Early warning of precessing compact binary merger with third-generation gravitational-wave detectors

Rapid localization of gravitational-wave events is important for the success of the multimessenger observations. The forthcoming improvements and constructions of gravitational-wave detectors will enable detecting and localizing compact-binary coalescence events even before mergers, which is called early warning. The performance of early warning can be improved by considering modulation of gravitational wave signal amplitude due to the Earth’s rotation and the precession of a binary orbital plane caused by the misaligned spins of compact objects. In this paper, for the first time we estimate localization precision in the early warning quantitatively, taking into account an orbital precession. We find that a neutron star—black hole binary at $z=0.1$ can typically be localized to $100{\mathrm{deg}}^2$ and $10{\mathrm{deg}}^2$ at the time of 12–15 minutes and 50–300 seconds before merger, respectively, which cannot be achieved without the precession effect.

Figure 1

Power spectral densities for advanced LIGO (blue), ET-D (orange), and CE (green).

Figure 2

Precessing binary. $\overrightarrow{J}$, $\overrightarrow{L}$, and $\overrightarrow{S}$ are, respectively, total, orbital, and spin angular momentum.

Figure 3

Precession angles for different mass ratios as a function of frequency. The top panel is for $\alpha$, the middle panel is for $\beta$, and the bottom panel is for $\zeta$.

Figure 4

Medians of localization errors for NSBH with $m_1/m_2=10$ as a function of time to merger. Left column is for the single detector case (ET). Right column is for the double detector case (ET and CE). From the top to the bottom, the sky localization error, the distance error, and the error volume as a function of time to merger. Blue (Orange) lines are without (with) a precession effect.

Figure 5

The same as Fig. 4 but for $m_1/m_2=5$.

Figure 6

Distributions of time to merger of detectable events when sky localization reaches $100{\mathrm{deg}}^2$ for NSBH with $m_1/m_2=10$ (top) and 5 (bottom). Left column is for the single detector case (ET). Right one is for the double detector case (ET and CE).

Figure 7

Medians of localization errors for BNS in the single detector case (ET) as a function of time to merger. From the top to the bottom, the sky localization error, the distance error, and the error volume as a function of time to merger. Blue (Orange) lines are without (with) the precession effect.

Figure 8

Distributions of SNR (top), $\mathrm{\Delta }\mathrm{\Omega }$ (middle), and $\mathrm{\Delta }{d}_L/d_L$ (bottom) for NSBH with $m_1/m_2=10$. Left column is for the single detector case (ET). Right one is for the double detector case (ET and CE).

Figure 9

Distributions of SNR (left), $\mathrm{\Delta }\mathrm{\Omega }$ (middle), and $\mathrm{\Delta }{d}_L/d_L$ (right) for BNS.

Figure 10

SNR dependences of sky localization errors for NSBH with $m_1/m_2=10$. Left panel is for single detector case, whereas Right panel is for double detectors case. Blue (Red) dots are with the earth rotation without (with) precession effect.

Figure 11

$\beta -{\theta }_J$ vs $|Z{|}^2$ for $\alpha (v)=0$, $F_{\times }=0$, $F_{+}=1$.