The search for those elusive gravitational waves LIGO-G060192-00-R The search for those elusive gravitational waves Recent results from interferometric detectors Nergis Mavalvala IAS, Oct. 2006 (on behalf of the LIGO Scientific Collaboration)

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

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 ) MIT WA 4 km 2 km Caltech 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

Gravitational-wave searches

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) underway 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 12 to 14 Mpc (33 to 39 million light years) H2 6 Mpc (16 million light years) L1 12 to 14 Mpc (26 to 33 million light years) Duty factor 60% (L1), 72% (H1), 79% (H2) individual 45% triple coincidence 1 light year = 9.5e12 km 1 pc = 30.8e12 km 1 Mpc = 3.26e6 l.y.

S5 Goal: one year of coincident data, at design sensitivity S5 Run Sensitivity S5 Goal: one year of coincident data, at design sensitivity

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

Known pulsar searches S1 Crab pulsar S1 Setting upper limits on the strength of periodic GW from PSR J1939 2134 using time domain and frequency domain techniques Phys. Rev. D 69 (2004) 082004 S2  Limits on GW emission from 28 known pulsars in the time domain 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

Analysis method Heterodyne time domain data using the known phase evolution of the pulsar to remove Doppler/spin-down effects Joint Bayesian parameter estimation of unknown pulsar parameters: GW amplitude h0, initial phase f0, polarisation angle y and inclination angle i, using data from all interferometers Produce probability distribution functions for unknown parameters and marginalise over angles to set 95% upper limit on h0 Set limits on the ellipticity of the pulsar and compare with limits from spin-down arguments  assuming all energy lost as the pulsar spins-down is dissipated via GWs R. Jones: University of Glasgow

S3 and S4 76 known radio pulsars S5 Method 32 isolated frequency (Hz) h0 S5 76 known radio pulsars 32 isolated 44 in binary systems 30 in globular clusters Method Accurate timing data coherently follow phases Coherently combine data from all detectors Method: * Accurate timing data, provided by Jodrell Bank Observatory and the ATNF, to coherently follow their phases over the run * Coherently combine the data from all detectors (including GEO600 for the two fastest pulsars)

S5 95% upper limits GW amplitude S5 Ellipticity Spindown (PSR J1603-7202) f = 134.8 Hz, r = 1.6kpc Ellipticity (PSR J2124-3358) f = 405.6 Hz, r = 0.25kpc Spindown 2.1 x above spindown limit for Crab pulsar f = 59.6 Hz, dist = 2.0 kpc S5 All values assume I = 10^38 kgm^2 and no error on distance.

Astrophysically interesting? Upper limits for most of these pulsars are generally well above those permitted by spin-down constraints and neutron star eqns of state Crab pulsar is nearing the spin-down upper limit Some others within < 100 x Provide the limits independent of the cluster dynamics for 29 globular cluster pulsars Apparent spin-ups due to accelerations within the cluster Cannot set spin-down limits Most stringent ellipticity limits (4.0x10-7) are starting to approach the range of neutron star structures for some NPE models (B. Owen, PRL, 2005 Maximum globular cluster frequency derivative seen ~ 4.6x10-13Hz/s

Light reading tonight... B. Abbott et al. (LIGO Scientific Collaboration): S1: Setting upper limits on the strength of periodic gravitational waves from PSR J1939 2134 using the first science data from the GEO 600 and LIGO detectors Physical Review D 69, 082004, (2004) S2: Limits on gravitational wave emission from selected pulsars using LIGO data (LSC+M. Kramer and A. G. Lyne) Phys. Rev. Lett. 94, 181103 (2005) S2: First all-sky upper limits from LIGO on the strength of periodic gravitational waves using the Hough transform Phys. Rev. D 72, 102004 (2005) S3, S4, S5: in progress (S3 searched with Einstein@home)

Gravitational-wave Searches Binary Inspirals

Search for Inspirals Sources Search method Binary neutron stars (~1 – 3 Msun) Binary black holes (< 30 Msun) Primordial black holes (< 1 Msun) Search method Waveforms calculable (depend on mass and spin), so use templates and optimal filtering Templates generated by population synthesis Horizon distance (inspiral range) The distance to which an optimally oriented and located (1.4 + 1.4) Msun NS binary is detectable with SNR = 8 For binary black hole searches the effective distance is for tow 5 Msun BHs optimally oriented with SNR =8.

