Intrinsic properties of a complete sample of HETE-2 gamma-ray bursts^*

A measure of the GRB rate in the Local Universe

¹ Laboratoire d'Astrophysique de Toulouse-Tarbes, Université de Toulouse, CNRS, 14 Av. Edouard Belin, 31400 Toulouse, France e-mail: [alexandre.pelangeon;atteia]@ast.obs-mip.fr
² Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan
³ RIKEN (Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
⁴ Space Sciences Laboratory, University of California at Berkeley, 7 Gauss Way, Berkeley, CA, 94720-7450, USA
⁵ Center for Space Research, Massachusetts Institute of Technology, 70 Vassar Street, Cambridge, MA, 02139, USA
⁶ Tsukuba Space Center, National Space Development Agency of Japan, Tsukuba, Ibaraki, 305-8505, Japan
⁷ Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8551, Japan
⁸ INAF/IASF Bologna, via Gobetti 101, 40129 Bologna, Italy
⁹ Observatoire de Haute-Provence (CNRS/OAMP), Saint Michel l'Observatoire, France
¹⁰ Instituto Nacional de Pesquisas Espaciais, Avenida Dos Astraunotas 1758, São Jose dos Campos 12227-010, Brazil
¹¹ Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
¹² Centre d'Étude Spatiale des Rayonnements, Université de Toulouse, CNRS, 9 Av. du Colonel Roche, 31028 Toulouse, France
¹³ Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM, 87545, USA
¹⁴ Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400 005, India
¹⁵ NASA Goddard Space Flight Center, Greenbelt, MD, 20771, USA
¹⁶ Center for Research and Exploration in Space Science and Technology (CRESST), NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
¹⁷ Joint Center for Astrophysics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
¹⁸ National Astronomical Observatory, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588, Japan
¹⁹ Department of Physics, Aoyama Gakuin University, Chitosedai, 6-16-1, Setagaya-ku, Tokyo, 157-8572, Japan
²⁰ Faculty of Engineering, Miyazaki University, Gakuen Kibanadai Nishi, Miyazaki, 889-2192, Japan
²¹ Department of Astronomy and Astrophysics, Univ of California at Santa Cruz, 477 Clark Kerr Hall, Santa Cruz, CA, 95064, USA

Received: 4 March 2008
Accepted: 19 August 2008

Abstract

Context. As a result of the numerous missions dedicated to the detection of Gamma-ray bursts (GRBs), the observed properties of these events are now well known. However, studying their parameters in the source frame is not simple since it requires having measurements of both the bursts' parameters and of their distances.

Aims. Taking advantage of the forthcoming Catalog of the High Energy Transient Explorer 2 (HETE-2) mission, the aim of this paper is to evaluate the main properties of HETE-2 GRBs – the peak energy , the duration (T₉₀) and the isotropic energy – in their source frames and to derive their unbiased distribution.

Methods. We first construct a complete sample containing all the bursts localized by the Wide-Field X-ray Monitor (WXM) on-board HETE-2, which are selected with a uniform criterion and whose observed parameters can be constrained. We then derive the intrinsic E_peak, T₉₀ and E_iso  distributions using their redshift when it is available, or their pseudo-redshift otherwise. We finally compute the “volume of detectability” V_max of each GRB, i.e. the volume of the universe in which the burst is bright enough to be part of our sample, and the corresponding number of GRB within their visibility volume , in order to derive a weight for each detected burst accounting both for the detection significance and the star formation history of the universe.

Results. We obtain unbiased distributions of three intrinsic properties of HETE-2 GRBs: , and the isotropic energy of the burst. These distributions clearly show the predominence of X-ray flashes (XRFs) in the global GRB population. We also derive the rate of local GRBs:   11 Gpc^-3 yr^-1, which is intermediate between the local rate obtained by considering only the “high-luminosity” bursts (~1 Gpc^-3 yr^-1) and that obtained by including the “low-luminosity” bursts (200 Gpc^-3 yr^-1).

Conclusions. This study shows that the XRFs are predominent in the GRB population and are closely linked to the “classical” GRBs. We show that HETE-2 detected no low-luminosity GRB like GRB 980425 or XRF 060218, due to the small size of its detectors, excluding this type of burst from our statistical analysis. The comparison of the GRB rate derived in this study with the known rate of type Ib/c supernovae clearly shows that the progenitors of SNe Ib/c must have some special characteristics in order to produce a gamma-ray burst or an X-ray flash.