Qi, Shi 2011 E_p-tau_RT-L关系

主要内容:
在多个关系里找一个致密的关系。
（方法可以借鉴，没有提供具体的数据）

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多个关系

找到了一个较致密的关系

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· arXiv e-print (arXiv:1111.6249)

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Title:		Toward tight gamma-ray burst luminosity relations
Authors:		Qi, Shi; Lu, Tan
Publication:		eprint arXiv:1111.6249
Publication Date:		11/2011
Origin:		ARXIV
Keywords:		Astrophysics - Cosmology and Extragalactic Astrophysics, Astrophysics - High Energy Astrophysical Phenomena
Comment:		8 pages, 1 figure, 1 table
Bibliographic Code:		2011arXiv1111.6249Q

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, we investigated 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 found the 3D correlation of $E_{\mathrm{peak}}$--$\tau_{\mathrm{RT}}$--$L$ to be significantly tighter (at $2 \sigma$ confidence level) than its corresponding 2D correlations, i.e., the $E_{\mathrm{peak}}$--$L$ and $\tau_{\mathrm{RT}}$--$L$ correlation. 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 exactly opposite to each other. Inputting this situation as a prior reduces the relation to $L \propto (E_{\mathrm{peak}}^{'} / \tau_{\mathrm{RT}}^{'})^{0.842 \pm 0.064}$, where $E_{\mathrm{peak}}^{'}$ and $\tau_{\mathrm{RT}}^{'}$ denote the peak energy and minimum rise time in the GRB rest frame. We discussed that what we found 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.

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