Gravitational-wave Detection with Interferometers LIGO, LISA, and the like Nergis Mavalvala IAP, 2003

Global network of gravitational wave interferometers GEO VIRGO LIGO TAMA AIGO LIGO LISA

Newton’s gravity Universal gravitation Three laws of motion and law of gravitation (centripetal force) eccentric orbits of comets cause of tides and variations precession of the earth’s axis perturbation of motion of the moon by gravity of the sun Solved most problems of astronomy and terrestrial physics known then Unified the work of Galileo, Copernicus and Kepler Worried about instantaneous action at a distance (Aristotle) How could objects influence other distant objects? Fg

Clocks tick more slowly Einstein’s gravity The Special Theory of Relativity (1905) said outrageous things about space and time Relative to an observer traveling near the speed of light space and time are altered The General Theory of Relativity and theory of Gravity (1916) No absolute motion  only relative motion Space and time not separate  four dimensional space-time Gravity is not a force acting at a distance  warpage of space-time Gravitational radiation (waves) Distances stretched and Clocks tick more slowly

Gravitational Waves GR predicts transverse space-time distortions propagating at the speed of light In TT gauge and weak field approximation, Einstein field equations  wave equation Conservation laws Conservation of energy  no monopole radiation Conservation of momentum  no dipole radiation Lowest moment of field  quadrupole (spin 2) Radiated by aspherical astrophysical objects Radiated by “dark” mass distributions  black holes, dark matter

Astrophysics with GWs vs. E&M Very different information, mostly mutually exclusive Difficult to predict GW sources based on EM observations E&M (photons) GW Space as medium for field Spacetime itself ripples Accelerating charge Accelerating aspherical mass Absorbed, scattered, dispersed by matter Very small interaction; matter is transparent 10 MHz and up 10 kHz and down Light = not dark (but >95% of Universe is dark) Radiated by dark mass distributions  black holes, dark matter

Gravitational waves measured? Emission of gravitational radiation from PSR1913+16 due to loss of orbital energy period sped up 14 sec from 1975-94 measured to ~50 msec accuracy deviation grows quadratically with time Nobel prize in 1997  Taylor and Hulse

Astrophysical sources of GWs Coalescing compact binaries Classes of objects: NS-NS, NS-BH, BH-BH Physics regimes: Inspiral, merger, ringdown Other periodic sources Spinning neutron stars  numerically hard problem Burst events Supernovae  asymmetric collapse Stochastic background Primordial Big Bang (t = 10-43 sec) Continuum of sources The Unexpected Coalescing compact binaries  chirp sources NS-NS  far away; long periods; final inspiral gives GW chirp NS-BH  tidal disruption of NS by BH; merger  GRB triggers Inspiral  accurate predition with PPN proportional to (v/c)^11 Merger  nonlinear dynamics of highly curved spacetime Ringdown  ringdown of modes of coalesced object Periodic sources Spinning NS  axisymmetry unknown Galactic pulsars in SN remnant gases  non-axisymmetry unknown LMXBs  mass accretion from companion Is accretion spin-up balanced by GW spin-down? Issues  axisymmetric distortion from radiation reaction force Supernovae Collapse  Dynamics not understood. If instability makes star into tumblong bar, then GWs Core convection  detect via correlations with neutrinos GWs neutrinos photons now

Strength of GWs: e.g. Neutron Star Binary Gravitational wave amplitude (strain) For a binary neutron star pair M R Quadrupole formalism is accurate to order of magnitude for most sources. Involves computing wave generation and radiation reaction from Einstein eqn. Weak internal gravity and stresses  nearly Newtonian source Kepler’s third law of planetary motion: period^2 = 4*pi^2*radius^3/(G*Msun) Distances  1 parsec = 3.26 l.y. = 3e18 cm r ~ 10^23 m ~ 10 Mpc (center of Virgo cluster) Distance of earth to center of galaxy ~ 30000 l.y. ~ 10 kpc h ~10-21 r

GWs meet Interferometers Laser interferometer DL = h L (h ~ 10-21) Earth diameter 1011 107 104 100 10-2 10-10 10-5 10-18 10-15 Earth-Sun distance USA E-W Short person Pea Width of hair Size of atom Size of nucleus LIGO measurement m Delta_L = h * L 10^-16 m = 10^-21 * 10^5 m

