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) LANL January 2006

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

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

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.

New rate predictions from SHBs? 4 Short Hard gamma ray Bursts since May 2005 Detected by Swift and HETE-2, with rapid follow-up using Hubble, Chandra, and look-back at BATSE Find that SHB progenitors are too old (>5 Gyr) to be supernova explosions (cause of long GRBs) Remaining candidates for progenitors of SHBs: old double neutron star (DNS) or neutron star-black hole (NS-BH) coalescences Predicted rates for Initial LIGO (S5) could be as high as But great uncertainty in rate estimates Progenitors are older (>5 Gyr) binaries Observed galactic DNS not a representative sample for SHB progenitors Merger rates of observed DNS dominated by short-lived (<100 Myr) systems while SHB progenitors >3 to 5 Gyr Possible that there is a large undetected population of older DNS in the galaxy Or NS-BH are progenitors of SHBs Nakar, Gal-Yam, Fox, astro-ph/0511254

Gravitational-wave searches Pulsars

Continuous Wave Sources Nearly-monochromatic continuous GW radiation, e.g. neutron stars with Spin precession at Excited modes of oscillation, e.g. r-modes at Non-axisymmetric distortion of shape at Signal frequency modulated by relative motion of detector and source Amplitude modulated by the motion of the antenna pattern of the detector Search for gravitational waves from a triaxial neutron star emitted at

Summary of pulsar searches S1 Setting upper limits on the strength of periodic gravitational waves from PSR J1939 2134 using GEO600 and LIGO data Phys. Rev. D 69 (2004) 082004 S2  Limits on GW emission from 28 selected pulsars using LIGO data Phys. Rev. Lett. 94 (2005) 181103 S1 Crab pulsar Time-domain analysis of 28 known pulsars with 2 frot > 50 Hz completed for S2 data Limit on strain amplitude h0 < 1e-24 to 1e-22 Stars  upper limits found using S2 data. Compare to... Circles  spindown upper limits assuming all measured rotational energy loss due to GWs and assuming moment of inertia Izz = 1e45 gm-cm^2 Results on h0 can be interpreted as upper limit on equatorial ellipticity Assume a rigid rotator with Izz ~ 1045 g cm2 and where all observed spindown is due to GW emission Distance to pulsar is known Limit on ellipticity epsilon < 1e-6 to 1e-1

Gravitational-wave Searches Binary Inspirals

Sources Search method Search for Inspirals Orbital-decaying neutron star binaries Black hole binaries MACHOs Search method Waveforms calculable Use optimal matched filtering  correlate detector output with template waveform Template inputs from population synthesis

Binary Neutron Star Inspiral (S2) Upper limit on binary neutron star coalescence rate Express the rate as a rate per Milky-Way Equivalent Galaxies (MWEG) Express as the distance to which radiation from a 1.4 Msun pair would be detectable with a SNR of 5 Important to look out further, so more galaxies can contribute to population of NS Theoretical prediction: R < 2 x 10-5 / yr /MWEG BNS inspiral paper for S2: Phys.Rev. D72 (2005) 082001 We use 373 hours ($\approx$ 15 days) of data from the second science run of the LIGO gravitational-wave detectors to search for signals from binary neutron star coalescences within a maximum distance of about 1.5 Mpc, a volume of space which includes the Andromeda Galaxy and other galaxies of the Local Group of galaxies. This analysis requires a signal to be found in data from detectors at the two LIGO sites, according to a set of coincidence criteria. The background (accidental coincidence rate) is determined from the data and is used to judge the significance of event candidates. No inspiral gravitational wave events were identified in our search. Using a population model which includes the Local Group, we establish an upper limit of less than 47 inspiral events per year per Milky Way equivalent galaxy with 90% confidence for non-spinning binary neutron star systems with component masses between 1 and 3 $M_\odot$. BBH search paper (gr-qc/0509129) abstract: We report on a search for gravitational waves from binary black hole inspirals in the data from the second science run of the LIGO interferometers. The search focused on binary systems with component masses between 3 and 20 solar masses. Optimally oriented binaries with distances up to 1 Mpc could be detected with efficiency of at least 90%. We found no events that could be identified as gravitational waves in the 385.6 hours of data that we searched. Phys.Rev. D72 (2005) 082001

Gravitational-wave searches Stochastic Background

Stochastic Background Waves now in the LIGO band were produced 10-22 sec after the Big Bang WMAP 2003

