The NANOGrav 15-year Data Set: Search for Anisotropy in the Gravitational-Wave Background (2306.16221v1)

Abstract: The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has reported evidence for the presence of an isotropic nanohertz gravitational wave background (GWB) in its 15 yr dataset. However, if the GWB is produced by a population of inspiraling supermassive black hole binary (SMBHB) systems, then the background is predicted to be anisotropic, depending on the distribution of these systems in the local Universe and the statistical properties of the SMBHB population. In this work, we search for anisotropy in the GWB using multiple methods and bases to describe the distribution of the GWB power on the sky. We do not find significant evidence of anisotropy, and place a Bayesian $95\%$ upper limit on the level of broadband anisotropy such that $(C_{l>0} / C_{l=0}) < 20\%$. We also derive conservative estimates on the anisotropy expected from a random distribution of SMBHB systems using astrophysical simulations conditioned on the isotropic GWB inferred in the 15-yr dataset, and show that this dataset has sufficient sensitivity to probe a large fraction of the predicted level of anisotropy. We end by highlighting the opportunities and challenges in searching for anisotropy in pulsar timing array data.

Insights into the NANOGrav 15-year Data: Anisotropy in the Gravitational-Wave Background

The paper "The NANOGrav 15-year Data Set: Search for Anisotropy in the Gravitational-Wave Background" presents an in-depth investigation into the anisotropic characteristics of the gravitational-wave background (GWB) using the extensive dataset from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). This document offers a detailed assessment of potential anisotropies emanating from the GWB, hypothesized to be driven predominantly by inspiraling supermassive black-hole binaries (SMBHBs).

Methodology Overview

The analysis employed both Bayesian and frequentist methodologies to interrogate the NANOGrav 15-year dataset for anisotropy signals in the GWB. The gravitational wave data was modeled using a combination of spherical harmonic and radiometer pixel basis frameworks to capture the spatial distribution of GWB power. The auto- and cross-correlations of pulsar timing data form the core of the dataset, allowing researchers to discern inconsistencies from an isotropic GWB. The paper utilized a considerable subset—67 pulsars—evaluated across multiple Bayesian and frequentist structures to probe the data's anisotropy spectrum. The Bayesian analysis leveraged a power-law model and frequency-resolved analyses to derive evidence for or against anisotropic characteristics within the GWB, while the frequentist analysis employed signal-to-noise (S/N) ratio calculations and upper limits to ascertain anisotropy.

Key Findings and Numerical Results

A central conclusion of the paper is the lack of significant evidence for anisotropy within the GWB based on the dataset analyzed. The Bayesian analysis yielded odds ratios not markedly in favor of an anisotropic model, while frequentist approaches resulted in an anisotropic S/N coinciding with a non-significant $p$-value. The derived 95% Bayesian upper limit on broad-spectrum anisotropy was established as $(C_{l>0} / C_{l=0}) < 20\%$, which remains below the thresholds predicted by theoretical models of anisotropy from SMBHBs at similar nHz frequencies.

Theoretical and Practical Implications

The findings have substantial implications for our understanding of the GWB's structure and the possible distribution of SMBHBs across the universe. Practically, these results underscore the existing limitations in current pulsar timing array datasets to unambiguously delineate between isotropic and anisotropic GWB. The constraint $(C_{l>0}/C_{l=0})\lesssim20\%$ serves as an empirical benchmark for future studies targeting anisotropy detection. Theoretically, given the prediction that anisotropy may surface from SMBHB clusters' distribution patterns, the absence of observed anisotropy is indicative of either uniform SMBHB distribution or limitations in sensitivity at the current dataset's frequency ranges.

Future Directions in Research

As the sensitivity and range of PTA datasets evolve, there is optimism regarding the enhanced capacity to detect or refute anisotropy within the GWB. This points to future work with IPTA's third data release, which integrates global datasets across the Parkes, European, and Indian arrays, expanding both pulsar count and observational timespan. Improved methodologies and computationally efficient algorithms, possibly leveraging advanced Markov Chain Monte Carlo and data-driven Bayesian-frequentist hybrids, could potentially enhance the search for anisotropy. Addressing these challenges will be pivotal in advancing nanohertz GW astronomy, refining constraints on cosmic structures, and potentially disentangling the GWB's constituents from cosmological models involving cosmic strings and other exotic sources.

In summary, while the paper did not conclusively demonstrate anisotropy presence within the GWB, it delineated significant constraints and methodological advancements relevant to the astrophysical community. As datasets grow longitudinally and methodologically, the pursuit of anisotropic signatures in the pulsar timing data remains a fertile ground for future exploration, promising insights into the universe's GW dynamics.