Detection of Gravitational Waves with Interferometers Giant detectors Precision measurement The search for the elusive waves Nergis Mavalvala (on behalf of the LIGO Scientific Collaboration)

Global network of detectors GEO VIRGO LIGO TAMA AIGO LIGO Detection confidence Source polarization Sky location 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?

Einstein’s gravity The Special Theory of Relativity (1905) said revolutionary 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 Transverse distortions of the space-time itself  ripples of space-time curvature Propagate at the speed of light Push on freely floating objects  stretch and squeeze the space transverse to direction of propagation Energy and momentum conservation require that the waves are quadrupolar  aspherical mass distribution

Astrophysics with GWs vs. E&M Very different information, mostly mutually exclusive Difficult to predict GW sources based on EM observations E&M GW Accelerating charge Accelerating aspherical mass Wavelength small compared to sources  images Wavelength large compared to sources  no spatial resolution Absorbed, scattered, dispersed by matter Very small interaction; matter is transparent 10 MHz and up 10 kHz and down

Astrophysical sources of GWs Periodic sources Pulsars  Spinning neutron stars Low mass Xray binaries Coalescing compact binaries Classes of objects: NS-NS, NS-BH, BH-BH Physics regimes: Inspiral, merger, ringdown Burst events Supernovae with asymmetric collapse GWs neutrinos photons now Stochastic background Primordial Big Bang (t = 10-43 sec) Continuum of sources The Unexpected

Astrophysical sources of GWs Periodic sources Pulsars  Spinning neutron stars Low mass Xray binaries Coalescing compact binaries Classes of objects: NS-NS, NS-BH, BH-BH Physics regimes: Inspiral, merger, ringdown Burst events Supernovae with asymmetric collapse GWs neutrinos photons now Stochastic background Primordial Big Bang (t = 10-43 sec) Continuum of sources The Unexpected

Pulsar born from a supernova PULSAR IS BORN: A supernova is associated with the death of a star about eight times as massive as the Sun or more. When such stars deplete their nuclear fuel, they no longer have the energy (in the form of radiation pressure outward) to support their mass. Their cores implode, forming either a neutron star (pulsar) or if there is enough mass, a black hole. The surface layers of the star blast outward, forming the colorful patterns typical of supernova remnants. ACCRETION SPINS UP THE PULSAR: When a pulsar is created in a supernova explosion, it is born spinning, but slows down over millions of years. Yet if the pulsar -- a dense star with strong gravitational attraction -- is in a binary system, then it can pull in, or accrete, material from its companion star. This influx of material can eventually spin up the pulsar to the millisecond range, rotating hundreds of revolutions per second. GWs LIMIT ACCRETION INDUCED SPIN UP: As the pulsar picks up speed through accretion, it becomes distorted from a perfect sphere due to subtle changes in the crust, depicted here by an equatorial bulge. Such slight distortion is enough to produce gravitational waves. Material flowing onto the pulsar surface from its companion star tends to quicken the spin, but loss of energy released as gravitational radiation tends to slow the spin due to the principle of conservation of energy. This competition may reach an equilibrium, setting a natural speed limit for millisecond pulsars beyond which they cannot be spun up. Courtesy of NASA (D. Berry)

Astrophysical sources of GWs Periodic sources Pulsars  Spinning neutron stars Low mass Xray binaries Coalescing compact binaries Classes of objects: NS-NS, NS-BH, BH-BH Physics regimes: Inspiral, merger, ringdown Burst events Supernovae with asymmetric collapse GWs neutrinos photons now Stochastic background Primordial Big Bang (t = 10-43 sec) Continuum of sources The Unexpected

Millisecond pulsar accretion As the pulsar picks up speed through accretion, it becomes distorted from a perfect sphere due to subtle changes in the crust, depicted here by an equatorial bulge. Such slight distortion is enough to produce gravitational waves. Material flowing onto the pulsar surface from its companion star tends to quicken the spin, but loss of energy released as gravitational radiation tends to slow the spin due to the principle of conservation of energy. This competition may reach an equilibrium, setting a natural speed limit for millisecond pulsars beyond which they cannot be spun up. Courtesy of NASA (D. Berry)

Astrophysical sources of GWs Periodic sources Pulsars  Spinning neutron stars Low mass Xray binaries Coalescing compact binaries Classes of objects: NS-NS, NS-BH, BH-BH Physics regimes: Inspiral, merger, ringdown Burst events Supernovae with asymmetric collapse GWs neutrinos photons now Stochastic background Primordial Big Bang (t = 10-43 sec) Continuum of sources The Unexpected

Neutron Stars spiraling toward each other This is a simulation of two inspiralling neutron stars using the Newtonian high resolution shock capturing code.  The green/blue portion is the density and the red/orange portion is the volumetric isolevels of the internal energy. Courtesy of WUStL GR group

Gravitational waves -- the Evidence Neutron Binary System – Hulse & Taylor PSR 1913 + 16 -- Timing of pulsars 17 / sec · ~ 8 hr · NS rotates on its axis 17 times/sec  pulse period is 59 msec. Reaches periastron (minimum separation of binary pair) every 7.75 hours. Systematic variation in arrival time of pulses. Variation in arrival time had a 7.75 hour period  binary orbit with another star. Pulsar clock slowed when traveling fastest and in strongest part of grav field (periastron). Figure shows decrease in orbital period of 76 usec/year. Shift in periastron due to decay of orbit. Neutron Binary System separated by 106 miles m1 = 1.4m; m2 = 1.36m; e = 0.617 Prediction from general relativity spiral in by 3 mm/orbit rate of change orbital period

