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

TL;DR

The paper investigates gravitational-wave detectability of equal-mass black-hole binaries with spins aligned or anti-aligned to the orbital angular momentum using numerical-relativity simulations extended by PN amplitudes. It quantifies how the total spin projection along the orbital momentum affects SNR, horizon distances, and event rates across LIGO/Virgo, AdLIGO/eLIGO, and LISA, and examines the role of higher-order modes in the signal. Key findings include a strong spin-dependent increase in SNR for aligned spins (maximally aligned binaries can be over three times louder than maximally anti-aligned ones), the existence of degeneracies in waveform morphology for opposite spins, and robust, simple fitting formulas for the SNR and radiated energy. These results have practical implications for GW searches and parameter estimation, highlighting the prominence of spin effects in detector reach and the necessity of accurate waveform models that include higher modes.

Abstract

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.

Figures (11)

• Figure 1: Schematic representation in the $(a_1,\,a_2)$ plane, also referred to as the "spin diagram", of the initial data collected in Table \ref{['tableone']}. These sequences cover most important portions of the space of parameters which is symmetric with respect to the $a_1=a_2$ diagonal.
• Figure 2: Noise strain for the Advanced LIGO and Virgo detectors and the Fourier-transformed amplitude of the PN and NR waveform at $\theta=0, \phi=0$ for a total mass $M=200\,M_{\odot}$ at a distance $d=100\,{\rm Mpc}$ for the maximally spinning model $s_8$. The glueing frequency is at $f_{\rm glue}=27.14$ Hz.
• Figure 3: Averaged and maximum horizon distance $d_H=d_H(a, M)$ for the LIGO detector (top left panel), for the Virgo detector (top right panel), and for the advanced versions of both detectors (bottom left and right panels, respectively). The horizon distance has been computed at a reference SNR $\rho=8.0$.
• Figure 4: Maximum SNR $\rho_{\rm max}=\rho(a,\,M)$ for the LIGO detector for a given set of masses at a distance $d=100\,{\rm Mpc}$. Note that the growth of $\rho_{\rm max}$ with $a$ is very well described with a low-order polynomial which is of $4$th order for the optimal mass (cf. discussion in Sect. \ref{['sec:fitSNR']}). Note also that the dependence on $a$ becomes stronger for masses $M>200 \,M_{\odot}$, for which the NR-part of the waveform and hence the plunge and ringdown phase dominate. In these cases, the SNR is more then doubled between $a=-1$ and $a=+1$.
• Figure 5: Averaged and maximum SNR $\rho=\rho(a, M)$ for the planned LISA mission and for sources at $d=6.4\,\mathrm{Gpc}\ (z=1)$.