A complete sample of bright Swift short Gamma-Ray Bursts
P. D'Avanzo, R. Salvaterra, M. G. Bernardini, L. Nava, S. Campana, S. Covino, V. D'Elia, G. Ghirlanda, G. Ghisellini, A. Melandri, B. Sbarufatti, S. D. Vergani, G. Tagliaferri
aa r X i v : . [ a s t r o - ph . H E ] M a y Mon. Not. R. Astron. Soc. , 1–17 (2014) Printed 21 May 2014 (MN L A TEX style file v2.2)
A complete sample of bright
Swift short Gamma–RayBursts
P. D’Avanzo ⋆ , R. Salvaterra , M. G. Bernardini , L. Nava , S. Campana , S. Covino ,V. D’Elia , G. Ghirlanda , G. Ghisellini , A. Melandri , B. Sbarufatti , , S. D. Vergani , & G. Tagliaferri INAF - Osservatorio Astronomico di Brera, via E. Bianchi 46, I-23807, Merate (LC), Italy INAF - IASF Milano, via E. Bassini 15, I-20133, Milano, Italy The Racah Institute of physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel ASI - Science Data Centre, via G. Galilei, I-00044, Frascati, Italy Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA, 16802, USA GEPI, Observatoire de Paris, CNRS, Univ. Paris Diderot, 5 place Jules Janssen, F-92190 Meudon, France
Accepted . Received ;
ABSTRACT
We present a carefully selected sample of short gamma-ray bursts (SGRBs) ob-served by the
Swift satellite up to June 2013. Inspired by the criteria we used to builda similar sample of bright long GRBs (the BAT6 sample), we selected SGRBs withfavorable observing conditions for the redshift determination on ground, ending upwith a sample of 36 events, almost half of which with a redshift measure. The redshiftcompleteness increases up to about 70% (with an average redshift value of z = 0 . Swift
Burst Alert Tele-scope energy band. Such flux-limited sample minimizes any redshift-related selectioneffects, and can provide a robust base for the study of the energetics, redshift distri-bution and environment of the
Swift bright population of SGRBs. For all the eventsof the sample we derived the prompt and afterglow emission in both the observer and(when possible) rest frame and tested the consistency with the correlations valid forlong GRBs. The redshift and intrinsic X-ray absorbing column density distributionswe obtain are consistent with the scenario of SGRBs originated by the coalescence ofcompact objects in primordial binaries, with a possible minor contribution ( ∼ Swift activity.
Key words: gamma-rays: bursts – X-rays: general.
Gamma-ray bursts (GRBs) are rapid, powerful flashes ofgamma-ray radiation occuring at an average rate of oneevent per day over the whole sky at cosmological distances.The high energy prompt emission is followed by a broadband(X-rays to radio ranges) fading emission, named afterglow,(Costa et al. 1997; van Paradijs et al. 1997; Frail et al. 1997;Bremer et al. 1998; Heng et al. 2008) that can be observedup to weeks and months after the onset of the event.The distribution of GRB durations observed by the ⋆ E-mail: [email protected]
BATSE instrument (Fishman et al. 1989) is bimodal, withpeaks at T ∼ . T ∼
20 s and a boundary at T ∼ . The two classes oflong (LGRBs, T > T z Burst and Transient Source Experiment, on board the
ComptonGamma Ray Observatory T is defined as the time during which the cumulative countsincrease from 5% to 95% above background, adding up to 90% ofthe total GRB counts.c (cid:13) P. D’Avanzo et al. a supernova (SN), are associated with core-collapse explo-sions of massive stars (see Hjorth & Bloom 2011, for a recentreview), the nature of SGRB progenitors is still under de-bate. Current models suggest that they are associated withthe merging of compact objects in binary systems, such asa double neutron star (NS), or a NS and a black hole (BH)system (Eichler et al. 1989; Narayan et al. 1992; Nakar 2007;Berger 2014). Such systems can originate from the evolutionof massive stars in a primordial binary (Narayan et al. 1992)or by dynamical interactions in globular clusters during theircore collapse (Grindlay et al. 2006; Salvaterra et al. 2008).Very recently, a direct evidence supporting the merger sce-nario has been claimed by Tanvir et al. (2013) and Berger,Fong & Chornock (2013) who reported the possible detec-tion of a kilonova associated to the SGRB 130603B (but seeJin et al. 2013 for further discussion).SGRBs are not distinguished from LGRBs only by theirduration. If we consider the observed prompt emission, neg-ligible spectral lag (Norris, Marani & Bonnell 2000; Norris,Scargle & Bonnell 2001) and harder spectra (Kouveliotou etal. 1993) are common for SGRBs. On the other hand, theprompt emission properties of short GRBs are similar to thefirst 1–2 s of long events (Ghirlanda, Ghisellini & Celotti2004) and both classes of objects show a similar spectralevolution (Ghirlanda, Ghisellini & Nava 2011). This mightsuggest a common emission mechanism for both long andshort GRBs.Since 2005, with the advent of the fast-repointing
Swift satellite (Gehrels et al. 2004), the discovery of SGRBs af-terglows and the identification of their host galaxies madepossible to study their distances, energy scales and environ-ments (Gehrels et al. 2005). SGRBs are found to be typicallyless energetic (their isotropic equivalent energy, E iso , is ofthe order of 10 − erg) than LGRBs and to occur at alower redshift (Nakar 2007; Berger 2011; Fong et al. 2013).Their afterglows tend to be significantly fainter on averagethan those of LGRBs (Kann et al. 2011; Nicuesa Guelbenzuet al. 2012; Margutti et al. 2013), but scaled to their E iso similar to faint LGRBs (Nysewander et al. 2009). Concern-ing the host galaxies, SGRBs occur in both early and latetype galaxies with low star formation rate and are associ-ated with an old stellar population (Berger 2009; Leibler &Berger 2010; Fong et al. 2013). A different origin for SGRBswith respect to the LGRB class is also supported by thelack of detection of the underlying SN in the light curvesof their optical afterglows down to very stringent magni-tude limits (Hjorth et al. 2005a; Hjorth et al. 2005b; Foxet al. 2005; Covino et al. 2006; Kann et al. 2011; D’Avanzoet al. 2009) and by their inconsistency with the correlation,valid for LGRBs, between the rest frame spectral peak en-ergy and E iso ( E peak − E iso correlation; Amati et al. 2008and references therein). On the other hand, Ghirlanda etal. (2009) showed that SGRBs are consistent with the same E peak − L iso correlation (where L iso is the prompt emissionisotropic peak luminosity) defined by LGRBs (Yonetoku etal. 2004). SGRBs are also consistent with the three param-eter E iso − E peak − E X correlation (with E X being the after-glow energy emitted in the soft X-ray band; Bernardini et al.2012; Margutti et al. 2013). Furthermore, the distributionsof the intrinsic X-ray absorbing column densities of long andshort GRBs do not show significant differences when com-pared in the same redshift range ( z
1; Kopac et al. 2012; Margutti et al. 2013). Finally, given that the measured du-ration of the GRB prompt emission can vary for differentinstrument (e.g. due to the different energy band used), ithas been recently proposed that the value of T used todivide the long and short GRBs should be reduced to about0.8 s for the Swift bursts (Bromberg et al. 2013). A recentreview of the properties of SGRBs has been presented byBerger (2014).The majority of the studies reported above is basedover the entire sample of SGRBs with measured redshifts.Although this approach has the clear advantage of describ-ing the intrinsic physical properties of these objects, it canbe severely affected by observational biases, given that al-most 3/4 of the
Swift
SGRBs are lacking a secure redshiftmeasurement (Berger 2014).In this paper, we present a carefully selected sub-sampleof the
Swift
SGRBs. Inspired by the criteria we followedto build a complete sample of LGRBs (the BAT6 sample;Salvaterra et al. 2012 and references therein), we selectedSGRBs with favorable observing conditions for redshift de-termination from the ground, ending up with a sample of 36events, almost half of which with a redshift measure. Theredshift completeness increases up to about 70% by restrict-ing to those events that are bright in the 15-150 keV
Swift
Burst Alert Telescope (BAT; Barthelmy et al. 2005) energyband, obtaining a sample of 16 SGRBs, which is completein flux and has the highest completeness in redshift withrespect to the SGRB samples presented in the literature todate. Such flux-limited sample provides a robust base forthe study of the energetics, redshift distribution and en-vironment of the
Swift population of SGRBs. A statisticalstudy of these properties is a useful tool to indirectly investi-gate their elusive progenitors, find additional parameters forthe GRB classification (that can go beyond the duration ofthe prompt emission) and check for the existence of possiblesub-classes.The paper is organized as follows. In section 2 we de-scribe the sample and the selection criteria and in sec-tion 3 the data analysis methods. The observed and rest-frame properties of the GRBs of the sample are discussedin section 4. Our conclusions are presented in section 5.Throughout the paper we assume a standard cosmology with h = Ω Λ = 0 . m = 0 .
