Horizon-absorption effects in coalescing black-hole binaries: An effective-one-body study of the nonspinning case

We study the horizon absorption of gravitational waves in coalescing, circularized, nonspinning black-hole binaries. The horizon-absorbed fluxes of a binary with a large mass ratio ($q=1000$) obtained by numerical perturbative simulations are compared with an analytical, effective-one-body (EOB) resummed expression recently proposed. The perturbative method employs an analytical, linear in the mass ratio, EOB-resummed radiation reaction, and the Regge-Wheeler-Zerilli formalism for wave extraction. Hyperboloidal layers are employed for the numerical solution of the Regge-Wheeler-Zerilli equations to accurately compute horizon fluxes up to the late plunge phase. The horizon fluxes from perturbative simulations and the EOB-resummed expression agree at the level of a few percent down to the late plunge. An upgrade of the EOB model for nonspinning binaries that includes horizon absorption of angular momentum as an additional term in the resummed radiation reaction is then discussed. The effect of this term on the waveform phasing for binaries with mass ratios spanning 1–1000 is investigated. We confirm that for comparable and intermediate-mass-ratio binaries horizon absorption is practically negligible for detection with advanced LIGO and the Einstein Telescope ($\mathrm{\text{faithfulness}}\ge 0.997$).

Figure 1

The function $\Omega$ for the two choices (18, 19). The dashed vertical lines (red online) indicate the interfaces at $R_{\pm }=12$. Infinity corresponds to $S_{\pm }=20$. The dashed (black online) curve denotes the $C^4$ transition (18), and the solid (black online) curve the smooth transition (19). The numerical results obtained later in the text are obtained with the smooth transition and with this choice of parameters.

Figure 2

Testing the accuracy of the updated time-domain RWZ code for a particle along a sequence of stable and unstable circular orbits. We plot the fractional difference in the horizon fluxes computed with the time-domain RWZ code using hyperboloidal layers and Akcay’s frequency-domain code [3, 44].

Figure 3

Comparing horizon and null infinity quadrupolar ($\ell =m=2$) RWZ waveforms for a coalescing binary with mass ratio $\nu ={10}^{-3}$. The horizontal axis corresponds to horizon anticipated time $u\equiv u^{+}=\tau +H$ for the horizon waveform and to null infinity retarded time, $u\equiv u^{-}=\tau -S$ for the asymptotic waveform. The leftmost (dash-dotted) vertical line marks the (dynamical) time when the particle crosses the LSO, while the rightmost (dashed) vertical line corresponds instead to the light-ring crossing. The horizon waveform (red online) becomes unreliable around the light-ring crossing ($u/M\gtrsim 4300$). See text for discussion.

Figure 4

Top panel: Comparison between RWZ horizon and asymptotic angular momentum fluxes for mass ratio $\nu ={10}^{-3}$ from Eq. (23) with ${\ell }_{\max }=8$. Bottom panel: The $\ell =2$ modes contribute to more than the 98% of the total absorbed flux up to LSO crossing (vertical dashed line).

Figure 5

Comparison between EOB resummed angular momentum flux and the RWZ one for the quadrupole ($\ell =2$) modes: $m=1$ (left panel) and $m=2$ (right panel). The dash-dotted vertical line marks the LSO crossing. The EOB-resummed (horizon) mechanical angular momentum loss shows very good consistency with the horizon flux computed from GWs. By contrast, the 1PN-accurate expressions, Eqs. (25, 26), underestimate horizon absorption by more than a factor of 2.

Figure 6

Test-mass limit ($\nu ={10}^{-3}$) including ${\mathcal{F}}_{\phi }^H(v;0)$ in the dynamics and its effect on the $\ell =m=2$ phasing. The top panel compares the $\ell =m=2$ EOB waveforms with (solid line) and without (dashed line) ${\mathcal{F}}_{\phi }^H(v;0)$. The accumulated phase difference (bottom panel) is of order 0.1 rad at LSO crossing (dash-dotted vertical line) and reaches a remarkable 1.5 rad at merger (dashed vertical line).

Figure 7

Accumulated phase difference due to horizon absorption for different mass ratios $q$ as obtained from EOB evolutions. The vertical lines mark the crossing of the EOB-defined LSO (leftmost line) and of the EOB-defined light ring (rightmost line). For all binaries, the initial separation is $r_0=15$, corresponding to $M{\omega }_{22}^0=0.0344$.

Figure 8

The evolution of the field for a radially infalling particle starting at $r_0=7$. The plot spans 13 orders of magnitude. Observers are located (from top to bottom) at $\mathcal{I}$, 30, and 15.

Figure 9

The local decay rates for the above evolution. The observers (from top to bottom) are located approximately at $\{\mathcal{I},250,80,50,35,25,20\}M$. The dashed lines indicate the theoretically expected asymptotic decay rates: $-4$ at $\mathcal{I}$, and $-7$ at finite distances.

Figure 10

The evolution of the real (solid line) and imaginary (dashed line) of the field for insplunge from $r_0=7$. The evolution spans 14 orders of magnitude. Observers are located (in units of $M$, from top to bottom) at $\mathcal{I}$, 35, and 18.