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

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 ($E_{\mathrm{iso}}$) 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 $T_L\equiv E_{\mathrm{iso}}/L_p$ as a hidden parameter to obtain a generalized Yonetoku relation as $(L_p/10^{52}\mathrm{erg}{\mathrm{s}}^{-1})=10^{-3.88\pm 0.09}(E_p/\mathrm{keV}{)}^{1.84\pm 0.04}(T_L/\mathrm{s}{)}^{-0.34\pm 0.04}$. 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 $({\Omega }_m,{\Omega }_{\Lambda })=(0.16_{-0.06}^{+0.04},1.20_{-0.09}^{+0.03})$, which is consistent with the concordance cosmological model within 2-$\sigma$ level.

5 pages, 6 figures, published in JCAP

References in corpus (8)

• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
• The Hubble Diagram to Redshift >6 from 69 Gamma-Ray Bursts
• Variation of the Amati Relation with the Cosmological Redshift: a Selection Effect or an Evolution Effect?
• Constraints on $w_0$ and $w_a$ of Dark Energy from High Redshift Gamma Ray Bursts
• Testing the E_p,i - L_p,iso - T_0.45 correlation on a BeppoSAX and Swift sample of gamma-ray bursts
• A universal GRB photon energy-peak luminosity relation
• Redshift Dependent Lag-Luminosity Relation in 565 BASTE Gamma Ray Bursts