Issues on Template Implementation for the BBH Inspiral Search - - PowerPoint PPT Presentation

Issues on Template Implementation for the BBH Inspiral Search Eirini Messaritaki (UW-Milwaukee) with

• S. Babak, P. Brady, D. Brown, T. Cokelaer
• J. Creighton, B. Sathyaprakash and D. Woods

BCV Templates

• Proposed by Buonanno, Chen and Vallisneri (PRD 67,

024016 (2003) ).

• Non-spinning BBH of total mass 10 − 40M⊙.
• Model the Fourier transform of the time-domain BBH

inspiral waveforms.

• Fitting factors in the range 0.85 - 0.97 .
• ˜

h(f) = f−7/6 (1 − αf2/3) θ(fcut − f) eiψ(f) ψ(f) = φ0 + 2πft0 + ψ0 f−5/3 + ψ3 f−2/3 = φ0 + ψ′(f)

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Template Parameters

• The BCV templates are not very good for physical

parameter estimation.

• Chirp mass: M ∼ 1

π

• 3

128 ψ0

3/5

• Extrinsic parameters: φ0, t0, α

– The SNR is maximized over those.

• Intrinsic parameters: ψ0, ψ3, fcut

– The template bank is generated for those.

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SNR Maximization

• Orthonormalize the two parts and normalize the template:

I1 =

fcut

f−7/3 S(f) d f

−1/2

I2 =

fcut

f−1 S(f) d f

−1/2

• Normalization factors a1, b1 and b2; depend on I1 and I2
• Maximize the SNR with respect to φ0 and α:

ρmax =

• F1
• 2 +
• F2
• 2 + 2ℑF1F ∗

2

+

• F1
• 2 +
• F2
• 2 − 2ℑF1F ∗

2

F1 =

fcut

a1f−7/6 S(f) eiψ′(f)˜ s∗(f) d f F2 =

fcut

[b1f−7/6 + b2f−1/2] S(f) eiψ′(f)˜ s∗(f) d f

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χ2-veto

• Assert that the chirp power is appropriately distributed
• ver the p frequency bins.
• χ2-statistic:

χ2 = p

p

• l=1
• fl+1

fl

a1f−7/6 S(f) eiψ′(f) ˜ s∗(f) d f − 1 p F1

• 2

+ p

p

• l=1
• fl+1

fl

[b1f−7/6 + b2f−1/2] S(f) eiψ′(f) ˜ s∗(f) d f − 1 p F2

• 2

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Current Status

• The BCV templates have been incorporated into the

template bank generation code and into the search code.

• The inspiral code is ready to be run for BBH inspiral

triggers.

• What total mass range can we ”safely” use the BCV

templates for?

6

Future Work

• Identify triggers and investigate:

– Future investigation will be required using the actual PN BBH inspiral models (for example for parameter estimation).

• Use the BCV templates for BH-NS inspiral.
• Incorporate the BCV-2 templates (spinning BBH) into the

search code.

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