A COMPARATIVE STUDY OF LONG AND SHORT GRBS. I. OVERLAPPING PROPERTIES

The most basic prompt emission property of GRBs is duration T₉₀, the timescale during which 5% to 95% of its γ-ray fluence is detected. It shows a clear bimodal distribution in the BATSE 50–300 keV band (Kouveliotou et al. 1993), which is used as the criterion to classify SGRBs and LGRBs. Columns 6 and 7 of Table 1 present the observed duration of the T₉₀ and related reference for each GRB. Also shown in Column 5 is the GRB detector from which the T₉₀ is derived. For Swift GRBs, T₉₀ values are derived in the 15–150 keV band, which are obtained from Sakamoto et al. (2011b) when possible, otherwise from the Swift GRB table.⁴ For Fermi GRBs without Swift detections, the T₉₀ (10–1000 keV) values from the Fermi GRB table (von Kienlin et al. 2014) are presented. For GRBs before the Swift era, the T₉₀ values from BeppoSAX (Frontera et al. 2009) and HETE-2 (Pélangeon et al. 2008) are adopted when possible. Some GRBs were detected from other detectors, e.g., Konus-Wind, INTEGRAL and Suzaku. Their T₉₀ values are obtained from GRB GCN circulars or related publications when available.

The broadband spectra of GRB prompt emission are usually fitted with the so-called "Band function" (Band et al. 1993), which is a smoothly joint broken power law (PL) defined by

$$\begin{eqnarray}N(E)=\left\{\begin{array}{ll}A{\left(\displaystyle \frac{E}{100\mathrm{keV}}\right)}^{\alpha }\exp \left(-\displaystyle \frac{E}{{E}_{0}}\right), & E\lt (\alpha -\beta ){E}_{0}\\ A{\left(\displaystyle \frac{E}{100\mathrm{keV}}\right)}^{\beta }{\left[\displaystyle \frac{(\alpha -\beta ){E}_{0}}{100\mathrm{keV}}\right]}^{\alpha -\beta }\exp (\beta -\alpha ), & E\geqslant (\alpha -\beta ){E}_{0}\end{array}\right.\end{eqnarray} \tag{ 1 }$$

where α is low energy photon index, β is high energy photon index, and E₀ is the break energy. Instead of E₀, more frequently quoted is ${E}_{{\rm{p}}}$, the peak energy in the energy spectrum ${E}^{2}N$, where ${E}_{{\rm{p}}}=(2+\alpha ){E}_{0}$. The spectral parameters α, β, and ${E}_{{\rm{p}}}$ in time-integrated spectra are provided in columns 4–6 of Table 2 when Band function fitting is available (Amati et al. 2002; Goldstein et al. 2013). Sometimes not all of these parameters are well constrained, due to the narrowness of the detector's energy band (Swift/BAT, Sakamoto et al. 2011b), and the low fluence of the bursts. In these cases, a cutoff power law (CPL) model, which is essentially the first half of Equation (1), or a simple PL model

$$\begin{eqnarray*}&&N(E)={{AE}}^{-{\rm{\Gamma }}}\end{eqnarray*}$$

are used for spectral fitting instead. If a CPL fitting is available, the parameters α and ${E}_{{\rm{p}}}$ are recorded. If the spectrum can be fitted with a PL model without an ${E}_{{\rm{p}}}$ estimation, the PL index Γ is recorded in the third column of Table 2. The PL Γ shows a systematic difference from Band α (Virgili et al. 2012). For sake of fair comparison, Γ is presented whenever available, regardless of whether α is provided or not.

Table 2.  Prompt Sample.

GRB	Detector	Γ	α	β	${E}_{{\rm{p}}}$	Fluence ${S}_{\gamma }$			Peak Flux ${F}_{{\rm{p}}}$ $({P}_{{\rm{p}}})$		Reference
	Fluence/Flux				(keV)	(${10}^{-7}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}$)	Band			Band
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)		(9)	(10)	(11)
140606B	Fermi	⋯	$-{1.24}_{-0.05}^{+0.05}$	$-{2.20}_{-0.52}^{+0.52}$	${554}_{-165}^{+165}$	75.9 ± 0.4	10−1000		$13.2\pm {0.3}^{{\rm{p}}}$	10−1000	103
140518A	Swift	1.89	$-{0.98}_{-0.53}^{+0.61}$	⋯	${47.9}_{-7.1}^{+12.7}$	10 ± 1	15−150		$1.0\pm {0.1}^{{\rm{p}}}$	15−150	107
140515A	Swift	1.78 ± 0.13	$-{0.98}_{-0.55}^{+0.64}$	⋯	${56.4}_{-9.9}^{+31.3}$	5.9 ± 0.6	15−150		$0.9\pm {0.1}^{{\rm{p}}}$	15−150	107
140512A	Fermi	1.45 ± 0.04	$-{1.22}_{-0.02}^{+0.02}$	$-{3.2}_{-1.6}^{+1.6}$	${682}_{-70}^{+70}$	293 ± 0	10−1000		$11.0\pm {0.3}^{{\rm{p}}}$	10−1000	$103,107$
140508A	Fermi	⋯	$-{1.19}_{-0.02}^{+0.02}$	$-{2.36}_{-0.10}^{+0.10}$	${263}_{-14}^{+14}$	614 ± 1	10−1000		$66.8\pm {1.0}^{{\rm{p}}}$	10−1000	103

Note. Col. (1) GRB name. Col. (2) Detector of fluence and/or peak flux. Col. (3) Spectral index of power law fitting. Col. (4–6) Spectral parameters of Band function. Col. (7) γ-ray fluence ${S}_{\gamma }$, in units of ${10}^{-7}$ erg cm⁻². Col. (8) The observational energy band of the fluence in col. (7). Col. (9) γ-ray 1 s peak flux ${F}_{{\rm{p}}}$, in units of ${10}^{-7}$ erg s⁻¹ cm⁻², or peak photon flux ${P}_{{\rm{p}}}$, in units of photons s⁻¹ cm⁻² (with superscript p). (¹-⁷) Fluxes from Konus-Wind are not 1 s peak flux. (1.) 0.004 s; (2.) 0.016 s; (3.) 0.064 s; (4.) 0.128 s; (5.) 0.256 s; (6.) 2.944 s; (7.) 3 s. Col. (10) The observational energy band of the flux in col. (9). Col. (11) Reference of prompt emission properties.

