Calibration of Gamma-Ray Burst Luminosity Correlations Using Gravitational Waves as Standard Sirens

Abstract

Gamma-ray bursts (GRBs) are a potential tool to probe the high-redshift universe. However, the circularity problem has encouraged people to find model-independent methods to study the luminosity correlations of GRBs. Here, we present a new method that uses gravitational waves (GWs) as standard sirens to calibrate GRB luminosity correlations. For the third-generation ground-based GW detectors (i.e., Einstein Telescope—ET), the redshifts of GW events accompanying electromagnetic counterparts can reach out to ∼4, which is more distant than type Ia supernovae ( z  ≲ 2). The Amati relation and Ghirlanda relation are calibrated using the mock GW catalog from ET. We find that the 1 σ  uncertainty of intercepts and slopes of these correlations can be constrained to less than 0.2% and 8% respectively. Using calibrated correlations, the evolution of the dark energy equation of state can be tightly measured, which is important for discriminating dark energy models.