S5 Inspiral Range

Analysis pipeline Tune pipeline using background, playground (10% of data) and injections Measure background by applying time slides before coincidence Add simulated signals to detector data to evaluate analysis performance Search for double or triple coincident “triggers” Estimate false alarm probability of resulting candidates: detection? Compare with expected efficiency of detection and surveyed galaxies: upper limit S5 Left: accidental coincidences and simulated signals Middle: Right: detection efficiency

Binary Neutron Stars S3 search S4 search 0.09 yr of data signal-to-noise ratio squared Rate < 47 per year per Milky-Way-like galaxy; 0.04 yr data, 1.27 Milky-Ways cumulative number of events S3 search 0.09 yr of data ~3 Milky-Way like galaxies S4 search 0.05 yr of data ~24 Milky-Way like galaxies Phys. Rev. D. 72, 082001 (2005)

Binary Black Holes S3 search S4 search 0.09 yr of data signal-to-noise ratio squared Rate < 38 per year per Milky-Way-like galaxy Log( cum. # of events ) S3 search 0.09 yr of data 5 Milky-Way like galaxies for 5 + 5 Msun S4 search 0.05 yr of data 150 Milky-Way like galaxies for 5 + 5 Msun Phys. Rev. D. 73, 062001 (2006) The upper limit is set by looking at the loudest event in the data. That sets the threshold. Then use injected simulated data to ask the question of how many galaxies can we reach at that threshold? The rate upper limit is set by R = 2.303/(T_obs*N_galaxies). In this case

Primordial Black Holes S3 search 0.09 yr of data 1 Milky-Way like halos for 0.5 + 0.5 Msun S4 search 0.05 yr of data 3 Milky-Way like halos for 0.5 + 0.5 Msun Rate < 63 per year per Milky-Way-like halo Total mass (Msun) Rate / MW halo / yr Phys. Rev. D. 72, 082002 (2005)

Light reading tonight... B. Abbott et al. (LIGO Scientific Collaboration) S1: Analysis of LIGO data for gravitational waves from binary neutron stars Phys. Rev. D 69, 122001 (2004) S2: Search for gravitational waves from primordial black hole binary coalescences in the galactic halo Phys. Rev. D 72, 082002 (2005) S2: Search for gravitational waves from galactic and extra-galactic binary neutron stars Phys. Rev. D 72, 082001 (2005) S2: Search for gravitational waves from binary black hole inspirals in LIGO data Phys. Rev. D 73, 062001 (2006) S2: Joint Search for Gravitational Waves from Inspiralling Neutron Star Binaries in LIGO and TAMA300 data (LIGO, TAMA collaborations) Phys. Rev. D, in press S3: finished searched for BNS, BBH, PBBH: no detection S4, S5: searches in progress

Gravitational-wave searches Stochastic Background

Stochastic GW Backgrounds Astrophysical backgrounds due to unresolved individual sources E.g.: BH mergers, inspirals, supernovae Cosmological background from Big Bang (analog of CMB) WMAP 3-year data GW spectrum due to cosmological BH ringdowns (Regimbau & Fotopoulos)

Cosmological GW Background 10-22 sec 10+12 sec 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

Isotropic search procedure Cross correlate two data streams x1 and x2 For isotropic search optimal statistic is “Overlap Reduction Function” (determined by network geometry) Detector noise spectra g(f) frequency (Hz)

Test other Wa(f) a = 0  inflationary or CS models a = 1  rotating NS Measured (S3, S4) Bayesian 90% upper limits Expected from S5 a = 0  inflationary or CS models a = 1  rotating NS a = 2  pre-BB cosmology

Predictions and Limits LIGO S1: Ω0 < 44 PRD 69 122004 (2004) LIGO S3: Ω0 < 8.4x10-4 PRL 95 221101 (2005) -2 Pulsar Timing CMB+galaxy+Ly-a adiabatic homogeneous BB Nucleo- synthesis LIGO S4: Ω0 < 6.5x10-5 (new) -4 (W0) -6 Initial LIGO, 1 yr data Expected Sensitivity ~ 4x10-6 -8 Log Cosmic strings CMB Adv. LIGO, 1 yr data Expected Sensitivity ~ 1x10-9 -10 Pre-BB model 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 Kamionkowski et al. (astro-ph/0603144-1) Use Lyman-alpha forest, galaxy surveys, and CMB data to constrain CGWBkgd, i.e. CMB and matter power spectrums. Assume either homogeneous initial conditions or adiabatic. Use neutrino degrees of freedom to constrain models. Adiabatic blue solid  CMB, galaxy and Lyman-alpha data currently available (Kamionkowski) Homogeneous blue dashed  CMB, galaxy and Lyman-alpha data currently available Adiabatic CMBPol (cyan solid)  CMB, galaxy and Lyman-alpha data when current CMB is replaced with expected CMBPol data Homogeneous CMBPol (cyan dashed)  CMB, galaxy and Lyman-alpha data when current CMB is replaced with expected CMBPol data -12 Inflation -14 Slow-roll Cyclic model EW or SUSY Phase transition -18 -16 -14 -12 -10 -8 -6 -4 -2 2 4 6 8 10 Log (f [Hz])