References. (1) Hurley et al. (2000b), (2) Jimenez et al. (2001), (3) Amati et al. (2002), (4) Price et al. (2002a), (5) Hurley et al. (2002a), (6) Hurley et al. (2002b), (7) Barraud et al. (2003), (8) Amati et al. (2004), (9) Nicastro et al. (2004), (10) Yonetoku et al. (2004), (11) Butler et al. (2004), (12) Golenetskii et al. (2004), (13) Galassi et al. (2004), (14) Sakamoto et al. (2005a), (15) Nakagawa et al. (2005), (16) Golenetskii et al. (2005b), (17) Sakamoto et al. (2005b), (18) Golenetskii et al. (2005c), (19) Boer et al. (2005), (20) Golenetskii et al. (2005a), (21) Crew et al. (2005), (22) Golenetskii et al. (2005d), (23) Golenetskii et al. (2005e), (24) Golenetskii et al. (2005f), (25) Golenetskii et al. (2005g), (26) Golenetskii et al. (2005h), (27) Villasenor et al. (2005), (28) Galli & Piro (2006), (29) Golenetskii et al. (2006b), (30) Golenetskii et al. (2006c), (31) Golenetskii et al. (2006d), (32) Golenetskii et al. (2006e), (33) Golenetskii et al. (2006f), (34) Golenetskii et al. (2006j), (35) Golenetskii et al. (2006g), (36) Golenetskii et al. (2006h), (37) Golenetskii et al. (2006a), (38) Bellm et al. (2006), (39) Golenetskii et al. (2006i), (40) Pal'Shin (2006), (41) Golenetskii et al. (2007a), (42) Golenetskii et al. (2007b), (43) Golenetskii et al. (2007i), (44) Golenetskii et al. (2007c), (45) Golenetskii et al. (2007d), (46) Golenetskii et al. (2007e), (47) Golenetskii et al. (2007f), (48) Golenetskii et al. (2007g), (49) Golenetskii et al. (2007j), (50) Golenetskii et al. (2007h), (51) Foley et al. (2008), (52) Pélangeon et al. (2008), (53) Golenetskii et al. (2008a), (54) Golenetskii et al. (2008b), (55) Golenetskii et al. (2008c), (56) Ohno et al. (2008), (57) Golenetskii et al. (2008d), (58) Golenetskii et al. (2008e), (59) Golenetskii et al. (2008f), (60) Golenetskii et al. (2008g), (61) Golenetskii et al. (2008h), (62) Pal'Shin et al. (2008), (63) Golenetskii et al. (2008i), (64) Nava et al. (2008), (65) Frontera et al. (2009), (66) Golenetskii et al. (2009b), (67) Golenetskii et al. (2009d), (68) Pal'Shin et al. (2009a), (69) Golenetskii et al. (2009c), (70) Golenetskii et al. (2009a), (71) Pal'Shin et al. (2009b), (72) Golenetskii et al. (2010a), (73) Golenetskii et al. (2010b), (74) Golenetskii et al. (2010c), (75) Sakamoto et al. (2011b), (76) Golenetskii et al. (2011a), (77) Golenetskii et al. (2011b), (78) Golenetskii et al. (2011c), (79) Golenetskii et al. (2011d), (80) Golenetskii et al. (2011e), (81) Golenetskii et al. (2011f), (82) Golenetskii et al. (2011g), (83) Sakamoto et al. (2011a), (84)Golenetskii et al. (2011h), (85) Golenetskii et al. (2011i), (86) Golenetskii et al. (2011j), (87) Lazzarotto et al. (2011), (88) Golenetskii et al. (2011k), (89) Guidorzi et al. (2011), (90) Goldstein et al. (2013), (91) Golenetskii et al. (2013e), (92) Golenetskii et al. (2013f), (93) Golenetskii et al. (2013g), (94) Golenetskii et al. (2013h), (95) Frederiks (2013), (96) Golenetskii et al. (2013i), (97) Golenetskii et al. (2013j), (98) Golenetskii et al. (2013a), (99) Golenetskii et al. (2013b), (100) Golenetskii et al. (2013c), (101) Golenetskii et al. (2013d), (102) Bošnjak et al. (2014), (103) Gruber et al. (2014), (104) Golenetskii et al. (2014a), (105) Golenetskii et al. (2014b), (106) Serino et al. (2014), (107) GRBtable.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

Table 2 also shows fluence ${S}_{\gamma }$ and peak flux ${F}_{{\rm{p}}}$ of each GRB, as well as the respective energy band and the detector used to derive them. The fluence ${S}_{\gamma }$ is given as energy fluence, in units of $\mathrm{erg}\ {\mathrm{cm}}^{-2}$. If not specified, the peak flux is energy flux at the peak time ${t}_{{\rm{p}}}$, in units of erg s⁻¹ cm⁻², with a time bin of 1 s. The photon peak flux ${P}_{{\rm{p}}}$, in units of photons s⁻¹ cm⁻², is shown with superscript "P." Peak flux from Konus-Wind is usually not binned in 1 s. The binning timescale is labelled in Table 2 using the following convention: (1) 0.004 s; (2) 0.016 s; (3) 0.064 s; (4) 0.128 s; (5) 0.256 s; (6) 2.944 s; (7) 3 s, respectively.

