Gamma-Ray Bursts are precise distance indicators similar to Type Ia Supernovae?

Abstract

We estimate the distance modulus to long gamma-ray bursts (LGRBs) using the Type I Fundamental Plane, a correlation between the spectral peak energy $E_{\mathrm{p}}$, the peak luminosity $L_{\mathrm{p}}$, and the luminosity time $T_{\mathrm{L}}$ ($\equiv E_{\mathrm{iso}}/L_{\mathrm{p}}$ where $E_{\mathrm{iso}}$ is isotropic energy) for small Absolute Deviation from Constant Luminosity(ADCL). The Type I Fundamental Plane of LGRBs is calibrated using 8 LGRBs with redshift $z<1.4$. To avoid any assumption on the cosmological model, we use the distance modulus of 557 Type Ia supernovae (SNeIa) from the Union 2 sample. This calibrated Type I Fundamental Plane is used to measure the distance moduli to 9 high-redshift LGRBs with the mean error ${\bar{\sigma }}_{\mu }=0.31$, which is comparable with that of SNe Ia ${\bar{\sigma }}_{\mu }=0.26$ where $\mu$ stands for the distance modulus. The Type I Fundamental Plane is so tight that our distance moduli have very small uncertainties. From those distance moduli, we obtained the constraint ${\Omega }_{\mathrm{M}}=0.22\pm 0.04$ for flat $\Lambda$CDM universe. Adding 9 LGRBs distance moduli ($z>1.4$) to 557 SNeIa distance moduli ($z<1.4$) significantly improves the constraint for non-flat $\Lambda$CDM universe from (${\Omega }_{\mathrm{M}},{\Omega }_{\mathrm{\Lambda }}$)=($0.29\pm 0.10$, $0.76\pm 0.13$) for SNeIa only to (${\Omega }_{\mathrm{M}},{\Omega }_{\mathrm{\Lambda }}$)=($0.23\pm 0.06$, $0.68\pm 0.08$) for SNeIa and 9 LGRBs.

arXiv comment12 pages, 5 figures. Submitted to JCAP. Some references added

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