A walk through some statistic details of LSC results

CBC (“inspiral”) papers S1: Analysis of LIGO data for gravitational waves from binary neutron stars. Phys. Rev. D 69 (2004) gr-qc/ Phys. Rev. D 69 (2004) gr-qc/ S2: Search for gravitational waves from galactic and extra-galactic binary neutron stars. Phys. Rev. D 72 (2005) gr-qc/ Phys. Rev. D 72 (2005) gr-qc/ S3/S4: Search for gravitational waves from binary inspirals in S3 and S4 LIGO dataPhys. Rev. D 77 (2008) arXiv: Phys. Rev. D 77 (2008) arXiv: S5/VSR1: Search for Gravitational Waves from Compact Binary Coalescence in LIGO and Virgo Data from S5 and VSR1 Phys. Rev. D 82 (2010) arXiv: Also Sensitivity to Gravitational Waves from Compact Binary Coalescences Achieved during LIGO's Fifth and Virgo's First Science Run, arXiv: Phys. Rev. D 82 (2010) arXiv: arXiv: 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: P Also Sensitivity Achieved by the LIGO and Virgo Gravitational Wave Detectors during LIGO’s Sixth and Virgo’s Second and Third Science Runs, arXiv: arXiv: P arXiv:

7/9/2003LIGO Scientific Collaboration - Amaldi 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)]

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

7/9/2003LIGO Scientific Collaboration - Amaldi “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:

Multiple detectors: S2 example

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

7/9/2003LIGO Scientific Collaboration - Amaldi 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):

7/9/2003LIGO Scientific Collaboration - Amaldi 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 = 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: ~ x /yr (Kalogera et al)

7/9/2003LIGO Scientific Collaboration - Amaldi 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

S2 run

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

S2 run: candidates

S2 run: background revisited

S2: upper limit

S3/S4: sensitivity, statistics

S3/S4: Bayesian upper limit

S3/S4: upper limit

S5: new statistic

S5 Results, upper limit

S5 Results – and blind injection

7/9/2003LIGO Scientific Collaboration - Amaldi 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

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