Power-recycled Interferometer Optical resonance: requires test masses to be held in position to 10-10-10-13 meter end test mass Light bounces back and forth along arms ~100 times  30 kW Light is “recycled” ~50 times  300 W input test mass Laser + optical field conditioning signal 6W single mode

The Laser Interferometer Gravitational-wave Observatory 2 km 4 km 3 k m ( ± 1 s ) WA LA 4 km

Initial LIGO Sensitivity Goal Strain sensitivity < 3x10-23 1/Hz1/2 at 200 Hz Displacement Noise Seismic motion Thermal Noise Radiation Pressure Sensing Noise Photon Shot Noise Residual Gas Facilities limits much lower

Limiting Noise Sources: Seismic Noise Motion of the earth few mm rms at low frequencies Passive seismic isolation ‘stacks’ amplify at mechanical resonances but get f-2 isolation per stage above 10 Hz

Limiting Noise Sources: Thermal Noise Suspended mirror in equilibrium with 293 K heat bath a kBT of energy per mode Fluctuation-dissipation theorem: Dissipative system will experience thermally driven fluctuations of its mechanical modes: Z(f) is impedance (loss) Low mechanical loss (high Quality factor) Suspension  no bends or ‘kinks’ in pendulum wire Test mass  no material defects in fused silica FRICTION

Limiting Noise Sources: Quantum Noise Shot Noise Uncertainty in number of photons detected a Higher input power Pbs a need low optical losses (Tunable) interferometer response  Tifo depends on light storage time of GW signal in the interferometer Radiation Pressure Noise Photons impart momentum to cavity mirrors Fluctuations in the number of photons a Lower input power, Pbs  Optimal input power for a chosen (fixed) Tifo Shot noise: Laser light is Poisson distributed  sigma_N = sqrt(N) dE dt >= hbar  d(N hbar omega) >= hbar  dN dphi >= 1 Radiation Pressure noise: Pressure fluctuations are anti-correlated between cavities

Displacement Sensitivity (Science Run 1, Sept. 2002)

The next-generation detector Advanced LIGO (aka LIGO II) Now being designed by the LIGO Scientific Collaboration Goal: Quantum-noise-limited interferometer Factor of ten increase in sensitivity Factor of 1000 in event rate. One day > entire 2-year initial data run Schedule: Begin installation: 2007 Begin data run: 2009

A Quantum Limited Interferometer Facility limits Gravity gradients Residual gas (scattered light) Advanced LIGO Seismic noise 4010 Hz Thermal noise 1/15 Optical noise 1/10 Beyond Adv LIGO Thermal noise: cooling of test masses Quantum noise: quantum non-demolition LIGO I LIGO II Seismic Suspension thermal Test mass thermal Quantum

Optimizing optical response: Signal Tuning Power Recycling Signal r(l).e i f (l) l Cavity forms compound output coupler with complex reflectivity. Peak response tuned by changing position of SRM Reflects GW photons back into interferometer to accrue more phase

Advance LIGO Sensitivity: Improved and Tunable Thorne… SQL  Heisenberg microscope analog If photon measures TM’s position too well, it’s own angular momentum will become uncertain.

Laser Interferometer Space Antenna (LISA) Three spacecraft triangular formation separated by 5 million km Constant solar illumination Formation trails Earth by 20° Approx. constant arm-lengths 1 AU = 1.5x108 km

LISA and LIGO

Science from gravitational wave detectors? Test of general relativity Waves  direct evidence for time-dependent metric Black hole signatures  test of strong field gravity Polarization of the waves  spin of graviton Propagation velocity  mass of graviton Different view of the Universe Predicted sources: compact binaries, SN, spinning NS Inner dynamics of processes hidden from EM astronomy Dynamics of neutron stars  large scale nuclear matter The earliest moments of the Big Bang  Planck epoch Precision measurements at and below the quantum limit set by Heisenberg on photons

New Instruments, New Field, the Unexpected…

Major research activities at the MIT LIGO Laboratory Initial LIGO (now!) Instrument science  lasers and optics, interferometry, optical metrology, optical resonant systems, photonics, control systems, low-noise electronics, vibration isolation systems, thermally induced dissipation, thermally adaptive optics Data analysis and astrophysical searches  signals of known and unknown signatures buried in noise, astrophysical source signatures, computing challenges Advance LIGO (beyond 2006) Instrument development  design and prototyping of mechanical and optical subsystems (R&D and implementation) Other things we work on LISA (advisory role at present) Quantum measurement  precision measurements at or below the quantum limit)