Parameters of BeppoSAX are obtained from Amati et al. (2002) and Frontera et al. (2009) in general. Parameters from BATSE are obtained from Yonetoku et al. (2004) and 5B BATSE catalog (Goldstein et al. 2013). The 5B BATSE catalog does not come with traditional GRB names, so we match 5B BATSE catalog burst IDs with traditional GRB names by requiring the positional difference smaller than 10 degree and a close temporal match (typically the difference is less than a few seconds). Spectral parameters from HETE-II are obtained from Sakamoto et al. (2005a) and Pélangeon et al. (2008), covering 2–400 keV in general. Spectral parameters from INTEGRAL are obtained from Bošnjak et al. (2014) and Foley et al. (2008), covering a time span from 2002 to 2012. While Bošnjak et al. (2014) makes a joint IBIS/SPI spectral fit covering 20–1000 keV, spectral fitting in Foley et al. (2008) uses data from IBIS only, covering 20–200 keV. So data from Bošnjak et al. (2014) are favored if parameters of the same burst are provided in both catalogs. Spectral parameters from Fermi/GBM are obtained from the Fermi GRB catalog (Gruber et al. 2014), typically covering 10–1000 keV. Sometimes, parameters from Konus-Wind, RHESSI or Suzaku/WAM are used, obtained from GCN circulars in general. Otherwise, Swift/BAT parameters are presented, including Γ, fluence and flux for those with PL as the best fit model, and α, ${E}_{{\rm{p}}}$, fluence and flux for those with CPL as the best fit model.

The isotropic gamma-ray energy ${E}_{\gamma ,\mathrm{iso}}$ and peak luminosity ${L}_{{\rm{p}},\mathrm{iso}}$ in the cosmological rest frame $1-{10}^{4}\,\mathrm{keV}$ are estimated with parameters presented in the previous sections. The estimated value are shown in Column 8 and 9 of Table 1.

The isotropic energy ${E}_{\gamma ,\mathrm{iso}}$ is estimated as

$$\begin{eqnarray}&&{E}_{\gamma ,\mathrm{iso}}=4\pi {D}_{{\rm{L}}}^{2}{S}_{\gamma }k/(1+z),\end{eqnarray} \tag{ 2 }$$

where ${S}_{\gamma }$ is the γ-ray fluence, in units of erg cm⁻², ${D}_{{\rm{L}}}$ is the luminosity distance estimated with redshift, and k is a k-correction factor from the lab frame to the bolometric rest frame, defined as

$$\begin{eqnarray}&&k=\displaystyle \frac{{\int }_{1/(1+z)}^{{10}^{4}/(1+z)}\ {EN}(E){dE}}{{\int }_{{e}_{\min }}^{{e}_{\max }}\ {EN}(E){dE}}.\end{eqnarray} \tag{ 3 }$$

Here ${e}_{\max }$ and ${e}_{\min }$ are the observational energy range of fluence, presented in Column 8 of Table 2, N(E) denotes the photon spectrum of GRBs. All the GRB spectra are assumed to be a Band function as shown in Equation (1), with the spectral parameters listed in Table 2. For those GRBs fitted with a CPL, $\beta =-2.3$ is assumed. For the GRBs with PL fitting only, the rough correlation between PL index Γ and the peak energy ${E}_{{\rm{p}}}$, i.e.,

$$\begin{eqnarray*}&&\mathrm{log}\ {E}_{{\rm{p}}}=(4.34\pm 0.48)-(1.32\pm 0.13){\rm{\Gamma }}\end{eqnarray*}$$

is used to estimate ${E}_{{\rm{p}}}$ (Zhang et al. 2007; Sakamoto et al. 2009; Virgili et al. 2012). For bursts without α and β, $\alpha =-1.0$ and $\beta =-2.3$ are assumed for LGRBs, and $\alpha =-0.5$, $\beta =-2.3$ for SGRBs (Band et al. 1993; Preece et al. 2000). For the bursts without redshift estimation, z = 2 is assumed for LGRBs, and z = 0.5 for SGRBs. One exception is GRB 020410, for which z = 0.5 is assumed according to the redshift estimation based on the possible SN detection in Levan et al. (2005).

The peak luminosity ${L}_{{\rm{p}},\mathrm{iso}}$ is estimated as

$$\begin{eqnarray}&&{L}_{{\rm{p}},\mathrm{iso}}=4\pi {D}_{{\rm{L}}}^{2}{F}_{{\rm{p}}}k,\end{eqnarray} \tag{ 4 }$$

with the same k correction as ${E}_{\gamma ,\mathrm{iso}}$ estimation, and the peak flux ${F}_{{\rm{p}}}$ in units of erg s⁻¹ cm⁻². For GRBs with photon peak flux ${P}_{{\rm{p}}}$ (in units of photon s⁻¹ cm⁻²) reported only, ${F}_{{\rm{p}}}$ is estimated from ${P}_{{\rm{p}}}$

$$\begin{eqnarray}&&{F}_{{\rm{p}}}={P}_{{\rm{p}}}\displaystyle \frac{{\int }_{{e}_{\min }}^{{e}_{\max }}{EN}(E){dE}}{{\int }_{{e}_{\min }}^{{e}_{\max }}N(E){dE}},\end{eqnarray} \tag{ 5 }$$

where ${e}_{\max }$ and ${e}_{\min }$ define the observational energy range of flux, presented in Column 10 of Table 2.

Lü et al. (2014) introduced the amplitude parameters f and ${f}_{\mathrm{eff}}$ to assist classification of GRBs. The f parameter is defined as the ratio between 1-s peak flux and background flux $f=\tfrac{{F}_{{\rm{p}}}}{{F}_{{\rm{B}}}}$, which measures how bright the brightest peak of a burst is above the background level. The effective amplitude parameter is defined as ${f}_{\mathrm{eff}}=\tfrac{{F}_{{\rm{p}}}^{\prime }}{{F}_{{\rm{B}}}}$, which is the amplitude of a pseudo GRB which was scaled down from the original burst until the new duration T₉₀ is shorter than 2 s. It reflects the measured f value for an intrinsically long GRB to be confused as a short GRB when the bulk of the emission is buried below the background. Since short GRBs already have ${T}_{90}\lt 2\,{\rm{s}}$, their ${f}_{\mathrm{eff}}$ parameter is the same as the f parameter. Lü et al. (2014) showed that the ${f}_{\mathrm{eff}}$ values of long GRBs are typically smaller than 2, which means that the "tip-of-iceberg" effect cannot give very high-amplitude short GRBs. In contrast, short GRBs typically have ${f}_{\mathrm{eff}}=f$ greater than 2. As a result, the f and ${f}_{\mathrm{eff}}$ parameters are useful to diagnose the physical origin of a burst. We include all the f and ${f}_{\mathrm{eff}}$ parameters published in Lü et al. (2014)⁵ in our analysis. The f and ${f}_{\mathrm{eff}}$ values of later Swift GRBs are also calculated using the same method of Lü et al. (2014). They are presented in the last two columns of Table 1.