3. Errors are given at the 68%confidence level unless stated differently.
We selected our sample among all the
Swift
GRBs with T < Swift -BAT light curve shows ashort-duration peak followed by a softer, long-lasting tail(the so-called “extended emission”). For these events, T can be longer than 2 s. We then selected: 1) all the eventspromptly re-pointed by the Swift
X-Ray Telescope (XRT; within 120 s from the trigger.c (cid:13) , 1–17 complete sample of Swift short GRBs Burrows et al. 2005) and 2) with favorable observing con-ditions for ground-based optical follow-up aimed at redshiftdetermination, i.e. events with low Galactic extinction inthe direction of the burst ( A V < . Swift -XRT).The sample built this way (the total sample from nowon) consists of 37 SGRBs, with a completeness in redshiftof 43% (Table 1). This total sample includes 5 SGRBs withextended emission (EE) and 19 with short-lived X-ray after-glow (SL) . We restricted this sample to those events with apeak photon flux P > . − cm − , computed using the15–150 keV Swift-
BAT light curves binned with δt = 64 ms.This further criterium selects 17 SGRBs, 12 with a measuredredshift, providing a sample that has, at the same time, asize large enough to perform statistical studies and a highlevel of redshift completeness (71%). An analogous, althoughless tight, cut was used in Salvaterra et al. (2012) to builtthe BAT6 sample of LGRBs. Being free of selection effects(except for the flux limit), this sample (the complete samplefrom now on), although relatively small, provides a usefulbenchmark to compare the rest-frame physical properties ofSGRB prompt and afterglow emission. The classification of three GRBs of our sample as SGRBevents is uncertain. GRB 090607 and GRB 100816A have T > T = 1 . σ with the E peak − E iso correlation (An-tonelli et al. 2009), which is followed by LGRBs (Amati et al.2002), making its classification uncertain (see also Levesqueet al. 2010; Th¨one et al. 2012). In the following sections,we will investigate the observer and rest-frame properties ofthese events, with the aim of shedding light on their classifi-cation either as long or short GRBs. As will be shown in Sect4.2, we propose GRB 100816A to be a LGRB, in light of itsconsistency with the E peak − E iso correlation coupled withits T > total and complete sample con-sist of 36 and 16 SGRBs, respectively, with a completenessin redshift of 42% (15/36) and 69% (11/16), respectively. Very recently, the redshift of the exceptionally bright shortGRB 130603B has been measured through spectroscopyof its optical afterglow. This is the first clean absorptionspectrum obtained for the optical afterglow of a securely-classified SGRB (Cucchiara et al. 2013; de Ugarte Postigo Defined by Sakamoto & Gehrels (2009) as those events forwhich the X-ray afterglow flux at 10 s after the trigger is lessthan 10 − erg cm − s − . et al. 2013). Optical afterglow spectroscopy of SGRBshave been reported in the past also for GRB 090426 andGRB 100816A (Antonelli et al. 2009; Levesque et al. 2010;Tanvir et al. 2010; Gorosabel et al. 2010), whose classifica-tion as SGRBs is however highly uncertain (see Sect. 2.1 and4.2), while with a T = 0 .
18 s, a hard spectrum and negligi-ble spectral lag, GRB 130603B can be classified as a SGRBbeyond any doubt (Barthelmy et al. 2013; Norris et al. 2013;Golenetskii et al. 2013). However, apart from such excep-tional event, the remaining SGRB redshifts are obtainedthrough spectroscopy of their associated host galaxies. Adirect consequence of this is that the SGRB-host galaxy as-sociation can only be secured when the optical afterglowis detected and found to lie within the host galaxy lightwith a sub-arcsecond precision or proposed on chance prob-ability arguments (and not, e.g., by matching the redshiftmeasured through spectroscopy of both the optical after-glow and the host galaxy). Throughout the paper, we willconsider as GRBs with a secure redshift measurement onlythose events for which an optical afterglow was found to liewithin the host galaxy light or those events having a hostgalaxy whose position is within a precise (radius < ′′ ) X-rayerror circle.These tight requirements we have put on the redshift re-liability can bias our sample against events with a large off-set with respect to their host galaxy. However, we note thatwith such criteria we exclude just one event whose redshiftis proposed on the basis of probabilistic association with anearby host galaxy (namely, GRB 090515; see Table 1). In Table 2 we report the prompt emission fluence observedin the 15-150 keV
Swift -BAT energy range, together withthe 0.3-10 keV X-ray fluence observed with
Swift -XRT. Wecollected the T and gamma-ray fluence values from the2nd Swift -BAT catalogue (Sakamoto et al. 2011) for GRBsbefore Dec 2009, while for events occuring later than thisdate, we referred to the refined analysis GCN circulars ofthe Swift -BAT team. For each GRB of our total sample weretrieved the 0.3-10 keV flux calibrated X-ray light curvesfrom the automated data products provided by the
Swift
Burst analyzer (Evans et al. 2009). These light curves werefitted with power laws, broken power laws or multiply bro-ken power laws. We then computed the early X-ray fluencesobserved in the first 500 s of the Swift -XRT observations andthe total X-ray fluences, obtained integrating the observed0.3-10 keV flux under the best light curve fit between 120sand 620 s after the BAT trigger and under the whole lightcurve (from the first to the last X-ray afterglow detection),respectively. For GRBs with just one detection of the X-ray http://gcn.gsfc.nasa.gov/gcn3.archive.html This choice is motivated by the will of having the earliest obser-vation time common to all the burst of the sample and to integrateover a time long enough to measure the early X-ray fluences withacceptable ( ∼ σ ) significance.c (cid:13)000
Burst analyzer (Evans et al. 2009). These light curves werefitted with power laws, broken power laws or multiply bro-ken power laws. We then computed the early X-ray fluencesobserved in the first 500 s of the Swift -XRT observations andthe total X-ray fluences, obtained integrating the observed0.3-10 keV flux under the best light curve fit between 120sand 620 s after the BAT trigger and under the whole lightcurve (from the first to the last X-ray afterglow detection),respectively. For GRBs with just one detection of the X-ray http://gcn.gsfc.nasa.gov/gcn3.archive.html This choice is motivated by the will of having the earliest obser-vation time common to all the burst of the sample and to integrateover a time long enough to measure the early X-ray fluences withacceptable ( ∼ σ ) significance.c (cid:13)000 , 1–17 P. D’Avanzo et al.
Table 1.
