arXiv:2407.06270v1 Announce Type: new
Abstract: A population of compact object binaries emitting gravitational waves that are not individually resolvable will form a stochastic gravitational wave signal. While the expected spectrum over population realizations is well known from Phinney (2001), its higher order moments have not been fully studied before or computed in the case of arbitrary binary evolution. We calculate analytic scaling relationships as a function of gravitational-wave frequency for the statistical variance, skewness, and kurtosis of a stochastic gravitational-wave signal over population realizations. If the time derivative of the binary orbital frequency can be expressed as a power-law in frequency, we find that these moment quantities also take the form of power-law relationships. We also develop a numerical population synthesis framework against which we compare our analytic results, finding excellent agreement. These new scaling relationships provide physical context to understanding spectral fluctuations in a gravitational-wave background signal and may provide additional information that can aid in explaining the origin of the nanohertz-frequency signal observed by pulsar timing array campaigns.
Future Roadmap for Readers
This article discusses the population of compact object binaries emitting gravitational waves and the formation of a stochastic gravitational wave signal. The author highlights that while the expected spectrum of the signal is well known, the higher order moments have not been fully studied before. The objective of the study is to calculate the statistical variance, skewness, and kurtosis of the stochastic gravitational wave signal and understand their scaling relationships as a function of gravitational-wave frequency. The findings of this study could provide insights into the nanohertz-frequency signal observed by pulsar timing array campaigns.
Challenges
- The calculation of higher order moments of a stochastic gravitational wave signal is a complex task and requires sophisticated analytical and numerical techniques.
- Obtaining accurate population synthesis data for comparing the results is a challenging endeavor.
- The assumed power-law relationship between the time derivative of binary orbital frequency and frequency may not hold true in all cases, which could affect the validity of the scaling relationships.
Opportunities
- Understanding the higher order moments of a stochastic gravitational wave signal can provide deeper insights into the origin and nature of the signal.
- The developed numerical population synthesis framework can be further refined and used for future studies on gravitational wave signals.
- These scaling relationships may help in explaining the nanohertz-frequency signal observed in pulsar timing array campaigns and contribute to the field of gravitational wave astronomy.