The Ins and Outs of Inspiral Searches Peter

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The Ins and Outs of Inspiral Searches Peter Shawhan Caltech / LIGO For the

The Ins and Outs of Inspiral Searches Peter Shawhan Caltech / LIGO For the LSC Inspiral Analysis Group Syracuse University March 3, 2006 LIGO-G 060036 -00 -Z 1

A Perfect Gravitational Wave Source To lowest order, gravitational wave emission is determined by

A Perfect Gravitational Wave Source To lowest order, gravitational wave emission is determined by second time derivative of mass quadrupole moment tensor Projection depending on wave direction See: Luc Blanchet, “Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries”, Living Rev. Relativity 5, (2002), 3. http: //www. livingreviews. org/lrr-2002 -3 A compact binary system is all quadrupole moment! Power emitted in gravitational waves: LIGO-G 060036 -00 -Z 2

“Newtonian” Inspiral Chirp To lowest order, as gravitational waves carry away energy: Coalescence time

“Newtonian” Inspiral Chirp To lowest order, as gravitational waves carry away energy: Coalescence time Frequency: (t) (t-tc)-3/8 Waveform: h(t) = A(t) cos( B (t-tc)5/8 + fc ) = A′( ) cos( B′ -5/3 + fc ) Y( ) LIGO-G 060036 -00 -Z 3

Chirp Waveform to Higher Order “Post-Newtonian” corrections change phase evolution: 1 PN 1. 5

Chirp Waveform to Higher Order “Post-Newtonian” corrections change phase evolution: 1 PN 1. 5 PN 2 PN where LIGO-G 060036 -00 -Z 4

Source Parameters vs. Signal Parameters Source parameters Masses (m 1, m 2) Spins →

Source Parameters vs. Signal Parameters Source parameters Masses (m 1, m 2) Spins → Assume negligible for now Orbital phase at coalescence → Maximize analytically when filtering Inclination of orbital plane Sky location Distance → Simply multiplicative for a given detector → Simply multiplicative Filter with orthogonal templates, take quadrature sum LIGO-G 060036 -00 -Z 5

Basic Matched Filtering LIGO-G 060036 -00 -Z 6

Basic Matched Filtering LIGO-G 060036 -00 -Z 6

Optimal Matched Filtering in Frequency Domain Data after FFT Template, generated in freq. domain

Optimal Matched Filtering in Frequency Domain Data after FFT Template, generated in freq. domain using stationary phase approx. Noise power spectral density Look for maximum of |z(t)| above some threshold trigger Search overlapping intervals to cover science segment, avoid wrap-around effects Estimate power spectrum from bin-by-bin median of fifteen 256 -sec data segments LIGO-G 060036 -00 -Z 7

Frequency Dealing with Non-Stationary Noise Time (sec) Inspiral filter output: -5 0 Time (sec)

Frequency Dealing with Non-Stationary Noise Time (sec) Inspiral filter output: -5 0 Time (sec) LIGO-G 060036 -00 -Z 5 8

Matched Filtering Susceptibility to Glitches LIGO-G 060036 -00 -Z 9

Matched Filtering Susceptibility to Glitches LIGO-G 060036 -00 -Z 9

Waveform Consistency Tests Divide template into p parts, calculate Frequency Chi-squared test Time Tests

Waveform Consistency Tests Divide template into p parts, calculate Frequency Chi-squared test Time Tests using filter output e. g. time above threshold LIGO-G 060036 -00 -Z 10

Analysis “Pipeline” for Computational Efficiency Computationally expensive tasks LIGO-G 060036 -00 -Z 11

Analysis “Pipeline” for Computational Efficiency Computationally expensive tasks LIGO-G 060036 -00 -Z 11

Template Bank Construction How did we come up with this set of templates? ?

Template Bank Construction How did we come up with this set of templates? ? ? LIGO-G 060036 -00 -Z 12

Template Bank Construction in (t 0, t 3) space LIGO-G 060036 -00 -Z 13

Template Bank Construction in (t 0, t 3) space LIGO-G 060036 -00 -Z 13

Ellipses in Mass Space LIGO-G 060036 -00 -Z 14

Ellipses in Mass Space LIGO-G 060036 -00 -Z 14

Different Bank Layout Methods LIGO-G 060036 -00 -Z 15

Different Bank Layout Methods LIGO-G 060036 -00 -Z 15

Uncertain Waveforms for High-Mass Inspirals Different models for 10+10 Msun black hole binary inspiral

Uncertain Waveforms for High-Mass Inspirals Different models for 10+10 Msun black hole binary inspiral (t) h(t) LIGO-G 060036 -00 -Z 16

BCV Detection Template Family Buonanno, Chen, and Vallisneri, Phys. Rev. D 67, 104025 (2003)

BCV Detection Template Family Buonanno, Chen, and Vallisneri, Phys. Rev. D 67, 104025 (2003) Analytically calculate a to maximize SNR Parameters of the search Can match the various waveform models rather well This is intended for binary components with negligible spin LIGO-G 060036 -00 -Z 17

Binary Systems with Spin Waveform can be much more complicated ! Another BCV detection

Binary Systems with Spin Waveform can be much more complicated ! Another BCV detection template family for systems with spin Six more analytically calculated parameters One more search parameter 4 -dimensional parameter space LIGO-G 060036 -00 -Z 18

Issues of Astrophysical Interpretation What population characteristics do we expect ? Neutron star binaries

Issues of Astrophysical Interpretation What population characteristics do we expect ? Neutron star binaries Mass distribution from population synthesis simulations Spatial distribution following blue light luminosity? Not certain Have placed limits on rate per Milky Way equivalent galaxy Primordial binary black holes in the galactic halo Can make a reasonable spatial model Don’t know mass distribution BH+BH and BH+NS binaries Don’t have a handle on mass and spatial distributions LIGO-G 060036 -00 -Z 19

Summary Searching for inspiral signals is simple in principle but fairly complicated in practice

Summary Searching for inspiral signals is simple in principle but fairly complicated in practice Have to deal with non-stationary noise Have to use a multi-stage pipeline to keep computational costs under control Astrophysical interpretation is nontrivial – but that’s where the excitement will be, eventually! LIGO-G 060036 -00 -Z 20