Localization of binary neutron star mergers with second and third generation gravitational-wave detectors

The observation of gravitational wave signals from binary black hole and binary neutron star mergers has established the field of gravitational wave astronomy. It is expected that future networks of gravitational wave detectors will possess great potential in probing various aspects of astronomy. An important consideration for successive improvement of current detectors or establishment on new sites is knowledge of the minimum number of detectors required to perform precision astronomy. We attempt to answer this question by assessing the ability of future detector networks to detect and localize binary neutron stars mergers on the sky. Good localization ability is crucial for many of the scientific goals of gravitational wave astronomy, such as electromagnetic follow-up, measuring the properties of compact binaries throughout cosmic history, and cosmology. We find that although two detectors at improved sensitivity are sufficient to get a substantial increase in the number of observed signals, at least three detectors of comparable sensitivity are required to localize majority of the signals, typically to within around $10{\mathrm{deg}}^2$—adequate for follow-up with most wide field of view optical telescopes.

Figure 1

Target noise curves for existing and future detectors [65]: advanced LIGO at design sensitivity (aLIGO); LIGO Voyager; Einstein Telescope (two proposed configurations, ET-B and ET-D) and Cosmic Explorer (CE).

Figure 2

Relative sensitivity of the different networks over the sky: Voyager, Voyager-ET, 3ET/3CE and CE-ET. Left: network response as a function of sky position and right: alignment factor as a function of sky position. Also shown are the locations of detectors in each network. Magenta markers are for Voyager detectors, white for ET, and red for CE. Since both ${\mathrm{N}}_R$ and the alignment factor are invariant under an overall scaling in network sensitivity with overall sensitivity of the network, 3ET and 3CE will have identical patterns.

Figure 3

The localization ellipses at different sky locations for face-on 1.4–1.4 BNS binaries at a redshift of: left—$z=0.2$ (luminosity distance of 1 Gpc) and right—$z=0.5$ (luminosity distance of 3 Gpc). The red crosses indicate that the BNS at this sky position would not be detected—either due to a network SNR less than 12, or not having $\mathrm{SNR}>5$ in at least two detectors. The $\mathrm{blue}+\mathrm{symbols}$ indicated sources that would be detected, but not well localized due to being identified in only two detectors. The ellipses give the 90% localization regions for a source from a given sky location. Detector locations are shown with golden markers.

Figure 4

The detection and localization efficiency as a function of redshift and luminosity distance of the Voyager, Voyager-ET and 3ET networks (left column) and the 3ET, CE-ET and 3CE networks (right column). For visual comparison, 3ET is plotted as a solid line in both. Left column: Voyager-ET and Voyager are the dashed and dotted lines respectively. Right column: CE-ET and 3CE are the dashed and dotted lines respectively. From bottom to top, the rows show the fraction of events at a given redshift/distance that will be detected and localized within 100, 10 and $1{\mathrm{deg}}^2$.

Figure 5

The number of BNS observations and localizations per year with future networks, as a function of redshift and luminosity distance. The y-axis is scaled so that the area under the curves gives the number of events per year. This assumes an isotropic redshift distribution that follows the star formation rate [122] shifted to account for the delay between star birth and BNS merger [120] and a distribution of possible delay times $P(t_D)\propto 1/t_D$, with a minimum delay of $t_D^{\min }=0.2\mathrm{Myr}$ [123]. The local merger rate density is taken as ${\mathrm{\Psi }}_{\mathrm{BNS}}(0)=1500{\mathrm{Gpc}}^{-3}{\mathrm{y}}^{-1}$ [3]. Note that the y-axis on $1{\mathrm{deg}}^2$ plot is different from the others. For visual comparison 3ET is plotted as a solid line in both column. Left column: Voyager-ET and Voyager are the dashed and dotted lines respectively. Right column: CE-ET and 3CE are the dashed and dotted lines respectively. From bottom to top, the rows show the number density of events at a given redshift/distance that will be detected and localized within 100, 10 and $1{\mathrm{deg}}^2$.