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 seconds, with a typical value about 10 4 seconds. 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 −0.9 b,z E 0.4 γ,iso . 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 −0.9 b,z E 0.5 p,i . 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 radiation physics of GRBs. The tight correlations are possible to be used as standard candles.

Statistical analyses on the energies of X-ray plateaus and flares in gamma-ray bursts

“…Currently, GRB central engines are still uncertain, but there are two leading models, i.e., the stellar-mass black hole (BH) hyperaccretion model (e.g., Woosley 1993;Popham et al 1999;Narayan et al 2001;Yi et al 2017;Liu et al 2018Liu et al , 2019 and for a review see Liu et al (2017) and the model of a rapidly rotating neutron star (NS) with a strong magnetic field of ∼ 10 15 G, et al 2007;Dainotti et al 2008Dainotti et al , 2010Dainotti et al , 2011aDainotti et al , 2013aDainotti et al , 2016Du 2020) and for a review see Dainotti & Del Vecchio (2017). A similar shallow decay also occurs in the optical light curves (e.g., Si et al 2018;Dainotti et al 2020) and Fermi -LAT GRBs (e.g., Dainotti et al 2021). The typical timescales of the X-ray plateaus in…”

The Optical Luminosity-Time Correlation for More Than 100 Gamma-Ray Burst Afterglows

“…We built a comprehensive sample of optical GRB LCs with known redshifts by searching the literature for all GRBs detected between May 1997 to January 2019 by several satellites such as the Swift Ultra-Violet/Optical Telescope (UVOT), or ground-based telescopes/detectors (e.g., GROND). In our final sample the redshifts of the GRBs span from z = 0.06 to z = 8.23 and the LCs employed are found in: Kann et al (2006Kann et al ( , 2010Kann et al ( , 2011Kann et al ( , 2021aKann et al ( , 2021b; Li et al (2012Li et al ( , 2015Li et al ( , 2018a; Oates et al (2009Oates et al ( , 2012; Zaninoni et al (2013);and Si et al (2018). We then determine the existence of a plateau by fitting the LCs with the phenomenological 2 W07 model, see Sec.…”

“…Below, we summarize the data analysis used by Li et al (2012Li et al ( , 2015Li et al ( , 2018a, Kann et al (2006Kann et al ( , 2010Kann et al ( , 2011, Oates et al (2012), Zaninoni et al (2013), andSi et al (2018). For GRBs that overlap between these samples, we choose the ones with the greatest coverage, especially in the plateau, and where the χ 2 value for the W07 fitting is the smallest.…”

Constraining Properties of GRB Central Engines with X-ray flares

“…The plateau phase of X-ray afterglow is still a puzzle, some theoretical models have proposed. A widely accepted model is the energy injection from a rapidly spinning magnetar (Usov 1992;Dai & Lu 1998a,b;Zhang & Mészáros 2001;Troja et al 2007;Dainotti et al 2010;Rowlinson et al 2014;Lü & Zhang 2014;Si et al 2018). The X-ray flares usually happen at 10 2 − 10 5 s after the prompt emission, the temporal behavior and spectral properties of flares are similar to that of prompt emissions.…”