List of GRBs matching the selection criteria of our total sample described in Sect. 2. GRB belonging to the complete (flux-limited) sub-sample are marked in boldface. Redshifts are provided in the following references: [1] Leibler & Berger (2010); [2] Soderberget al. (2006); [3] Berger et al. 2007; [4] Graham et al. (2009); [5] Berger et al. (2009); [6] D’Avanzo et al. (2009); [7] Leibler & Berger(2010); [8] Rowlinson et al. (2010); [9] Antonelli et al. (2009); [10] Levesque et al. (2010); [11] McBreen et al. (2010); [12] Fong et al.(2011); [13] Fong et al. (2013); [14] Tanvir et al. (2010); [15] Gorosabel et al. (2010); [16] Chornock & Berger (2011); [17] Margutti et al.(2012); [18] Sakamoto et al. (2013); [19] Cucchiara et al. (2013).GRB T P F EE SL/LL XRT err OA redshift Referencess ph cm s − ′′ . . a . . . − − N N051105A 0.06 2 . − − N N051210 1.30 1 . . . b . . .
547 2051227 115.40 1 . . . . . . a . . . . . . a . − − N N . . . . . . a . . a . − − N N071227 144.98 2 . . . . . . . . d c . . . . . . a c . . . . . . c . . . . . . . . . . . b . . . . . . . . Notes . a GRB with proposed redshift based on the association with the nearby galaxy with the lowest chance probability.GRB 050509B: z = 0 .
225 (Gehrels et al. 2005; Bloom et al. 2006); GRB 060502B: z = 0 .
287 (Bloom et al. 2007); GRB 061217: z = 0 . z = 0 . z = 0 .
473 (Berger 2010); GRB 090515: z = 0 . b Photometric redshift. c GRB with uncertain classification, possibly long (see Sect. 2.1 and 4.2.2). d Possibly underestimated redshift (see Sect. 4.3.1). afterglow (seven events, see Table 2) it was not possible toconstrain a decay and were not considered in this analysis. γ − and X − rays spectral analysis To collect the prompt emission spectral properties of thebursts in our complete sample we refer to the spectral anal-ysis reported in the GCN circulars or to the refined analysisreported in published papers, when available. Most of the GRBs in our sample have been detected not only by
Swift -BAT, but also by other high energy satellites, including
Konus -WIND,
Fermi -GBM and
Suzaku -WAM, providing acomplete information on the prompt spectrum (peak energy,fluence and peak flux). For the bursts with a measured red-shift it was possible to estimate the rest frame E peak , E iso ,and L iso and test the E peak − E iso and E peak − L iso correla-tions. E iso and L iso have been estimated in the (rest frame)energy range 1 keV – 10 MeV (Table 3).We retrieved the automated data products provided by c (cid:13) , 1–17 complete sample of Swift short GRBs Table 2.
High energy properties of the GRB of our total sample in the observer frame: prompt emission fluence measured by the
Swift-
BAT in the 15-150 keV energy range and X-ray fluence measured by the
Swift-
XRT in the 0.3-10 keV energy range. The early andtotal X-ray fluences are measured integrating the observed 0.3-10 keV flux under the best light curve fit between 120 s and 620 s afterthe BAT trigger and under the whole light curve (from the first to the last X-ray afterglow detection), respectively (see Sect. 3.1 fordetails). GRB belonging to the complete (flux-limited) sub-sample are marked in boldface.GRB γ prompt fluence X-ray early fluence X-ray total fluence10 − erg cm − erg cm − erg cm . ± .
02 0 . ± .
07 0 . ± . . ± .
11 0 . ± . − b . ± . − a − a . ± . − a − a . ± .
14 5 . ± .
16 7 . ± . . ± .
35 4 . ± .
96 20 . ± . . ± .
10 5 . ± .
10 10 . ± . . ± .
46 7 . ± .
73 27 . ± . . ± .
07 0 . ± . − b . ± .
10 2 . ± .
56 3 . ± . . ± .
28 12 . ± .
70 47 . ± . . ± .
08 0 . ± . − b . ± . − a − a . ± .
04 12 . ± .
39 34 . ± . . ± .
07 3 . ± .
83 7 . ± . . ± .
17 0 . ± . − b . ± .
15 0 . ± .
08 4 . ± . . ± . − a − a . ± .
23 4 . ± .
72 7 . ± . . ± .
70 16 . ± .
60 19 . ± . . ± .
49 25 . ± .
99 46 . ± . . ± .
19 4 . ± .
09 5 . ± . . ± .
27 1 . ± .
35 9 . ± . . ± .
40 14 . ± .
97 37 . ± . . ± .
04 7 . ± .
12 4 . ± . . ± .
19 4 . ± .
85 1 . ± . . ± .
13 10 . ± .
71 18 . ± . . ± .
20 0 . ± .
22 1 . ± . . ± .
00 7 . ± .
36 23 . ± . . ± .
30 4 . ± .
00 4 . ± . . ± .
11 0 . ± . − b . ± .
09 0 . ± .
11 1 . ± . . ± .
18 0 . ± .
21 1 . ± . . ± .
20 3 . ± .
84 16 . ± . . ± .
07 0 . ± . − b . ± .
20 0 . ± . − b . ± .
30 6 . ± .
42 42 . ± . Notes . a GRB without an XRT detected afterglow. b GRB with just one detection of the X-ray afterglow. the
Swift -XRT GRB spectrum repository to obtain the in-trinsic X-ray absorbing column densities for the GRBs ofour complete sample with measured redshift. Following theprocedure described in Kopac et al. (2012) we used datamostly from photon counting (PC) mode in the widest timeepoch where the 0 . − . . −
10 keV hardness ratiois constant, in order to prevent spectral changes that can af-fect the X-ray column density determination. Each spectra isfitted with the phabs*zphabs*pow model within the XSPECpackage. The first absorbtion component ( phabs ) is frozen atthe Galactic contribution to the X-ray N H in the directionof each GRB (using the value computed by Kalberla et al.2005). The second (intrinsic) absorption component ( zphabs ) is left free to vary, with the redshift frozen to the value re-ported in the literature for any given GRB (Table 1). Thethird component ( pow ) is a simple power-law model withphoton index and normalization free to vary. The results ofour analysis are shown in Table 4. Using the automated data products provided by the
Swift
Burst analyzer (Evans et al. 2009) we estimated the af-terglow X-ray integral fluxes in the 2-10 keV rest framecommon energy band and computed the corresponding restframe X-ray luminosities at different rest frame times forall the GRBs of our complete sample with a measured red-shift. The 2-10 keV rest frame fluxes were computed fromthe observed 0.3-10 keV unabsorbed fluxes and the time- c (cid:13) , 1–17 P. D’Avanzo et al.
Table 3.
Prompt emission rest frame spectral properties for the SGRBs of the complete sample with measured redshift. Spectralparameters, rest frame peak energies ( E peak ), isotropic energies ( E iso ) and luminosities ( L iso ) are listed. Columns 7 and 8 report thename of the mission from which the spectral properties have been derived (F= Fermi , K=
Konus/Wind ,Su=
Suzaku , S=
Swift ) and thewidth of the temporal bin chosen to rebin the prompt emission light curve (∆ t ), respectively. Reference in the last column are for thespectral properties: [1] Golenetskii et al. (2005), [2] Ohno et al. (2007), [3] Uehara et al. (2008), [4] Nava et al. (2011), [5] Antonelli etal. (2009), [6] Bhat et al. (2010), [7] Fitzpatrick (2010), [8] Golenetskii et al. (2010), [9] Sakamoto et al. (2013), [10] Golenetskii et al.(2013).GRB z α [ β ] E peak E iso L iso Mission ∆ t Ref.keV 10 erg 10 erg s − ms051221A 0.547 − . ± .
13 621 . ± .
77 2 . ± .
33 5 . ± .
89 K 4 1070714B 0.92 − . ± .
10 2150 . ± .
48 9 . ± .
38 1 . ± .
14 Su 1000 2080123 0.495 − . ± .
38 104 . a . a . a Su 880 3080905A 0.122 − . ± .