Strength of GWs: e.g. Neutron Star Binary Gravitational wave amplitude (strain) For a binary neutron star pair M r 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

Effect of a GW on matter

Measurement and the real world How to measure the gravitational-wave? Measure the displacements of the mirrors of the interferometer by measuring the phase shifts of the light What makes it hard? GW amplitude is small External forces also push the mirrors around Laser light has fluctuations in its phase and amplitude

GW detector at a glance L ~ 4 km For h ~ 10–21 Seismic motion -- DL ~ 10-18 m Seismic motion -- ground motion due to natural and anthropogenic sources Thermal noise -- vibrations due to finite temperature Shot noise -- quantum fluctuations in the number of photons detected

LIGO: Laser Interferometer Gravitational-wave Observatory 3 k m ( ± 1 s ) WA 4 km 2 km 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 is a few mm at low frequencies Passive and active seismic isolation Amplify mechanical resonances Get isolation above a few 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: Low mechanical loss (high Quality factor) Suspension  no bends or ‘kinks’ in pendulum wire Test mass  no material defects in fused silica Z(f) is mechanical impedance (loss) FRICTION

Limiting Noise Sources Optical Noise Shot Noise Uncertainty in number of photons detected Higher circulating power Pbs a low optical losses Frequency dependence a light (GW signal) storage time in the interferometer Radiation Pressure Noise Photons impart momentum to cavity mirrors Fluctuations in the number of photons Lower input power, Pbs Frequency dependence a response of mass to forces 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  Optimal input power depends on frequency

Gravitational-wave searches

Reaching LIGO’s Science Goals Interferometer commissioning Intersperse commissioning and data taking consistent with obtaining one year of integrated data at h = 10-21 by end of 2006 Science runs and astrophysical searches Science data collection and intense data mining interleaved with commissioning S1 Aug 2002 – Sep 2002 duration: 2 weeks S2 Feb 2003 – Apr 2003 duration: 8 weeks S3 Oct 2003 – Jan 2004 duration: 10 weeks S4 Feb 2005 – Mar 2005 duration: 4 weeks S5 Nov 2005 – ... duration: 1 yr integrated Advanced LIGO

Science runs and sensitivity 1st Science Run Sept 02 (17 days) S2 2nd Science Run Feb – Apr 03 (59 days) S3 3rd Science Run Nov 03 – Jan 04 (70 days) Strain (sqrt[Hz]-1) LIGO Target Sensitivity S5 5th Science Run Nov 05 onward (1 year integrated) S4 4th Science Run Feb – Mar 05 (30 days) Frequency (Hz)

Science Run 5 (S5) begins Schedule Started in November, 2005 Get 1 year of data at design sensitivity Small enhancements over next 3 years Typical sensitivity (in terms of inspiral distance) H1 10 to 12 Mpc (33 to 39 million light years) H2 5 Mpc (16 million light years) L1 8 to 10 Mpc (26 to 33 million light years) Sample duty cycle (12/13/05 to 12/26/05) 68% (L1), 83% (H1), 88% (H2) individual 58% triple coincidence 1 light year = 9.5e12 km 1 pc = 30.8e12 km 1 Mpc = 3.26e6 l.y.

Advanced LIGO

Why a better detector? Astrophysics Factor 10 better amplitude sensitivity (Reach)3 = rate Factor 4 lower frequency bound Hope for NSF funding in FY08 Infrastructure of initial LIGO but replace many detector components with new designs Expect to be observing 1000x more galaxies by 2013 NS Binaries Initial LIGO: ~15 Mpc Adv LIGO: ~300 Mpc BH Binaries Initial LIGO: 10 Mo, 100 Mpc Adv LIGO : 50 Mo, z=2 Stochastic background Initial LIGO: ~3e-6 Adv LIGO ~3e-9

A Quantum Limited Interferometer LIGO I LIGO II Seismic Suspension thermal Test mass thermal Quantum

How will we get there? Seismic noise Thermal noise Optical noise Active isolation system Mirrors suspended as fourth (!!) stage of quadruple pendulums Thermal noise Suspension  fused quartz; ribbons Test mass  higher mechanical Q material, e.g. sapphire; more massive (40 kg) Optical noise Input laser power  increase to ~200 W Optimize interferometer response  signal recycling

Signal-recycled Interferometer ℓ Cavity forms compound output coupler with complex reflectivity. Peak response tuned by changing position of SRM 800 kW 125 W Reflects GW photons back into interferometer to accrue more phase Signal Recycling signal

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

Laser Interferometer Space Antenna LISA Laser Interferometer Space Antenna

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

LISA and LIGO

Astrophysical searches from early science data runs completed In closing... Astrophysical searches from early science data runs completed The most sensitive search yet (S5) begun with plan to get 1 year of data at initial LIGO sensitivity Advanced LIGO approved by the NSB Construction funding expected (hoped?) to begin in FY2008 Joint searches with partner observatories in Europe and Japan

Ultimate success… New Instruments, New Field, the Unexpected…

The End