GRB satellites are relatively inefficient detectors of dim hard bursts because they trigger on photon counts, which are number-biased against hard photons. Therefore, for example, given two bursts of identical peak luminosity near the detection threshold, a dim soft burst will be preferentially detected over a dim hard burst. This detector bias can create or skew an apparent correlation where increasingly hard GRBs appear increasingly bright. Although such correlations may be obfuscated by a middle step where GRBs need to be bright enough to have their actual redshifts determined, it is found that the bias is generally pervasive. This result is derived here through simulations convolving a wide variety of possible GRB brightnesses and spectra with the BATSE Large Area Detectors (LAD) detection thresholds. The presented analyses indicate that the rest-frame $\nu F_{\nu}$ spectrum peak energy of long-duration GRBs, $\epi$, is not a good cosmological standard candle without significant corrections for selection effects. Therefore, the appearance of $\epi$ in seeming correlations such as the Amati ($E_{iso}-\epi$), Ghirlanda ($E_{\gamma}-\epi$), and $L_{iso}-\epi$ relations is statistically real but strongly influenced by so far uncalibrated GRB detector thresholds.
Deep Dive into The Possible Impact of GRB Detector Thresholds on Cosmological Standard Candles.
GRB satellites are relatively inefficient detectors of dim hard bursts because they trigger on photon counts, which are number-biased against hard photons. Therefore, for example, given two bursts of identical peak luminosity near the detection threshold, a dim soft burst will be preferentially detected over a dim hard burst. This detector bias can create or skew an apparent correlation where increasingly hard GRBs appear increasingly bright. Although such correlations may be obfuscated by a middle step where GRBs need to be bright enough to have their actual redshifts determined, it is found that the bias is generally pervasive. This result is derived here through simulations convolving a wide variety of possible GRB brightnesses and spectra with the BATSE Large Area Detectors (LAD) detection thresholds. The presented analyses indicate that the rest-frame $\nu F_{\nu}$ spectrum peak energy of long-duration GRBs, $\epi$, is not a good cosmological standard candle without significant co
The existence of correlations among the spectral parameters of Long-duration Gamma-Ray Bursts (LGRBs) has been touted as providing clues to the underling physics of GRB prompt emission and making LGRBs a useful tool for probing cosmology in the distant universe. Recently reported attempts to use these correlations to construct a GRB Hubble diagram include those by Cardone et al. (2009), Amati et al. (2008a), Basilakos & Perivolaropoulos (2008), Cuesta et al. (2008), Liang et al. (2008), Schaefer (2007) -hereafter S07 -& Firmani et al. (2006). The investigation of possible correlations among the parameters of LGRBs, however, dates back to the BATSE era when the cosmological origins of LGRBs was not yet established. Specifically in an early effort, Lloyd, Petrosian, & Mallozzi (2000) did an analysis to determine the degree of correlation between the observerframe νFν spectrum peak energy (E p,obs ) and the bolometric fluence of bright BATSE LGRBs (S bol ) and to investigate E-mail: ashahmor@mtu.edu; nemiroff@mtu.edu to what extent the correlation is either intrinsic or cosmological. After accounting for the data truncation due to the detection threshold, they concluded that there is probably a significant correlation between the rest-frame νFν spectrum peak energy (Ep,int) and isotropic-equivalent radiated energy (Eiso).
While there is still no unique and robust interpretation of these results (e.g. Levinson & Eichler 2005;Rees & Mészáros 2005;Eichler & Levinson 2004), the discovery of some outliers to these relations (e.g. Urata et al. 2009;Sugita et al. 2009;Bellm et al. 2008;McBreen et al. 2008;Campana et al. 2007;Rizzuto et al. 2007;Gehrels et al. 2006;Vaghuan et al. 2006;Sazonov et al. 2004;Soderberg et al. 2004;Ghirlanda et al. 2004a -hereafter G04a) has raised two possibilities: that these correlations belong to only a sub-population of LGRBs, or that they are an artifact of the GRB detection process. The latter idea is bolstered by recent reports from several independent groups (Butler et al. 2009a;Bagoly et al. 2009;Bagoly et al. 2008;Nava et al. 2008, hereafter N08;Butler et al. 2007, hereafter B07). Moreover, Nakar & Piran (2005a) (hereafter NP05a), found that a significant number of BATSE LGRBs are inconsistent with two of these relations known as the ‘Amati relation’ (Amati 2006;Amati 2002) and the ‘Ghirlanda relation’ (Ghirlanda et al. 2007 -hereafter G07;G04a) which relate Ep,int of LGRBs to their isotropic-equivalent radiated energy (Eiso) and the collimation-corrected energy (Eγ) respectively. Following their analysis, Band & Preece (2005), analyzed a large sample of BATSE LGRBs and found that about 88% and 1.6% of their sample were inconsistent with the Amati and Ghirlanda relations respectively. Kaneko et al. (2006) -hereafter K06 -also reported an inconsistency of bright BATSE bursts with these correlations.
Responding to these results, Ghirlanda et al. (2005a) argued that taking into account the intrinsic scatter of the Amati relation, the BATSE bursts may still be consistent. This claim, however, has also been challenged (Nakar & Piran 2005b). Although all the above mentioned reports generally conclude that the Amati and Ghirlanda relations are statistically non-compelling, the matter still remains controversial whether the reported correlations are completely due to selection effects in the detection process, or whether there is some real, statistically strong correlation between the LGRBs spectral parameters. It is noteworthy that Yonetoku et al. (2004) -hereafter Y04 -have also tried to estimate the redshifts of 745 BATSE LGRBs using a relation between Liso and Ep,int. However, these estimates resulted in 21 GRBs being located beyond z > 12, and 35 even having no solution satisfying the Liso -Ep,int relation, indicating that these 35 bursts show a large observer-frame peak energy (E p,obs ) while being very dim. In addition, Tsutsui et al. (2008) have shown that the redshifts derived from the lag-luminosity & Liso -Ep,int for 565 BATSE LGRBs are totally inconsistent with each other.
Most recently, N08 and Ghirlanda et al. (2008) -hereafter G08 -have reported the triggering threshold limits for several GRB detectors, including BATSE, SWIFT, Konus-Wind, BeppoSAX and HETE-II in the plane of peak energy vs. bolometric fluence (S bol -E p,obs ) and peak energy vs. bolometric 1-second peak flux (P bol -E p,obs ) of LGRBs. They also obtain the minimum fluence limits required for spectral analysis of a burst on these planes and conclude, contrary to the previous reports, that only 6% of BATSE LGRBs are certain outliers with respect to the Amati relation at > 3σ, while there are apparently no outliers to the Ghirlanda relation. They also find that the slope and the distribution of LGRBs are significantly different from the slopes of the curves of the minimum fluences and peak fluxes required for triggering and spectral analysis on these planes. Their analysis, however, is limited to about 3
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