16 578 . ± .
42 0 . ± .
003 0 . ± .
002 F 64 4090426 2.609 − − .
3] 176 . ± . b . ± . b . ± . b S 1000 5090510 0.903 − . ± .
02 [ − . ± .
25] 8089 . ± .
74 74 . ± .
21 17 . ± .
17 F 64 4100117A 0.920 − . ± .
21 549 . ± .
48 0 . ± .
10 0 . ± .
13 F 64 4100625A 0.452 − . ± .
11 701 . ± .
71 0 . ± .
03 0 . ± .
01 F 64 6100816A 0.805 − . ± .
05 [ − . ± .
17] 247 . ± .
48 7 . ± .
25 0 . ± .
01 F 1024 7101219A 0.718 − . ± .
27 841 . ± .
62 4 . ± .
68 6 . ± .
86 K 16 8111117A 1.3 c − . ± .
28 966 . ± .
00 3 . ± .
06 4 . ± .
28 F 50 9130603B 0.356 − . ± .
15 894 . ± .
60 2 . ± .
23 4 . ± .
87 K 16 10
Notes . a Lower limit. b Values obtained from fitting with a Band function with α = − β = − . c Photometric redshift.
Table 4.
Intrinsic X-ray absorbing column densities of the SGRB of our complete sample with measured redshift. Columns are: GRBindentifier, redshift, Galactic X-ray absorbing column density, X-ray spectrum exposure time and time interval, spectral photon index,intrinsic X-ray absorbing column desity. Errors are at 90% confidence level.GRB z N H Gal. Exp. (interval) Γ N H ( z )10 cm − ks (s) 10 cm − .
547 5 . . − × ) 2 . +0 . − . . +0 . − . .
923 6 . . − × ) 1 . +0 . − . . +1 . − . .
495 2 . . − . +0 . − . < . UL .
122 9 . . − . +0 . − . < . UL .
609 1 . . − . × ) 2 . +0 . − . < . UL .
903 1 . .
14 (100 − . +0 . − . . +1 . − . .
915 2 . .
05 (105 − . +0 . − . . +4 . − . .
452 2 . .
65 (61 − . +0 . − . < . UL .
805 4 . . − × ) 1 . +0 . − . . +1 . − . .
718 4 . . − . +0 . − . . +3 . − . . a . .
58 (89 − . +0 . − . . +6 . − . .
356 1 . . − × ) 2 . +0 . − . . +0 . − . a Photometric redshift. resolved measured photon spectral index, Γ, (that we re-trieved from the
Swift
Burst Analyzer) in the following way(see also Gehrels et al. 2008): f X,rf (2 −
10 keV) = f X (0 . −
10 keV) (cid:0) (cid:1) − Γ − (cid:0) (cid:1) − Γ − Γ − . − Γ (1)The best-fit of each GRB X-ray light curve was interpo-lated or extrapolated to the given rest frame times. These af-terglow X-ray luminosities were compared with the promptemission isotropic energies E iso , the isotropic peak luminosi-ties L iso and the rest frame peak energies E peak for the burstsof our complete sample. The obtained 2-10 keV rest frameX-ray luminosities are reported in Table 5. In the following sections, we will show the results obtainedby testing the existence of correlations among the observedand rest-frame physical properties of the SGRBs of our sam-ple. We computed for each case the Spearman rank corre-lation coefficient r (Spearman 1904; Press et al. 1986) and,in order to determine the significance of the correlation, theassociated null-hypothesis probability P null . Given the largescatter of the data points (larger than the uncertainties oneach value) and that, in principle, any of the quantities atplay can be assumed as the independent variable, we fit thedata using the ordinary least squares bisector method (Isobeet al. 1990). c (cid:13) , 1–17 complete sample of Swift short GRBs Table 5.
X-ray luminosities in the 2–10 keV rest frame energy band computed at four different rest frame times (5 min, 1 hr, 11 hr and24 hr) for the SGRBs of the complete sample with measured redshift (see Sect. 2 for details).GRB z L X, L X, err L X, L X, err L X, L X, err L X, L X, errerg s − erg s − erg s − erg s − erg s − erg s − erg s − erg s − . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × a . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × a Photometric redshift.
We note that, for the events of our complete sample, therest-frame properties like luminosities and energies can becorrelated with the redshift and this could give rise to spu-rious correlations. Indeed, for any flux-limited sample (as inour case) there will be an inevitable and tight correlationbetween luminosity and redshift. This arises because, for afixed flux limit, only the more powerful sources can be de-tected out to great distances (see, e.g., Blundell, Rawlings& Willot 1999 and references therein). In order to properlyhandle this problem the correlations between luminosities orbetween luminosity and energy should be examined takinginto account the common redshift dependence. This can bedone with a partial correlation analysis. If r ij is the cor-relation coefficient between x i and x j , in the case of threevariables the correlation coefficient between two of them,excluding the effect of the third one is: r , = r − r r p − r p − r (2)(Kendall & Stuart 1979; see also Padovani 1992) where, forour study, the coefficients 1 and 2 refer to the luminosityand energy, respectively, and the coefficient 3 to the redshift.We also performed a linear fit to each data distribution inlogarithmic space. The results of such correlation analysisare reported in Table 6 and Table 7. Total sample: properties in the observer frame
As discussed in Sect. 1, SGRB progenitors (binary systemsof compact objects) can originate from the evolution of mas-sive stars in a primordial binary or by dynamical interactionsand capture in globular clusters during their core collapse. Inprimordial systems, the delay between binary formation andmerging is driven by the gravitational wave inspiral time,which is strongly dependent on the initial system separa-tion. Some systems are thus expected to drift away from thestar–forming regions in which they formed, before mergingtakes place, also because they experience a natal kick at thetime of the formation of the compact object. Simulations(Belczynski, Bulik & Kalogera 2002; Belczynski et al. 2006) −10 −9 −8 −7 −6 −10 −9 −8 −7 −6 F l u e n ce s t s X R T ( e r g c m − ) Fluence BAT (erg cm −2 )EESLPossible LGRB Figure 1.
X-ray (0.3–10 keV) fluence during the first 500 s of
Swift -XRT observation vs. gamma–ray (15-150 keV) prompt flu-ence of the SGRBs of the total sample (dots). The dashed lineshows where the two quantities are equal (even if in different en-ergy bands). Sample sub-classes are also shown: no XRT promptdetection (lower limits); extended emission SGRBs (open circles);short lived SGRBs (open squares); possible LGRBs (open trian-gles). show that a large fraction of the merging events should takeplace in the outskirts or even outside the galaxies, in lowdensity environments. A low density circumburst environ-ment is expected also for short GRBs of dynamical originoccurring in globular clusters. For these events, the result-ing time delay between star-formation and merging wouldbe dominated by the cluster core-collapse time and thus becomparable to the Hubble time (Hopman et al. 2006). Amuch faster evolutionary channel has been proposed (Bel-czynski & Kalogera 2001; Perna & Belczynski 2002; Belczyn-ski et al. 2006), leading to merging in only ∼ − yr,when most systems are still immersed in their star-formingregions. According to the above scenario, with the exceptionof the events originated by the “fast” primordial channel,SGRBs are generally expected to occur in regions where thedensity of the diffuse medium is low, giving rise to fainterafterglows, setting in at later times than those of long GRBs c (cid:13) , 1–17 P. D’Avanzo et al. −10 −9 −8 −7 −6 −10 −9 −8 −7 −6 F l u e n ce t o t X R T ( e r g c m − ) Fluence BAT (erg cm −2 )EESLPossible LGRB Figure 2.
