Scientific Results from the first LIGO Science Run

Scientific Results from the first LIGO Science Run Introduction to GW s,ligo, and the science runs The LIGO S1 run Analysis Organization Physics goals and S1 analysis results:» Burst (Unmodeled transient) Sources» Binary Coalescence» Pulsars and CW Sources» Stochastic Background Prospects for S2, S3 analyses "Colliding Black Holes" National Center for Supercomputing Applications (NCSA) Alan Weinstein Caltech for the LIGO Scientific Collaboration (special thanks to Albert Lazzarini) HEP Seminar, January 5, 2004

gravitational radiation: propagating waves of space-time curvature gravitational radiation from inspiral of compact stellar-mass binary objects (black holes, neutron stars)

Nature of Gravitational Radiation General Relativity predicts : transverse space-time distortions, freely propagating at speed of light mass of graviton = 0 Stretches and squashes space between test masses strain Conservation laws: h = L/L cons of energy no monopole radiation cons of momentum no dipole radiation quadrupole wave (spin 2) two polarizations plus ( ) and cross ( ) Spin of graviton = 2 Contrast with EM dipole radiation: xˆ (( )) ŷ )) ))

Interferometric detection of GWs GW acts on freely falling masses: laser mirrors For fixed ability to measure L, make L as big as possible! Beam splitter Dark port photodiode P out = P in sin 2 (2k L) Antenna pattern: (not very directional!)

LIGO Observatories Hanford: two interferometers in same vacuum envelope (4km, 2km) Livingston: one interferometer (4km)

International network LIGO GEO Virgo TAMA detection confidence locate the sources verify light speed propagation decompose the polarization of gravitational waves AIGO Open up a new field of astrophysics!

LIGO, VIRGO, GEO, TAMA LHO4K LHO2K GEO 600 VIRGO 3000 LLO 4K TAMA 300

LIGO Noise-limited Sensitivity The noise in the LIGO interferometers is dominated by three different processes depending on the frequency band Shaking of ground transfers through the suspension into movement of the test mirrors thermal noise in mirrors and suspensions At present, noise in the LIGO detectors is dominated by technical sources, associated with as-yet-imperfect implementation of the design Fluctuations in the number of photons arriving at the photodiode

LIGO Sensitivity progress Livingston 4km Interferometer May 2001 Jan 2003

Commissioning and the First Science Runs 1999 2000 2001 2002 2003 2004 3Q 4Q 1Q 2Q 3Q 4Q 1Q 2Q 3Q 4Q 1Q 2Q 3Q 4Q 1Q 2Q 3Q 4Q 1Q 2Q 3Q Inauguration First Lock Full Lock all IFO's Now strain noise density @ 200 Hz [Hz-1/2 ] 10-17 10-18 10-19 10-20 10-21 10-22 Engineering E1 Runs Science E2 E3 E4 E5 E6 E7 E8 E9 S1 First Science Data S2 E10 S3

Sensitivity in 3 Science Runs S1 1 st Science Run end Sept. 2002 17 days S2 2 nd Science Run end Apr. 2003 59 days LIGO Target Sensitivity S3 3 rd Science Run end Jan. 2004 64 days

Sensitivity during S1 During S1 the 3 LIGO interferometers offered the first opportunity for the most sensitive coincidence observations ever made in the low frequency band around a few hundred Hertz LHO 2Km LLO 4Km LHO 4Km

In-Lock Data Summary from S1 Red lines: integrated up time Green bands (w/ black borders): epochs of lock H1: 235 hrs H2: 298 hrs L1: 170 hrs 3X: 95.7 hrs August 23 September 9, 2002: 408 hrs (17 days). H1 (4km): duty cycle 57.6% ; Total Locked time: 235 hrs H2 (2km): duty cycle 73.1% ; Total Locked time: 298 hrs L1 (4km): duty cycle 41.7% ; Total Locked time: 170 hrs Double coincidences: L1 && H1 : duty cycle 28.4%; Total coincident time: 116 hrs L1 && H2 : duty cycle 32.1%; Total coincident time: 131 hrs H1 && H2 : duty cycle 46.1%; Total coincident time: 188 hrs Triple Coincidence: L1, H1, and H2 : duty cycle 23.4% ; Total coincident time: 95.7 hrs

