Upper limits on persistent gravitational waves using folded data and the full covariance matrix from Advanced LIGO$'$s first two observing runs

TL;DR

This paper develops a method to set upper limits on anisotropic stochastic gravitational-wave backgrounds using the full pixel-to-pixel covariance matrix from Advanced LIGO data, confirming previous results and validating the approach with injection tests.

Contribution

It introduces a novel analysis using the full Fisher information matrix in the pixel basis for SGWB anisotropy, improving upon previous spherical harmonic methods.

Findings

Results are consistent with previous LIGO-Virgo upper limits.

No evidence for persistent directional gravitational-wave sources was found.

Injection tests confirm the validity of the new upper limits.

Abstract

The stochastic gravitational-wave background (SGWB) created by astrophysical sources in the nearby Universe is likely to be anisotropic. Upper limits on SGWB anisotropy have been produced for all major data-taking runs by the ground-based laser interferometric detectors. However, due to the challenges involved in numerically inverting the pixel-to-pixel noise covariance matrix, which is necessary for setting upper limits, the searches accounted for angular correlations in the map by using the spherical harmonic basis, where regularization was relatively easier. This approach is better suited though for extended sources. Moreover, the upper-limit maps produced in the two different bases are seemingly different. While the upper limits may be consistent within statistical errors, it was important to check whether the results would remain consistent if the full noise covariance matrix was used in the pixel basis. Here, we use the full pixel- to-pixel Fisher information matrix to create upper-limit maps of SGWB anisotropy. We first perform an unmodeled search for persistent, directional gravitational-wave sources using folded data from the first (O1) and second (O2) observing runs of Advanced LIGO and show that the results are consistent with the upper limits published by the LIGO-Virgo Collaboration (LVC). We then explore various ways to account for the pixel-to-pixel Fisher information matrix using singular-value decomposition and Bayesian regularization schemes. We do not find evidence for any SGWB signal in the data and the upper limits are consistent with the LVC results within statistical errors. Through an injection study, we show that they are all valid 95\% upper limits, that is, the upper limit in a pixel is less than the injected signal strength in less than 5\% of the pixels.