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Black Holes and Gravitational Waves

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Black Holes and Gravitational Waves 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 Review 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 6 10 x10 M 5 5 10 x10 M Gravity's Standard Sirens 10 -5 10 -4 10 -3 Hz 10 -2 10 -1 1 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.
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