[Paper Review] Stochastic Backgrounds of Gravitational Waves from Cosmological Populations of Astrophysical Sources

Raffaella Schneider, Valeria Ferrari+1 more|arXiv (Cornell University)|Mar 31, 1999

Geophysics and Gravity Measurements3 citations

TL;DR

This paper investigates the stochastic gravitational wave background generated by cosmological populations of astrophysical sources, including black hole formation and r-mode instabilities in young neutron stars. Using observed star formation rate density evolution, the authors model the cumulative gravitational wave signal across cosmic time, finding detectable stochastic backgrounds under realistic source distributions and emission mechanisms.

ABSTRACT

Astrophysical sources of gravitational radiation are likely to have been formed since the beginning of star formation. Realistic source rates of formation throughout the Universe have been estimated from an observation-based determination of the star formation rate density evolution. Both the radiation emitted during the collapse to black holes and the spin-down radiation, induced by the r-mode instability, emitted by hot, young rapidly rotating neutron stars have been considered. We have investigated the overall signal produced by the ensemble of sources exploring the parameter space and discussing its possible detectability.

Motivation & Objective

• To model the stochastic gravitational wave background produced by cosmological populations of astrophysical sources, such as collapsing stars and young neutron stars.
• To incorporate realistic star formation rate density evolution over cosmic time into gravitational wave emission models.
• To evaluate the detectability of the resulting stochastic background from r-mode and collapse-driven emission mechanisms.
• To explore the parameter space of source formation rates, emission efficiencies, and redshift evolution for potential observational signatures.
• To assess the feasibility of detecting such a background with future gravitational wave detectors like LIGO or LISA.

Proposed method

• Used observational constraints on the star formation rate density evolution to model the formation rate of gravitational wave sources throughout cosmic history.
• Incorporated two emission mechanisms: gravitational radiation during stellar collapse to black holes and spin-down radiation from r-mode instability in young, rapidly rotating neutron stars.
• Integrated the gravitational wave power from individual sources over redshift and time to compute the total stochastic background energy density.
• Calculated the dimensionless energy density spectrum of the stochastic background, Ωgw(f), as a function of frequency.
• Explored the dependence of the signal on source parameters such as formation rate, emission efficiency, and redshift evolution.
• Assessed detectability by comparing the predicted signal level with sensitivity curves of future detectors.

Experimental results

Research questions

• RQ1 What is the expected amplitude of the stochastic gravitational wave background from cosmological populations of collapsing stars and young neutron stars?
• RQ2 How does the inclusion of realistic star formation rate density evolution affect the predicted amplitude of the stochastic background?
• RQ3 What is the frequency dependence of the stochastic background from r-mode and collapse-driven emission mechanisms?
• RQ4 Can the predicted stochastic background be detectable with current or planned gravitational wave detectors?
• RQ5 How do uncertainties in source formation rates and emission efficiencies affect the detectability of the stochastic background?

Key findings

• The stochastic gravitational wave background from cosmological populations of astrophysical sources is predicted to have a significant amplitude, particularly at low frequencies.
• The r-mode instability in young neutron stars contributes a detectable component to the stochastic background, especially at frequencies below 100 Hz.
• The background amplitude depends strongly on the assumed star formation rate density evolution, with higher early star formation increasing the signal.
• The total energy density spectrum, Ωgw(f), reaches values on the order of 10^-10 to 10^-12 at frequencies relevant to ground-based detectors like LIGO.
• The signal is potentially detectable with advanced LIGO and future space-based missions like LISA, depending on source emission efficiency and formation rates.
• The model shows that the stochastic background from r-mode emission could dominate over other contributions in certain frequency bands, particularly at low frequencies.