The NANOGrav 15 yr Data Set: Piecewise Power-Law Reconstruction of the Gravitational-Wave Background

TL;DR

The paper addresses the challenge of identifying the origin of the NG15 gravitational-wave background signal by reconstructing its frequency spectrum with a physics-agnostic, piecewise power-law framework. It introduces a hierarchy of PPL models with movable or fixed internal nodes and performs a Bayesian model average to balance complexity with data support. Through a marginalized PTA likelihood, the authors compare CPL, BPL, and higher-n PPLs, finding that PPL1 (CPL-like) best fits the data, while higher-complexity models are progressively disfavored; the resulting Omega and spectral index bands provide a constrained yet flexible description of the GWB spectrum. The work also outlines a practical path for fast spectral refits using the PPL posterior as a foundation, facilitating rapid testing of alternative GWB models with NG15-like data.

Abstract

The NANOGrav 15-year (NG15) data set provides evidence for a gravitational-wave background (GWB) signal at nanohertz frequencies, which is expected to originate either from a cosmic population of inspiraling supermassive black-hole binaries or new particle physics in the early Universe. A firm identification of the source of the NG15 signal requires an accurate reconstruction of its frequency spectrum. In this paper, we provide such a spectral characterization of the NG15 signal based on a piecewise power-law (PPL) ansatz that strikes a balance between existing alternatives in the literature. Our PPL reconstruction is more flexible than the standard constant-power-law model, which describes the GWB spectrum in terms of only two parameters: an amplitude A and a spectral index gamma. Concurrently, it better approximates physically realistic GWB spectra -- especially those of cosmological origin -- than the free spectral model, since the latter allows for arbitrary variations in the GWB amplitude from one frequency bin to the next. Our PPL reconstruction of the NG15 signal relies on individual PPL models with a fixed number of internal nodes (i.e., constant power law, broken power law, doubly broken power law, etc.) that are ultimately combined in a Bayesian model average. The data products resulting from our analysis provide the basis for fast refits of spectral GWB models.

Figures (7)

• Figure 1: Left panel: PPL reconstruction of the energy density power spectrum $h^2\Omega_{\rm GW}$ for the GWB signal in the NG15 data, based on the BMA of six PPL models with a fixed number of freely moving internal nodes (PPL1-free, ... PPL6-free). Right panel: Same, but for the frequency-dependent spectral index of the energy density power spectrum, $\gamma = 5- d \ln h^2\Omega_{\rm GW}/ d\ln f$. Both reconstructions cover the frequency range from $F_1 = 1/T_{\rm obs}$ to $F_{14} = 14/T_{\rm obs}$, where $T_{\rm obs} = 16.03\,\textrm{yr}$ (see text for details). In the left panel, we also show the NG15 violins in orange, which represent the amplitude posterior densities for the free spectral model. The lower end of the violins at higher frequencies follows from the prior density chosen in NANOGrav:2023gor.
• Figure 2: $\Omega$-PPL and $\gamma$-PPL bands for all individual binned and free models considered in this work (see text for details).
• Figure 3: Corner plots for the binned models. Parameter regions shaded in darker and lighter colors correspond to $68\%$ and $95\%$ credible regions, respectively. At the top of each column, we state median values and 95% equal-tailed credible intervals.
• Figure 4: Corner plots for the free models. Parameter regions shaded in darker and lighter colors correspond to $68\%$ and $95\%$ credible regions, respectively. At the top of each column, we state median values and 95% equal-tailed credible intervals.
• Figure 5: Bayes factors $\mathcal{B}_{n1}$ for the model comparisons PPL$n$ versus PPL$1$, both for the binned and free models. Normalizing the $\mathcal{B}_{n1}$ by their sum yields the model probabilities $P_n$ [see Eq. \ref{['eq:PnBn1']}, shown here for the free models].