Stellar mass, ${M}_{* }$, which is the main control of luminosity, SFR, and metallicity of a galaxy, is the most important host galaxy parameter. It is also used to estimate the sSFR, defined as SFR per unit stellar mass (SFR/${M}_{* }$), which shows the intrinsic star formation status of a galaxy. Broadband SED fitting to stellar population synthesis models is the most common method to estimate ${M}_{* }$. For most of the bursts in our sample, the SED-fitted ${M}_{* }$ is collected from the catalogs of Savaglio et al. (2009) and Leibler & Berger (2010). Others are obtained from individual papers. When SED estimated ${M}_{* }$ is not available, a single band luminosity such as the K band magnitude (Svensson et al. 2010) or infrared magnitude (Laskar et al. 2011) is used as the indicator of stellar mass. In these cases, the uncertainty is larger than one order of magnitude. For GRBs from Laskar et al. (2011), upper limits of ${M}_{* }$ are used when only upper limits are available. For those with detections, ${M}_{70\mathrm{Myr}}$ are used since 70 Myr is a typical age of LGRB hosts at $z\sim 1$ (Leibler & Berger 2010). The values of ${M}_{* }$ and the method to estimate them are presented in columns 4 and 5 of Table 3.

Table 3.  SFR

GRB	z	Instrument	log ${M}_{* }$			SFR		sSFR	[X/H]			${A}_{{\rm{V}}}$		reference
		(Spectrum)	(${M}_{\odot }$)	Method		(${M}_{\odot }\,{\mathrm{yr}}^{-1}$)	Method	[Gyr−1]		Method		(mag)	method
(1)	(2)	(3)	(4)	(5)		(6)	(7)	(8)	(9)	(10)		(11)	(12)	(13)
140606B	0.384	GTC/OSIRIS	⋯	⋯		0.052 ± 0.005	Hα	⋯	⋯	⋯		${0.3}_{-0.30}^{+0.89}$	Balmer	87
140518A	4.707	Gemini/GMOS	⋯	⋯		⋯	⋯	⋯	$\gt -1.06$	A/S		⋯	⋯	79
140515A	6.32	GTC/OSIRIS	⋯	⋯		⋯	⋯	⋯	$\lt -1.1$	A/O		0.11 ± 0.02	AG-SED	75
140512A	0.725	NOT/ALFOSC	⋯	⋯		⋯	⋯	⋯	⋯	⋯		⋯	⋯	0
140508A	1.027	NOT/ALFOSC	⋯	⋯		⋯	⋯	⋯	⋯	⋯		⋯	⋯	0

Notes. Col. (1) GRB name. Col. (2) Redshift. Col. (3) The instrument which obtained the optical spectrum. Col. (4–5) Stellar mass ${M}_{* }$ and the methods which derive it. Col. (6-7) Star formation rate and the methods which derive it. Col. (8) Specific SFR, SFR/${M}_{* }$. Col. (9-10) Metallicity and the methods which derive it. (E)mission line and (A)bsorption line. Two values before and after the back slash are estimated with the lower and upper branches of the R₂₃−[X/H] relation, respectively. Col. (11–12) Extinction and the methods which derive it. Col. (13) Reference.

References. (1) Fynbo et al. (2002), (2) Fynbo et al. (2003), (3) Vreeswijk et al. (2004), (4) Jakobsson et al. (2004), (5) Vreeswijk et al. (2006), (6) Pellizza et al. (2006), (7) Jakobsson et al. (2006a), (8) Berger et al. (2006), (9) Penprase et al. (2006), (10) Watson et al. (2006), (11) Della Valle et al. (2006), (12) Stratta et al. (2007), (13) Prochaska et al. (2007b), (14) Cenko et al. (2008b), (15) Prochaska et al. (2008), (16) D'Avanzo et al. (2009), (17) Berger (2009), (18) Chen et al. (2009), (19) Savaglio et al. (2009), (20) Han et al. (2010), (21) Zafar et al. (2010), (22) McBreen et al. (2010), (23) Castro-Tirado et al. (2010), (24) D'Avanzo et al. (2010), (25) Thöne et al. (2010), (26) Levesque et al. (2010b), (27) Rau et al. (2010b), (28) Tanvir et al. (2010a), (29) Leibler & Berger (2010), (30) Levesque et al. (2010a), (31) Schady et al. (2010), (32) Chornock et al. (2010c), (33) Schulze et al. (2011), (34) Greiner et al. (2011), (35) Krühler et al. (2011a), (36) Vergani et al. (2011), (37) Fong et al. (2011), (38) Laskar et al. (2011), (39) Levesque et al. (2011), (40) De Cia et al. (2011), (41) Cano et al. (2011), (42) Götz et al. (2011), (43) Mannucci et al. (2011), (44) Guidorzi et al. (2011), (45) Basa et al. (2012), (46) De Cia et al. (2012), (47) Milvang-Jensen et al. (2012), (48) Perley et al. (2012a), (49) Savaglio et al. (2012), (50) Svensson et al. (2012), (51) Niino et al. (2012), (52) Krühler et al. (2013), (53) de Ugarte Postigo et al. (2013a), (54) Zauderer et al. (2013), (55) Fong et al. (2013), (56) Jin et al. (2013), (57) Kelly et al. (2013), (58) Xu et al. (2013a), (59) Perley et al. (2013); (60) Thöne et al. (2013), (61) Elliott et al. (2013b), (62) de Ugarte Postigo et al. (2014b), (63) D'Elia et al. (2014), (64) Hunt et al. (2014), (65) Schulze et al. (2014), (66) Cano et al. (2014), (67) Jeong et al. (2014a), (68) Fynbo et al. (2014), (69) Rossi et al. (2014), (70) Sparre et al. (2014), (71) Morgan et al. (2014), (72) Olivares et al. (2015), (73) Schady et al. (2015), (74) Hartoog et al. (2015), (75) Melandri et al. (2015), (76) Vergani et al. (2015), (77) Krühler et al. (2015), (78) Michałowski et al. (2015), (79) Cucchiara et al. (2015), (80) Hashimoto et al. (2015), (81) Greiner et al. (2015), (82) Arabsalmani et al. (2015), (83) Stanway et al. (2015), (84) van der Horst et al. (2015), (85) Kohn et al. (2015), (86) Friis et al. (2015), (87) Cano et al. (2015), (88) Piranomonte et al. (2015), (89) GHOST.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

