Cosmological Constraints from calibrated Yonetoku and Amati relation implies Fundamental plane of Gamma-ray bursts

TL;DR

This paper introduces a new fundamental plane relation for Gamma-Ray Bursts that reduces systematic errors and improves cosmological parameter constraints by incorporating a hidden parameter, T_L.

Contribution

The paper proposes a generalized Yonetoku relation including a hidden parameter, T_L, establishing a fundamental plane for GRBs with smaller systematic errors and better cosmological constraints.

Findings

The new relation has 30% smaller systematic error.

It suggests the existence of a hidden parameter in GRBs.

Cosmological constraints are consistent with the standard model within 2-sigma.

Abstract

We consider two empirical relations using data only from the prompt emission of Gamma-Ray Bursts (GRBs), peak energy ($E_p$) - peak luminosity ($L_p$) relation (so called Yonetoku relation) and $E_p$-isotropic energy ($E_{\rm iso}$) relation (so called Amati relation). We first suggest the independence of the two relations although they have been considered similar and dependent. From this viewpoint, we compare constraints on cosmological parameters, $\Omega_m$ and $\Omega_{\Lambda}$, from the Yonetoku and Amati relations calibrated by low-redshift GRBs with $z < 1.8$. We found that they are different in 1-$\sigma$ level, although they are still consistent in 2-$\sigma$ level. This and the fact that both Amati and Yonetoku relations have systematic errors larger than statistical errors suggest the existence of a hidden parameter of GRBs. We introduce the luminosity time $T_L$ defined by $T_L\equiv E_{\rm iso}/L_p$ as a hidden parameter to obtain a generalized Yonetoku relation as $(L_p/{10^{52} \rm{erg s^{-1}}}) = 10^{-3.88\pm0.09}(E_p/{\rm{keV}})^{1.84\pm0.04} (T_L/{\rm{s}})^{-0.34\pm0.04}$. The new relation has much smaller systematic error, 30%, and can be regarded as "Fundamental plane" of GRBs. We show a possible radiation model for this new relation. Finally we apply the new relation for high-redshift GRBs with $1.8 < z < 5.6$ to obtain $(\Omega_m,\Omega_{\Lambda}) = (0.16^{+0.04}_{-0.06},1.20^{+0.03}_{-0.09})$, which is consistent with the concordance cosmological model within 2-$\sigma$ level.