Scientific Results from the first LIGO Science Runs

Scientific Results from the first LIGO Science Runs Introduction to GW s and LIGO The LIGO Science runs Physics, astrophysics, and S1 analysis results:» Binary inspirals» Pulsars and CW Sources» Bursts (Unmodeled transients)» Stochastic Background Prospects and preliminary results for S2, S3 analyses "Colliding Black Holes" National Center for Supercomputing Applications (NCSA) Alan Weinstein Caltech for the LIGO Scientific Collaboration CERN EP Seminar, July 12, 2004

Nature of Gravitational Radiation General Relativity predicts that rapidly changing gravitational fields produce ripples of curvature in the fabric of spacetime gravitational waves transverse space-time distortions, freely propagating at speed of light mass of graviton = 0 Stretches and squeezes space between test masses strain h = L/L GW are tensor fields (EM: vector fields) two polarizations: plus ( ) and cross ( ) (EM: two polarizations, x and y ) Spin of graviton = 2 Conservation laws: h = L / L Contrast with EM dipole radiation: xˆ (( )) ŷ )) cons of energy no monopole radiation cons of momentum no dipole radiation lowest multipole is quadrupole wave (spin 2) ))

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!)

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

Resonant Bar detectors around the world International Gravitational Event Collaboration (IGEC) Baton Rouge, Legarno, CERN, Frascati, Perth, LA USA Italy Suisse Italy Australia

LIGO Observatories 4 km (H1) + 2 km (H2) Hanford (LHO) : two interferometers in same vacuum envelope Both sites are relatively seismically quiet, low human noise 4 km L1 Livingston (LLO): one interferometer

LIGO Scientific Collaboration ~ 350 scientists from ~ 41 institutions

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

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 E2 E3 E4 E5 E6 E7 E8 E9 E10 Runs Science S1 First Science Data S2 S3 S4fi

Data Runs We have carried out three Science Runs (S1--S3) interspersed with commissioning. S1 run: 17 days (August / September 2002) Four detectors operating: LIGO (L1, H1, H2) and GEO600 Triple-LIGO-coincidence (96 hours) 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 Four S1 astrophysical searches published (Phys. Rev. D 2004):» Inspiraling neutron stars 122001» Bursts 102001» Known pulsar (J1939+2134) with GEO 082004» Stochastic background 122004

Data Runs S2 and S3 S2 run: 59 days (February April 2003) Four interferometers operating: LIGO (L1, H1, H2) and TAMA300 plus Allegro bar detector at LSU Triple-LIGO-coincidence (318 hours) S2 searches under way some preliminary results for today:» Inspiraling compact binaries» Bursts» Pulsars»Stochastic background S3 run: 70 days (October 2003 January 2004) Analysis in progress

LIGO Sensitivity progress 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

LIGO 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

Frequency-Time Characteristics of GW Sources frequency Bursts Broadband Stochastic Background CW (quasi-periodic) Ringdowns Mergers 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! δf f 2.6 10 4 frequency Chirps Earth s orbit time frequency Earth s rotation time δf f time 4 10 6 Unmodeled broad-band bursts Modeled bursts (chirps, ringdowns) Continuous broadband Continuous quasi-periodic Each waveform morphology requires very different data analysis techniques.

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 Gravitational Waves Compact-object binary systems lose energy due to gravitational waves. Waveform traces history. h Chirp waveform In LIGO frequency band (40 2000 Hz) for a short time before merging: anywhere from a few minutes to <<1 second, depending on mass Waveform is known accurately for objects up to ~3 M? Post-Newtonian expansion in powers of (Gm/rc 2 ) is adequate Use matched filtering

Illustration of Matched Filtering Arbitrary units Bank of 2110 post 2 Newtonian stationary-phase templates for 1< m 1 m 2 < 3 M with 3% maximum mismatch

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

The loudest events in S1 For S1, limit search to NS/NS binaries (1< m1 m2 < 3 M ) 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 (most sensitive, but 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 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)

Compact binary sources Upper limit on coalescence rate during S1 No candidate events seen! Sensitive to most of the Milky Way, some LMC,SMC Limit on binary neutron star coalescence rate:»t = 236 h = 0.027 y + 0.12»N G = 0.6 (= ε 1.13 MWEGs) - 0.10 (systematic) = 0.5 (min) 90% confidence upper limit in the (m 1, m 2 ) range of 1 to 3 M sun gr-qc/0308069, PRD 69 122001 (2004) 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, 28th International Cosmic Ray Conference Proc, p3059.

