Toward tight gamma-ray burst luminosity relations

Abstract

The large scatters of luminosity relations of gamma-ray bursts (GRBs) have been one of the most important reasons that prevent the extensive applications of GRBs in cosmology. Many efforts have been made to seek tight luminosity relations. With the latest sample of 116 GRBs with measured redshift and spectral parameters, we investigate 6 two-dimensional (2D) correlations and 14 derived three-dimensional (3D) correlations of GRBs to explore the possibility of decreasing the intrinsic scatters of the luminosity relations of GRBs. We find the 3D correlation of $E_{\mathrm{peak}}$--${\tau }_{\mathrm{RT}}$--$L$ to be evidently tighter (at the $2\sigma$ confidence level) than its corresponding 2D correlations, i.e., the $E_{\mathrm{peak}}$--$L$ and ${\tau }_{\mathrm{RT}}$--$L$ correlations. In addition, the coefficients before the logarithms of $E_{\mathrm{peak}}$ and ${\tau }_{\mathrm{RT}}$ in the $E_{\mathrm{peak}}$--${\tau }_{\mathrm{RT}}$--$L$ correlation are almost exact opposites of each other. Inputting this situation as a prior reduces the relation to $L\propto (E_{\mathrm{peak}}^{{}^{\prime }}/{\tau }_{\mathrm{RT}}^{{}^{\prime }}{)}^{0.842\pm 0.064}$, where $E_{\mathrm{peak}}^{{}^{\prime }}$ and ${\tau }_{\mathrm{RT}}^{{}^{\prime }}$ denote the peak energy and minimum rise time in the GRB rest frame. We discuss how our findings can be interpreted/understood in the framework of the definition of the luminosity (energy released in units of time). Our argument about the connection between the luminosity relations of GRBs and the definition of the luminosity provides a clear direction for exploring tighter luminosity relations of GRBs in the future.

9 pages, 1 figure, 1 table, added discussion and clarification, added references, minor language edit, published in The Astrophysical Journal

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Cited by in corpus (7)

• Determination of the intrinsic Luminosity Time Correlation in the X-ray Afterglows of GRBs
• Selection effects in Gamma Ray Bursts correlations: consequences on the ratio between GRB and star formation rates
• The High-z Quasar Hubble Diagram
• Correlation between Peak Energy and Peak Luminosity in Short Gamma-Ray Bursts
• On the Correlation of Low-energy Spectral Indices and Redshifts of Gamma-ray Bursts
• Prospects for the detection of the prompt very-high-energy emission from $\gamma$-ray bursts with the High Altitude Detection of Astronomical Radiation experiment
• Gamma-Ray Bursts with Extended Emission: Classifications, Energy Correlations and Radiation Properties