Parameter estimation for binary black holes with networks of third-generation gravitational-wave detectors

The two binary black hole (BBH) coalescences detected by LIGO, GW150914, and GW151226, were relatively nearby sources, with a redshift of $\sim 0.1$. As the sensitivity of Advanced LIGO and Virgo increases in the next few years, they will eventually detect stellar-mass BBHs up to redshifts of $\sim 1$. However, these are still relatively small distances compared with the size of the Universe, or with those encountered in most areas of astrophysics. In order to study BBH during the epoch of reionization, or black holes born from population III stars, more sensitive instruments are needed. Third-generation gravitational-wave detectors, such as the Einstein Telescope or the Cosmic Explorer, are already in an advanced R&D stage. These detectors will be roughly a factor of 10 more sensitive in strain than the current generation, and they will be able to detect BBH mergers beyond a redshift of 20. In this paper we quantify the precision with which these new facilities will be able to estimate the parameters of stellar-mass, heavy, and intermediate-mass BBHs as a function of their redshifts and the number of detectors. We show that having only two detectors would result in relatively poor estimates of black hole intrinsic masses: a situation improved with three or four instruments. Larger improvements are visible for the sky localization, although it is not yet clear whether BBHs are luminous in the electromagnetic or neutrino band. The measurement of the spin parameters, on the other hand, does not improve significantly as more detectors are added to the network since redshift information is not required to measure spin.

Figure 1

The amplitude spectral density of the ET-D and CE, compared with the Advanced LIGO design. The curves can be downloaded from Ref. [24].

Figure 2

The redshift distribution used to generate the simulated events. This curve is also used as a prior for the parameter estimation algorithm.

Figure 3

Violin plots for the 90% sky localization uncertainties ($y$ axis). Each panel focuses on a different redshift bin, indicated at the top. The labels on the $x$ axis identify the 3G networks.

Figure 4

Violin plots for the 90% relative uncertainties for the luminosity distance ($y$ axis). Each panel focuses on a different redshift bin, indicated at the top. The labels on the $x$ axis identify the 3G networks.

Figure 5

The distribution of uncertainties for the spin magnitude of the primary (top) and secondary (bottom) black hole versus the injected redshift. All networks are shown together with different symbols since they yield very similar distributions. The histogram on the right reports the distribution of the uncertainties for the LCAI network with a dashed green (red) line at the 50% (10%) percentile.

Figure 6

Violin plots for the 90% relative uncertainties for the source-frame chirp mass ($y$ axis). Each panel focuses on a different redshift bin, indicated at the top. The labels on the $x$ axis identify the 3G networks.

Figure 7

Violin plots for the 90% relative uncertainties for the source frame $m_1$ ($y$ axis). Each panel focuses on a different redshift bin, indicated at the top. The labels on the $x$ axis identify the 3G networks.

Figure 8

Violin plots for the 90% relative uncertainties for the source frame $m_2$ ($y$ axis). Each panel focuses on a different redshift bin, indicated at the top. The labels on the $x$ axis identify the 3G networks.