Black hole remnant of black hole-neutron star coalescing binaries

We present a model for determining the dimensionless spin parameter and mass of the black hole remnant of black hole-neutron star mergers with parallel orbital angular momentum and initial black hole spin. This approach is based on the Buonanno, Kidder, and Lehner method for binary black holes, and it is successfully tested against the results of numerical-relativity simulations: the dimensionless spin parameter is predicted with absolute error $\lesssim 0.02$, whereas the relative error on the final mass is $\lesssim 2\%$, its distribution in the tests being pronouncedly peaked at 1%. Our approach and the fit to the torus remnant mass reported in [57] thus constitute an easy-to-use analytical model that accurately describes the remnant of black hole-neutron star mergers. The space of parameters consisting of the binary mass ratio, the initial black hole spin, and the neutron star mass and equation of state is investigated. We provide indirect support to the cosmic censorship conjecture for black hole remnants of black hole-neutron star mergers. We show that the presence of a neutron star affects the quasinormal mode frequency of the black hole remnant, thus suggesting that the ringdown epoch of the gravitational wave signal may virtually be used to (1) distinguish black hole-black hole from black hole-neutron star mergers and to (2) constrain the neutron star equation of state.

Figure 1

$|a_{\mathrm{f}}-a_{\mathrm{f}}^{\mathrm{NR}}|$ is shown for all entries in Tables . The horizontal axis is the dummy that runs through both tables.

Figure 2

$a_{\mathrm{f}}-a_{\mathrm{f}}^{\mathrm{NR}}$ distribution for all entries in Tables .

Figure 3

$|a_{\mathrm{f}}-a_{\mathrm{f}}^{\mathrm{NR}}|$ distribution for all entries in Tables .

Figure 4

Same as Fig. 1, but using the predictions of 57 for $M_{\mathrm{b},\mathrm{torus}}$ in Eq. (11).

Figure 5

$|a_{\mathrm{f}}-a_{\mathrm{f}}^{\mathrm{NR}}|$ distribution obtained when using the predictions of 57 for $M_{\mathrm{b},\mathrm{torus}}$ in Eq. (11).

Figure 6

Distribution of the relative errors $ϵ(M_{\mathrm{f}}/M)$, $ϵ(M_{\mathrm{irr},\mathrm{f}}/M)$, $ϵ(f_{220}^{\mathrm{QNM}})$, and $ϵ({\tau }_{220}^{\mathrm{QNM}})$ obtained from Eqs. (9, 11, 12) in combination with 57 for test cases in Tables  for which information on the BH remnant mass is provided in the references.

Figure 7

The final spin parameter of BH-NS systems is shown as a function of the NS mass and the symmetric mass ratio; the initial spin parameter of the BH is set to 0.75. Results in the left/right panel refer to the PS/WFF1 EOS.

Figure 8

Final spin parameter for binaries with a primary spinning BH and a secondary nonspinning BH. From left to right, the initial spin parameter of the spinning BH is set to 0, 0.75, and 0.9. The curves were obtained with the fitting formula of 83.

Figure 9

Difference, in Hz, between the $l=m=2$, $n=0$ quasinormal mode frequency, $f_{220}^{\mathrm{QNM}}$, of the BH remnant of a BH-NS merger and of a BH-BH merger with the same secondary mass $M_2$, symmetric mass ratio $\nu$, and initial spin parameters. The NS and secondary BH initial spin is always set to zero. The primary BH initial spin parameter is 0.4 and 0.8 in the top and bottom panels, respectively.

Figure 10

NS equilibrium sequences in the radius-mass plane for several equations of state. The sequences shown are compatible with the recent measurement $M_{\mathrm{NS}}=(2.01\pm 0.04)M_{\odot }$ (horizontal, dashed line). Results for the WFF1/PS EOS, which yields the most/least compact NSs, are shown in blue/red. The APR2 sequence is shown in orange, while sequences obtained with other equations of state are shown with thinner, continuous gray lines.

Figure 11

Same as Fig. 10, but in the compactness-mass plane.