Astrophysical Sources of Gravitational Waves Compact binary systems» Black holes and neutron stars» Inspiral merger ringdown» Probe internal structure, nuclear eqn of state of NS crust, populations, and spacetime geometry Spinning neutron stars» known & unknown pulsars» LMXBs» Probe internal structure and populations Neutron star birth» Supernova core collapse» Instabilities: tumbling, convection» Correlations with EM observations Stochastic background» Big bang & other early universe» Background of GW bursts Analog from cosmic microwave background -- WMAP 2003

LIGO Data analysis LIGO is a broad-band amplitude detector, measures waveforms. The experimentalist thinks not in terms of astrophysical sources, but in terms of waveform morphologies. Specific astrophysical sources suggest specific waveforms, but we don t want to miss the unexpected! Four different waveform morphologies being considered:» Bursts (of limited duration), for which we have models (chirps, ringdowns)» Bursts, for which we have no reliable models (supernovas, )» Continuous waves, narrow bandwidth - periodic (pulsars)» Continuous waves, broad bandwidth - stochastic (BB background) Each requires radically different data analysis techniques. Algorithms, implementation development is in its adolescence. Marching into the unknown look out for surprises!

Frequency-Time Characteristics of GW Sources Ringdowns frequency Bursts Broadband Stochastic Background CW (quasi-periodic) Mergers Chirps Earth s orbit Earth s rotation time δf f 2.6 10 4 frequency frequency δf f 4 10 6 time time

S1,S2 Data Analysis Groups LIGO Scientific Collaboration (LSC) Analysis Groups» Typically ~30 physicists / group» One experimentalist / One theorist co-lead each group Compact binary inspiral: chirps Supernovae / GRBs / mergers: bursts Pulsars in our galaxy: periodic Cosmological Signal stochastic background

Analysis generalities Analysis pipeline development still very much in progress for all searches! adolescence Most analyses start with single-ifo data, then combine for coincidences (exception: stochastic search correlates IFO pairs from the start) Veto particularly noisy, unstable, or uncalibrated data epochs (stringent cuts for burst search) Design and tune analysis pipeline on playground data, freeze analysis before looking at full data Playground was not very representative many important lessons learned about stability of the detectors None of the searches with S1 data were prepared for detection; aim for upper limits Apply lessons learned, and aim for detection in S2 and beyond

Event search pipeline Example from bursts -- prototypical for other searches

1. Compact binary sources Coalescence inspirals Detectability of coalescing binary sources during S1 (for optimal location & orientation relative to antenna pattern)

Inspiral and Merger of Compact Binaries NS/NS @ 10Mpc BBH (40M ) 500 Mpc LIGO is sensitive to:» GR from binary systems containing neutron stars & stellar mass black holes» Last several minutes of inspiral driven by GW emission» Test PPN-predictions, consistency Neutron Star Binaries» Known to exist (Hulse-Taylor)» merger waveform provides info on nuclear eqn of state of NS crust NS/BH, BH/BH» New science: rates, dynamics of gravitational field, merger waves» GR in non-linear, non-perturbative regime» BH/BH collisions: particle physics

Chirp signal from Binary Inspiral determine distance from the earth r masses of the two bodies orbital eccentricity e and orbital inclination I spins of the compact objects Over-constrained parameters: TEST GR

Compact Binary detection range and Diurnal variation during S1 S1: Sensitive to whole Milky Way and SMC (~ 1.13 MWEG) (Andromeda ~ 800 kpc) L1 oriented with best sensitivity to sources at Galactic core in middle of sidereal day

Compact binary sources What is expected? NOTE: Rate estimates DO NOT include most recent relativistic pulsar discovery, J0737-3039.. Estimates will increase ~> 10X Table from: V. Kalogera (population synthesis) astro-ph/001238, astro-ph/ 0012172, astro-ph/ 0101047

Optimal Wiener Filtering Matched filtering (optimal) looks for best overlap between a signal and a set of expected (template) signals in the presence of the instrument noise -- correlation filter Replace the data time series with an SNR time series Look for excess SNR to flag possible detection Theoretical challenge: compute banks of waveforms to sufficient accuracy ξ p [ ] = ˆ t c T p *( f ) s ˆ ( f ) S ˆ e 2πift c df n ( f ) For S1, limit search to NS/NS binaries: Bank of 2110 post 2 - Newtonian stationary-phase templates for 1< m 1 m 2 < 3 M sun with 3% maximum mismatch Parallel PC Linux Cluster +

