduction to Gravitational Waves What are gravitational waves Gravitational wave detectors: Current status and future plans Science from Standard Sirens Speed of gravitational waves and mass of the graviton Seeds of galaxy formation, star formation rate Mass function of neutron stars and star formation rate Black hole “no-hair” theorem Cosmological parameters with standard sirens Black hole spectroscopy

Gravity's Standard Sirens p2 What are Gravitational Waves?

In Newton’s law of gravity the gravitational potential is given by Poisson’s equation:

V2Φ(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| << 1, Einstein’s equations reduce to wave equations:

hαβ = 8πGTαβ . Gravitational waves are caused by asymmetric motion and non-stationary fields According to Einstein’s general relativity gravity is not a force but a warping of spacetime: Gravitational waves are ripples in the curvature of spacetime that carry information about changing gravitational fields

Gravity's Standard Sirens p3 Gravitational Wave Observables

Luminosity L = (Asymm.) v10 Frequency f = √ρ Dynamical frequency in the Luminosity is a strong function of velocity: A black hole binary system: twice the orb. freq. source brightens up a million Binary chirp rate times during merger Many sources chirp during Amplitude observation: chirp rate depends only chirp mass h = (Asymm.) (M/R) (M/r) Chirping sources are The amplitude gives strain standard candles caused in space as the wave Polarisation propagates h = dL/L In Einstein’s theory two For binaries the amplitude polarisations - plus and cross depends only on

chirpmass/distance

Gravity's Standard Sirens p4 Comparison of Gravitational Waves with Electromagnetic Waves EM waves are transverse waves, GW waves are also transverse with two polarisations, travel at the waves, with two polarisations, travel speed of light at the speed of light Production: electronic transitions in Production: coherent motion stellar atoms and accelerated charges – and super-massive black holes, what we observe comes from supernovae, big bang, … physics of small things Often, a single coherent wave, but Incoherent superposition of many, many waves stochastic background expected Detectors sensitive to the intensity GW detectors are sensitive to the of the radiation amplitude of the radiation Normally EM waves cannot be Normally, waves followed in phase, followed in phase great increase in signal visibility Intensity falls off as inverse square Amplitude falls off as inverse of the of the distance to source distance to source Directional telescopes Sensitive to wide areas over the sky

Gravity's Standard Sirens p5 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 period Observed decrease in period - about 10 micro seconds per year - is in agreement with Einstein’s theory to fraction of a percent

Gravity's Standard Sirens p6 Accumulated orbital phase shift in PSR 1913+16

Taylor and Weisberg, 2000, Will Living ReviewTaylor and Weisberg, Eventually the two stars will coalesce, but that will take another 100 million years Gravity's Standard Sirens p7 Tidal Gravitational Forces

Gravitational effect of a distant source can only be felt through its tidal forces Gravitational waves are traveling, time- dependent tidal forces . Tidal forces scale with size, typically produce elliptical deformations.

Gravity's Standard Sirens p8 Tidal Action of Gravitational Waves

Plus polarization Cross polarization

Gravity's Standard Sirens p9 Interferometric gravitational-wave detectors

τ τ 3τ t = 0 t = t = t = 4 2 4 δl For Typical Astronomical sources l h 2δ l δ l = l h ≤= 10 − 22 2 l

Gravity's Standard Sirens p10 Gravitational Waves Detectors

Gravity's Standard Sirens p11 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/Sqrt(Hz)

Frequency (Hz) G070221-00-Z S5 Sensitivity

G070221-00-Z Future Improvements

Enhanced Detectors (2009-11) 2 x increase in sensitivity 8 x increase in rate Advanced Detectors, LIGO and Virgo (2014- …) 12 x increase in sensitivity Over 1000 x increase in rate 3G Detectors: Einstein Telescope (2018+) 10 x increase in sensitivity Over 1000 x increase in rate

Gravity's Standard Sirens p19 Einstein Telescope

ET 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 observatory Sensitivity of the apparatus~10 better than advanced detectors

Gravity's Standard Sirens p20 Gravity's Standard Sirens p21 Expected Future Sensitivities

10-19 (a) 3rd Generation Virgo+ 2008 LIGO 2005 (b)AURIGA LCGT 2005 10-20 (c) advanced LIGO Virgo Design (d) advanced Virgo (e) LIGO -21 (f) Virgo 10 (g) GEO600 (g) (f) GEO-HF 10-22 2009 (e) -23 h(f) [1/sqrt(Hz)] h(f) 10 DUAL Mo (a) (Quantum Limit) (d) Ad LIGO/Virgo NB -24 Advanced(b) LIGO/Virgo(c) (2014) 10

