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Exploring Nonlinear Couplings in LIGO Data: Insights from S1 Analysis at Penn State University

This study investigates potential nonlinear couplings in LIGO data, particularly focusing on the S1 dataset. By applying a structured model to classify data points as "events," we explore the deviations from expected distributions due to nonlinearity parameters. The analysis reveals varying performance across detectors H1, H2, and L1, with implications for understanding noise characteristics in gravitational wave observations. Results highlight the impact of violin modes and glitches, emphasizing the need for refined data whitening techniques and robust methods for handling anomalies.

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Exploring Nonlinear Couplings in LIGO Data: Insights from S1 Analysis at Penn State University

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  1. A Test for Nonlinear Couplings: Results from S1 Tiffany Summerscales Penn State University

  2. Coupling in LIGO data Noise may couple to signal linearly . . . Slope = linear coupling Penn State University

  3. Coupling in LIGO data Or non-linearly: e.g., hysteresis Gain = • : nonlinearity parameter Penn State University

  4. Test for Non-Linear Coupling: Summary • Model: xj=nj(1+nj-k)xj=(cos)nj(1+(tan)nj-k) • tan more sensitive to small effects • Apply a threshold and classify above-threshold data points as “events” • A nonzero  will cause the events to deviate from a Poisson distribution • A nonzero  will cause the intervals between events to deviate from an exponential distribution • Evaluate 2 fit to exponential distribution • 2 per degree of freedom  will be  1 to be consistent with  = 0 • Use value of 2 statistic to set confidence bounds on  Penn State University

  5. Apply test to S1 data • Test applied to all lock stretches of S1 Playground data • Applied to 2 min and 1 min long segments • Data first restricted to 256-1024Hz frequency band • Whitened using an AR model with 28 coefficients • First and last 50 samples thrown out to avoid end effects of the whitening filter • For calculating 2 statistic: threshold = 2.5, number of bins = 100 Penn State University

  6. Results:H1 • H1 “best behaved” of all of the detectors • 2/<3 almost all of the time • Small deviations from  consistent with 0 probably mostly due to inadequate whitening Penn State University

  7. Results: H2 • H2’s average 2/ higher than H1 • 2/ range mostly between 1 and 4 • Higher average may be due to larger power lines • 2/ > 6 present at the same time as rung up violin modes Penn State University

  8. Results: L1 • Highest values of 2/ • Some high values correspond to violin mode ringup • Most of the highest values seem to be caused by glitches • Attempted removal of glitches since they skewed the normalization of the data causing the 2 test program to crash • Evidently, not all effects of the glitches removed Penn State University

  9. Results from S1: Correlation between violin mode ringup and high 2 • All detectors have lock stretches with large amplitude violin modes • H1 – Lock01 • H2 – Lock01, Lock05, Lock07 • L1 – Lock10, Lock12 • Kalman filter used to remove the violin modes • Times of high violin mode excitation still produce the highest values of c2/n. • For most lock stretches, c2/n jumps by an order of magnitude. • Evidently, the effects of the violin mode are not removed completely with the Kalman filter. Penn State University

  10. Conclusions • High amplitude violin modes have effects which cannot be easily filtered out • Insufficient whitening and glitches can fool the test • Need to perfect whitening techniques and remove sources of large glitches • Complete set of results posted on the web • Available at http://gravity.phys.psu.edu/PSURG/ • Login/Password: Available upon request, subject to collaboration data policy • Under Summerscales • Test made into Matlab toolbox • Available at http://gravity.phys.psu.edu/~tzs/toolbox/ Penn State University

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