On the interpretation of spectral-energy correlations in long gamma-ray bursts

Free access article

Issue		A&A Volume 450, Number 2, May I 2006


Page(s)		471 - 481
Section		Extragalactic astronomy
DOI		http://dx.doi.org/10.1051/0004-6361:20054211

A&A 450, 471-481 (2006)
DOI: 10.1051/0004-6361:20054211

On the interpretation of spectral-energy correlations in long gamma-ray bursts

L. Nava^{1, 2}, G. Ghisellini¹, G. Ghirlanda¹, F. Tavecchio¹ and C. Firmani^{1, 3}

¹ Osservatorio Astronomico di Brera, via Bianchi 46, 23807 Merate, Italy
e-mail: gabriele@merate.mi.astro.it
² Univ. di Milano-Bicocca, P.za della Scienza 3, 20126 Milano, Italy
³ Instituto de Astronomía, U.N.A.M., A.P. 70-264, 04510 México, D.F., México

(Received 15 September 2005 / Accepted 6 November 2005 )

Abstract
Context.Recently, Liang & Zhang found a tight correlation involving only observable quantities, namely the isotropic emitted energy $E_{\rm \gamma, iso}$ , the energy of the peak of the prompt spectrum $E^\prime_{\rm p}$ , and the jet break time $t^\prime_{\rm j}$ of Gamma Ray Bursts. This phenomenological correlation can have a first explanation in the framework of jetted fireballs, whose semiaperture angle $\theta_{\rm j}$ is measured by the jet break time $t^\prime_{\rm j}$ . By correcting $E_{\rm \gamma, iso}$ for the angle $\theta_{\rm j}$ one obtains the so-called Ghirlanda correlation, linking the collimation-corrected energy $E_\gamma$ and $E^\prime_{\rm p}$ .
Aims.There are two ways to derive $\theta_{\rm j}$ from $t^\prime_{\rm j}$ in the "standard" scenario, corresponding to a homogeneous or to a wind-like circumburst medium. We compute and compare the $E^\prime_{\rm p}$ - $E_\gamma$ correlations derived in these two conditions and study the consistency of these model-dependent correlations with the empirical Liang & Zhang correlation. We consider the difference between the observed correlations and the ones in the comoving frame.
Methods.We study 18 GRBs with firmly measured z, $E_{\rm peak}$ and $t_{\rm break}$ and discuss the differences with previously published samples. We compute the correlations accounting for the errors on all the relevant quantities.
Results.We show that the Ghirlanda correlation with a wind-like circumburst medium is as tight as (if not tighter) than the Ghirlanda correlation for a homogeneous medium. These two Ghirlanda correlations are both consistent with the phenomenological Liang & Zhang relation. The wind-like Ghirlanda relation, which is linear, remains linear also in the comoving frame, independently of the distribution of bulk Lorentz factors. Instead, in the homogeneous density case, one is forced to assume the existence of a strict relation between the bulk Lorentz factor and the total energy, which in turn places constraints on the radiation mechanisms of the prompt emission. The wind-like Ghirlanda correlation, being linear, corresponds to different bursts having the same number of photons.

Key words: gamma rays: bursts -- radiation mechanisms: non-thermal -- X-rays: general

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