Detectability of subsolar mass neutron stars through a template bank search

We study the detectability of gravitational-wave signals from subsolar-mass binary neutron star systems by the current generation of ground-based gravitational-wave detectors. We find that finite size effects from large tidal deformabilities of the neutron stars and lower merger frequencies can significantly impact the sensitivity of the detectors to these sources. By simulating a matched-filter based search using injected binary neutron star signals with tidal deformabilities derived from physically motivated equations of state, we calculate the reduction in sensitivity of the detectors. We conclude that the loss in sensitive volume can be as high as 78.4% for an equal mass binary system of chirp mass $0.17M_{\odot }$, in a search conducted using binary black hole template banks. We use this loss in sensitive volume, in combination with the results from the search for subsolar-mass binaries conducted on data collected by the LIGO-Virgo observatories during their first three observing runs, to obtain a conservative upper limit on the merger rate of subsolar-mass binary neutron stars. Since the discovery of a low-mass neutron star would provide new insight into formation mechanisms of neutron stars and further constrain the equation of state of dense nuclear matter, our result merits a dedicated search for subsolar-mass binary neutron star signals.

Figure 1

Left panel shows the match between binary neutron star and binary black hole waveforms as a function of chirp mass ${\mathcal{M}}_C$ and effective tidal deformability $\tilde{\mathrm{\Lambda }}$ of the binary system, for equal mass binaries. The binary neutron star signals are terminated at the frequency of gravitational-wave emission at the innermost stable circular orbit for a point particle orbiting a Schwarzschild black hole. Low match values in the region bounded by the equation of state curves indicate that ignoring the tidal deformability of subsolar-mass neutron stars can reduce the sensitivity of LIGO searches to gravitational-wave signals from these sources. Right panel shows the match between binary neutron star and binary black hole waveforms as a function of the chirp mass of the system, for equal mass binaries, and for three different neutron star equations of state. The lower frequency cutoff for match evaluation is 15 Hz.

Figure 2

Comparison of mass-radius curves for neutron stars, obtained by integrating the Tolman-Oppenheimer-Volkoff system of differential equations for the three different equations of state being considered in this work. The large radii of the low-mass neutron stars impact the merger frequency of their gravitational waveforms as they are tidally disrupted by the companion at lower frequencies than higher-mass neutron stars.

Figure 3

Gravitational binding energy $E_b$ for an equal mass binary neutron star system with $M_1=M_2=1M_{\odot }$ as computed with LORENE (accounting for matter effects) and in the point-particle limit at 3PN. The APR equation of state is used in this calculation. The Roche lobe overflow frequency (vertical dashed line) is estimated as the frequency beyond which no equilibrium solution can be found.

Figure 4

Gravitational-wave frequency at Roche lobe overflow for binaries with different masses $m_1\ge m_2$ and three equations of state: APR, SLy4, and BSk21. Each point represents a binary neutron star system, and is colored according to the gravitational-wave frequency at the point of Roche lobe overflow.

Figure 5

The shaded region in the figure shows the fitting factor [Eq. (3)] as a function of component masses $(m_1,m_2)$ of injected binary black hole signals. Fitting factors are highest for signals located closest to the templates, and lowest for those located equidistant from two nearest templates.

Figure 6

Left panel shows fitting factors obtained on performing template bank simulations, for injected binary neutron star signals with the component neutron stars having tidal deformabilities derived from the APR, SLy4 and BSk21 equations of state, and terminated at their Roche Lobe overflow frequencies, plotted as a function of the primary mass $m_1$ and secondary mass $m_2$. Right panel shows a plot of effective tidal deformability of the binary neutron star systems, as a function of $m_1$ and $m_2$. The fitting factors are lower for systems having higher tidal deformabilities, indicating greater mismatch between the binary black hole templates and the injected binary neutron star signals.

Figure 7

Left panel: Blue curve shows the upper limit on merger rate for subsolar-mass binaries obtained in [32] for the O1 to O3b observing runs. Red curve shows an upper limit on the rate of subsolar-mass binary neutron star mergers, obtained using the sensitive volume reduced by a factor of $(\text{average fitting factor}{)}^3$. Right panel: The ratio of upper limit on the rate of binary neutron star mergers to the upper limit on the rate of binary black hole mergers, plotted as a function of chirp mass of the binary system.