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

S2 Binary Neutron Star Inspiral Search Average distance at which an optimally oriented 2 x 1.4 M sun neutron star binary gives r = 8:» LLO 4k: 1.8 Mpc reaches M31, M33, M32, M110» LHO 4k: 0.9 Mpc just reaches M31 in Andromeda» LHO 2k: 0.6 Mpc Recorded over 1200 hours of data» Did not use single IFO or H1/H2 only data» Applied data quality cuts» Applied auxiliary channel vetoes Used 355 hours of data in search Required triggers to be coincident in time and in mass from at least two detectors

S2 Background Estimation Using Time Slides Preliminary Result ρ H ρ L

S2 Empirical Coherent Statistic For Gaussian noise, optimal coherent statistic would be Background Triggers Simulated Signals ρ H ρ L

Preliminary S2 Triggers in Coincidence Preliminary Result ρ H ρ max ρ L

S2 BNS inspiral search efficiency From detailed simulations: waveform injection into S2 data Galactic and extra-galactic source distribution m 1 /m 2 distribution (pop synth) antenna pattern response full search pipeline ρ 2 max

Preliminary Upper Limit Result R 90% = 2.303 T obs ε + ln P N b MWEG Observation time (T obs ) : 345 hours Conservative lower bound on the product (ε N MWEG ) : 1.2 Omit background correction term (ln P b ) Conservative upper limit: Rate < 50 per year per MWEG (90% frequentist C.L.) Preliminary c.f. S1 result: < 170 per year per MWEG

Binary mass space coverage m 2 BH/BHs S2 & S3 Much better sensitivity in S3: all three LIGO detectors have greater reach than the best detector in S2 NS/NS S2 S3 SPINNING BBHs S3 MACHOs S2 & S3 MACHO/NS S3 Extreme Mass Ratio Inspirals S3 m 1 0.1 1 3 20 M AJW, CERN EP Seminar, July 12, 2004

2. Periodic signals Rotating neutron stars make gravitational waves, if they aren t symmetric about their rotation axis. Mechanisms include:» spin precession at ~f rot» excited oscillatory modes such as the r-mode at 4/3 * f rot» triaxial distortion of crystalline structure, at 2f rot For now, we limit our search to gravitational waves from a triaxial neutron star emitted at twice its rotational frequency. h 0 16π = c 4 2 G I zz f R 2 0 ε ε I1 I2 = I 3 Mountain on neutron star Wobbling neutron star Accreting neutron star <10 5 R-modes

Sensitivity to periodic sources h 0 LIGO design (1 yr) Crab pulsar h 0 : Amplitude detectable with 99% confidence during observation time T There are ~28 known isolated pulsars in LIGO band which are spinning down; targeted in S2 search PSR J1939+2134 P = 0.00155781 s. f GW = 1283.86 Hz P = 1.0519 10-19 s/s D = 3.6 kpc Known EM pulsars Values of h 0 derived from measured spin-down IF spin-down were entirely attributable to GW emissions Rigorous astrophysical upper limit from energy conservation arguments

Search for quasi-periodic signals Long lasting quasi-periodic signals from known (radio) pulsars» 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

Pulsar Analysis techniques Coherent searches» Time-domain method (best if source ephemeris is known) Target known pulsars with frequencies (2f rot ) in detector band» Frequency-domain method (optimal for blind detection of unknown signal) All-sky, broadband search Targeted searches (e.g. galactic core) LMXB (e.g. ScoX-1) search Incoherent searches» Account for frequency modulation of source by appropriate averages of short-time power spectra.» Stack-slide, Hough transform, Power Flux methods In the future, we will implement hierarchical analyses that layer coherent and incoherent methods.

Time-domain method Heterodyne data with fixed frequency, down-sample to 4 samples/second Heterodyne data with doppler/spindown, to 1 sample/minute B k Compare B k with source model (antenna pattern amplitude modulation ) Calculate χ 2 (h 0, ι, ϕ, ψ) for source model, easily related to probability (noise Gaussian) Marginalize over ι, ϕ, ψ to get PDF for (and Bayesian upper limit on) h 0 Verify that B k data are Gaussian and uncorrelated Validate procedure with software and hardware injections (as in all LIGO searches)

o S1 Search for Quasi-Periodic GW s Start small: attempt to detect GW s from one source: PSR J1939+2134 located 3.6 kpc from Earth (fastest known rotating neutron star)» Frequency, spindown, sky coordinates (α, δ) : known» Amplitude h 0 : unknown (though spindown implies h 0 < 10-27 )» Orientation ι, Phase, polarization ϕ, ψ : unknown S1 Analysis:» Search for emission at 1283.86 Hz (2 f EM ).» 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 searches for unknown pulsars (frequency domain method)» Observe with L1, H1, H2, GEO for ~ 200 hrs» Set upper limits on strain amplitude h 0 < 1.4 10-22 at 95% CL PSR J1939+2134 P = 0.00155781 s. f GW = 1283.86 Hz P = 1.0519 10-19 s/s D = 3.6 kpc