X-ray (0.3–10 keV) total fluence vs. gamma–ray (15-150 keV) prompt fluence of the SGRBs of the total sample. Thedashed line shows where the two quantities are equal (even if indifferent energy bands). Sample sub-classes are also shown: ex-tended emission SGRBs (open circles); short lived SGRBs (opensquares); possible LGRBs (open triangles). (e.g. Vietri 2000; Panaitescu, Kumar & Narayan 2001; Sal-vaterra et al. 2010).Four events (i.e., 13% of the total sample) have no X-ray afterglow detected, in spite of the prompt
Swift
XRTfollow-up. This marks a significant difference with respectto the LGRBs, where only ∼
2% of the events promptlyobserved by the
Swift
XRT is missing an X-ray afterglowdetection (Evans et al. 2009). The lack of detection of anX-ray afterglow for these four events can have multiple ex-planations. It can be ascribed to a difference in the GRBenergetics (they could be sub-energetic GRBs), to the lowdensity of the circumburst medium or to a high-redshift ori-gin. For each GRB of the total sample we computed theobserved 0.3-10 keV X-ray fluence during the first 500 s ofthe
Swift -XRT observation (between 120 s and 620 s afterthe burst; Table 2). We then compared it with the promptemission fluence computed in the 15-150 keV
Swift -BAT en-ergy band (Table 2). As can be seen in Fig. 1 and Table 6,the two quantities scale linearly, with the highest X-ray flu-ences corresponding to the highest gamma-ray fluences. Thefour X-ray fluence upper limits lay in the faint end of theBAT fluence distribution, suggesting that these events wereprobably less energetic, rather than occurred in low-densityenvironments. A similar explanation was proposed also byNysewander et al. (2009) for SGRBs with faint X-ray af-terglows. However, if we assume that the early time X-rayemission is the tail of the prompt emission (i.e. originated byinternal shocks; Kumar & Panaitescu 2000; Tagliaferri et al.2005), then its intensity should be unrelated to the densityof the circumburst medium and clearly tightly correlated tothe energetic of the prompt emission. Actually, as we willshow in the next sections, the early time X-ray luminosityfor the SGRBs of the complete sample is found to stronglycorrelate with the isotropic energy of the prompt emission. Auseful test to check for the role of the density of the circum-burst medium could come from the emission in the opticalband (if any), which is expected to be pure external shockafterglow emission even at early times. Unfortunately, noneof these SGRBs without an early X-ray detection have an optical afterglow (Berger 2014). Finally, we note that a highredshift origin for these events (all missing a redshift mea-surement) cannot be ruled out anyway (see, e.g., Berger etal. 2007).We also compared the
Swift -BAT fluence with the totalX-ray fluence, computed by integrating the 0.3-10 keV X-ray flux under each light curve best fit (see Sect. 3.1). Againthe two quantities follow a broadly linear correlation, sug-gesting that the X-ray afterglow brightness is a proxy of theprompt emission energy (Fig. 2, Table 6). Such results aresimilar to what found for the observed gamma and X-rayproperties of LGRBs (Gehrels et al. 2008; Nysewander etal. 2009; Margutti et al. 2013). In particular, we find thatSGRBs with extended emission and SGRBs with short livedX-ray afterglows follow the correlation as the other eventsof the sample, with the former having sistematically larger γ − ray fluences, as expected given their longer duration interms of T . According to these findings, the prompt emis-sion or the X-ray afterglow duration do not seem to providea unique indicator of a specific progenitor and/or environ-ment for SGRBs. Complete sample: properties in the rest frame
One of the key properties characterizing the SGRBs is theirprompt emission spectrum, which is found to be typicallyharder with respect to LGRBs (Kouveliotou et al. 1993).Considering the GRB prompt emission spectrum as de-scribed by a Band function (Band et al. 1993), the SGRBspectral hardness is found to be due to a combination ofan harder low-energy spectral component (the α index ofthe Band function) and to a higher spectral peak energy(Ghirlanda et al. 2009). However, these differencies becomeless significant when the analysis is restricted to the first1-2 s of the LGRBs prompt emission (Ghirlanda, Ghisellini& Celotti 2004; Ghirlanda et al. 2009). At the same time,Ghirlanda, Ghisellini & Celotti (2004) showed that for thebrightest SGRBs, the difference in the spectral hardnesswith respect to LGRBs is mainly driven by a harder lowenergy spectral index present in short bursts, rather thandue to a different peak energy. To further investigate thisissue, we compared the low-energy spectral indices ( α ) andthe peak energies ( E peak ) of the SGRBs of our complete sample (Table 3) with the equivalent values of the LGRBsof the BAT6 sample (Nava et al. 2012). The obtained dis-tributions have average α SGRB = − . σ = 0 .
4) versus α LGRB = − . σ = 0 .
2) and E SGRB peak = 1557 ( σ = 2352)keV versus E LGRB peak = 737 ( σ = 510) keV. A Kolmogorv-Smirnov (K-S) test gives a 1% and 29% probability for thetwo distributions of α and E peak to be drawn from the samepopulation, respectively. This provides a moderate indica-tion (although both distributions are rather scattered) thatfor a sub-sample of bright events, the spectral hardness ofSGRBs (compared to LGRBs) is mainly due to a differentlow-energy spectral index (in agreement with the findings ofGhirlanda, Ghisellini & Celotti 2004). c (cid:13) , 1–17 complete sample of Swift short GRBs Table 6.
Correlation fits and coefficients for the observer frame properties of the total sample. Data distributions shown in Fig. 1 andFig. 2 were fitted with the function y = 10 A x B (see Sect. 2.1 for details).Correlation A B r P null DispersionX − ray early vs. γ − ray − . ± .
02 1 . ± .
11 0.65 5 . × − − ray total vs. γ − ray − . ± .
74 0 . ± .
07 0.74 1 . × − We checked the consistency with the E peak − L iso (Yonetokuet al. 2004), and with the E peak − E iso relations (Amati etal. 2002) for all the bursts of our complete sample with ameasured redshift. The results are shown in the upper panelsof Fig. 3.All events are found to be consistent with the E peak − L iso correlation, which is valid also for LGRBs (Yonetoku etal. 2004; Nava et al. 2012). A fit to the LGRBs with redshift(taken from Nava et al. 2012) together with the SGRBs ofthe complete sample with the function y = 10 A x B provides anormalization A = − . ± .
81 and a slope B = 0 . ± . σ from the best fit. This is the event with the lowestredshift of our sample (Table 1) and, consequently, with thelowest values of L iso and E iso . However, such redshift mea-surement comes from the association with a spiral galaxy at z = 0 .
