Great Impostors: Extremely Compact, Merging Binary Neutron Stars in the Mass Gap Posing as Binary Black Holes

Can one distinguish a binary black hole undergoing a merger from a binary neutron star if the individual compact companions have masses that fall inside the so-called mass gap of $3–5M_{\odot }$? For neutron stars, achieving such masses typically requires extreme compactness and in this work we present initial data and evolutions of binary neutron stars initially in quasiequilibrium circular orbits having a compactness $C=0.336$. These are the most compact, nonvacuum, quasiequilibrium binary objects that have been constructed and evolved to date, including boson stars. The compactness achieved is only slightly smaller than the maximum possible imposed by causality, $C_{\max }=0.355$, which requires the sound speed to be less than the speed of light. By comparing the emitted gravitational waveforms from the late inspiral to merger and postmerger phases between such a binary neutron star vs a binary black hole of the same total mass we identify concrete measurements that serve to distinguish them. With that level of compactness, the binary neutron stars exhibit no tidal disruption up until merger, whereupon a prompt collapse is initiated even before a common core forms. Within the accuracy of our simulations the black hole remnants from both binaries exhibit ringdown radiation that is not distinguishable from a perturbed Kerr spacetime. However, their inspiral leads to phase differences of the order of $\sim 5\mathrm{rad}$ over an $\sim 81\mathrm{km}$ separation (1.7 orbits) while typical neutron stars exhibit phase differences of $\ge 20\mathrm{rad}$. Although a difference of $\sim 5\mathrm{rad}$ can be measured by current gravitational wave laser interferometers (e.g., aLIGO/Virgo), uncertainties in the individual masses and spins will likely prevent distinguishing such compact, massive neutron stars from black holes.

Figure 1

Rest-mass density profile across the $x$ axis for the NSNS system with the ALF2cc EOS. Horizontal red line corresponds to nuclear density ${\rho }_{0\text{nuc}}$. The inset enlarges the area close to the surface where the density drops from ${\rho }_{0\text{nuc}}$ to zero in a steep manner.

Figure 2

Evolution of an $M=7.90M_{\odot }$ binary NSNS system. Isocontours of rest-mass density ${\rho }_0=2.263\times {10}^{13}\mathrm{gr}/{\mathrm{cm}}^3$, which corresponds to $0.998R_x(0)$ and therefore is a accurate representation of the surface of the star.

Figure 3

Top panel: strain vs retarded time for the ($\ell =2$, $m=2$) dominant mode. R1nsns and R2nsns correspond to the two resolutions of the NSNS system and Rbhbh to the BHBH simulation. Bottom panel shows the phase ${\mathrm{\Phi }}_{22}(t)$ of the strain up until its maximum vs the GW frequency.

Figure 4

Top panel: Fourier spectra of numerical waveforms (colored lines). Vertical blue lines correspond to the frequency of the (2,2) mode at the initial separation and at the ringdown. Bottom panel: Spin of the remnant BHs.