Credit: M.Punturo Einstein GW Telescope 10-25 1 10 100 1000 10000 Frequency [Hz]

Gravity's Standard Sirens p22 Laser Interferometer Space Antenna

Gravity's Standard Sirens p23 Laser Interferometer Space Antenna

ESA-NASA collaboration Intended for launch in 2017 3 space craft, 5 million km apart, in heliocentric orbit Test masses are passive mirrors shielded from solar radiation Crafts orbit out of the ecliptic always retaining their formation

Gravity's Standard Sirens p24 Gravity's Standard Sirens p25 Gravity's Standard Sirens p26 LISA’s Sensitivity

6 M  6 10 10 x 5 M  5 10 10 x

10-5 10-4 10-3 10-2 10-1 1 Gravity's Standard Sirens Hz p27 Science from Standard Sirens Burst Sources

Gravitational wave bursts Black hole collisions Supernovae gamma-ray bursts (GRBs) Short-hard GRBs could be the result of merger of a neutron star with another NS or a BH Long-hard GRBs could be triggered by supernovae

Gravity's Standard Sirens p29 Continuous Wave Sources

Gravitational wave bursts Black hole collisions Supernovae gamma-ray bursts (GRBs)

Continuous waves Rapidly spinning neutron stars or other objects

Gravity's Standard Sirens p30 Stochastic Backgrounds

Gravitational wave bursts Black hole collisions Supernovae gamma-ray bursts Continuous waves Rapidly spinning neutron stars or other objects Stochastic background Primordial background Astrophysical background

Gravity's Standard Sirens p31 Compact Binary Mergers

Compact binary mergers Binary neutron stars Binary black holes Neutron star–black hole binaries

Loss of energy leads to steady inspiral whose waveform has been calculated to order v7 in post- Newtonian theory

Knowledge of the waveforms allows matched filtering

Gravity's Standard Sirens p32 Why are compact binaries standard sirens? Schutz 86 Compact binaries are standard sirens

Amplitude of gravitational waves depends on the combination of Chirp-mass/Distance: Chirp-mass=μ3/5M2/5 Gravitational 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 distance However, GW observations alone cannot determine the red-shift to a source Joint gravitational-wave and optical observations can facilitate a new cosmological tool

Gravity's Standard Sirens p34 What do we know about the waveforms from compact binaries? Compact Binary Waveforms Increasing Spin Amplitude

Time Gravity's Standard Sirens p36 Do compact binaries exist in nature? J0737-3039: Fastest binary pulsar Burgay et al Nature 2003 The fastest

Strongly relativistic, Pb =2.5 Hrs Mildly eccentric, e=0.088 Highly 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 century Orbit is shrinking by a few millimeters each year due to gravitational radiation reaction

Gravity's Standard Sirens p38 How often do we expect to detect compact binaries? Expected Annual Coalescence Rates

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

BNS NS-BH BBH Initial LIGO 0.015-0.15 0.004-0.13 0.01-1.7 (2002-06) Enhanced LIGO 0.15-1.5 0.04-1.4 0.11-18 x2 sensitivity (2009-10)

Advanced LIGO 20-200 5.7-190 16-2700 x12 sensitivity (2014+)

Gravity's Standard Sirens p40 Compact binaries in LIGO S5 (5th science run)

S5 data being analyzed Horizon distance (in Mpc) binary neutron star versus total mass (in M ) horizon distance  for binary black holes 145 Average over run

120 1 sigma variation 90

60

30 binary black hole horizon distance 0 Gravity's Standard Sirens Image: R. Powell 1 20 40 60 80 100p41 Do supermassive black hole binaries exist? Sagittarius A: A Galactic SMBH

Gravity's Standard Sirens p43 Super-massive black hole mergers

Gravity's Standard Sirens p44 SMBH binary in NGC 6240

NGC6240, Kamossa et al X-ray observations have revealed that the nucleus of NGC 6240 contains an SMBH binary that will coalesce within the Hubble time The high visibility of the signal means we can see SMBH binaries anywhere in the Universe We 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.