12, given that the position (known with sub-arcsecondprecision) of the optical afterglow of GRB 080905 falls in thelight of this galaxy. As shown in Rowlinson et al. (2010), theproposed host galaxy is seen face-on and the optical after-glow of this burst falls in a region between two spiral arms(and near, but not inside, the bulge). These authors estimatea chance probability alignment of < complete sample are consis-tent with the E peak − L iso relation, we note that they almostall lie to the left of the best fit of long GRBs. On the basis ofthis consideration, Tsutsui et al. (2013) suggested that the E peak − L iso correlation followed by short bursts is 5 timesfainter than the same correlation defined by long bursts. Theestimate of the peak luminosity depends on the width of thetemporal bin ∆ t chosen to rebin the light curve: by choos-ing smaller and smaller bins, the estimate of L iso tends toincrease. For this reason a more uniform estimate of L iso should refer to a peak luminosity estimated for all GRBson the same rest frame temporal bin. In our sample, thepeak fluxes have been estimated on different temporal bins,from 4 ms to 1024 ms in the observer frame. In Fig. 3 (rightpanel) we divided our sample in bursts with ∆ t > ∆ t t = 16ms(yellow triangles) and ∆ t = 4ms (purple upside down tri-angle). Bursts with smaller ∆ t systematically tend to havelarger L iso , and to be more consistent with the best fit oflong bursts. For most long bursts the peak flux has beenestimated on a ∆ t ∼
1s timescale. Any consideration about the existence of an E peak − L iso correlation for short GRBsand its comparison with the same correlation for long GRBsshould take this effect into account. The conclusion can bedifferent depending on the choice of ∆ t . When L iso is esti-mated on similar timescales both for long and short GRBs,short GRBs lie on the extreme left side of the correlationdefined by long bursts. By reducing ∆ t for short bursts (forexample for ∆ t ∼ E peak − L iso plane improves. Our preliminaryresults might suggest that a consistency between the longand short E peak − L iso correlation can be reached by con-sidering for both classes of events a ∆ t which is a (proper)fraction of their T (see also Tsutsui et al. 2013).Concerning the E peak − E iso plane, most of the SGRBsof our sample lie at more than 3 σ from the correlation de-fined by LGRBs, and systematically on the left with respectto the best fit line of LGRBs (Fig. 3). This suggests forthe existence of a SGRB region that has the same slopeas the LGRBs relation, but a different normalization (seealso Amati 2008; Piranomonte et al. 2008; Ghirlanda etal. 2009; Zhang et al. 2012). Two significant exceptions areGRB 090426 and GRB 100816A both placed at the border ofthe 2 σ confidence region of the relation holding for LGRBs.As discussed in Sect. 2.1, both these events have an uncer-tain classification. We note, however, that GRB 090426 isone of the few events of our complete sample whose promptemission was observed by the Swift satellite only. Given therelatively limited energy range of the BAT telescope (15-150 keV) and to the lack of detection by other high-energysatellites, the E peak and E iso for this event were obtained byfitting the BAT spectrum with a Band function with photonindexes fixed to α = − β = − . α and β free to vary, only pro-vides a lower limit to E peak (with the rest frame E peak > E iso = [2 . − . × erg; Antonelli et al. 2009),thus leaving some uncertainty about the position of thisevent on the E peak − E iso plane. The situation is differentfor GRB 100816A, whose prompt emission was observed bythe Fermi and
Konus-Wind satellites in the 10 − E peak − E iso relation, coupled with its T of 2.9 s, points toward a clas-sification as a LGRB. Excluding the events whose classifi-cation or redshift is uncertain, a fit to the SGRBs of the complete sample in the E peak − E iso plane with the function y = 10 A x B provides a normalization A = − . ± .
91 anda slope B = 0 . ± .
06. As a comparison, as reported in Navaet al. (2012), the same fit performed on the total sample ofLGRBs provides A = − . ± .
13 and B = 0 . ± . z . For these c (cid:13) , 1–17 P. D’Avanzo et al.
Figure 3. E peak − E iso ( left panels ) and E peak − L iso ( right panels ) correlations valid for LGRBs (dots; data taken from Nava et al.2012). The power-law best fit is shown as a solid dark line. The shaded region represents the 3 σ scatter of the distribution. SGRBs ofour complete sample are marked as empty squares. In the lower panels the consistency of the two correlations of SGRBs with unknownredshift is shown. The test is performed by varying the redshift from 0.01 to 10. Different colours refers to different ranges of redshift(see legend). Two possible LGRBs belonging to our complete sample (GRB 090426 and GRB 100816A) and a possible outlier of the E peak − L iso correlation (GRB 080905A) are also marked. GRBs we tested their consistency with the Amati and Yo-netoku correlations by varying the redshift from 0.01 to 10(Fig. 3, bottom panel). Independently of the chosen redshift,they are inconsistent with the Amati correlation (only GRB061201 can by marginally consistent if its redshift is largerthan ∼ z > . E peak and, consequently on E iso can be estimated fromthe spectral analysis (arrows in Fig. 3, bottom panel). ForGRB 080503 it was not possible to test its consistency with the correlations since the spectrum is well described by apower law function and the redshift is unknown.All the events of our complete sample are consistentwith the SGRB region of the three parameter E iso − E peak − E X,iso correlation (Bernardini et al. 2012 and Margutti etal. 2013), with the two debated SGRBs 090426 and 100816Alying close to the region defined by LGRBs (Fig. 4).
In Fig. 5 we show the X-ray light curves of the SGRBs ofthe complete sample with redshift normalized to their E iso . c (cid:13) , 1–17 complete sample of Swift short GRBs Figure 4. E iso − E peak − E X,iso correlation. The power-law best fit is shown as a solid dark line. The shaded region represents the3 σ scatter of the distribution. SGRBs of our complete sample are marked as squares. Two possible LGRBs belonging to our complete sample (GRB 090426 and GRB 100816A) are also marked. Figure 5.
Best fit of the X-ray luminosity light curves of theSGRBs with redshift of our complete sample normalized to their E iso . The X-ray luminosities were computed for each GRB inthe common rest frame 2 −
10 keV energy band following theprecedure described in Sec. 3.2.2. The rest frame times at whichwe computed L X − E iso , L X − E peak and L X − L iso correlationsare marked with vertical dashed lines. The dark (light) shadedarea represent the 1 σ (2 σ ) scatter of the same plot obtained forthe LGRBs of the BAT6 sample (D’Avanzo et al. 2012). The distribution of the E iso -normalized X-ray light curvesfor the LGRBs of the BAT6 sample (taken from D’Avanzo etal. 2012) is also represented in the background for compar- ison. This plot shows that the E iso − normalized X-ray lightcurves of long and short GRBs are rather clustered, with anintrinsic scatter that changes with the rest frame time. Withthe aim of investigating such evolution in time between theprompt and X-ray afterglow emission, different correlations( L X − E iso , L X − L iso and L X − E peak ) were tested for theSGRBs of the complete sample at four different rest frametimes. Following the procedure described in D’Avanzo et al.(2012), the early X-ray afterglow luminosity was measuredat t rf = 5 min and at t rf = 1 hr, while the late time af-terglow flux was measured at t rf = 11 hr and t rf = 24 hr(Fig. 5).As a general trend, we note that the afterglow X-rayluminosity at early times ( t rf = 5 min) correlates with theprompt emission quantities E iso , L iso and E peak with nullprobabilities of 10 − − − and dispersion ∼ . − . t rf = 1, 11 and 24 hr) the scatter increasesand these correlations become much less significant. Theearly time prompt-afterglow correlation we find (Table 7) arerather similar to the same correlations found for the BAT6sample of LGRBS (D’Avanzo et al. 2012). In particular, theearly time L X − E iso correlations for short and long GRBsfrom the two samples have the same slope, with the SGRBslying on the faint end of the correlation (in agreement withwhat found by Nysewander et al. 2009). To compare themqualitatively, we show in Fig. 6 the time resolved prompt-afterglow correlations for the SGRBs of our complete sam-ple and for the LGRBs of the BAT6 sample. Concerning the L X − L iso plane we note that at all times, assuming the same L iso , SGRBs have on average lower X-ray luminosity withrespect to LGRBs. However, we note that the systematics inthe procedure of L iso estimate for SGRBs discussed in Sect.4.2.1 for the E peak − L iso relation might amplify this effect.Similarly, compared to LGRBs, for a given E peak , SGRBsare found at an average lower X-ray luminosity. Consider-ing the correlation found between L X and E iso , such a result c (cid:13) , 1–17 P. D’Avanzo et al.
Table 7.
Correlation fits and coefficients for the prompt vs. early afterglow emission rest frame properties of the complete sample. Datadistributions were fitted with the function y = 10 A x B (see Sect. 2.1 for details).Correlation A B r P null Dispersion L X, vs. E iso − . ± .
67 1 . ± .
09 0.67 7 . × − L X, vs. E iso − . ± .
48 1 . ± .
25 0.43 2 . × − L X, vs. L iso . ± .
07 0 . ± .
20 0.40 3 . × − L X, vs. L iso − . ± .
06 1 . ± .
