A redshift–observation time relation for gamma-ray bursts: evidence of a distinct subluminous population

E. J. Howell 0 D. M. Coward 0 0 School of Physics, University of Western Australia , Crawley, WA 6009, Australia A B S T R A C T We show that the redshift and peak flux distributions of gamma-ray bursts (GRBs) have an observation time dependence that can be used to discriminate between different burst populations. We demonstrate how observation time relations can be derived from the standard integral distributions and that they can differentiate between GRB populations detected by both the Burst and Transient Source Experiment (BATSE) and Swift satellites. Using Swift data, we show that a redshift-observation time relation (log Z- log T ) is consistent with both a peak flux-observation time relation (log P - log T ) and a standard log N - log P brightness distribution. As the method depends only on rarer small-z events, it is invariant to high-z selection effects. We use the log Z- log T relation to show that subluminous GRBs are a distinct population occurring at a higher rate of the order of 150+19800 Gpc3 yr1. Our analysis suggests that GRB 060505 - a relatively nearby GRB observed without any associated supernova - is consistent with a subluminous population of bursts. Finally, we show that our relations can be used as a consistency test for some of the proposed GRB spectral energy correlations. 1 I N T R O D U C T I O N Multiwavelength observations have shown that gamma-ray bursts (GRBs) are the most luminous1 and distant transient events in the Universe (Greiner et al. 2008; Cucchiara et al. 2011). GRBs have been generally categorized into two populations: spectrally soft long-duration bursts related to core-collapse events (LGRBs/ Type II) and harder short-duration bursts possibly resulting from compact star mergers (SGRB/Type I). In addition to these two main populations of bursts, it has been suggested that there exist two subpopulations: subluminous GRBs (SL-GRBs) and SGRBs with extended emissions (SGRB-EE). SLGRBs are of the long-duration type and have isotropic equivalent gamma-ray luminosities two to three orders of magnitude below classical LGRBs (Coward 2005; Murase et al. 2006; Guetta & Della Valle 2007; Imerito et al. 2008). The lower energy emissions mean they are only detected at low z as such, four of the six GRBs with unambiguous spectroscopically confirmed GRBsupernova associations were from this category. SGRB-EE emissions have been given a separate classification in the second Swift catalogue (Sakamoto et al. 2011). These bursts show an initial SGRB-like short hard spike (<2 s) followed by a faint softer emission ( 100 s; E-mail: 1 In terms of electromagnetic radiation per unit solid angle. Norris & Bonnell 2006; Page et al. 2006; Perley et al. 2008; Norris, Gehrels & Scargle 2011; Zhang 2011). There is still no clear consensus that these subcategories arise from different progenitor systems or are simply rarer events from the tail of the respective short/long burst distributions. Attempts to address this have generally been based on statistical arguments (Soderberg et al. 2006; Guetta & Della Valle 2007), fits to the log N log P , peak flux or brightness distribution of bursts (Pian et al. 2006) or through simulation (Coward 2005; Virgilii, Liang & Zhang 2008). The goal of this paper is to demonstrate an alternative strategy using the relative time records of the bursts. This approach exploits the fact that different astrophysical transient populations will have different local rate densities. We show that by recording the arrival times of the rarest events in a time series, for example the closest or brightest of a cosmological population, one can produce a ratedependent data set with a unique statistical signature (Coward & Burman 2005). By constraining the data using an observation-timedependent model that is highly sensitive to the rate density, we demonstrate how this alternative approach can untangle different source populations. In this study, we will specifically address the issue of whether SL-GRBs are a distinct population of GRBs. The outline of the paper is as follows. In Section 2, we present an overview of GRB population studies. Section 3 will set the scene in regard to the observation time dependence of transient events, and Section 4 will describe the data extraction methodologies used in this study. A standard theoretical framework will follow in Section 5. Section 6 describes observation-time-dependent models for both peak flux (log P log T ) and redshift (log Z log T ), showing how they follow seamlessly from the relative integral distributions of transient sources. In Section 7, parameters for both the BATSE2 and Swift LGRB populations will be obtained using a standard differential log N log P distribution. These parameters will be used in Section 8 to constrain the peak fluxobservation time data from both detectors using a log N log P model. Doing so demonstrates that the method is both consistent with a standard brightness distribution and detector independent. Section 9 will demonstrate the use of the previously derived parameters in the redshiftobservation time domain to constrain Swift data using the log Z log T model. In Section 10, we apply our methods to the Swift SL-GRB population to further demonstrate how the method can be used as a tool to discriminate between different source populations. We show that the method uses only the closest or brightest of a population; thus, many of the selection biases that plague GRB observations can be bypassed. We discuss our findings and present our conclusions in Section 11. 2 G A M M A - R AY B U R S T P O P U L AT I O N S The categorization of GRBs was traditionally based on the bimodal distribution of T90 durations observed by BATSE3 (Kouveliotou et al. 1993) and their hardness ratio in the spectral domain. These criteria separated GRBs into hard SGRBs (T90 < 2 s; hard spectra) and softer LGRBs (T90 2 s; soft spectra). Electromagnetic observations of LGRBs and SGRBs have provided strong evidence for different progenitors. LGRBs have been associated with the deaths of massive stars (Hjorth 2003; Stanek 2003; Woosley & Bloom 2006) and have subsequently been found in or near dense regions of active star formation, predominantly dwarf starburst field galaxies (Fruchter et al. 2006). For SGRBs, which have contributed around 25 and 10 per cent of the BATSE and Swift GRB samples, respectively (Guetta & Stella 2009), the leading progenitor model is the merger of compact neutron star (NS) and/or black hole binaries. The association of an older stellar population with these bursts is supported by their occurrence in both early- and late-type galaxies, as well as field and cluster galaxies. There exist, however, a number of ambiguities in the categorization schemes of GRB populations. LGRBs, such as GRB 060614 and GRB 060505, showed no evidence of a supernova (SN), despite extensive follow-up campaigns (Zhang 2006). Additionally, it has been suggested that the tw (...truncated)