SFR indicates average rate of star formation in a "recent" time range. It can be estimated with emission lines, ultraviolet (UV) light, infared, radio, and X-rays (see Kennicutt 1998 and Kennicutt & Evans 2012 for reviews). Among different diagnostics, emission lines such as Hα, Hβ, and [O ii] represent the most recent 0–10 Myr SFR, best matching the life of LGRB progenitor stars with >30 M_☉ (Kennicutt & Evans 2012). Among different emission lines, Hα is the best indicator of SFR, due to its relative strength, small dust extinction, and independence of metallicity. However, for objects with redshift larger than 0.4, Hα shifts out of the optical band and requires an infrared detection. For these cases, Hβ and [O ii] emission lines become good indicators instead in the optical band, which are applicable up to the redshift 0.9 and 1.4, respectively. The benefit of Hβ over [O ii] is its independence of metallicity. Moustakas et al. (2006) show that the dependence of [O ii] estimated SFR on metallicity is weak in the range of 8.2 < 12 + log(O/H) < 8.7, but is significant in the range of 12 + log(O/H) < 8.2 and 12 + log(O/H) > 8.7. Since a lot of GRB hosts show 12 + log(O/H) < 8.2 (Savaglio et al. 2009; Krühler et al. 2015), Hβ is in general a better indicator than [O ii]. However, [O ii] is usually stronger than Hβ. So [O ii] is more frequently used as the SFR indicator for galaxies with redshifts as high as 1.4. For objects with redshifts higher than 2, the Lyα emission line shifts into optical and may be used as an SFR indicator (Milvang-Jensen et al. 2012). The SFR and the method used to estimate it are shown in columns 6 and 7 of Table 3, with column 3 presenting the instrument offering the spectrum. For those without SFR information, column 3 gives the instruments of spectral observations that provide redshift information. The criteria mentioned above are used.

The two largest LGRB SFR catalogs are from Savaglio et al. (2009) and Krühler et al. (2015). Savaglio et al. (2009) summarized emission line information of GRBs before December 2006 and presented a systematic estimation of SFR using Hα, Hβ, [O ii], and UV, respectively. We record the SFR of each GRB host according to the criteria mentioned above. Krühler et al. (2015) estimated the host galaxy SFR for GRBs later than April 2005, with emission line luminosities obtained from the VLT/X-Shooter spectra. Due to the infrared coverage of VLT/X-Shooter, Krühler et al. (2015) extended Hα detection to z ∼2.5. It enables SFR estimation with Hα and better dust extinction ${A}_{{\rm{V}}}$ estimation. There are only two objects presented in both of these two catalgs, GRB 050416A and GRB 051022A, with redshift 0.653 and 0.807 respectively. Krühler et al. (2015) showed that their Balmer decrementd estimated ${A}_{{\rm{V}}}$ are ${1.62}_{-0.36}^{+0.36}$ mag and ${1.86}_{-0.13}^{+0.17}$ mag, respectively, and made dust extinction correction with these values. It turns out that the estimated SFR of these two bursts by Krühler et al. (2015) are around two times larger than those estimated by Savaglio et al. (2009), who applied a mean ${A}_{{\rm{V}}}=0.53$ to their LGRB sample due to the lack of ${A}_{{\rm{V}}}$ estimate for both bursts. As both GRB 050416A and GRB 051022A have dust extinction ${A}_{{\rm{V}}}$ much larger than ${A}_{{\rm{V}}}=0.53$, the diversity between these two papers can be easily accounted for by the discrepancy of the ${A}_{{\rm{V}}}$ applied. On the other hand, the average ${A}_{{\rm{V}}}$ and SFR for the same redshift range are consistent with each other between Krühler et al. (2015) and Savaglio et al. (2009), so that these two GRBs do not indicate statistical inconsistency between these two catalogs.

Two largest SGRB SFR catalogs are from Savaglio et al. (2009) and Berger (2009), each presenting five bursts. Three of their host galaxies, GRB 051221, GRB 050709, and GRB 061006, show active star formation with emission lines and their emission-line-estimated SFRs show consistency between these two papers. The other two, GRB 050509B and GRB 050724, have passive hosts without emission lines. While the emission-line-estimated SFR upper limits are <0.1 and <0.05 ${M}_{\odot }\ {\mathrm{yr}}^{-1}$, respectively (Berger 2009), their UV-estimated SFRs are as high as 16.87 and 18.76 ${M}_{\odot }\ {\mathrm{yr}}^{-1}$, respectively (Savaglio et al. 2009). The discrepancy could be understood by the difference of the age of stars that emission lines and UV light trace, i.e., $0\mbox{--}10\,\mathrm{Myr}$ for emission lines and $10\mbox{--}200\,\mathrm{Myr}$ for UV light. Since LGRBs originate from stars with mass >30 M_☉ and age ∼10 Myr, emission lines are better diagnostics than UV light. As a result, we do not include UV SFRs in our analysis even though we still list them in Table 3 for completeness.