GW Channel + simulated inspiral Data analysis: matched filtering SNR ρ Filter to suppress high/low freq Coalescence Time χ 2

Compact binary sources Discrimination against non-stationary noise artifacts Time dependence of signal strengths»snr - ρ» χ 2 Can distinguish true events vs. noise with same ρ and χ 2 S1 data loudest trigger S1 data+injected chirp r(t) c 2 (t) h(t)

The loudest events observed Hundreds of inspiral event triggers were recorded during S1 NO inspiral events above threshold seen in coincidence (more than one IFO) The loudest (SNR) events were observed in L1 only (relatively noisy; PD saturation); NONE were loud enough to have been detected in H1 NONE of these events are consistent with expected clean signals Set final threshold just above loudest event (0 candidates remain) Upper limit at 90% CL = 2.3 events Evaluate detection efficiency for 1.13 MWEG using that threshold

Compact binary sources Upper limit on coalescence rate during S1 Limit on binary neutron star coalescence rate:»t = 236 h = 0.027 y + 0.12»N G = 0.6 (= ε 1.13 L G /L G )- 0.10 (systematic) = 0.5 (min) No event candidates found in coincidence 90% confidence upper limit in the (m 1, m 2 ) range of 1 to 3 M sun 26X lower than best published observational limit 40m prototype at Caltech 1 :»R 90% (Milky Way) < 4400 /yr Comparable to recent TAMA analysis (1000 hr run) 2 :»R < 123 /yr for MW Galaxy 1 1994 data, Allen et al., Phys.Rev.Lett. 83 (1999) 1498 2 TAMA Collaboration, 28 th International Cosmic Ray Conference Proc, p3059.

2. Periodic sources S1 sensitivities -- GEO -- H2 2km -- H1 4km -- L1 4km Crab pulsar h 0 h 0 : Amplitude detectable with 99% confidence during observation time T PSR J1939+2134 P = 0.00155781 s. f GW = 1283.86 Hz P = 1.0519 10-19 s/s D = 3.6 kpc Limit of detectability for rotating NS with equatorial ellipticity, ε = δi/i zz : 10-3, 10-4, 10-5 @ 10 kpc Known EM pulsars Values of h 0 derived from measured spindown IF spin-down were entirely attributable to GW emissions Rigorous astrophysical upper limit from energy conservation arguments

Spinning Neutron Stars ε = I 3 I 3 I 1 θ w ε = I1 I2 I 3 <10 5 Known isolated pulsars:» waves from crustal strain or wobbling» Accretion driven instabilities or asymmetries EM-quiet or newborn pulsars» Probe population/birth rate of neutron stars in Galaxy» R-mode instabilities in nascent NS; combine with supernova triggers Probe:» Nature of neutron star crust via gravitational ellipticity» Strength and nature of magnetic fields inside neutron stars» Origin of clustered spin-period (~300 Hz) observed for low-mass x-ray binaries (Bildsten) h 0

Search for quasi-periodic signals Long lasting quasi-periodic signals» Account for Doppler induced frequency shifts and intrinsic spin evolution» Account for modulation of amplitude due to detector antenna pattern» Must know pulsar position in sky, and period P, dp/dt» Amplitude h 0, Orientation ι, Phase, polarization ϕ, ψ : usually unknown» Can infer, from Doppler induced frequency shifts, deviation of v GW from c light, and can test prediction that only two transverse polarizations are present For small numbers of pulsars observed in EM spectrum, can analyze in time domain, integrating demodulated signal over long observation times For large numbers of pulsars, or unknown source direction and period (most pulsars!), frequency domain analysis is best, but is very much computationally bound!» stay tuned for Einstein@home! Earth s orbit Earth s rotation δf f 2.6 10 4 frequency frequency δf f 4 10 6 time time

