The three-parameter correlations about 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 (${\alpha }_1$ and ${\alpha }_2$), the break times ($T_{\mathrm{b}}$), and the corresponding optical fluxes ($F_{\mathrm{b}}$) 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 $E_{\gamma ,\mathrm{iso}}$ into the $L_{\mathrm{b},\mathrm{z}}-T_{\mathrm{b},\mathrm{z}}$ relation. The best fit correlation is obtained to be $L_{\mathrm{b},\mathrm{z}}\propto T_{\mathrm{b},\mathrm{z}}^{-0.9}{E}_{\gamma ,\mathrm{iso}}^{0.4}$. We next explored the possible correlations among $L_{\mathrm{b},\mathrm{z}}$, $T_{\mathrm{b},\mathrm{z}}$ and $E_{\mathrm{p},\mathrm{i}}$, and found there is also a tight correlation between them, which takes the form of $L_{\mathrm{b},\mathrm{z}}\propto T_{\mathrm{b},\mathrm{z}}^{-0.9}{E}_{\mathrm{p},\mathrm{i}}^{0.5}$. We argue that these two tight $L_{\mathrm{b},\mathrm{z}}-T_{\mathrm{b},\mathrm{z}}-E_{\gamma ,\mathrm{iso}}$ and $L_{\mathrm{b},\mathrm{z}}-T_{\mathrm{b},\mathrm{z}}-E_{\mathrm{p},\mathrm{i}}$ 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.

arXiv commentAccepted for publication in The Astrophysical Journal; 26 pages, 8 figures, 3 tables

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