Zitouni 2010 假设内急波的情况下模拟伽马暴的光度函数

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Title:		The GRB luminosity function: predictions from the internal shock model and comparison with observations
Authors:		Zitouni, H.; Daigne, F.; Mochkovich, R.; Zerguini, T. H.
Affiliation:		AA(Institut d'Astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie-Paris 6, 98 bis boulevard Arago, 75014 Paris, France; Université des Sciences et Technologies Houari Boumebedienne, BP 32 16123 Bab-Ezzouar Alger, Algeria), AB(Institut d'Astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie-Paris 6, 98 bis boulevard Arago, 75014 Paris, France; Institut Universitaire de France), AC(Institut d'Astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie-Paris 6, 98 bis boulevard Arago, 75014 Paris, France), AD(Université des Sciences et Technologies Houari Boumebedienne, BP 32 16123 Bab-Ezzouar Alger, Algeria)
Publication:		Monthly Notices of the Royal Astronomical Society, Volume 386, Issue 3, pp. 1597-1604. (MNRAS Homepage)
Publication Date:		05/2008
Origin:		MNRAS
MNRAS Keywords:		methods: statistical , stars: luminosity function, mass function , gamma-rays: bursts
DOI:		10.1111/j.1365-2966.2008.13136.x
Bibliographic Code:		2008MNRAS.386.1597Z

Abstract

We compute the expected luminosity function of gamma-ray bursts (GRBs) in the context of the internal shock model. We assume that GRB central engines generate relativistic outflows characterized by the respective distributions of injected kinetic power and contrast in Lorentz factor κ = Γ_max/Γ_min. We find that if the distribution of contrast extends down to values close to unity (i.e. if both highly variable and smooth outflows can exist), then the luminosity function has two branches. At high luminosity it follows the distribution of while at low luminosity it is close to a power law of slope -0.5. We then examine if existing data can constrain the luminosity function. Using the logN-logP curve, the E_p distribution of bright Burst and Transient Source Experiment (BATSE) bursts and the X-ray flash (XRF)/GRB ratio obtained by High Energy Transient Explorer 2 (HETE2), we show that single and broken power laws can provide equally good fits of these data. Present observations are therefore unable to favour one form or the other. However, when a broken power law is adopted they clearly indicate a low-luminosity slope ~= -0.6 +/- 0.2, compatible with the prediction of the internal shock model.

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