33 0.15 7 . × − L X, vs. E peak . ± .
83 1 . ± .
55 0.51 2 . × − L X, vs. E peak . ± .
71 1 . ± .
06 0.15 7 . × − can be considered a natural consequence of the inconsistencyof SGRBs with the E peak − E iso correlation (Fig. 3, upperpanel). Another feature arising from the comparison of theshort and long GRB samples is that the SGRBs prompt-afterglow correlations show a scatter much larger than whatobserved for LGRBs, especially at late times ( t − t > E iso and L iso asgood as it is found to be for the LGRBs (D’Avanzo et al.2012). Such phenomenon might be indicative of a lower ra-diative efficiency of the central engine related to the differentprogenitor or be the consequence of a different circumburstmedium.Finally, we note from Fig. 6 that the two debated shortGRB 090426 and GRB 100816A always fall in the LGRBsregion of the different correlation planes. While this can beconsidered as a further evidence against the classificationof GRB 100816A as a SGRB, we stress that the same rea-soning cannot be applied safely to GRB 090426 given thepoor constraints on its prompt emission spectrum (see Sect.4.2.1). The redshift distribution of SGRBs can provide an indi-rect tool to constrain the nature of their progenitors anddiscriminate among the evolutionary channels. The redshiftdistribution of merger events of dynamically formed dou-ble compact object systems is expected to be different fromthat of primordial binaries. In particular, given the rela-tively short delay between formation and merging ( < complete sample is < z > = 0 .
85 (0.72). This value is higherthan the one obtained by Fong et al. (2013) by consideringthe whole
Swift
SGRB sample ( < z > ∼ .
5) while it is inagreement with the mean redshift ( < z > = 0 .
72) reportedby Rowlinson et al (2013) for their SGRB sample limited tothe events with T
2s (which is thus excluding all SGRBwith extended emission). Indeed, the average redshift of our complete sample is consistent with the expected peak for theredshift distribution of SGRBs originated by the primordialformation channel (Salvaterra et al. 2008). Including GRB 050709, discovered by the
HETE-II satellite
In the primordial binary scenario, the intrinsic forma-tion rate, defined as the number of bursts per unit time andunit comoving volume at redshift z , Ψ SGRB ( z ) , is given bythe convolution of the massive star binary formation rateand a delay time distribution function f F ( t ). The delay isthe time interval between the formation of the massive starbinary and the merging of the compact objects. The forma-tion rate is assumed to be proportional to the cosmic starformation rate, ˙ ρ ⋆ , parametrized as in Hopkins & Beacom(2006). Ψ SGRB ( z ) is then given by:Ψ SGRB ( z ) ∝ Z ∞ z dz ′ dtdz ′ ( z ′ ) ˙ ρ ⋆ ( z ′ ) f F [ t ( z ) − t ( z ′ )] , (3)where t ( z ) is the age of the Universe at redshift z . For thedelay time distribution function f F ( t ), we adopt the sim-ple expression: f F ( t ) ∝ t n with n = −
1, as suggested froman updated analysis of double compact object mergers per-formed using population synthesis methods (Portegies Zwart& Yungeson 1998; Schneider et al. 2001; Belczynski et al.2006; O’Shaughnessy et al. 2008). However, some uncer-tainty remains on the exact value of the n exponent (Berger2014, and references therein). For a comparison with thedata, we compute the observed distribution of SGRBs forthree different values of n , namely n = − . n = − n = − . ∼
20 Myr to ∼
10 Gyr. Given that a t − distribution would diverge as t get close to zero, we will consider an initial time cutoff of 10Myr. As noted by Behroozi, Ramirez-Ruiz & Fryer (2014),the choice of the time cutoff has little effect on the meantime delay value.The observed photon flux, P , in the energy band E min The L X − E iso , L X − L iso and L X − E peak correlations studied in the present paper for the complete sample of SGRBs atdifferent rest-frame times (stars). GRB 090426 and GRB 100816A, found to be marginally consistent with the E peak − E iso correlation,are marked with stars. As a comparison, the 3 σ scatter for the correlations found for the LGRBs of the BAT6 sample is also shown(shaded area; from D’Avanzo et al. 2012). dNdt ( P < P < P ) = Z ∞ dz dV ( z ) dz ∆Ω s π k SGRB Ψ SGRB ( z )1 + z × Z L ( P ,z ) L ( P ,z ) dL ′ φ ( L ′ ) , (5)where dV ( z ) /dz = 4 πc d L ( z ) / [ H ( z )(1 + z ) ] is the comovingvolume element, and H ( z ) = H [Ω M (1 + z ) + Ω Λ + (1 − Ω M − Ω Λ )(1 + z ) ] / . ∆Ω s is the solid angle covered onthe sky by the survey, and the factor (1 + z ) − accounts forcosmological time dilation. Ψ SGRB ( z ) is the comoving burstformation rate normalized to unity at z = 0 as computed inEq. 3 and k SGRB is the SGRB formation rate at z = 0. Fi-nally, we assume that the luminosity function of short GRBsis well described by a single power-law of power-index ξ forluminosity in the range 10 − erg s − . Following Sal-vaterra et al. (2008), we obtain the value of ξ by fitting thedifferential photon flux distribution of SGRBs with T < 2s detected by BATSE in the 50-300 keV band (Paciesas etal. 1999). We obtain a reasonable fit to BATSE data in allformation scenarios with ξ = − . ± . − . ± . 08, and − . ± . 08 (errors at 1 σ confidence level) for n = − . − − . 5, respectively.We then compute the expected redshift distribution ofshort GRBs matching the selection criteria of our complete sample, i.e. those with photon fluxes P > . − cm − in the 15–150 keV band of Swift- BAT (see Sect. 2). We notethat having a flux-limited sample, with a clear photon fluxcut, is an asset for the comparison with the model predic-tions. Model results computed for the primordial formationchannel with different time delay distributions are shown inFig. 7. The shaded area accounts for the observed cumulativeredshift distribution including the uncertainties due the lackof a secure redshift determination for ∼ 30% of the SGRBs of the complete sample. From the plot it is clear that themodel with n = − . n = − f F ( t ) ∝ t − . looks to be favoured in ac-counting for the observed redshift distribution of the SGRBsof our sample, suggesting that they are mainly originated byprimordial double compact object systems merging in a rel-atively short time. This differs from the results of a similaranalysis carried on for the BAT6 sample of long GRBs: toaccount for their observed redshift distribution, the rate oflong GRB formation has to increase with redshift on the topof the known evolution of the SFR density as (1 + z ) . ± . (Salvaterra et al. 2012).Finally, we note that a significant contribution ofSGRBs with dynamical origin would require a lower meanredshift (Salvaterra et al. 2008; Guetta et al. 2008), suggest-ing that the contribution of this formation channel to theSGRBs should be negligible and/or limited to the faintestevents (which are not included in our flux-limited sam-ple). On the other hand one can conclude that dynamicallyformed SGRBs should be intrinsically sub-energetic giventhat, occurring at an average lower redshift, they shouldshow a relatively high observed flux (and, in principle, fallin a flux-limited sample like the one presented in this paper).A tentative estimate of the fraction of SGRBs with dynam-ical origin in our sample is given in the next subsection. The distribution of the intrinsic X-ray absorbing columndensities of the SGRB of our complete sample has a meanvalue log N H ( z ) = 21 . σ log N H ( z ) =0 . com- c (cid:13) , 1–17 P. D’Avanzo et al. Figure 7. Redshift distribution of our complete sample ofSGRBs. The shaded are takes into account the uncertainties dueto the lack of redshift measurement for five bursts in the sam-ple. Model results for n = − . 