Numerical relativity estimates of the remnant recoil velocity in binary neutron star mergers

We present, for the first time, recoil velocity estimates for binary neutron star mergers using data from numerical relativity simulations. We find that binary neutron star merger remnants can have recoil velocity of the order of a few tens of kilometers per second and as high as 150 kilometers per second in our dataset. These recoils are attained due to equivalent contributions from the anisotropic gravitational wave emission as well as the asymmetric ejection of dynamical matter during the merger. We provide fits for net recoil velocity as well as its ejecta component as a function of the amount of ejected matter, which may be useful when constraints on the ejected matter are obtained through electromagnetic observations. We also estimate the mass and spin of the remnants and find them to be in the range $[2.34,3.38]M_{\odot }$ and [0.63, 0.82], respectively, for our dataset.

Figure 1

The distribution of mass ratio ($q$), total mass ($M$), and reduced tidal deformability parameter ($\tilde{\mathrm{\Lambda }}$) for the 84 binaries in our dataset.

Figure 2

The neutron star equations of state used in our numerical relativity simulations.

Figure 3

The distribution of the net remnant recoil velocity (top panel) and the ratio of ejecta to GW recoil velocity (bottom panel). Six binaries with remnant recoils greater than $70\mathrm{km}/\mathrm{s}$ are not shown in the top panel histogram; refer to Table 1 for their details.

Figure 4

The variation of BNS remnant recoils with binary’s mass ratio, total mass, and the reduced tidal deformability parameter. The size of the markers corresponds to the magnitude of the net remnant recoil. The shaded gray region and the region contained within solid gray lines represent the 90% credible intervals of the respective parameters estimated for GW170817 [3] and GW190425 [4], respectively. For GW170817, we consider parameter estimates using the low-spin prior as described in [71]. Different neutron star EoSs are represented using different colors as indicated in the legend.

Figure 5

A scatter plot showing the variation of the ejecta component of the remnant recoil (blue) and the net recoil (orange) with the net ejected mass. Both quantities are correlated and can be fitted with a linear curve (piecewise linear in the net recoil case) on this logarithmic scale: the solid blue (orange) lines represent the fitting function given in Eq. (12) [Eq. (13)].

Figure 6

The distribution of dynamical ejecta across a sphere at $r=200M_{\odot }\sim 295\mathrm{km}$ around the remnant for cases where the recoils due to ejecta are low (top row, a and b) and high (bottom row, c and d). The left (right) part of the subplot displays the molleweide (polar) projection of the healpix map. The color intensity represents the ejecta momentum flux density corresponding to each pixel. The star and dot markers indicate the direction of the GW and ejecta components of the remnant recoils, respectively.

Figure 7

Quantification of the asymmetry in the ejecta distribution using the antipodal symmetry parameter, $\alpha$.

Figure 8

Comparison of BNS remnant recoils with the recoils of nonspinning BBHs having the same mass ratio. The solid blue line shows the BBH recoils calculated through the GW emission using surrkick. This line terminates at $v=2.88\mathrm{km}/\mathrm{s}$ (dashed horizontal line) for $q=1$, which represents numerical errors in the surrkick calculation. The scatter of points represent BNS recoils from our dataset, with green circles considering just the BNS’s GW recoil while the orange stars consider the net BNS recoil.

Figure 9

The variation of BNS remnant recoils with the EoS for comparable mass binaries ($q>0.9$) lying in the total mass $M=[2.63,2.75]M_{\odot }$ bin.