Light reading tonight... B. Abbott et al. (LIGO Scientific Collaboration): S1: Analysis of first LIGO science data for stochastic gravitational waves Phys. Rev. D 69, 122004 (2004) S3: Upper Limits on a Stochastic Background of Gravitational Waves Phys. Rev. Lett. 95, 221101 (2005)

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)

Gravitational-Wave Bursts Expected from catastrophic events involving solar-mass (1-100 Mo) compact objects core-collapse supernovae accreting/merging black holes gamma-ray burst engines other … ??? Sources typically not well understood, involving complicated (and interesting!) physics Dynamical gravity with event horizons Behavior of matter at supra-nuclear densities Lack of signal models makes GWBs more difficult to detect SN 1987 A

Burst Search Techniques Two main types of burst searches: Untriggered: Scan ~all data, looking for excess power indicative of a transient signal Robust way to detect generic waveforms Triggered: Scan small amount of data around time of astronomical event (e.g., GRB), by cross-correlating data from pairs of detectors Exploits knowledge of time of and direction to astronomical event Always: Use techniques that make minimal assumptions about the signal Be open to the unexpected!

Excess-Power Detection Look for transient jump in power in some time-frequency region: frequency ~ [60,2000] Hz (determined by noise curves of instruments) duration ~ [1,100] ms (time scale associated with solar-mass COs) Anderson et al. PRD 63 042003 (2001) Many different implementations in LIGO: Fourier modes, wavelets, Gaussian-modulated sinusoids Multiple time-frequency resolutions Provide redundancy & robustness Also time-domain & optimal filter searches Simulated binary inspiral signal in S5 data Chatterji: Q Pipeline search for GWBs with LIGO

time, frequency coincidence Schematic Typically require coincident detection in all 3 LIGO interferometers: frequency detector 2 time detector 3 detector 1 time, frequency coincidence range of time-freq resolutions 8 - 256 Hz  candidate event 1/128 – 1/4 s 2

Upper Limits No GWBs detected through S4. So, set limit on GWB rate vs. signal strength: h = upper limit on event number T = observation time e(hrss) = efficiency vs strength Progress: Central Frequency Lower rate limits from longer observation times Rate Limit (events/day) Lower amplitude limits from lower detector noise

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 predeterimined 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

Procedure: GRBs Cross correlate data between pairs of detectors around time of event 25 – 100 ms target signal duration [-2,+1] min around GRB Compute probability of largest measured CC using distribution of CCs from neighboring times (no GRB, with time shifts). Improbably large CC equals candidate GWB sample GRB lightcurve (BATSE) trigger time detector 2 detector 1

most significant excess at 9th least probable event: Statistical Tests No loud signals seen. Look also for weak cumulative effect from population of GRBs. Use binomial test to compare to uniform distribution. No significant deviation from expected distribution. Max-likelihood test also used. Mohanty, CQG 22 S1349 (2005) 54 GRB tests most significant excess at 9th least probable event: P≥ 9 (p9 ) = 0.102 Leonor / Sannibale, Session W11

Short Hard Bursts? 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

Light reading tonight... B. Abbott et al. (LIGO Scientific Collaboration): S1: First upper limits from LIGO on gravitational wave bursts Phys. Rev. D 69, 102001 (2004) S2: A Search for Gravitational Waves Associated with the Gamma Ray Burst GRB030329 Using the LIGO Detectors Phys. Rev. D 72, 042002 (2005) S2: Upper Limits on Gravitational Wave Bursts in LIGO's Second Science Run Phys. Rev. D 72, 062001 (2005) S2: Upper Limits from the LIGO and TAMA Detectors on the Rate of Gravitational-Wave Bursts Phys. Rev. D 72, 122004 (2005) S3: Search for gravitational wave bursts in LIGO's third science run Class. Quant. Grav. 23, S29-S39 (2006)

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