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, and which therefore do not exhibit precession effects, 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 “3 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 ${\mathit{S}}_1=-{\mathit{S}}_2$ cannot be distinguished, whereas binaries with spin ${\mathit{S}}_1={\mathit{S}}_2$ 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 $E_{\mathrm{rad}}/M\gtrsim 3.6\%$, which can become as large as $E_{\mathrm{rad}}/M\simeq 10\%$ for maximally spinning binaries with spins aligned with the orbital angular momentum. These binaries are therefore among the most efficient sources of energy in the Universe.