The 28 pulsars targeted for S2 B0021-72C B0021-72D B0021-72F B0021-72G B0021-72L B0021-72M B0021-72N B0531+21 (Crab) B1516+02A B1820-30A B1821-24 B1937+21 (S1) B1951+32 B0030+0451 J0711-6830 J1024-0719 J1629-6902 J1721-2457 J1730-2304 J1744-1134 J1748-2446C J1910-5959B J1910-5959C J1910-5959D J1910-5959E J1913+1011 J2124-3358 J2322+2057 There are 38 known isolated radio pulsars with f GW > 50 Hz, including PSR J1939+2134 (used in S1) and the Crab pulsar» Timing information for 28 pulsars: Radio observations collected over S2/S3 for 18 of these (Michael Kramer, Jodrell Bank) ATNF catalogue used for 10 others» The remaining 10 pulsars have not been included in the analysis because of outdated spin parameters (would require more that one template)

Summary of S2 results h 0 16π = c 4 2 G I zz f R 2 0 ε Best upper-limits: J1910 5959D: h 0 = 1.7 x 10-24 J2124 3358: ε = 4.5 x 10-6 How far are S2 results from spin-down limit? Crab: a factor ~ 30 Dots: UL on h 0 Squares: UL on ε Red and magenta refer to PSRs with no info on fdot

4. Stochastic gravitational waves Waves now in the LIGO band were produced 10-22 sec after the big bang WMAP 2003

Stochastic signals Stochastic backgrounds can arise either from» Cosmological processes, such as inflation, phase transitions, or cosmic strings, or from» Astrophysical processes, as the superposition of many signals from the other signal classes already described in this talk. Characterize the strength by its energy density Ω gw, defined as Strain power spectrum: strain amplitude: 0 d(ln f ) Ω GW ( f ) = ρ GW ρ critical 2 3H0 Sgw( f ) = Ω ( ) 2 3 gw f 10π f

Stochastic models, limits LIGO S1 data 2 Cryo Bars 0-2 -4 Log 10 [ W gw ] -6-8 Cosmic strings Pulsar LIGO, 1 yr data Nucleosynthesis Adv. LIGO, 1 yr -10 CMBR String cosmology LISA -12 phase transition -14 Inflation slow-roll limit -16-14 -12-10 -8-6 -4-2 0 2 4 6 8 Log [ f (Hz) ] 10

Detecting a stochastic background In a single detector, a stochastic signal is indistinguishable from noise. To detect it, we cross-correlate the outputs of multiple detectors. Signal model:» Isotropic, Gaussian, stationary (appropriate for cosmological background)» Signal and noise uncorrelated, as is noise among detectors» Ω GW (f) ~ constant in LIGO band (a weak assumption) Cross-correlation statistic combine signal outputs from two detectors using optimal filter to optimize SNR Y = s% ( f) Q% ( f) s ( f) df where Q% ( f) 1 2 γ ( f) S ( f) gw P( f) P( f) 1 2

90% CL Upper Limits on Ω 0 h 100 2

LIGO limits and expectations on Ω GW LIGO S1 data 2 Cryo Bars S1 result: W GW < 23 0-2 -4 S2 prelim: W GW < 0.02 S3 expect: W GW <~ 10-3 Log 10 [ W gw ] -6-8 -10 CMBR Cosmic strings Pulsar String cosmology LISA LIGO, 1 yr data Nucleosynthesis Adv. LIGO, 1 yr LIGO design, 1 year: W GW <~ 10-5 - 10-6 Advanced LIGO, 1 year: W GW <~ 10-9 -12 phase transition -14 Inflation slow-roll limit -16-14 -12-10 -8-6 -4-2 0 2 4 6 8 Log [ f (Hz) ] 10 Challenge is to identify and eliminate noise correlations between H1 and H2!

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

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

S1 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

Burst search in S2 Burst Analysis looks for unmodeled signals» No waveforms or other known characteristics Two approaches» Externally-triggered: gw burst associated with γ-ray burst 030329» Anonymous gravitational wave bursts: self-triggered Expect S2 constraint on bursts with h RSS ~10-20 Hz -1/2» x15 Improvement over S1: x10 for data quality, x1.5 for more sophisticated analysis

S3 and beyond All 3 LIGO Interferometers at Extragalactic Sensitivity for binary inspirals AdvLIGO funding request is at the NSF. 15 sensitivity 1000 rate!

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