Measurement of Hubble constant with stellar-mass binary black holes

The direct detections of gravitational waves (GW) from merging binary black holes (BBH) by aLIGO have brought us a new opportunity to utilize BBH for a measurement of the Hubble constant. In this paper, we point out that there exists a small number of BBH that gives significantly small sky localization volume so that a host galaxy is uniquely identified. Then a redshift of a BBH is obtained from a spectroscopic follow-up observation of the host galaxy. Using these redshift-identified BBH, we show that the Hubble constant is measured at a level of precision better than 1% with advanced detectors like aLIGO at design sensitivity. Since a GW observation is completely independent of other astrophysical means, this qualitatively new probe will help resolve a well-known value discrepancy problem on the Hubble constant from cosmological measurements and local measurements.

Figure 1

Probability distributions of source parameters in a source catalog with the mass distributions ($\alpha =2.35$ and $\alpha =1$), observed by the HLV detector network. The horizontal axes are from the left, the chirp mass, redshift, and SNR. The colors are all binaries (blue, solid), binaries with $N_{\text{host}}<100$ (green, dot-dashed), and binaries with $N_{\text{host}}<1$ (red, dotted).

Figure 2

Probability distributions of parameter estimation errors for sources from the mass distributions ($\alpha =2.35$ and $\alpha =1$), observed by HLV detector network. The horizontal axes are a relative error in luminosity distance (left) and sky localization error in the unit of square degrees (right). The line colors are the same as Fig. 1.

Figure 3

Probability distributions of the number of host-galaxy candidates for a BBH merger event observed by the HLV network. The color shows the mass distributions, $\alpha =2.35$ (orange) and $\alpha =1$ (blue).

Figure 4

Measurement precision of the Hubble constant as a function of the observed number of golden BBH in the case of $\alpha =2.35$ mass distribution. The detector networks are HLV (red) and HLVK (blue). The solid and dotted lines are with/without the systematic error from peculiar velocity. The horizontal line shows 1% precision.