Gravitational waves from cosmological compact binaries

TL;DR

This paper estimates the stochastic gravitational-wave background from cosmological populations of compact binaries during their early-inspiral phase by combining a quadrupole-level single-source spectrum with population-synthesis results (SeBa) and a star-formation-history-based birth/merger-rate evolution. It distinguishes multiple binary types (bh-bh, ns-ns, wd-wd, and mixed pairs) and finds a two-component background: a primary low-frequency peak and a secondary higher-frequency component, with WD-WD and NS-NS binaries potentially detectable by LISA in the $1$–$10$ mHz range, where they also act as a confusion noise source. The study shows monolithic star-formation histories yield amplitudes $\sim$20–25% higher than hierarchical ones, reflecting the sensitivity of the background to assumptions about early galaxy evolution. It highlights the practical impact on LISA’s sensitivity to other signals and outlines future work to incorporate more realistic waveforms and to compare with relic backgrounds from the early Universe.

Abstract

We consider gravitational waves emitted by various populations of compact binaries at cosmological distances. We use population synthesis models to characterize the properties of double neutron stars, double black holes and double white dwarf binaries as well as white dwarf-neutron star, white dwarf-black hole and black hole-neutron star systems. We use the observationally determined cosmic star formation history to reconstruct the redshift distribution of these sources and their merging rate evolution. The gravitational signals emitted by each source during its early-inspiral phase add randomly to produce a stochastic background in the low frequency band with spectral strain amplitude between 10^{-18} Hz^{-1/2} and 5 10^{-17} Hz^{-1/2} at frequencies in the interval [5 10^{-6}-5 10^{-5}] Hz. The overall signal which, at frequencies above 10^{-4}Hz, is largely dominated by double white dwarf systems, might be detectable with LISA in the frequency range [1-10] mHz and acts like a confusion limited noise component which might limit the LISA sensitivity at frequencies above 1 mHz.

Figures (14)

• Figure 1: The cumulative probability distribution for the time delay $\tau_s$ (in Myr) between the formation of the progenitor system and the formation of the corresponding degenerate binary obtained for the (bh, wd), (ns, wd) and (wd, wd) samples.
• Figure 2: The cumulative probability distribution for the merger time $\tau_m$ (in Myr) is shown for the (ns, ns), (ns, wd) and (wd, wd) samples.
• Figure 3: The probability distribution for the orbital parameters of (bh, bh) systems ( left panel) is compared to that obtained for the (ns, ns) ( right panel) population.
• Figure 4: The Log of the star formation rate density in units of $M_\odot \hbox{yr}^{-1} \hbox{Mpc}^{-3}$ as a function of redshift for a cosmological background model with $\Omega_{M}=1$, $\Omega_{\Lambda}=0$, $H_0=50 \,\hbox{km}\hbox{s}^{-1} \hbox{Mpc}^{-1}$ and a Scalo (1986) IMF. Left: The data points correspond to UV, H$\alpha$ and IR observations of field galaxies. ( Filled dots) UV observations of Treyer et al. (1998), Lilly et al. (1996), Connolly et al. (1997), HDF Madau et al. (1996), Steidel et al. (1996),(1999); ( asterisks) H$\alpha$ observations of Gallego et al. 1995, Gronwall 1999, Tresse & Maddox 1998, Glazebrook et al. 1998, Yan et al. 1999); ( triangles): ISO IR observations (Flores et al. 1999) and the lower limit of SCUBA data (Hughes et al. 1998). ( Right): The dust-corrected SFR density as derived from UV data in the two models most favoured by observations predicted by Calzetti & Heckman ( asterisks) and by Pei, Fall & Hauser filled dots (see text).
• Figure 5: The rest-frame frequency of core-collapse SNae vs redshift predicted by the monolithic and hierarchical models. The predictions are consistent with the observed value for the present-day galaxy population (see text).