Status of Stochastic Analyses within the LIGO Scientific - - PowerPoint PPT Presentation

Status of Stochastic Analyses within the LIGO Scientific Collaboration

J.D. Romano, Cardiff University Joseph.Romano@astro.cf.ac.uk

• n behalf of the Stochastic Souces Analysis Group

Presented at the 8th GWDAW 2003 December 19 G030674-00-Z

Outline

• Introduction
• S1 Analysis
• S2 Analysis

– Preliminary results – Refinements under consideration

• Parallel projects

– ALLEGRO-LLO, GEO-LIGO stochastic analyses

• S3 Preview

– E10 coherence

Introduction

• Set upper limit on a stochastic background Ωgw(f) = Ω0
• Use standard optimally-filtered cross-correlation method:

Y ≡

• dt1
• dt2 s1(t1)Q(t1 − t2)s2(t2) ≈
• d

f ˜ s1(f) ˜ Q(f)˜ s∗

2(f)

• Science runs:

– S1: August - September 2002 – S2: February - April 2003 – S3: November 2003 - January 2004

• Analysis to date has focused on LIGO-LIGO correlations
• Extend analysis to include ALLEGRO-LLO, GEO-LIGO

S1 Analysis

• Paper almost submitted to gr-qc
• Improves direct broadband and narrow band upper limits
• Freq range: 40-314 Hz (LLO-LHO), 40-300 Hz (H1-H2)
• Observed instrumental correlations between H1-H2
• GEO data not included in the analysis

IFO Pair Obs time Estimate Error bar Upper limit H1-L1 64 hr 32 18 Ω0 h2

100 ≤ 55 ± 11

H2-L1 51.25 hr 0.16 18 Ω0 h2

100 ≤ 23 ± 4.6

H1-H2 100.25

• 8.3

0.95 —

S2 Analysis

• Preliminary analyses underway (search parameters not final)
• Preliminary upper limits ∼ 1000 times better (as expected

from improved sensitivity and longer observation)

• H1-H2 still dominated by instrumental correlations
• Refinements to the analysis pipeline—to be discussed
• Verifying/validating new version of LDAS code against S1

code & injected signals (K. Reilly)

• Analyze together with S3 data before writing up

Key quantities

• CC statistic values:

YI =

• d

f ˜ sI 1(f) ˜ QI(f)˜ s∗

I 2(f)

• Optimal filter:

˜ QI(f) = NI γ(f) f3PI 1(f)PI 2(f) NI ∝

• d

f γ2(f) f6PI 1(f)PI 2(f)

−1

• Theoretical variance:

σ2

I ∝

• d

f γ2(f) f6PI 1(f)PI 2(f)

−1

• Weighted avg of CC measurements & error bar:

Yopt =

• I σ−2

I

YI

• I σ−2

I

σ2

• pt =

1

• I σ−2

I

Possible S2 Pipeline Enhancements

• High-pass filtering:

– To reduce spectral leakage from low-frequency seismic noise consider time-domain hi-pass filter

• Overlapping Hann windows:

– Replace (flat top) Tukey windows with Hann windows for better leakage protection – Non-overlapping Hann windows lose 50% of effective obs time; overlapping windows recover almost all of this

• Combining measurements from multiple IFO pairs:

– How to combine H1-L1 and H2-L1 given instrumental cor- relations in H1-H2? (See Lazzarini/Whelan talk)

• Monte Carlo simulations: (S. Bose, T. Regimbau)

– Many long weak injections to check weak-signal limit to determine detection efficiency – Signals now continuous in time-domain (spliced IFFTs)

Parallel projects

• 1. GEO-LIGO correlation:
• Coherence measurements to access data quality
• Stand-alone search code: (A. Mercer)

– 2-3 hours for S2 analysis at B’ham (200 nodes) – Validation/verification against LDAS code, injections – Monte Carlo simulation capability (T. Regimbau) – Handles calibrated and uncalibrated data

• Hardware injections to be implemented in future
• 2. ALLEGRO-LLO correlation: See Whelan’s talk

S3 Preview: E10 Coherence (40–201 Hz)

E10 H1-H2 coherence lower than S2 despite reduction in PSD. Most stringent S3 limit from H1-H2?

S3 Preview: E10 Coherence (200–361 Hz)

S2 Preliminary Data Analysis Pipeline

Detector #1 data Decimate to 1024 s/sec divide into 60-sec segments Detector #2 data Decimate to 1024 s/sec divide into 60-sec segments window PSD estimate (0.25Hz bins) PSD estimate (0.25Hz BW) window clean, contiguous, coincident data calibrate calibrate zero pad zero pad FFT Frequency mask FFT Optimal Filter theoretical variance σI cross correlation statistic Y

I

Y optimal (best estimate

• f ΩT)

error bars