o S1 Search for Quasi-Periodic GW s Start small: attempt to detect GW s from one source: PSR J1939+2134 (fastest known rotating neutron star) located 3.6 kpc from Earth» Frequency of source: known» Rate of change of frequency (spindown): known» Sky coordinates (α, δ) of source: known» Amplitude h 0 : unknown (though spindown implies h 0 < 10-27 )» Orientation ι: unknown» Phase, polarization ϕ, ψ: unknown S1 Analysis goals:» Search for emission at 1283.86 Hz (2 f EM ). Set upper limits on strain amplitude h 0.» Develop and test an analysis pipeline optimized for efficient known target parameter searches (time domain method)» Develop and test an efficient analysis pipeline that can be used for blind searches (frequency domain method) PSR J1939+2134 P = 0.00155781 s. f GW = 1283.86 Hz P = 1.0519 10-19 s/s D = 3.6 kpc

Search for Continuous Waves S1 Search Methods:»Performed for four interferometers: L1, H1, H2, GEO»No joint interferometer result (timing problems, L1 best anyway)»time-domain method (sets Bayesian upper limit): <- REST OF THIS DISCUSSION Heterodyne data (with fixed freq) and down-sample to 4 samples/second Heterodyne data (with doppler/spindown) to 1 sample/minute Calculate χ 2 (h 0, ι, ϕ, ψ) for source model, antenna pattern Easily related to probability (noise Gaussian) Marginalize over ι, ϕ, ψ to get PDF for (and upper limit on) h 0»Frequency-domain method (optimal for blind detection, frequentist UL): Take SFTs of (high-pass filtered) 1-minute stretches of GW channel Calibrate in the frequency domain, weight by average noise in narrow band Compute F == likelihood ratio (worst-case values for ι, ϕ, ψ) Obtain upper limit using Monte-Carlo simulations, by injecting large numbers of simulated signals at nearby frequencies

Power spectra near pulsar f GW Noise level versus time during S1 run: sensitivity varies PSR J1939+2134 at 1283.8564877 Hz

Statistics of noise near pulsar f GW Noise in narrow band around 1284 Hz appears Gaussian, uncorrelated in time and frequency: L1 Histogram of power in bins (0.01 Hz x 60-second) has exponential distribution 60-sec SFT s: Histogram of phase difference between adjacent frequency bins, every 60 seconds, is uniform For Gaussian amplitude noise: -exponential (Rayleigh) power dist. -uniform phase dist.

Time domain behavior of data follow ideal behavior for Gaussian noise at pulsar f GW y(t k ; a) is source model a = {h,ι, ψ, φ 0 } - parameters B k are the down-sampled & heterodyned data series Residuals are normal deviates with N[0,1]. χ 2 per DOF ~ 1

Bayesian upper limits from time domain analysis in concordance with frequentist results Upper limit on h 0 implies upper limit on ε:

3. Burst sources GW s from asymmetric supernova collapse gravitational waves Expected SNe Rate 1/50 yr - our galaxy 3/yr - Virgo cluster

Burst Sources General properties.» Duration << observation time.» Modeled systems are dirty, i.e. no accurate gravitational waveform Possible Sources» NS merger» Supernovae hang-up (Muller, Brown...) in rapidly spinning core-collapse events; may not see EM explosion!» Instabilities in nascent NS (Burrows )» Cosmic string cusps (Damour/Vilenkin) Promise» Unexpected sources and serendipity.» Detection uses minimal information.» Possible correlations with γ-ray and/or neutrino observations GRBs, SNEWS No optimal analysis approach! Much more background!

Search for clusters of excess power in pixelized t-f plane: tfclusters Identify GW burst while attempting to avoid bias in assumed waveform, making full use of detector bandwidth: Compute t-f spectrogram, in 1/8-second bins Threshold on power in a pixel, get uniform black-pixel probability Simple pattern recognition of clusters in B/W plane; threshold on size, or on size and distance for pairs of clusters

Time-frequency spectrogram of GW signal stationary? This is an example of a very glitchy 128-sec interval during E7. Much less bursty for S1! Still, cannot distinguish instrumental bursts from GWs, except by coincidence between widely-separated detectors:» tight time coincidence (~10 msec)» consistent waveforms between detectors Make very tight data quality cuts:» cut noisy data epochs» cut GW triggers coincident with glitches in IFO monitoring channels Data quality during S1 was insufficient to feel confident in detection.

