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LIGO Hanford. Estimating the Accidental Coincidence Rates in Searches for Gravitational Waves from Compact Binary Coalescences with LIGO. Sarah Caudill for the LSC. LIGO Livingston. Fifth Gulf Coast Gravity Meeting, Baton Rouge, LA, Apr 2009. LIGO- G0900348.

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Sarah Caudill for the LSC

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Sarah caudill for the lsc

LIGO Hanford

Estimating the Accidental Coincidence Rates in Searches for Gravitational Waves from Compact Binary Coalescences with LIGO

Sarah Caudill for the LSC

LIGO Livingston

Fifth Gulf Coast Gravity Meeting, Baton Rouge, LA, Apr 2009

LIGO-G0900348


Sarah caudill for the lsc

The Compact Binary Coalescence Search

  • Binary Neutron Stars (BNS)

  • Binary Black Holes (BBH)

  • Black Hole-Neutron Star Binary (BHNS)

Chirp

Signal

h (strain)

time (sec)

H1

Data

Generate Template Bank

Matched Filtering

CBC

Search

Pipeline

f (Hz)

GW Candidates

H2

Data

Generate Template Bank

Matched Filtering

Coincidence Tests; Data Quality

time (sec)

L1

Data

Generate Template Bank

Matched Filtering


Sarah caudill for the lsc

Statistical Significance

The statistical significance of the cbc candidates is estimated from time-shifted triggers

Combined SNR ρ Histogram*

IFO 1

+

Δ

t1

IFO 2

+

Δ

t2

In-time Coincident trigger: potential gravitational wave

IFO 1

Δt

+

Δ

t1’=t1+Dt

IFO 2

+

Δ

t2

ρ

“Real” data false alarms - SNR

Gaussian noise prediction – SNR

(width comes from coincidence tolerances)

Time-shifted coincident trigger: not a gravitational wave; accidental coincidence

“Real” data false alarms – effective SNR

ρeff

  • 100 time slides = 100 independent experiments

*LIGO Technical Doc. T070109-01-Z


Sarah caudill for the lsc

Utilizing Time-shifted Triggers

Histogram of coincident triggers versus statistic

100

Ex: S4 Binary Neutron

Star search

[Phys. Rev. D 77

(2008) 062002]

Total analyzed time = 576 hrs;

No detection found

Candidates’ distribution

Region where outlier candidates would appear

10

Number of events

1

Accidental coincidences distribution

80

90

100

110

120

Combined effective SNR statistic

(ρeff)2


Sarah caudill for the lsc

Problems with ρeff ranking:

Solution:

Rank by False Alarm Rate (FAR)

Combine double, triple coincidences

Plot IFAR = 1/FAR

Cum. hist of num. events vs combined ρeff H1H2L1

10

loudest triple coinc. in triple obs. time

1

Number of Events

Cum. hist of num. events vs combined IFAR for triple obs. time

0.1

1000

90

50

60

70

80

100

110

120

combined eff snr

Number of Events

We expect a real GW to lie at high IFAR

Cum. hist of num. events vs combined ρeff H1L1

100

1000

10

100

loudest double coinc. in triple obs. time

1

10

Number of Events

10-4

10-3

10-2

10-1

100

1

IFAR (yr)

0.1

80

20

40

60

100

120

160

180

140

combined eff snr

plots from s5 1st yr low mass search [arXiv:0901.0302]


Sarah caudill for the lsc

Problems with ρeff ranking:

Solution:

Rank by False Alarm Rate (FAR)

Combine double, triple coincidences

Plot IFAR = 1/FAR

Cum. hist of num. events vs combined ρeff H1H2L1

10

We only do 100 timeshifts.

1

Number of Events

Cum. hist of num. events vs combined IFAR for triple obs. time

FAR??

0.1

1000

90

50

60

70

80

100

110

120

+

combined eff snr

Number of Events

Cum. hist of num. events vs combined ρeff H1L1

100

1000

10

100

loudest double coinc. in triple obs. time

?

?

1

10

Number of Events

10-4

10-3

10-2

10-1

100

1

IFAR (yr)

0.1

80

20

40

60

100

120

160

180

140

combined eff snr

plots from s5 1st yr low mass search [arXiv:0901.0302]


Sarah caudill for the lsc

Better Estimation of Accidental Coincidence Rate

Combined Effective SNR

H1 Single Detector SNR*

Tail of distribution provides valuable info

10

Number of triggers

1

Map to account for coinc. in time and mass

Map from single detector ρ dist.’s to single detector ρeff dist.’s

Convert to IFAR dist.

Cumulative IFAR

110

80

100

90

If the information in the tails of the single detector ρ dist. is not lost due to time-shifts, we can determine the correct accidental coincidence distribution at large IFAR.

Combined SNR statistic

*S4 Primordial Black Hole Search [Phys. Rev. D 77 (2008) 062002]


Sarah caudill for the lsc

Meaningful False Alarm Rates

Histogram of coincident triggers versus statistic

100

10

Number of events

What we hope to see soon!

1

1

Find meaningful FAR!

80

100

120

Combined effective SNR statistic

(ρeff)2

Correct distribution at high SNR!


Sarah caudill for the lsc

THANK YOU!


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