Gravity's Standard Sirens p45 Visibility of SMBH binary mergers

Gravity's Standard Sirens p46 Cutler and Vecchio What can we expect to learn by observing compact binaries? Capture of Small Black Holes by Super- massive Black Holes

Gravity's Standard Sirens p48 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

Gravity's Standard Sirens p49 Counting the Polarization States

Only two states in GR: h+ and hx

Plus polarization Cross polarization

Gravity's Standard Sirens p50 Polarization States in a Scalar-Tensor Theory

Will

Gravity's Standard Sirens p51 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 function Stellar mass functions Star 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

Gravity's Standard Sirens p52 Testing the No-Hair Theorem Ryan

Gravity's Standard Sirens p53 Gravitational Capture and Testing Uniqueness of Black Hole Spacetimes

Ryan; Finn and Thorne

Glampedakis and Babak

Gravity's Standard Sirens p54 Concordant Cosmological Model

The early universe went through a hot initial phase Hubble expansion, cosmic microwave background, nucleosynthesis, Most of the universe is dark Galaxy rotation curves, gravitational lensing, cluster dispersion velocities, … The universe has undergone an accelerated expansion Measurement of luminosity distance Vs red-shift relation using type-Ia supernovae as standard candles

Many steps involved in setting up the cosmic distance ladder which is necessary to calibrate standard candles Current paradigm needs independent verifications and cross-checks Gravitational wave astronomy can provide a calibration of the distance scale without the need for multiple steps Black hole binaries are ideal standard sirens

Gravity's Standard Sirens p55 How can we measure cosmological parameters?

Luminosity distance Vs. red shift has cosmological parameters H0, ΩM, Ωb, ΩΛ, w, etc.

+ zc )1( dz L D = 3 + w 2/1)1(3 H 0 ∫ M z Λ +Ω++Ω z ])1()1([

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.

Gravity's Standard Sirens p56 Solving the Enigma of Dark Energy Hughes and Holz 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-shift Weak gravitational lensing could limit the LISA’s ability to measure the dark energy equation of state parameter w Arun Et Al

Higher Harmonics will enable better point of sources Should measure, masses, luminosity distance and sky position more accurately LISA should be able to measure w to within a few percent

Gravity's Standard Sirens p57 Spectrum of the signal

Arun et al (2007a)

Gravity's Standard Sirens p58 −3 6 Trias and Sintes x 10 (0.1, 0.1) 10 M 2 1  1

1 0.5 0.5

0 0 0 0 1000 2000 −6 −4 −2 −5 0 5 log10 ΔΩ / srad log10 ΔΩ / srad SNR N L 2 2 2

1 1 1

0 0 0 −3 −2 −1 0 1 −2 −1 0 −1.5 −1 −0.5 0 0.5 log10 Δ D / D L L log10 Δβ log10 Δσ 1.5 2 2 1

1 1 0.5

0 0 0 −0.5 0 0.5 1 1.5 −5 −4 −3 −5 −4 −3 −2 −1 Gravity's Standardlog10 Sirens Δ t / sec c log10 Δ cm / cm log10 Δ μ / μ p59 −3 6 Trias and Sintes x 10 (0.1, 1) 10 M 4 1 1

2 0.5 0.5

0 0 0 0 500 1000 −5 −4 −3 −2 −1 −5 0 5 log10 ΔΩ / srad log10 ΔΩ / srad SNR N L 1.5 3 3

1 2 2

0.5 1 1

0 0 0 −2 0 2 −1.5 −1 −0.5 0 0.5 −1.5 −1 −0.5 0 0.5 log10 Δ D / D L L log10 Δβ log10 Δσ 3 2 2 2

1 1 1

0 0 0 1 2 −4.5 −4 −3.5 −3 −2.5 −3 −2 −1 0 Gravity's Standardlog10 Sirens Δ t / sec c log10 Δ cm / cm log10 Δ μ / μ p60 (0.1, 10) 106 M Trias and Sintes 0.015 3 1 0.01 2 0.5 0.005 1

0 0 0 0 100 200 −4 −3 −2 −1 −3 −2 −1 0 1 log10 ΔΩ / srad log10 ΔΩ / srad SNR N L 3 4 2 2 2 1 1

0 0 0 −2 −1 0 −1 0 1 2 0 1 2 log10 Δ D / D L L log10 Δβ log10 Δσ 3 3 2 2 2 1 1 1

0 0 0 3 4 5 −3 −2 −1 −2 −1 0 1 Gravity's Standardlog10 Sirens Δ t / sec c log10 Δ cm / cm log10 Δ μ / μ p61 Measuring the Dark Energy with LISA

Arun et al 2008

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

5 6 (10 , 10 ) M ∆w/|w| 0.050 0.033 0.0096 0.011 0.0062 0.014 0.025

6 7 (10 , 10 ) M

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

Gravity's Standard Sirens p62 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 astrophysics What is the origin of gamma ray bursts? What is the structure of neutron stars and other compact objects? Cosmology What is dark energy? How did massive black holes at galactic nuclei form? Fundamental questions What were the physical conditions at the big bang? Are there really ten spatial dimensions?

Gravity's Standard Sirens p63