Investigating the noise residuals around the gravitational wave event GW150914

Alex B. Nielsen^1,2, Alexander H. Nitz^1,2, Collin Capano^1,2, and Duncan A. Brown³

<sub>1. Albert-Einstein-Institut, Max-Planck-Institut for Gravitationsphysik, D-30167 Hannover, Germany
2. Leibniz Universitat Hannover, D-30167 Hannover, Germany
3. Department of Physics, Syracuse University, Syracuse, NY 13244, USA</sub>

Introduction

We use the Pearson cross-correlation statistic proposed by Liu and Jackson, and employed by Creswell et al., to look for statistically significant correlations between the LIGO Hanford and Livingston detectors at the time of the binary black hole merger GW150914. We compute this statistic for the calibrated strain data released by LIGO, using both the residuals provided by LIGO and using our own subtraction of a maximum-likelihood waveform that is constructed to model binary black hole mergers in general relativity. To assign a significance to the values obtained, we calculate the cross-correlation of both simulated Gaussian noise and data from the LIGO detectors at times during which no detection of gravitational waves has been claimed. We find that after subtracting the maximum likelihood waveform there are no statistically significant correlations between the residuals of the two detectors at the time of GW150914.

Analysis Details

Details of the analaysis can be found in our preprint paper.

Description of Supplemental Material

This repository contains Jupyter notebooks that reproduce the results in our paper. Running the notebooks requires installation of PyCBC v1.12.4 and LALSuite 6.49, which contains version 1.8.0 of the LALSimulation library used to generate the maximum likelihood waveform. Both of these libraries can be installed using pip with the command:

pip install 'pycbc==1.12.4' 'lalsuite==6.49'

The notebooks available in this repository are:

1. CreateResiduals.ipynb creates the data used in the paper starting from data publically available from GWOSC and the supplemental materials from Biwer et al for the maximum likelihood waveform parameters.
2. Fig1_Fig2_Correlation.ipynb generates Figures 1 and 2 that show the correlations between timeseries data of the Hanford and Livingston detectors and the various residuals.
3. Fig3_Background.ipynb generates Figure 3 and the data used to measure the statistical significance of the correlation statistic in simulated Gaussian noise and LIGO detector data.
4. Fig4_Fig5_Robustness.ipynb generates Figures 4 and 5 that explore the robustness of the correlation statistic to various choices of parameters.
5. Fig6_Fig7_WhitenedData.ipynb generates Figures 6 and 7 that explore the effect of whitening on the correllation statistic.

The residual file is also included in the repository. This is stored with git-lfs so a checkout of this repository is required to directly download the file. Instructions for installing git-lfs.

The residual file residuals.hdf contains the maximum-likelihood subtracted residuals for each detector (in {detector}/residual, where {detector} is H1 and L1), as well as the maximum-likelihood waveform projected into each detector (in {detector}/maxl_waveform). Both of these datasets are 4096 seconds long, spanning the same time range as the GW150914 datasets that are available from GWOSC. The start time and time step of the datasets are stored in their respective attrs.

The parameters of the maximum-likelihood waveform are also stored in residuals.hdf, in the top-level .attrs. You can obtain them from within python by doing:

import h5py
with h5py.File('residuals.hdf', 'r') as fp:
    maxl_params = dict(fp.attrs.items())

License and Citation

This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 United States License.

We encourage use of these data in derivative works. If you use the material provided here, please cite the paper using the reference:

@article{Nielsen:2018bhc,
      author         = "Nielsen, Alex B. and Nitz, Alexander H. and Capano,
                        Collin D. and Brown, Duncan A.",
      title          = "{Investigating the noise residuals around the
                        gravitational wave event GW150914}",
      journal        = "JCAP",
      volume         = "1902",
      year           = "2019",
      pages          = "019",
      doi            = "10.1088/1475-7516/2019/02/019",
      eprint         = "1811.04071",
      archivePrefix  = "arXiv",
      primaryClass   = "astro-ph.HE",
      SLACcitation   = "%%CITATION = ARXIV:1811.04071;%%"
}

Acknowledgements

We thank Sylvia Zhu and Sebastian Khan for carefully reading an earlier version of this work. ABN and DAB thank Andrew Jackson, Hao Liu and Pavel Naselsky for helpful discussions and the 2017 Kavli Summer Program in Astrophysics at the Niels Bohr Institute in Copenhagen and DARK University of Copenhagen for support during this work. The 2017 Kavli Summer Program program was supported by the the Kavli Foundation, Danish National Research Foundation (DNRF), the Niels Bohr International Academy and DARK. DAB thanks Will Farr for helpful discussions and NSF award PHY-1707954 for support.