Eccentric binary neutron star search prospects for Cosmic Explorer

We determine the ability of Cosmic Explorer, a proposed third-generation gravitational-wave observatory, to detect eccentric binary neutron stars and to measure their eccentricity. We find that for a matched-filter search, template banks constructed using binaries in quasicircular orbits are effectual for eccentric neutron star binaries with $e_7\le 0.004$ ($e_7\le 0.003$) for CE1 (CE2), where $e_7$ is the binary’s eccentricity at a gravitational-wave frequency of 7 Hz. We show that stochastic template placement can be used to construct a matched-filter search for binaries with larger eccentricities and construct an effectual template bank for binaries with $e_7\le 0.05$. We show that the computational cost of both the search for binaries in quasicircular orbits and eccentric orbits is not significantly larger for Cosmic Explorer than for Advanced LIGO and is accessible with present-day computational resources. We investigate Cosmic Explorer’s ability to distinguish between circular and eccentric binaries. We estimate that for a binary with a signal-to-noise ratio of 20 (800), Cosmic Explorer can distinguish between a circular binary and a binary with eccentricity $e_7\gtrsim {10}^{-2}$ (${10}^{-3}$) at 90% confidence.

Figure 1

The normalized signal-to-noise ratio integrand as a function of frequency for Cosmic Explorer (CE1/CE2), Einstein Telescope (ETD) and Advanced LIGO (aLIGO). This gives a visual representation of what the matched filter sees when it is integrating up the signal-to-noise ratio. A majority of the signal-to-noise ratio for Cosmic Explorer and Advanced LIGO is accumulated between 10 and 50 Hz, while the signal-to-noise ratio for the ETD is accumulated below 10 Hz.

Figure 2

The cumulative fraction of signal-to-noise ratio as a function of frequency. Cosmic Explorer (CE1/CE2) and aLIGO have accumulated more than 99.9% of their total signal-to-noise ratio from frequencies above 7 Hz. At 7 Hz, the ETD accumulated more than 85% of their total signal-to-noise ratio. Since more than 99.9% of the total signal-to-noise ratio is accumulated, we use a low-frequency cutoff of 7 Hz to generate the waveforms in our template banks.

Figure 3

The fitting factor as a function of eccentricity correlated with chirp mass for CE1. A noneccentric template bank was used to calculate the fitting factor. For Cosmic Explorer the fitting factor decreases for increasing values of eccentricity. The noneccentric template bank is effective in detecting eccentric systems with a fitting factor greater than 97% for $e\lesssim 0.004$.

Figure 4

As in Fig. 3, but we use the CE2 noise curve. A noneccentric template bank was used to calculate the fitting factor. The noneccentric template bank is effective in detecting eccentric systems with a fitting factor greater than 97% for $e\lesssim 0.003$.

Figure 5

The match as a function of eccentricity for Cosmic Explorer (CE1/CE2) and aLIGO. This gives a representation of the match between a circular waveform and an eccentric waveform for various eccentricities. The match for Cosmic Explorer at an eccentricity of 0.05 is about a factor of 3 smaller than that of Advanced LIGO.

Figure 6

A cumulative histogram that shows the fraction of points where the fitting factor is less than the value on the $x$ axis for each template bank. Using the eccentric template bank, a majority of the samples are at a fitting factor $\gtrsim 95\%$. For our eccentricity range, the eccentric template banks appear to do a better job at detecting eccentric systems than the noneccentric template banks.

Figure 7

The signal-to-noise ratio as a function of eccentricity. The black dot is at a signal-to-noise ratio of 32.4 [20] and eccentricity of 0.035 at 90% confidence [32]. For each detector, we show the signal-to-noise ratio needed to resolve the signal with eccentricity on the eccentricity axis at 90% confidence. For $e\ge 5\times {10}^{-3}$, a signal-to-noise ratio of 20 would be needed to resolve the signal at 90% confidence in Cosmic Explorer. As the eccentricity decreases, the signal-to-noise ratio needed to resolve the signal increases.