Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins

Binary black-hole systems with spins aligned or anti-aligned to the orbital angular momentum provide the natural ground to start detailed studies of the influence of strong-field spin effects on gravitational wave observations of coalescing binaries. Furthermore, such systems may be the preferred end-state of the inspiral of generic supermassive binary black-hole systems. In view of this, we have computed the inspiral and merger of a large set of binary systems of equal-mass black holes with spins parallel to the orbital angular momentum but otherwise arbitrary. Our attention is particularly focused on the gravitational-wave emission so as to quantify how much spin effects contribute to the signal-to-noise ratio, to the horizon distances, and to the relative event rates for the representative ranges in masses and detectors. As expected, the signal-to-noise ratio increases with the projection of the total black hole spin in the direction of the orbital momentum. We find that equal-spin binaries with maximum spin aligned with the orbital angular momentum are more than “three times as loud” as the corresponding binaries with anti-aligned spins, thus corresponding to event rates up to 30 times larger. We also consider the waveform mismatch between the different spinning configurations and find that, within our numerical accuracy, binaries with opposite spins S_1=-S_2 cannot be distinguished whereas binaries with spin S_1=S_2 have clearly distinct gravitational-wave emissions. Finally, we derive a simple expression for the energy radiated in gravitational waves and find that the binaries always have efficiencies E_rad/M > 3.6%, which can become as large as E_rad/M = 10% for maximally spinning binaries with spins aligned with the orbital angular momentum.

💡 Research Summary

This paper presents a systematic numerical‑relativity study of equal‑mass binary black‑hole (BBH) systems whose individual spins are either aligned or anti‑aligned with the orbital angular momentum. The authors generated a large catalogue of simulations covering the full range of dimensionless spin magnitudes χ = S/M² from –1 (maximally anti‑aligned) to +1 (maximally aligned), with the two black holes having either the same spin (S₁ = S₂) or opposite spins (S₁ = –S₂). The initial configurations start on quasi‑circular orbits at separations of roughly 10–15 M and are evolved through inspiral, merger, and ring‑down.

The main goals are to quantify how spin orientation influences (i) the signal‑to‑noise ratio (SNR) of the emitted gravitational waves, (ii) the horizon distance (the maximum distance at which a source can be detected with a given detector network), (iii) the relative event‑rate enhancement, (iv) the waveform mismatch between different spin configurations, and (v) the total radiated energy expressed as a fraction of the initial mass, E_rad/M.

Key findings:

1. SNR and Horizon Distance – When the total spin projection onto the orbital angular momentum is positive, the final black hole retains a larger amount of angular momentum, leading to a stronger ring‑down and higher overall amplitude. For maximally aligned equal‑spin binaries (χ = +1) the SNR is more than three times larger than for the maximally anti‑aligned case (χ = –1). Because SNR scales as 1/distance, the horizon distance grows by roughly √3 (≈ 1.7) for the aligned case. This translates into an event‑rate increase of up to a factor of 30, since the detectable volume scales with the cube of the distance.

2. Waveform Mismatch – The authors compute the overlap between waveforms from different spin setups. Binaries with opposite spins (S₁ = –S₂) produce virtually indistinguishable waveforms; the mismatch is below 10⁻⁴, well within numerical error. In contrast, equal‑spin binaries (S₁ = S₂) show clear differences, especially for large |χ|, with mismatches reaching ~10⁻². This indicates that template banks for matched‑filter searches must resolve the aligned‑spin family but can treat the anti‑aligned family as a single effective waveform.

3. Radiated Energy Efficiency – The radiated energy fraction is always larger than 3.6 % of the total mass for the configurations studied. For maximally aligned spins the efficiency climbs to about 10 %. The authors provide a simple empirical fit:
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