The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget (2306.16218v1)

Abstract: Pulsar timing arrays (PTAs) are galactic-scale gravitational wave detectors. Each individual arm, composed of a millisecond pulsar, a radio telescope, and a kiloparsecs-long path, differs in its properties but, in aggregate, can be used to extract low-frequency gravitational wave (GW) signals. We present a noise and sensitivity analysis to accompany the NANOGrav 15-year data release and associated papers, along with an in-depth introduction to PTA noise models. As a first step in our analysis, we characterize each individual pulsar data set with three types of white noise parameters and two red noise parameters. These parameters, along with the timing model and, particularly, a piecewise-constant model for the time-variable dispersion measure, determine the sensitivity curve over the low-frequency GW band we are searching. We tabulate information for all of the pulsars in this data release and present some representative sensitivity curves. We then combine the individual pulsar sensitivities using a signal-to-noise-ratio statistic to calculate the global sensitivity of the PTA to a stochastic background of GWs, obtaining a minimum noise characteristic strain of $7\times 10^{-15}$ at 5 nHz. A power law-integrated analysis shows rough agreement with the amplitudes recovered in NANOGrav's 15-year GW background analysis. While our phenomenological noise model does not model all known physical effects explicitly, it provides an accurate characterization of the noise in the data while preserving sensitivity to multiple classes of GW signals.

• The paper details a comprehensive noise budget analysis of pulsar timing data over 15 years, employing power-law spectral models and Gaussian processes to isolate gravitational wave signals.
• It quantifies a minimum noise strain of 7×10⁻¹⁵ at 5 nHz, validating the detector’s sensitivity and consistency with earlier gravitational wave amplitude recoveries.
• The study identifies key pulsars with intrinsic red noise or common gravitational wave contributions, setting the stage for improved noise mitigation and future detection strategies.

Overview of the NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget

In the paper titled "The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget," the NANOGrav collaboration presents an extensive analysis of the noise budget associated with their pulsar timing array (PTA) over 15 years of data collection. This research is critical in advancing the understanding and detection capabilities of PTAs, which are galactic-scale detectors of gravitational waves (GWs) working in the nanohertz frequency domain.

Pulsar Timing Arrays and Their Noise Components

PTAs exploit the exceptionally stable rotation of millisecond pulsars (MSPs) as cosmic timekeepers to detect low-frequency gravitational waves, primarily emitted by supermassive black hole binaries (SMBHBs). The goal is to observe the stochastic gravitational wave background (GWB) formed by the aggregate of signals from unresolved SMBHBs. Such observations necessitate meticulous noise modeling to discern gravitational wave signals from other sources of time-variable noise.

Methodological Approach to Noise Analysis

The paper provides an in-depth characterization of both white and red noise components within the detector. White noise, treated as uncorrelated over time, is detailed with three parameters that adjust the timing uncertainties of recorded pulsar observations. These include the Error Factor (EFAC), EQUAD, and ECORR adjusted across various backend and receiver combinations to ensure data reliability.

Red noise, typifying time-correlated stochastic processes, is modeled using Gaussian process regression. This involves capturing low-frequency signals, which may include contributions from GWBs, through power-law spectral models characterized by amplitude and spectral indexes.

Key Findings and Analytical Results

The research shows that the noise budget is essential for ensuring the accurate characterization of the PTA’s sensitivity to the stochastic GWB. The noise budget analysis was substantiated by demonstrating its alignment with previously recovered GW amplitudes, underscoring the validity of the phenomenological noise model.

Highlighted findings include:

• A minimum noise characteristic strain was identified at $7 \times 10^{-15}$ at 5 nHz, pivotal for the PTA's sensitivity curve assessment.
• Sensitivity to the stochastic GWB was calculated using a power law-integrated approach, emphasizing agreement with recovered amplitudes from the historic data set.
• Key pulsars were identified with either intrinsic red noise or significant contributions to a common GW signal, helping refine future sensitivity estimates.

Implications and Future Developments

The implications of this research lie both in improving PTA techniques for gravitational wave detection and in advancing theoretical understanding of GW signals in the low-frequency domain. The paper suggests possible improvements via future wideband observations and noise reduction strategies, which include more comprehensive data analysis methodologies such as cyclic spectroscopy and real-time cyclic spectral processing.

Future developments will focus on maximizing the use of emerging wideband receivers, which could offer significant enhancements in signal precision and noise mitigation. Additionally, adaptive analysis techniques to exclude GWB as background noise for future GW detections from isolated sources will become increasingly relevant.

By accurately modeling and interpreting noise within PTAs, researchers can push the boundaries of gravitational wave astronomy, unlocking insights into the universe's most enigmatic phenomena. This paper not only establishes a methodological foundation for analyzing PTA data sets but also opens avenues for refined exploration of gravitational waves at previously inaccessible frequencies.