Modern View of Gravitation Newtonian instantaneous action at a distance G µ = 8 µ # General Relativity information carried by gravitational radiation at the speed of light
Gravitational Waves GR predicts existence of propagating waves of spacetime curvature traveling at the speed of light Emitted by any (nonspherical) changing distribution of masses An important example Two orbiting objects Gravitational waves carry energy and angular momentum away from orbit causes orbit to decay
Electromagnetic Analogy Given a charge distribution, what is the electromagnetic power far away? P(l) = 2cF(l) ω c 2l+2 Q 2 lm, Q lm = where F(l) = (l+1)/{l[(2l+1)!!] 2 }, n!! = 1x3x5x7x The leading terms are P e dipole ~ ω 4 q 2 l 2 r l Y lm * (θ,φ)ρdv multi-pole expansion, P c 3 e quadrupole ~ P m dipole ~ ω 6 q 2 l 4 c 5 Gravitational interactions are mediated by gravitons of spin 2, so there is no dipole emission of gravitational waves. The quadrupole emission is, by analogy, given by P grav ~ ω 6 M 2 l 4 c 5
Binary Pulsar If the typical separation between two neutron stars is l, the mass of each of them is M, and they orbit around each other with angular frequency, the luminosity is L = 16Gω 6 M 2 l 4 5c 5 Since the total energy E tot ~ l -1 and the angular frequency ~ l -3/2 (for Keplerian motion), one expects the orbital period P ~ -1 ~ l 3/2 ~ E -3/2. Therefore, 1 P dp dt = 3 2 1 d E tot E tot dt = 3 2 L E tot = 24 5 ω 6 l 5 For PSR B1913+16, the measured rate of change in P is dp dt = ( 2.422 ± 0.006) 10 12 in agreement with dp dt GR = 2.40 10 12
Hulse-Taylor Pulsar 59ms pulsar in eccentric orbit around another neutron star (7.75 hour period) Can determine orbits accurately by timing pulsar Find that orbit is decaying; period is decreasing Fits prediction of GR perfectly GWs are carrying away orbital energy Agrees to <3% Only unambiguous detection of the effects of gravitational radiation PSR B1913+16 1993 Nobel Prize in Physics
Detecting Gravitatonal Waves Numerous experiments currently being built to detect gravitational waves All based on detecting characteristic changes in the separation of a several masses as a GW passes by Two polarizations Measure the strength of a gravitational wave via the strain h= x/x. Most modern attempts based on laser interferometry
Expected Signal Strength When gravitational waves of luminosity L and angular frequency from a source that is at a distance R from the detector, the strain h is roughly h 2 ~ GL c 3 ω 2 R h ~ GMl 2 ω 2 2 c 4 R The product Ml 2 2 is the second derivative of the quadrupole moment of the source and is equal to the kinetic energy E kin ~ Mv 2 associated with the source oscillations. In terms of orbital period, more rigoriously, we have h 10 22 M 2.8M 5/3 0.01s P 2/3 100Mpc R
Gravitational Wave Interferometers Precision laser beams in the interferometers will sense small motions of the mirrors that are caused by a gravitational wave. Ly M L=Laser M=Mass Mirror D=Detector S=Beam Splitter L S D Lx M Constructive: L=Lx-Ly=nλ Destructive: L=Lx-Ly=(n+1/2)λ n=0,1,2, Δa(t) a = c + h + (t) + c h (t)
From the Ground Laser Interferometer Gravitational-wave Observatory (LIGO)
Limitations of interferometors
International Endeavor GEO600 (British-German) Hannover, Germany TAMA (Japan) Mitaka LIGO (USA) Hanford, WA and Livingston, LA AIGO (Australia), Wallingup Plain, 85km north of Perth VIRGO (French-Italian) Cascina, Italy
From Space An interferometer in space: 5 million km baseline: VERY long!.makes for very low frequency detection band. A NASA-ESA joint project, looking for a successful take off by 2013.
Differences Test masses are freely floating within the spacecraft (not suspended with wires as in a ground-based interferometer) LISA doesn't use beam splitters: The two laser beams from the main spacecraft is transmitted to the other two spacecrafts, which act as the end mirrors Because of the large distances between the spacecraft, rather than reflecting the received beams back to the main spacecraft, the secondaries transmit new laser beams (in phase)
Detecting Gravitational Waves Gravitational Wave Astrophysical Source Detectors in space LISA Terrestrial detectors Virgo, LIGO, TAMA, GEO AIGO
Sensitivities
What to See? LIGO - detects high frequency GWs Final stages of merging neutron star binaries Final stages of stellar mass BHs merging with other stellar mass BHs or neutron stars (Possibly) core collapse supernovae, GRBs, LISA - detects lower frequency GWs Merging supermassive black holes Infall of a stellar-mass BH or neutron star into a supermassive black hole Galactic Binary star system (esp. binary white dwarfs)
Types of Signals Stochastic Background Compact binary inpiral - chirps Supernova/GRB - Bursts Pulsars - Periodic
Gravity Waves from Inflation Like all quantum fields, the gravitational field (the structure of spacetime) undergoes quantum fluctuations due to the Uncertainty Principle. For the most part, these are only appreciable on submicroscopic lengthscales (the gravitational field of the Earth does not fluctuate wildly, fortunately for us). Recall, that we defined the Planck length (~10-43 cm) as the scale over which these spacetime fluctuations are large. During inflation, however, these gravitational fluctuations are stretched from submicroscopic to astronomical scales (just as the fluctuations of the inflaton field itself). These long wavelength gravity fluctuations are gravitational waves.
Gravity Waves from Inflation Gravity waves from inflation are not expected to be seen by the coming generation of Laser interferometer gravity wave detectors, because they probe relatively short wavelength waves. Gravity waves from inflation do, however, produce a distinctive signature in the Cosmic Microwave Background anisotropy. Searching for this subtle effect (polarization) is another experimental challenge for the decade ahead.
Upper Limits
Inflationary GW s Summary of the times probed by the various gravitational wave experiments. Assuming initial primordial perturbation in matter density Wavelengths larger than horizon are frozen no communication between crest and trough Later, the mode enters horizon
BH-BH Merger The merger of two black holes is a violent process that emits very strong gravitational waves. Three stages Inspiral of the two black holes Merging of their event horizons Ringdown to a final relaxed black hole
Expected Waveform