Lorentz Invariance Violation Test from Time Delays Measured with Gravitationally Lensed GRB Candidates 950830 and 200716C

Abstract

The spectral lag features in gamma-ray bursts (GRBs) have been widely used to investigate possible Lorentz invariance violation (LIV). However, these constraints could depend on the unknown source-intrinsic time delays in different energy bands. Biesiada & Piórkowska theoretically proposed that gravitational lensing time delays in a strongly lensed GRB can become a tool for testing LIV free from the intrinsic time lag problem. Recently GRB 950830 and GRB 200716C have been proposed to be lensed by an intermediate-mass black hole. They should still be considered as candidates of strongly lensed bursts, since no angular offset (i.e., the evidence for multiple images) was detected, but only a double peak structure in the light curve. The redshift of the burst z s and of the lens z l have not been measured in either case; hence we assumed a reasonable guess of z l = 1.0, z s = 2.0 for GRB 950830 and z l = 0.174, z s = 0.348 for GRB 200716C. Bearing all this in mind, we attempted to constrain LIV theories in a prospective way based on the two GRBs by considering time delays between two pulses in different energy channels. By directly fitting the time delay data of GRBs 950830 and 200716C we obtained the following limits on LIV energy scale: E QG,1 ≥ 3.2 × 109 GeV and E QG,1 ≥ 6.3 × 109 GeV, respectively. Sensitivity analysis regarding the (unknown) redshifts leads to the most conservative estimate, E QG,1 ≥ 1.5 × 108 GeV for GRB 950830 and E QG,1 ≥ 4.8 × 108 GeV for GRB 200716C, when they would be located at z s ∼ 5.