How will our knowledge on short gamma-ray burst affect the distance measurement of binary neutron star?. (arXiv:2101.12371v3 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Du_M/0/1/0/all/0/1">Minghui Du</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Xu_L/0/1/0/all/0/1">Lixin Xu</a>
Binary neutron star associated with short gamma-ray burst has drawn wide
attention ever since the observation of GW170817, due to its prospect in
cosmology. While further application of this sort of event suffers from the
problem of degeneracy between luminosity distance and inclination angle. To
address this issue, proposed in previous research is the utilization of
information from short gamma-ray burst. In this paper, we aim to investigate
the effect of different Gaussian priors of the inclination angle. To test the
property of resulting posterior distribution, we generate four catalogues of
1000 events by varying the number of third-generation detectors and the scale
of prior. It turns out that a network of detectors tends to recognize more and
farther events than a single detector. Besides, adopting tighter prior and
employing multiple detectors both lead to lower error at given redshifts. Also
considered is the validity of a widely adopted formula $sigma_{Delta d_{rm
L}0} = 2d_{rm L} / rho$, which undergoes the change from overestimating to
underestimating with the increase of redshift. In the case of $Lambda$CDM
cosmology, 800, 300, 800 and 600 events are required for the four
configurations to achieve $1%$ $H_0$ accuracy. With all 1000 events in each
catalogue, $H_0$ can be constrained to $0.90%$, $0.60%$, $0.91%$ and
$0.77%$, while the errors of $Omega_m$ are 0.014, 0.010, 0.018 and 0.016
respectively. Besides, adopting $sigma_{Delta d_{rm L}0}$ leads to
underestimation on the errors of cosmological parameters for tighter prior and
overestimation in the opposite case. Results of Gaussian process also show that
gravitational wave standard siren can reach higher redshift than traditional
standard candles, especially when a network of detector is available, while
alteration of the prior only has moderate impact.
Binary neutron star associated with short gamma-ray burst has drawn wide
attention ever since the observation of GW170817, due to its prospect in
cosmology. While further application of this sort of event suffers from the
problem of degeneracy between luminosity distance and inclination angle. To
address this issue, proposed in previous research is the utilization of
information from short gamma-ray burst. In this paper, we aim to investigate
the effect of different Gaussian priors of the inclination angle. To test the
property of resulting posterior distribution, we generate four catalogues of
1000 events by varying the number of third-generation detectors and the scale
of prior. It turns out that a network of detectors tends to recognize more and
farther events than a single detector. Besides, adopting tighter prior and
employing multiple detectors both lead to lower error at given redshifts. Also
considered is the validity of a widely adopted formula $sigma_{Delta d_{rm
L}0} = 2d_{rm L} / rho$, which undergoes the change from overestimating to
underestimating with the increase of redshift. In the case of $Lambda$CDM
cosmology, 800, 300, 800 and 600 events are required for the four
configurations to achieve $1%$ $H_0$ accuracy. With all 1000 events in each
catalogue, $H_0$ can be constrained to $0.90%$, $0.60%$, $0.91%$ and
$0.77%$, while the errors of $Omega_m$ are 0.014, 0.010, 0.018 and 0.016
respectively. Besides, adopting $sigma_{Delta d_{rm L}0}$ leads to
underestimation on the errors of cosmological parameters for tighter prior and
overestimation in the opposite case. Results of Gaussian process also show that
gravitational wave standard siren can reach higher redshift than traditional
standard candles, especially when a network of detector is available, while
alteration of the prior only has moderate impact.
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