Metallicity, abundance of elements other than hydrogen and helium, is generally described by the number density ratio between a specific element and hydrogen. It may be estimated with absorption lines or emission lines. Although these two methods provide metallicity estimation for somewhat different regimes in GRB host galaxies, they show consisteny in GRB 121024A, which has both emission- and absorption-line estimated metallicities (Friis et al. 2015). The two methods also cover complementary redshift ranges, so we include both of them here. We caution that one needs more objects with both absorption lines and emission lines to provide metallicity estimates to confirm the consistency between the two methods. Metallicities estimated by absorption lines are generally described by $[{\rm{X}}/{\rm{H}}]=\mathrm{log}({N}_{{\rm{X}}}/{N}_{{\rm{H}}})-\mathrm{log}({N}_{{{\rm{X}}}_{\odot }}/{N}_{{{\rm{H}}}_{\odot }})$, where ${N}_{{\rm{X}}}$ indicates column density of element X. Metallicities estimated by emission lines, on the other hand, are generally described by $12+\mathrm{log}({\rm{O}}/{\rm{H}})$, with solar value $12+\mathrm{log}{({\rm{O}}/{\rm{H}})}_{\odot }=8.69$. In order to be consistent with each other, we convert $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ to [X/H] with X = O by $12+\mathrm{log}({\rm{O}}/{\rm{H}})-8.69$ (Asplund et al. 2009). The estimated values as well as corresponding methods are presented in columns 8 and 9 of Table 3.

Emission line ratios are the most common diagnostics for late type galaxy metallicity (Kewley & Dopita 2002; Kobulnicky & Kewley 2004; Pettini & Pagel 2004). This method estimates the metallicities in H ii regions of the host galaxy. It is based on photoionization models (Kewley & Dopita 2002) and local H ii region and galaxies observations (Pettini & Pagel 2004). If the host galaxy redshift is larger than 0.2, it is hard to obtain a spatially resolved spectrum of a specific point. Since most GRBs have redshifts greater than 0.2, emission-line-estimated metallicity is generally the luminosity-weighted metallicity of the hosts.

The largest two LGRB samples with metallicity measurements are Savaglio et al. (2009) and Krühler et al. (2015). Savaglio et al. (2009) used different emission line diagnostics for different GRBs, due to different available emission lines. A direct estimation comes from electron temperature ${T}_{{\rm{e}}}$, which requires a comparison of different ionization lines with the same elements (Izotov et al. 2006). This is only valid for a few cases where both [O iii]λ4363 and [O iii]λ4959, 5007 are available. For most cases, other indicators with higher uncertainties are generally used. If Hα is detected, for GRBs with z < 0.4 in general, ${\rm{O}}3{\rm{N}}2\ =\mathrm{log}\{([{\rm{O}}\,{\rm{III}}]\lambda 5007/{\rm{H}}\beta )/([{\rm{N}}\,{\rm{II}}]\lambda 6583/{\rm{H}}\alpha )\}$ is used, with (Pettini & Pagel 2004)

$$\begin{eqnarray*}&&12+\mathrm{log}({\rm{O}}/{\rm{H}})=8.73-0.32\times {\rm{O}}3{\rm{N}}2.\end{eqnarray*}$$

If Hα is not available, for most high redshift GRBs,

$$\begin{eqnarray*}&&\mathrm{log}\ {R}_{23}=\mathrm{log}\{([{\rm{O}}\,{\rm{II}}]\lambda 3727+[{\rm{O}}\,{\rm{III}}]\lambda 4959,5007)/{\rm{H}}\beta \}\end{eqnarray*}$$

are used for metallicity estimation, with

$$\begin{eqnarray*}&&\mathrm{log}\ {O}_{32}=\mathrm{log}\{([{\rm{O}}\,{\rm{III}}]\lambda 4959,5007)/([{\rm{O}}\,{\rm{II}}]\lambda 3727)\}\end{eqnarray*}$$

as an indicator of the ionization parameter. However, the relation between R₂₃ and 12 + log(O/H) is double-valued. Following Kewley & Ellison (2008), Equation (18) of Kobulnicky & Kewley (2004) is applied for the upper branch and Kewley & Dopita (2002) for the lower branch. These R₂₃ metallicities are corrected to ${\rm{O}}3{\rm{N}}2$ values as suggested by Kewley & Ellison (2008). Due to the lack of [N ii], which is usually needed to decouple the double value effect, the two values are sometimes both listed (Savaglio et al. 2009). Krühler et al. (2015) used a combination of the methods by estimating the probability density profile of metallicities for each GRB. Benefiting from infrared spectra with Hα lines and [N ii] lines, their values do not encounter the double value problem.

The largest SGRB sample is from Berger (2009). The R₂₃ method is used and only the upper branch is presented, as suggested by Kobulnicky & Kewley (2004). However, the event available for O3N2, i.e., GRB 061210, shows 12 + log(O/H) = 8.47 by the method applied in Savaglio et al. (2009), which is 0.35 smaller than the value 12 + log(O/H) = 8.82 estimated with the upper R₂₃ branch. It indicates that the upper R₂₃ branch method may overestimate the metallicities of SGRB host galaxies, and the diversity of SGRB and LGRB metallicities may not be as significant as shown. However, due to the complexity of metallicity estimation and the lack of Hα and [N ii] line information of other three events, GRB 061006, GRB 070724, and GRB 051221A, we still present the values of Berger (2009) in Table 3. We note here that the true metallicities may be a factor of 0.4 smaller than the listed values. More observations, especially of the infrared spectra, are required to verify the metallicities of these SGRBs.

With the absorption line equivalent width and line profile, column densities of various elements ${N}_{{\rm{X}}}$ along the line of sight can be estimated (Draine 2011). By comparing with hydrogen column density ${N}_{{\rm{H}}}$ obtained from Lyα, metallicities [X/H] = log(${N}_{{\rm{X}}}$/${N}_{{\rm{H}}}$)−log(${N}_{{{\rm{X}}}_{\odot }}$/${N}_{{{\rm{H}}}_{\odot }}$) can be estimated for various elements X, such as oxygen. The condition to produce absorption lines is that the probed regions are cooler than those probed with emission lines. These absorption line regions are estimated to be around 100 pc away from GRBs (Vreeswijk et al. 2012; Krühler et al. 2013; D'Elia et al. 2014), so that they can reveal the properties of local environment of GRBs. Since generally the detection of a Lyα absorption line is needed, the absorption line metallicity estimation is generally valid for high redshift GRBs, i.e., z > 1.8 in general. If metallicity is estimated for more than one element, the value for the most abundant element is recorded, e.g., in the order of O, C, N, Mg, Si, Fe, S (Asplund et al. 2009). The largest absorption line estimated metalllicity catalog is from Cucchiara et al. (2015), and other cases are obtained from individual papers. These values are labelled as "A" in the metallicity method column and the specific elements used to estimate it is also recorded. Lower limits for metallicity are usually due to saturation of the absorption lines, e.g., in GRB 140515A. Although these values are lower limits in definition, they are generally used as the metallicity in the literature, so we treat them as the measured metallicity in the rest of the paper. The upper limits are usually due to non-detection of metal lines, e.g., in GRB 140518A.

