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A walk through some statistic details of LSC results

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CBC (“inspiral”) papers S1: Analysis of LIGO data for gravitational waves from binary neutron stars. Phys. Rev. D 69 (2004) 122001 gr-qc/0308069 Phys. Rev. D 69 (2004) 122001 gr-qc/0308069 S2: Search for gravitational waves from galactic and extra-galactic binary neutron stars. Phys. Rev. D 72 (2005) 082001 gr-qc/0505041 Phys. Rev. D 72 (2005) 082001 gr-qc/0505041 S3/S4: Search for gravitational waves from binary inspirals in S3 and S4 LIGO dataPhys. Rev. D 77 (2008) 062002 arXiv:0704.3368Phys. Rev. D 77 (2008) 062002arXiv:0704.3368 S5/VSR1: Search for Gravitational Waves from Compact Binary Coalescence in LIGO and Virgo Data from S5 and VSR1 Phys. Rev. D 82 (2010) 102001 arXiv:1005.4655 Also Sensitivity to Gravitational Waves from Compact Binary Coalescences Achieved during LIGO's Fifth and Virgo's First Science Run, arXiv:1003.2481Phys. Rev. D 82 (2010) 102001arXiv:1005.4655arXiv:1003.2481 S6/VSR2, 3: Search for Gravitational Waves from Low Mass Compact Binary Coalescence in LIGO's Sixth Science Run and Virgo's Science Runs 2 and 3 arXiv:1111.7314 P1100034. Also Sensitivity Achieved by the LIGO and Virgo Gravitational Wave Detectors during LIGO’s Sixth and Virgo’s Second and Third Science Runs, arXiv:1203.2674arXiv:1111.7314P1100034arXiv:1203.2674

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7/9/2003LIGO Scientific Collaboration - Amaldi 20033 How to detect inspiral waves Use template based matched filtering algorithm Template waveforms for non-spinning binaries – 2.0 post-Newtonian approx. D: effective distance; a: phase Discrete set of templates labeled by I=(m1, m2) – 1.0 Msun < m1, m2 < 3.0 Msun – 2110 templates – At most 3% loss in SNR s(t) = (1Mpc/D) x [ sin(a) h I s (t-t0) + cos(a) h I c (t-t0)]

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7/9/20034 Optimal Filtering Using FFTs Transform data to frequency domain : Calculate template in frequency domain : Combine, weighting by power spectral density of noise, and then inverse Fourier transform gives the filter output at all times: Find maxima of over arrival time and phase

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7/9/2003LIGO Scientific Collaboration - Amaldi 20035 “Chi-Squared Veto” Many large glitches in the data can lead to a filter output with large SNR The essence of a “chirp” is that the signal power is distributed over frequencies in a particular way Divide template into sub-bands (p=8) and calculate 2 : Correct for large signals which fall between points in template bank and apply a threshold cut:

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Multiple detectors: S2 example

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Results of a search Candidates and their significance (detections?). Upper limits on rate of coalescences (frequentist or Bayesian).

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7/9/2003LIGO Scientific Collaboration - Amaldi 20039 S1 Inspiral Search: results Use triggers from H 4km and L 4km interferometers: – T = 236 hours – Max SNR observed: 15.9 An event seen in L1 only, with effective distance = 95 kpc There are no event candidates in the coincidence category – Monte Carlo simulation efficiency for SNR=15.9: = 53% – Effective number of Milky Way-equivalent galaxies surveyed: N G = (L pop /L G )=0.53x1.13=0.60 – Uncertainties (calibration, etc):

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7/9/2003LIGO Scientific Collaboration - Amaldi 200310 Inspiral Search: results Limit on binary neutron star coalescence rate: – R90% (Milky Way) < = 2.3 x (1/N G ) (1/T) = 140 (0.60/N G ) /yr – With N G =0.60-0.10 we derive R< 170 /yr /MWEG Compare with: – Previous experimental results: LIGO 40m ‘94: 0.5/hr (25hrs, D<25kpc, Allen et al., PRD 1998) TAMA300 ’99: 0.6/hr (6 hr, D<6kpc, Tagoshi et al., PRD 2001) TAMA300 DT6: 82/yr (1,038 hr, D<33 kpc, GWDAW 2002) – Expected Galactic rate: ~10 -6 - 5 x 10 -4 /yr (Kalogera et al)

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7/9/2003LIGO Scientific Collaboration - Amaldi 200311 S1 search: Loudest Surviving Event Candidate Not NS/NS inspiral event! 2 Sep 2002, 00:38:33 UTC S/N = 15.9, 2 /dof = 2.2 (m1,m2) = (1.3, 1.1) Msun What caused this? Appears to be saturation of a photodiode SNR 2 test GW channel Actual trigger Injected signal

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S2 run

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S2 run: a new statistic, and an estimate of the background

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S2 run: candidates

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S2 run: background revisited

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S2: upper limit

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S3/S4: sensitivity, statistics

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S3/S4: Bayesian upper limit

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S3/S4: upper limit

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S5: new statistic

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S5 Results, upper limit

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S5 Results – and blind injection

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7/9/2003LIGO Scientific Collaboration - Amaldi 200324 Days in S1 LIGO sensitivity S1: 23 Aug – 9 Sep, 2002 Inspiral sensitivity measured in distance to 2 x 1.4 Msun optimally oriented inspiral at signal to noise = 8 – Livingston: = 176 kpc – Hanford: = 46 kpc Sensitive to inspirals in – Milky Way, LMC & SMC

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Keeping interferometer locked S1 run: 17days (408 hrs) Seismic Noise in theband

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