5, -1, and -0.5 are shown with thelong-dashed, short-dashed and dotted line, respectively. In com-puting the expected redshift distribution for the different modelwe apply the same photon flux cut, P > . − cm − inthe Swift- BAT 15–150 keV band, used in the definition of our complete sample. plete sample of LGRBs presented in Campana et al. (2012).In order to make a proper comparison, we considered onlythose LGRBs whose redshift is lower or equal to z = 1 . com-plete sample) obtaining a mean log N H ( z ) = 21 . σ log N H ( z ) = 0 . N H might be a good proxy ofthe GRB host galaxy global properties but not for the spe-cific properties of the circumburst medium. Furthermore,the possibility that gas along the line of sight in the diffuseintergalactic medium or intervening absorbing systems cancontribute to the absorption observed in the X-ray emis-sion of GRBs has to be taken into account (Behar et al.2011; Campana et al. 2012; Starling et al. 2013). However,such effect is expected to dominate at z > 3, while at lowerredshifts, comparable to the values found for our complete sample, the absorption within the GRB host galaxy is ex-pected to dominate (Starling et al. 2013). For LGRBs, themassive star progenitor is expected to significantly enrich the surrounding environment with metals (whose X-ray N H is a proxy) before the collapse with its stellar wind. Alterna-tively, it has been recently proposed that the Helium in theH II regions where the burst may occur is responsible for theobserved X-ray absorption in LGRBs (Watson et al. 2013).Under these hypothesis, a high intrinsic X-ray N H , can beinterpreted as the evidence of a dense circumburst medium.Something similar can happen for SGRBs, under the con-dition that a short time (of the order of Myrs) separatesthe supernova explosions which gave origin to the compactobjects in the primordial binary system progenitor and itscoalescence, with the result that the burst would occur insideits host galaxy and near its star forming birthplace (Perna& Belczynski 2002). Such formation channel of “fast merg-ing” primordial binaries is in agreement with the observedredshift distribution of our complete sample discussed above.Indeed, the only case for which combined X-ray and opti-cal afterglow spectroscopy could be performed for a genuineSGRBs (GRB 130603B, which is included in our sample),provided evidence for a progenitor with short delay time ora low natal kick (de Ugarte Postigo et al. 2013).SGRBs originated by double compact object systemswhich experienced a large natal kick or which are dynami-cally formed in globular clusters are expected to be associ-ated with a low-density environments. As shown in Table 4,four SGRBs of the complete sample have only upper limitson the intrinsic X-ray N H . Among these, GRB 100625A isthe only event whose upper limit is significantly below theaverage N H of the distribution. Assuming that such limitis indicative of a low-density circumburst medium, we canestimate that at least 10% of the events of our sample areoriginated by coalescing binaries formed via the dynamicalchannel (or having experienced a large natal kick). Further-more, three (out of five) events of the complete sample miss-ing a robust redshift measure (GRB 061201, GRB 080503,GRB 090515) have no detected host galaxy coincident withthe afterglow position in spite of the precise (sub-arcsecond)location and the deep magnitude limits (Berger 2010 andreferences therein). As discussed in Berger (2010) “hostless”SGRBs may lie at moderately high redshifts z > 1, and havefaint hosts, or represent a population where the progenitorhas been kicked out from its host or is sited in an outly-ing globular cluster. A statistical study carried out recentlyby Tunnicliffe et al. (2014) pointed out that the proximityof these events to nearby galaxies is higher than is seen forrandom positions on the sky, in contrast with the high red-shift scenario. Following this interpretation, up to 4 events(25% of the SGRBs of the complete sample) might haveoccurred in low-density environments.Finally, we remark that the complete sample presentedin this paper is built by selecting the events with a brightprompt emission that, according to the standard GRBmodel, is independent on the type of circumburst environ-ment. Namely, GRB 100625A and the three “hostless” bursts.c (cid:13) , 1–17 complete sample of Swift short GRBs Figure 8. Distribution of the intrinsic X-ray absorbing columndensities for the SGRBs of the complete sample (filled histogram)and of the LGRB with z < . The statistical study of the rest-frame properties of SGRBsgives the best opportunity to characterize the physics ofthese events, although such studies are often biased by thefact that almost 3/4 of GRBs are lacking a secure redshiftmeasurement. In this paper, we overcome this problem work-ing with a carefully selected sample of Swift SGRBs havinga completeness in redshift of ∼ 42% which increases up to ∼ 70% by considering the events with the brightest γ − rayprompt emission. From the study of the observer and rest-frame properties of this sample we obtained the followingmain results:- The SGRBs X-ray afterglow fluence correlates linearly withthe prompt emission fluence at all times, with no differencefor the SGRBs with extended emission or with a short/long-lived X-ray afterglow.- The percentage of Swift SGRBs lacking an X-ray afterglowdetection at early times is more than 6 times higher thanfor LGRBs. These events lay in the faint end of the γ − rayfluences distribution suggesting that their lack of an X-rayafterglow is likely due to the intrinsic faintness of the promptemission, although a high redshift origin for these eventscannot be excluded.- Compared to bright LGRBs (BAT6 sample) the spectralhardness of the SGRBs of the complete sample seems tobe mainly due to a harder low energy spectral componentpresent in short bursts, rather than to a higher peak energy.- All the SGRBs of our complete sample are consistent withthe E peak − L iso and the E iso − E peak − E X,iso correlations,with the significant exception of GRB 080905A. We notethat such event has the lowest values for E iso and L iso amongthe burst of our sample. We speculate that the redshift ofthis GRB might be higher than the value inferred from itsassociation with a nearby ( z = 0 . E peak − L iso correlation followed by SGRBs being sistem-atically fainter than the correlation defined by LGRBs. Al-though such finding is intriguing, we caution that it can beaffected by the choice of the temporal bin in the estimate ofthe isotropic peak luminosity for both long and short GRBs. - On the E peak − E iso plane, SGRBs define a region withthe same slope measured for the correlation holding forLGRBs but with a different normalization. Two exceptionsare GRB 090426 and GRB 100816A, both consistent within2 σ with the E peak − E iso LGRB correlation.- The rest-frame afterglow X-ray luminosity at early times( t rf = 5 min) correlates well with the prompt emission E iso and L iso . At later times ( t rf > L X − E iso and L X − L iso correlations hold at all times. Such effect mightbe indicative of a lower radiative efficiency of the SGRBcentral engine related to the different progenitor or be theconsequence of a different circumburst medium for long andshort GRBs.- In light of its duration, prompt emission and X-ray af-terglow properties, GRB 100816A (initially classified as aSGRB) is likely a long-duration event. No firm conclusioncan be derived for the classification of GRB 090426, mainlydue to the lack of strong constraints on the properties of itsprompt emission spectrum.- The redshift distribution of the SGRBs of our sample hasa mean value of z = 0 . 85. No evidence for a different en-vironment for long and short GRBs can be derived fromthe rest-frame X-ray column densities. When compared onthe same redhift bin, the distributions for long and shortGRBs are fully comparable. Both these results are consis-tent with the scenario of “primordial binary” progenitors,with short coalescence times. However, a minor contribu-tion (10%–25%) of dynamically formed (or with large natalkicks) compact binaries progenitors cannot be excluded.The complete sample of SGRBs presented in this paperconsists of 16 events observed by the Swift satellite over 8.5years. As can be evinced from Table 1, the efficiency of red-shift measurements almost doubled (from ∼ 30% to ∼ Swift operations wewill handle a well-selectd sample of ∼ 30 SGRBs with aredshift completeness higher than 70%. With such numbers,the statistics of this SGRB sample will become comparableto, e.g., the LGRB BAT6 sample, opening the possibilityto study, e.g., the SGRBs luminosity function and measur-ing their intrinsic extinction through their optical and near-infrared spectral energy distributions (Salvaterra et al. 2012;Covino et al. 2013). ACKNOWLEDGMENTS This work made use of data supplied by the UK Swift Sci-ence Data Centre at the University of Leicester. 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