Final dataset for analysis Very stringent data quality cuts: S1 run: 408.0 hours 3 IFOs in coincidence: 96.0 hours Set aside playground: 86.7 hours Granularity in pipeline (360 sec): 80.8 hours BLRMS cut: 54.6 hours Keep only well-calibrated data: 35.5 hours Vetos: no attempt (for S1) to veto triggers based on time coincidence with instrumental glitches, for fear of vetoing GWs. Veto safety (no false dismissals), and efficacy (suppression of false triggers) under careful study for S2 and beyond.

Background Estimation and Upper Limits Number of triple-coincident event triggers in 35.5 hours: Use time-shift analysis to estimate background rates Feldman-Cousins to set upper limits or confidence belts Rate < 1.6 events/day at 90% CL

Interpretation of Burst rate upper limit Zwerger-Müller core collapse waveforms Compare with what we might expect from, eg, Galactic SN Instead of using astrophysical simulations (which might bias the search, since those waveforms are not reliable), use simple ad-hoc waveforms:» broadband Gaussians and narrow-band sine-gaussians, of 2 amplitude h rss h rss = h( t) dt Monte-Carlo simulation to determine detection efficiency for triple coincidence as a function of signal strength h rss and waveform model, averaged over source direction and polarization Upper bound: R(h) N / (ε(h) T) N: number observed events ε(h): detection efficiency for amplitude h T: observation time -- livetime Proportionality constant depends on confidence level (CL) -- of order 1 for 90%

Efficiency determination using Monte Carlo TFCLUSTERS -- Single and triple coincidences Optimal Wave & Polarization Orientation Detection threshold vs. frequency Average over Wave & Polarization Orientation SG 554, Q = 9

Efficiency vs. Rate Interpret result as an upper limit on event rate vs. rss strain Efficiency depends on signal frequency content

4. Stochastic gravitational wave background Sources Early universe sources (inflation, cosmic strings, etc) produce very weak, non-thermal (eg, power-law spectrum), unpolarized, isotropic, incoherent (stochastic) background spectrum Contemporary sources (unresolved SN & inspiral sources) produce power-law spectrum Analog from cosmic microwave background -- WMAP 2003 0 d(ln f ) Ω GW ( f ) = ρ GW ρ critical The integral of [1/f Ω GW (f)] over all frequencies corresponds to the fractional energy density in gravitational waves in the Universe

Stochastic Background sensitivities S1

Stochastic background radiation Current best upper limits:» Inferred: From Big Bang nucleosynthesis: (Kolb et al., 1990)» Measured: Garching-Glasgow interferometers (Compton et al. 1994): Ω GW ( f ) d ln f <1 10 5 Ω GW ( f ) < 3 10 5» Measured: EXPLORER-NAUTILUS (cryogenic bars -- Astone et al., 1999): Ω GW (907Hz) < 60 Cross-correlation technique enables one to dig signal below individual interferometer noise floors

o Stochastic background radiation S1 search method» Calculate cross-correlations between detector- pairs (H1-L1, H2-L1, H1-H2), using filter optimal for Ω GW (f) f 0 (constant)» Good sensitivity requires wavelength l GW > 2D (detector baseline) f < 50 Hz for L - H pair» Initial LIGO limiting sensitivity: W < 10-6» Analyze data in (2-detector coincident) 900-second stretches» Partition each of these into 90-second stretches to characterize statistics» Window, zero pad, FFT, estimate power spectrum for 900 sec» Notch out frequencies containing instrumental artifacts Very narrow features - 0.25 Hz bins n X16 Hz, n X 60 Hz, 168.25 Hz, 168.5 Hz, 250 Hz» Extensive statistical analysis to set 90% confidence upper limit S1 Analysis goals:» Directly constrain Ω GW (f) for 40 Hz = f = 300 Hz» Expect for S1: W < Order(1)» Investigate instrumental correlations

Stochastic background radiation Measurement technique: detector cross-correlation Mean of Y proportional to Ω GW Variance due to instrument noise floors Optimal filter, Q(τ), depends on noise floors and a geometrical factor relating detector orientations and antenna patterns» Perfectly aligned colocated detectors have γ(f) == 1

Stochastic background radiation Selection of measurement band Contribution to total SNR, µ/σ Y, as a function of frequency for the three detector pairs

