Selection Effects in Gamma-Ray Burst Correlations: Consequences on the Ratio Between Gamma-Ray Burst and Star Formation Rates

Abstract

Gamma Ray Bursts (GRBs) visible up to very high redshift have become attractive targets as potential new distance indicators. It is still not clear whether the relations proposed so far originate from an unknown GRB physics or result from selection effects. We investigate this issue in the case of the L X − T * a correlation (hereafter LT) between the X-ray luminosity L X (T a ) at the end of the plateau phase, T a , and the rest frame time T * a . We devise a general method to build mock data sets starting from a GRB world model and taking into account selection effects on both time and luminosity. This method shows how not knowing the efficiency function could influence the evaluation of the intrinsic slope of any correlation and the GRB density rate. We investigate biases (small offsets in slope or normalization) that would occur in the LT relation as a result of truncations, possibly present in the intrinsic distributions of L X and T * a . We compare these results with the ones in Dainotti et al. (2013) showing that in both cases the intrinsic slope of the LT correlation is ≈ −1.0. This method is general, therefore relevant to investigate if any other GRB correlation is generated by the biases themselves. Moreover, because the farthest GRBs and star-forming galaxies probe the reionization epoch, we evaluate the redshift-dependent ratio Ψ(z) = (1 + z) α of the GRB rate to star formation rate (SFR). We found a modest evolution −0.2 ≤ α ≤ 0.5 consistent with Swift GRB afterglow plateau in the redshift range 0.99 < z < 9.4.

Gamma Ray Burst afterglow and prompt-afterglow relations: An overview

“…The 8 upper envelope points are shown as red squares, while the IC GRBs are represented by green triangles. Dainotti et al (2015b) also confirmed previous results of Dainotti et al (2013a) but with a larger sample of 123…”

“…In fact, they obtained a E γ,prompt − E X,af terglow relation with slope b ∼ 1 using 43 SGRBs and 232 GRBs with spectroscopic redshifts detected by Swift respectively. Finally, Dainotti et al (2015b) analyzed this relation to find some constraints on the ratio of E X,af terglow to E γ,prompt , considering a sample of 123…”

The pulse luminosity function ofSwiftgamma-ray bursts

“…LGRBs the preferred mechanism is that of a collapsar: massive stars that undergo catastrophic core collapse into blackholes (Woosley 1993;Paczyński 1998;MacFadyen & Woosley 1999), favoured because of the observed association with Type Ib/c supernovae (Galama et al 1998;Stanek et al 2003) with Wolf-Rayet stars the favoured progenitor type. With their high mass (M > 25M ), and subsequently short main-sequence lifespans, Wolf-Rayet stars closely trace the local star formation rate; as such, for type I/II models, we take the Cole (Cole et al 2001) functional form for the CSFRD:…”

“…Early Swift GRB LF papers continued to develop the LGRB luminosity function by utilising either small numbers of LGRBs with measured redshifts (Li 2008;Kistler et al 2008), with poor constraints on fitted parameters; or by artificially boosting the LGRB redshift sample by combining real and pseudo redshift data from Swift and BATSE (Butler, Bloom & Poznanski 2010;Salvaterra et al 2012). Over time, the sample size of GRBs with observed redshifts has increased 1 and contemporary GRB LF studies utilise larger datasets with entirely observed redshifts (Wanderman & Piran 2010;Cao et al 2011;Robertson & Ellis 2012;Howell & Coward 2013;G. Dainotti et al 2014;Petrosian, Kitanidis & Kocevski 2015;Pescalli et al 2015;Yu et al 2015;Deng et al 2016).…”

Gamma-ray bursts with afterglow plateau phases associated with supernovae

“…20 In order to test appropriately theoretical models it is also necessary to correctly distinguish among physically different subsamples taken into consideration into the analysis, because if these mentioned subsamples (short with extended emission, for example) are caused by different emission mechanisms this may have consequences on the tightness of the correlation itself and therefore on its use as redshift estimator 11 as cosmological tool 4,5,14,27 and as indicator of the ratio between GRB rate and star formation rate. 15 The problem of selecting homogeneous samples in terms of similar observational properties usually helps to reduce the scatter of correlations, 10 and it is a general issue which can equally applied to the prompt-afterglow correlations 12,16 and prompt correlations. 1,21,24 With this issue in mind we focused on the updated sample of 176 GRBs with known redshift and observed plateau emission looking for a subset with high degree of correlation in the LT space.…”