Observational upper limits on the gravitational wave production of core collapse supernovae

The upper limit on the energy density of a stochastic gravitational wave (GW) background obtained from the two-year science run (S5) of the Laser Interferometer Gravitational-wave Observatory (LIGO) is used to constrain the average GW production of core collapse supernovae (ccSNe). We assume that the ccSNe rate tracks the star formation history of the universe and show that the stochastic background energy density depends only weakly on the assumed average source spectrum. Using the ccSNe rate for $z\leq10$, we scale the generic source spectrum to obtain an observation-based upper limit on the average GW emission. We show that the mean energy emitted in GWs can be constrained within $< (0.49-1.98){1mm} M_{\odot} c^{2}$ depending on the average source spectrum. While these results are higher than the total available gravitational energy in a core collapse event, second and third generation GW detectors will enable tighter constraints to be set on the GW emission from such systems.

💡 Research Summary

The paper exploits the upper limit on the stochastic gravitational‑wave (GW) background derived from the two‑year science run (S5) of the Laser Interferometer Gravitational‑Wave Observatory (LIGO) to place an observational constraint on the average GW emission of core‑collapse supernovae (ccSNe). The authors begin by assuming that the cosmic ccSN rate follows the star‑formation history (SFH) of the Universe. Using a modern SFH model together with a standard initial‑mass function, they calculate the redshift‑dependent ccSN rate R(z) for redshifts up to z = 10, incorporating the fraction of massive stars (M > 8 M⊙) that end their lives as core‑collapse events. Cosmological parameters (Ωm = 0.3, ΩΛ = 0.7, H0 = 70 km s⁻¹ Mpc⁻¹) are adopted to convert comoving rates into an integrated GW background.

For the GW signal from an individual supernova the authors adopt a “generic” source spectrum. This is represented either by a Gaussian centered at a characteristic frequency f0 with a width Δf, or by a simple broken power‑law. The choice is motivated by the fact that detailed numerical simulations of core‑collapse produce spectra that are broadly similar in shape, and the exact form has only a weak impact on the final stochastic background because redshift stretching and the redshift‑dependent event rate partially cancel spectral differences in the integral.

The stochastic background energy density Ωgw(f) is obtained by integrating the product of the source spectrum and the event rate over redshift. The integral includes the (1+z) factor accounting for the redshift of GW energy and the cosmological volume element. The authors demonstrate that Ωgw depends only mildly on the assumed spectral shape, which justifies using a single representative spectrum for the whole analysis.

LIGO’s S5 result provides an upper limit Ωgw < 6.9 × 10⁻⁶ in the band 41.5–169 Hz. Substituting this limit into the integral expression for Ωgw and solving for the average GW energy per supernova, EGW, yields an observational upper bound. The derived bound varies with the chosen generic spectrum, ranging from 0.49 M⊙c² to 1.98 M⊙c². This is substantially larger than the total gravitational binding energy released in a typical core‑collapse event (≈0.1 M⊙c²) and far above the values predicted by most theoretical models (10⁻⁸–10⁻⁶ M⊙c²). Consequently, the current S5 constraint does not yet challenge existing supernova GW emission models, but it establishes a clear, data‑driven ceiling.

The paper then discusses the prospects for tighter constraints with next‑generation detectors. Advanced LIGO, Virgo+, KAGRA, and third‑generation observatories such as the Einstein Telescope are expected to improve the stochastic background limit by two to three orders of magnitude. If Ωgw can be reduced to ≲10⁻⁸, the corresponding upper limit on EGW would fall to ≲10⁻³ M⊙c², entering the regime where it can discriminate between different core‑collapse mechanisms (e.g., rapid rotation, strong magnetic fields, or asymmetric neutrino emission). Moreover, a more precise measurement of the spectral shape of the stochastic background could allow separation of the ccSN contribution from other astrophysical sources (binary black holes, binary neutron stars, etc.).

In summary, the authors provide the first observationally anchored upper limit on the average GW energy emitted by core‑collapse supernovae, based on the LIGO S5 stochastic background bound. While the present limit is far above theoretical expectations, the methodology demonstrates that stochastic GW background measurements are a viable tool for probing the collective GW output of distant supernovae. Future improvements in detector sensitivity will tighten these bounds dramatically, potentially turning stochastic background observations into a powerful diagnostic of the physics of core collapse.