How will our knowledge of short gamma-ray bursts affect the distance measurement of binary neutron stars?

Gravitational waves from binary neutron stars associated with short gamma-ray bursts have drawn considerable attention due to their prospect in cosmology. For such events, the sky locations of sources can be pinpointed with techniques such as identifying the host galaxies. However, the cosmological applications of these events still suffer from the problem of degeneracy between luminosity distance and inclination angle. To address this issue, a technique was proposed in previous study, i.e., using the collimation property of short gamma-ray bursts. Based on the observations, we assume that the cosine of inclination follows a Gaussian distribution, which may act as a prior in the Bayes analysis to break the degeneracy. This paper investigates the effects of different Gaussian priors and detector configurations on distance measurement and cosmological research. We first derive a simplified Fisher information matrix for demonstration, and then conduct quantitative analyses via simulation. By varying the number of third-generation detectors and the scale of prior, we generate four catalogs of 1000 events. It is shown that, in the same detecting period, a network of detectors can recognize more and farther events than a single detector. Besides, adopting tighter prior and employing multiple detectors both decrease the error of luminosity distance. Also considered is the performance of a widely adopted formula in the error budget, which turns out to be a conservative choice in each case. As for cosmological applications, for the ?CDM model, 500, 200, 600, and 300 events are required for the four configurations to achieve 1% H-0 accuracy. With all 1000 events in each catalog, H-0 and omega(m) can be constrained to (0.66%, 0.37%, 0.76%, 0.49%), and (0.010, 0.006, 0.013, 0.010), respectively. The results of the Gaussian process also show that the gravitational wave standard siren can serve as a probe of cosmology at high redshifts.