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 − 40 M ⊙ . • 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 − αf 2 / 3 ) θ ( f cut − f ) e iψ ( f ) • ˜ ψ ( f ) = φ 0 + 2 πft 0 + ψ 0 f − 5 / 3 + ψ 3 f − 2 / 3 = φ 0 + ψ ′ ( f ) 2

Template Parameters • The BCV templates are not very good for physical parameter estimation. � 3 / 5 � • Chirp mass: M ∼ 1 3 π 128 ψ 0 • Extrinsic parameters: φ 0 , t 0 , α – The SNR is maximized over those. • Intrinsic parameters: ψ 0 , ψ 3 , f cut – The template bank is generated for those. 3

SNR Maximization • Orthonormalize the two parts and normalize the template: � − 1 / 2 � − 1 / 2 � � f cut � � f cut f − 7 / 3 f − 1 I 1 = S ( f ) d f I 2 = S ( f ) d f 0 0 • Normalization factors a 1 , b 1 and b 2 ; depend on I 1 and I 2 • Maximize the SNR with respect to φ 0 and α : �� 2 + 2 + 2 ℑ F 1 F ∗ � � � ρ max = � F 1 � F 2 � � � � 2 � � �� 2 + 2 − 2 ℑ F 1 F ∗ � � � + � F 1 � F 2 � � � � 2 � � � f cut a 1 f − 7 / 6 e iψ ′ ( f ) ˜ s ∗ ( f ) d F 1 = f S ( f ) 0 � f cut [ b 1 f − 7 / 6 + b 2 f − 1 / 2 ] e iψ ′ ( f ) ˜ s ∗ ( f ) d F 2 = f S ( f ) 0 4

χ 2 -veto • Assert that the chirp power is appropriately distributed over the p frequency bins. • χ 2 -statistic: � f l +1 p a 1 f − 7 / 6 2 f − 1 � � χ 2 = p e iψ ′ ( f ) ˜ s ∗ ( f ) d � � � p F 1 � � S ( f ) f l � � l =1 p � f l +1 [ b 1 f − 7 / 6 + b 2 f − 1 / 2 ] 2 f − 1 � � e iψ ′ ( f ) ˜ s ∗ ( f ) d � � � + p p F 2 � � S ( f ) f l � � l =1 5

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. 7