Stochastic Background of GWs Given an energy density spectrum Wgw(f ), there is a GW strain power spectrum For standard inflation (rc depends on present day Hubble constant) Search by cross-correlating output of two GW detectors: L1-H1, H1-H2, L1-ALLEGRO The closer the detectors, the lower the frequencies that can be searched (due to overlap reduction function) Omega_GW(f) = (1/rho_critical) d(rho_GW)/d(ln f) Ratio of energy density in GWs to total energy density needed to close the universe Rho_c depends on the present day Hubble expansion rate H0. H100 = H0/(100 km/sec/Mpc) ~ 0.72

Cross-correlated instrumental noise found LIGO results for 0h1002 LIGO run 0h1002 Comments Frequency Range Observation Time S1 PRD 69 (2004) < 23  4.6 (H2-L1) Cross-correlated instrumental noise found 40 to 314 Hz 64 hours (08/02 – 09/02) S2 < 0.018 (H1-L1) 50 to 300 Hz 387 hours (02/03 – 04/03) S3 PRL 95 (2005) < 8 x 10-4 a = 0  inflationary or CS models a = 1  rotating NS a = 2  pre-BB cosmology 70 to 160 Hz (H1-L1) 200 hrs (H1-L1) (10/03 – 01/04) S4 Analysis underway 447 hrs (H1-L1) 510 hrs (H1-H2) (02/05 – 03/05) Initial LIGO (1 yr) 0h1002 < 2 x 10-6 Advanced LIGO (1 yr) 0h1002 < 7 x 10-10 For S2: the positive error is larger in magnitude than the negative error owing to a bias we found in the SW and HW injection pt. Est, that lowered its value. This was later found to be caused by the fact that we were using the PSD of the same interval on which the CC statistic was being computed -> so we graduated to doing sliding PSDs. For S3: ====== Phys.Rev.Lett. 95 (2005) 221101 The Laser Interferometer Gravitational Wave Observatory (LIGO) has performed a third science run with much improved sensitivities of all three interferometers. We present an analysis of approximately 200 hours of data acquired during this run, used to search for a stochastic background of gravitational radiation. We place upper bounds on the energy density stored as gravitational radiation for three different spectral power laws. For the flat spectrum, our limit of Omega_0<8.4e-4 in the 69-156 Hz band is ~10^5 times lower than the previous result in this frequency range.

Limits on Wgw from astrophysical observations LIGO S2 data LIGO S3 data , at design sensitivity Accuracy of big-bang nucleosynthesis model constrains the energy density of the universe at the time of nucleosynthesis  total energy in GWs is constrained integral_f<1e-8 d(ln f) Omega_GW Pulsar timing  Stochastic GWs would produce fluctuations in the regularity of msec pulsar signals; residual normalized timing errors are ~10e-14 over ~10 yrs observation Stochastic GWs would produce CMBR temperature fluctuations (Sachs Wolfe effect), Measured Delta_T constrains GW amplitude at very low frequencies H0 = 72 km/s/Mpc

Gravitational-wave Searches Transient or “burst’ events

Brief transients: unmodelled waveforms Time-frequency search methods GWs from burst sources Brief transients: unmodelled waveforms Time-frequency search methods Upper limit on rate, and rate as a function of amplitude for specific shapes Triggered searches Use external triggers (GRBs, supernovae) Untriggered searches compact binary system coalescences… (SN1987A Animation: NASA/CXC/D.Berry)

Gamma Ray Burst: GRB030329 Targeted search  NO detection A supernova at z ~ 0.17 ~ 800 Mpc Targeted search  NO detection H1 and H2 operational during S2 Integration time (logarithmic steps) Segment time (from HETE) The corrgram images show time vs. integration length (log scale). Color scale refers to degree of excess correlation, red being most correlated. Both false alarm rate (fixes threshold event strength) and efficiency determined from injection of simulated waveforms in both data streams. Waveforms used include sine Gaussians, as well as example astrophysically motivated ones, such as Dimmelmeier-Mueller ones. Upper left is a sine-Gaussian injection (250 Hz, Q~8.9) well above preset detection threshold, upper right is well below detection threshold. Lower images are both for different epochs of noise. The color scales are different on all quadrants. Event strength threshold for detection is 2, which gives false alarm rate of 5e-4 Hz with a 90% CL (determined from background data). Circles are SIGNAL REGION – duration of GRB. Yielded only events well below the predetermined threshold event strength. Diamonds are expected distribution based on BACKGROUND. Squares are expected distribution from TIME-SHIFTs – unphysical time shifts between H1 and H2. 11% error from calibration uncertainties. Fixed false alarm rate allows upper limits to be set directly from simulation results. hrss  6 x 10-21 Hz-1/2 (waveform-dependent) Phys. Rev. D 72 (2005) 042002

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

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