Stochastic Gravitational Wave Background from Cosmological Supernovae

TL;DR

This work assesses the stochastic gravitational-wave background produced by cosmological core-collapse supernovae and evaluates its significance for space-based detectors. It introduces a framework tying the background to the cosmic SN rate $R_{\rm SN}(z)$ and the single-event spectrum $|\tilde{h}(f)|$ via the memory effect from anisotropic neutrino emission, encapsulated in $\Omega_{\rm gw}(f)$ with a zero-frequency extension of the event signal. Using SN simulations (e.g., models s15r, s11nr180, pns180) and a speculative Population III scenario, the authors show that the SN background could be comparable to or even exceed the inflationary GW background in the sub-Hz range, potentially acting as a foreground for BBO. However, predictions are highly uncertain due to the poorly constrained neutrino anisotropy evolution $q(t)$, redshift evolution parameter $\alpha$, and PopIII rates, underscoring the need for longer, fully three-dimensional simulations with realistic neutrino transport. Depending on PopIII abundances, these early stars could dominate the GW background; if not, the inflationary background remains detectable but requires careful foreground modeling and mitigation.

Abstract

Based on new developments in the understanding of supernovae (SNe) as gravitational-wave (GW) sources we estimate the GW background from all cosmic SNe. For a broad range of frequencies around 1 Hz, this background is crudely comparable to the GW background expected from standard inflationary models. While our estimate remains uncertain within several orders of magnitude, the SN GW background may become detectable by second-generation space-based interferometers such as the proposed Big-Bang Observatory (BBO). By the same token, the SN GWs may become a foreground for searches of the inflationary GWs, in particular for sub-Hz frequencies where the SN background is Gaussian and where the BBO will be most sensitive. SN simulations lasting far beyond the usual cutoff of about 1 second are needed for more robust predictions in the sub-Hz frequency band. An even larger GW background can arise from a hypothetical early population of massive stars, although their GW source strength as well as their abundance are currently poorly understood.

Figures (8)

• Figure 1: Spectrum of GW background from Eq. (\ref{['los']}) for a simulation from Ref. Fryer:2004wi. Solid lines: the spectrum is continuously extended with the low-$f$ tail according to Eq. (\ref{['low_freq']}). The upper curve is obtained from Fig. 9 of Ref. Fryer:2004wi, whereas the lower is the same shifted downwards by a factor 100, which is considered a more realistic estimate. Horizontal lines: GW stochastic spectrum produced during slow-roll inflation and evaluated from Eq. (6) of Ref. Turner:1996ck. We assume $T/S=0.3$ for the ratio of the tensorial and scalar contributions to the cosmic microwave background radiation (CMBR) anisotropy and consider two values $\pm 10^{-3}$ of the running of the tensorial power-law index. Dotted lines: sensitivities of the indicated detectors. The BBO sensitivity is approximate and may change slightly in the final design.
• Figure 2: Neutrino luminosity $L_\nu(t)$, an-isotropy $q(t)$, and GW strain $h(t)$ times distance from anisotropic neutrino emission only, see Eq. (\ref{['Lnu']}), for model s15r of Ref. Mueller:2003fs, as functions of time after bounce. We also show the GW strain $h(t)$ times distance from anisotropic neutrino emission, using the average anisotropy $\langle q \rangle = 0.45 \%$.
• Figure 3: GW source spectra: Solid and dotted ragged lines are total and neutrino contribution, respectively, for model s15r of Ref. Mueller:2003fs at distance $D=10$ kpc. The straight solid line is the low-$f$ tail Eq. (\ref{['low_freq']}) with $h_\infty$ from Eq. (\ref{['memory']}), using $q(t)$ and $L_\nu (t)$ of Fig. \ref{['fig2']}, leading to $f|\tilde{h}(f)|\simeq2.21\times10^{-22}$. The dashed line is the schematic spectrum for PopIII stars of Eq. (\ref{['popIII']}).
• Figure 4: GW background for model s15r with rotation (colored bands and solid lines) and model s11nr180 without rotation (dashed line) from Ref. Mueller:2003fs. The source spectra have been continuously extended using the zero-$f$ tail, Eq. (\ref{['low_freq']}), for $f\lesssim1$ Hz, except for the solid lines. The blue band and lower solid lines for model s15r reflect the plausible range $6$--$36$ of the enhancement factor to correct for the limited time of the simulation. For model s11nr180 the lower enhancement factor of 6 was assumed. We always use $\alpha=0$ in Eq. (\ref{['evol']}), except for the red band and upper solid line which show the difference between $\alpha=0$ and $\alpha=2$ (for enhancement factor 36) for model s15r.
• Figure 5: GW source spectra from mass motions plus an-iso-tropic neutrino emission for the proto-neutron star model pns180 of Ref. Mueller:2003fs at a distance of 10 kpc. The blue curve is for the full simulation with the fluctuating $q(t)$ integrated over 1.2 s, whereas for the red curve $q(t)$ was replaced with $\left\langle q\right\rangle\sim3\times10^{-5}$.