Stochastic background radiation Best upper limit on Ω GW provided by H2-L1 f?df dω CC (f ) 0 dω CC (f)/df Days of observation Normalized residuals over S1 run Run-averaged spectrum of S1Measurements over S1 cross correlation (CC)

Summary of S1 The methodology of LIGO science The first upper limits results have been obtained using the LIGO interferometers in coincidence. These have resulted in four methodology papers: Papers submitted to Physical Review D: D Analysis of LIGO data for gravitational waves from binary neutron stars, gr-qc/0308069 Setting upper limits on the strength of periodic gravitational waves using the first science data from the GEO600 and LIGO detectors, gr-qc/0308050 First upper limits on gravitational wave bursts from LIGO, gr-qc/0312056 Analysis of First LIGO Science Data for Stochastic Gravitational Waves, gr-qc/0312088 A paper describing the instruments has also been accepted for publication by Nuclear Instruments and Methods. Detector Description and Performance for the First Coincidence Observations between LIGO and GEO, gr-qc/0308043

Papers in publication process 300 physicists and engineers; 40 institutions from eight countries

Plans for S2 and beyond Inspiral» (If no detections) get better upper limit, making use of longer observation time, additional sources in Andromeda» Improved data quality cuts and statistical testing; coherent analysis» Search for non-spinning BHs up to ~20 solar masses (or UL)» Search for MACHO binaries (low mass BHs) in Galactic Halo Bursts» Eyes wide open search for signals in the 1-100 msec duration» Triggered search for correlations with GRBs» Modeled search for Black hole ringdown Supernovae waveform catalog» Four-way coincidence with TAMA» Introduce amplitude constraints, tighter time coincidence windows, cross-correlation of time-series data from multiple interferometers near event candidates for better discrimination Periodic sources Time domain method:» Upper limits on all known pulsars > 50 Hz» Search for Crab» Develop specialized statistical methods (Metropolis-Hastings Markov Chain) to characterize PDF in parameter space Frequency domain method» Search parameter space (nearby all-sky broadband + deeper small-area)» Specialized search for SCO-X1 (pulsar in binary)» Incoherent searches: Hough, unbiased, stack-slide Stochastic» May optimally filter for power-law spectra: Ω GW (f) f β» Correlate ALLEGRO-LLO» Technical improvements: apply calibration data once/minute, overlapping lowerleakage windows, study H1-H2 correlations in more detail.

Sensitivity in 3 Science Runs S1 1 st Science Run end Sept. 2002 17 days S2 2 nd Science Run end Apr. 2003 59 days LIGO Target Sensitivity S3 3 rd Science Run end Jan. 2004 64 days

S3: All 3 LIGO Interferometers at Extragalactic Sensitivity Displacement spectral density

S3 -- reaching Andromeda M31 in Andromeda

Why will S2,S3 be so much better than S1? S2 -- Detector sensitivity» All three detectors showed dramatic improvement in sensitivity over S1 : ~10x» Well matched in sensitivity above ~250 Hz Better coincidence efficiencies for all sources Inspiral ranges more well-matched Stochastic sensitivity scales as 1/(P 1 P 2 ) Bursts-- greater ranges CW sources -- lower h 0 Data Yield» 4x longer run than S1 All sources will benefit from increased observation time Rate -limited: 1/T Background limited: 1/vT Triple coincidence is important for eliminating chance coincidences» S1 required stringent data quality cuts because of nonstationarity» S2 data cuts much less severe Partial implementation of WFS (wavefront sensing system) for alignment Better monitoring and greater automation of operational status Better stationarityfor interferometers S3 -- Detector sensitivity» H1, H2 improved at low frequencies to match L1 performance in S2» Better matching of sensitivities at low frequencies makes coincidence analysis more effective Duty cycle» Faster lock acquisition due to greater automation» Full implementation of WFS at LHO maintains optimum alignment» H1, H2 running 70-80% in science mode» L1 expected to run about 40% science mode (~ same as S2) Analysis» Greater experience will allow us to exercise and optimize the pipeline as a whole rather than in pieces

LIGO detectors are working better and better Sensitivity and duty cycle are approaching design values The worldwide network is joining in Analysis techniques and pipelines are becoming more powerful and streamlined Look for MORE, and MORE INTERESTING results from LIGO in near future! Conclusions