Erratum: "Charged Compact Binary Coalescence Signal and Electromagnetic Counterpart of Plunging BH–NS Mergers" (2019, ApJL, 873, L9)

In the published Letter, there was a typo in Equation (4). The reduced mass should be expressed as M_r, not μ, which is defined as the magnetic dipole moment later. The correct expression should read

$$\begin{eqnarray}&&{L}_{\mathrm{GW}}=\displaystyle \frac{32}{5}\displaystyle \frac{{G}^{4}}{{c}^{5}}\displaystyle \frac{{M}_{r}^{2}{M}^{3}}{{a}^{5}}f(e).\end{eqnarray} \tag{ 4 }$$

The discussion of neutron star (NS) charge in Section 3 contains errors. In particular, Equation (23) is incorrect. After correcting the error, the general conclusion of the Letter remains unchanged, even though the charge of NSs is systematically reduced by a factor of ∼4.5. The second paragraph of Section 3 should be revised as follows:

"As has been well known in pulsar theories (e.g., Michel 1982), rotating, magnetized NSs are charged. For a dipolar magnetic field, even though integrating the Goldreich–Julian spatial charge density distribution (${\rho }_{\mathrm{GJ}}\sim -({\boldsymbol{\Omega }}\cdot {\boldsymbol{B}})/2\pi c$, Goldreich & Julian 1969) over the volume contained within the magnetosphere gives no net charge (regardless of the inclination angle), the electric field ${\boldsymbol{E}}=-({\boldsymbol{v}}\times {\boldsymbol{B}})/c$ has a radial component at the NS surface. Gauss's law gives a net charge contained at the center of the NS (Michel 1982; Pétri 2012)

$$\begin{eqnarray}&&{Q}_{\mathrm{NS}}=\displaystyle \frac{1}{3}\displaystyle \frac{{\rm{\Omega }}{B}_{p}{R}^{3}}{c}\cos \alpha ,\end{eqnarray} \tag{ 23 }$$

where α is the inclination angle between the magnetic and rotational axes of the NS. If the NS is uniformly magnetized, the NS charge is ${Q}_{\mathrm{NS}}=-({\rm{\Omega }}{B}_{p})/(2\pi c)\cdot (4\pi /3){R}^{3}\cos \alpha =-(2/3)({\rm{\Omega }}{B}_{p}{R}^{3}/c)\cos \alpha$ (notice the opposite sign from the dipole case). Since the charged compact binary coalescence (cCBC) emission power scales with ${\hat{q}}^{2}$, only the absolute value of the charge enters the problem. For the uniformly magnetized NS, the NS dimensionless charge has an absolute value

$$\begin{eqnarray}&&\left|{\hat{q}}_{\mathrm{NS}}\right|\simeq \displaystyle \frac{{\rm{\Omega }}{B}_{p}{R}^{3}}{3c\sqrt{G}{M}_{\mathrm{ns}}}\cos \alpha \sim {10}^{-7}{B}_{13}{P}_{-2}^{-1}{R}_{6}^{3}{M}_{1.4}^{-1}\cos \alpha .\end{eqnarray} \tag{ 24 }$$

For the Crab pulsar (B₁₃ = 0.8 and P₋₂ = 3.3), one has ${\hat{q}}_{\mathrm{Crab}}=2.4\times {10}^{-8}\cos \alpha$."

I thank Kunihito Ioka, Kazuya Takahashi, and Tomoki Wada for pointing out the error and for discussing NS charge physics.