Morphological properties of GRB host galaxies are obtained from optical images. Due to the faintness of GRB hosts, it usually requires deep and high angular resolution photometric observations, e.g., with Hubble Space Telescope (HST). The identification of a GRB host galaxy is not straightforward (Bloom et al. 2002; Berger 2010; Church et al. 2011; Tunnicliffe et al. 2014). If the position uncertainty is large, there might be many galaxies within the error box. Sometimes, especially for SGRBs, the offset of the GRB location from the center of host galaxy may be larger than the size of host galaxy itself, so that it is not straightforward to identify the host galaxy without a probability argument. It is also possible that the host galaxy of a particular GRB is too faint to be detected, but there is a galaxy near the afterglow location by chance, so that it may be mis-identified as the GRB host. Following Bloom et al. (2002), a chance coincidence probability ${P}_{\mathrm{cc}}$ is usually defined as the possibility of a non-host galaxy identified as the host galaxy by chance

$$\begin{eqnarray*}&&{P}_{\mathrm{cc}}=1-\exp (-\pi {r}^{2}\sigma (\leqslant {m}_{{\rm{i}}})),\end{eqnarray*}$$

where $\sigma (\leqslant {m}_{{\rm{i}}})$ are the surface densities of the galaxies with magnitude $\leqslant {m}_{{\rm{i}}}$, and r is the effective radius, which is a function of position uncertainty, offset, and the size of a candidate host galaxy. In order to indicate how much the candidate host galaxy is trustable, we list the instrument used to take the image, and ${P}_{\mathrm{cc}}$ in columns 3 and 4 in Table 4 when possible.

Table 4.  Offset

GRB	z	Instrument	Pcc	R50	R50	n	${R}_{\mathrm{off}}$	${R}_{\mathrm{off}}$	${r}_{\mathrm{off}}$	${F}_{\mathrm{light}}$	Reference
		(Image)		('')	(kpc)		('')	(kpc)	$[{R}_{50}]$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
140606B	0.384	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	0
140518A	4.707	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	0
140515A	6.32	HST	0.014	${0.12}_{-0.04}^{+0.05}$	${0.680}_{-0.23}^{+0.27}$	⋯	0.210 ± 0.070	1.21 ± 0.40	1.776	⋯	47
140512A	0.725	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	0
140508A	1.027	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	0

Notes. Col. (1) GRB name. Col. (2) Redshift. Col. (3) The instrument which obtained the optical image. Col. (4) Probability of chance coincidence. Col. (5-6) Half light radius in unit of arcsec and kpc. Col. (7) Sérsic index ${\rm{\Sigma }}{(r)={{\rm{\Sigma }}}_{{\rm{e}}}\exp \{-{k}_{{\rm{n}}}[(r/{r}_{{\rm{e}}})}^{1/n}-1]\}$. Col. (8–9) Offset of GRB from the center of host galaxy, in unit of arcsec and kpc. Col. (10) Normalized offset ${r}_{\mathrm{off}}={R}_{\mathrm{off}}/{R}_{50}$. Col. (11) The fraction of area within host galaxy which is brighter than the GRB region. 1.0 indicates GRB is in the brightest region of the host and 0.0 indicates GRB is in the faintest region of the host. Col. (12) Reference. The values with * are roughly estimated from the images in the references.

^az = 0.5 is assumed for GRB 020410A, according to the possible detection of SN in Levan et al. (2005).References. (1) Burud et al. (2001), (2) Bloom et al. (2002), (3) Price et al. (2002b), (4) Price et al. (2002a), (5) Piro et al. (2002), (6) Castro et al. (2003), (7) Galama et al. (2003), (8) Bloom et al. (2003b), (9) Greiner et al. (2003), (10) Vreeswijk et al. (2004), (11) Cobb et al. (2004), (12) Gorosabel et al. (2005), (13) Masetti et al. (2005), (14) Jakobsson et al. (2005), (15) Fynbo et al. (2005), (16) Fruchter et al. (2006), (17) Wainwright et al. (2007), (18) Mirabal et al. (2007), (19) Perley et al. (2008a), (20) Cenko et al. (2008b), (21) Chen et al. (2009), (22) Levan et al. (2009b), (23) McBreen et al. (2010), (24) D'Avanzo et al. (2010), (25) Fong et al. (2010), (26) Holland et al. (2010), (27) Krühler et al. (2011a), (28) Tanvir et al. (2012b), (29) Levesque et al. (2012), (30) Perley et al. (2012a), (31) Elliott et al. (2013a), (32) de Ugarte Postigo et al. (2013a), (33) Fong et al. (2013), (34) Kelly et al. (2013), (35) Fong & Berger (2013), (36) Perley et al. (2013), (37) Thöne et al. (2013), (38) Greiner et al. (2014), (39) Rossi et al. (2014), (40) Levan et al. (2014b), (41) Levan et al. (2014a), (42) Tunnicliffe et al. (2014), (43) Schady et al. (2015), (44) Michałowski et al. (2015), (45) Dominik et al. (2015), (46) Stanway et al. (2015), (47) McGuire et al. (2015), (48) Blanchard et al. (2016), (49) Toy et al. (2016).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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The basic morphological property of host galaxies is size, represented by the half brightness radius R₅₀, which indicates the semimajor axis of the ellipse within which half flux of the entire galaxy is enclosed. Sometimes the host surface brightness is fitted with the Sérsic profile

$$\begin{eqnarray*}&&{\rm{\Sigma }}{(r)={{\rm{\Sigma }}}_{{\rm{e}}}\exp \{-{k}_{{\rm{n}}}[(r/{r}_{{\rm{e}}})}^{1/n}-1]\},\end{eqnarray*}$$

