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. Remarkably, we find that, due to nuances involved in the regularization schemes, the simplest method of using the convolved (dirty) map with a normalized variance, which was used in the LVC analysis, provides as good upper limits as the elaborate schemes with the full noise covariance matrix. Hence, we recommend continuing to use this simple method, though more regularization schemes may be explored to obtain stronger upper limits.

• Received 24 May 2021
• Accepted 26 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.123018