The Three-parameter Correlations About the Optical Plateaus of Gamma-Ray Bursts

Abstract

Well-sampled optical light curves of 50 gamma-ray bursts (GRBs) with plateau features are compiled from the literature. By empirical fitting, we obtained the parameters of the optical plateaus, such as the decay slopes ( α 1 and α 2 ), the break times ( T b ), and the corresponding optical fluxes ( F b ) at the break times. The break time of optical plateaus ranges from tens of seconds to 10 6 s, with a typical value of about 10 4 s. We have calculated the break luminosity, and it mainly ranges from 10 44 erg s −1 to 10 47 erg s −1 , which is generally two or three orders of magnitude less than the corresponding break luminosity of the X-ray afterglow plateaus. We reanalyzed the optical plateaus and also found that a significantly tighter correlation exists when we added the isotropic equivalent energy of GRBs E γ ,iso into the L b,z – T b,z relation. The best-fit correlation is obtained to be L b , z ∝ T b , z − 0.9 E γ , iso 0.4 . We next explored the possible correlations among L b,z , T b,z and E p,i , and found there is also a tight correlation between them, which takes the form of L b , z ∝ T b , z − 0.9 E p , i 0.5 . We argue that these two tight L b,z – T b,z – E γ ,iso and L b,z – T b,z – E p,i correlations are more physical, and it may be directly related to the radiation physics of GRBs. The tight correlations can possibly be used as standard candles.