with the effective radius ${r}_{{\rm{e}}}$ as the size indicator (Wainwright et al. 2007; Fong et al. 2010; Fong & Berger 2013). Sometimes, the size of a host galaxy is defined as the 80 percent radius R₈₀ (Fruchter et al. 2006; Svensson et al. 2010), which is the major axis radius of a similar ellipse that encloses 80 percent of flux. For these cases, we convert R₈₀ to R₅₀ by assuming that the surface brightness profile of the galaxy is a Sérsic profile. Since nearly all LGRB host galaxies and most SGRB host galaxies are disk (spiral) galaxies, n = 1 is assumed. This is equivalent to an exponential profile, which is consistent with the disk galaxy surface density profile. For n = 1, one has ${R}_{50}={R}_{80}/1.79$, and ${R}_{50}={r}_{{\rm{e}}}$. The host galaxies of three SGRBs, GRB 050509B, GRB 050724, and GRB 100117A, are obviously elliptical galaxies with $n\sim 4$, so that the conversion factor ${R}_{50}=0.968{r}_{{\rm{e}}}$ is applied. If R₅₀ of more than one band is given, the value for the band mostly close to optical is used since the blue band may be affected by dust extinction. Sometimes, no precisely defined radius is available, and only vaguely defined "size" or "radius" are quoted in the literature. In these cases, we treat them as R₈₀ which covers most flux of galaxy. R₅₀ in units of arcsec and kpc are presented in columns 5 and 6 of Table 4. The parameter n is also presented in column 7 when possible. Some GRBs with angular R₅₀ values do not have redshift detections. For these cases, z = 0.5 for SGRBs and z = 2.0 for LGRBs are assumed to estimate the physical size of the galaxy.

Angular and physical offsets, the angular/physical separation of a GRB from the center of its host galaxy, are given in columns 8 and 9 of Table 4, in units of arcseconds and kpc, respectively. If an offset is smaller than the positional uncertainty of the GRB or host galaxy, an upper limit is given. The largest samples of LGRB offsets are from Bloom et al. (2002) and Blanchard et al. (2016), and the largest SGRB offset samples are from Fong et al. (2010) and Fong & Berger (2013). For GRBs from Table 2 of Perley et al. (2013), the angular distance between the afterglow and the host galaxy is used to define the offset. Similar to ${R}_{50}$, z = 0.5 for SGRB and z = 2.0 for LGRB are also assumed for those without redshift detections. In some problems, one cares more about the relative offset with respect to the size of the host galaxy. The normalized offset (the true offset normalized to R₅₀ of the host galaxy) is shown in column 10 of Table 4.

Many GRB hosts are irregular and interacting galaxies. For these, the size R₅₀, the center, and hence, the offset of the galaxy are not well defined. In these cases, the fraction of brightness ${F}_{\mathrm{light}}$, which is the ratio between the area of the host fainter than the GRB position and the area of the entire host galaxy, is defined. It delineates how bright the GRB location is relative to the other regions of the host galaxy, and reveals the local SFR, especially if the UV band image is used. The largest LGRB ${F}_{\mathrm{light}}$ samples are from Fruchter et al. (2006), Svensson et al. (2010), and Blanchard et al. (2016), and the largest SGRB ${F}_{\mathrm{light}}$ samples are from Fong et al. (2010) and Fong & Berger (2013). Others are collected from individual papers. The parameter ${F}_{\mathrm{light}}$ is given in column 11 of Table 4. ${F}_{\mathrm{light}}=1$ indicates that the GRB is located in the brightest region of the host, and ${F}_{\mathrm{light}}=0$ indicates that the GRB is in the faintest region of the host.

The properties of galaxies are mainly controlled by their stellar mass ${M}_{* }$ (van der Wel et al. 2014; Ilbert et al. 2015). Host galaxy masses of the consensus and T₉₀-defined LGRBs and SGRBs are presented in the left and right columns of Figure 1, row 9. In order to be consistent, only stellar masses obtained with SED fitting are used here. Most SGRB and LGRB host galaxies are smaller than the turnover mass of galaxies extending to redshift 3 (Mortlock et al. 2015). Although the median of SGRB hosts is 0.6 dex larger than that of all LGRB hosts, their difference is not statistically significant. LGRB hosts with $z\lt 1.4$ show a 0.2 dex lower stellar mass than the whole sample. It may be a selection effect, since the galaxies with larger stellar masses are brighter and easier to be observed at high redshifts. It makes the low-z LGRBs more significantly different from SGRBs. Since the median redshift of low-z LGRBs is still larger than that of SGRBs, a true same-redshift comparison between LGRB and SGRB host stellar masses should show even more significant differences. Also, it indicates that there should be more small stellar mass host galaxies that have not been discovered yet, especially in the high redshift range. The overlapping fractions are around 90% for both LGRBs and SGRBs. The results of the consensus and T₉₀-defined LGRB and SGRB samples are consistent with each other.

The SFR represents the global star formation status of the entire galaxy. It is expected to be large in LGRB hosts, since LGRBs are presumed to be massive star collapsars and are expected to be associate with star formation. SGRBs are believed to be related to compact star mergers, so at least some of them are expected to be associated with the old stellar populations and no recent star formation is required for the presence of SGRBs. SFR of consensus and T₉₀-defined LGRBs and SGRBs are presented in Figure 1, row 10. In order to be consistent, only SFRs obtained with emission lines are used. The median SFR of LGRBs is around 0.4 dex larger than that of SGRBs, although their difference is not statistically significant, due to the large dispersion, both around 0.8 dex. It may be also due to the generally more massive host galaxies of SGRBs, since SFR is proportional to the stellar mass of the galaxies. The low-z LGRB hosts are similar to those of low-z SGRBs. It may be a result of the decrease of the LGRB host mass at low redshifts. Both LGRBs and SGRBs show around 90% overlapping fraction for SFR. The T₉₀-defined samples show even less difference and larger overlaps, suggesting the limitation of T₉₀ to define the physical category of GRBs.

In the sample of the consensus SGRBs, the one with an extremely large SFR is GRB 100816A. Its T₉₀ is reported to be 2.9 s in the Swift GRB table and 1.99 s in Pérez-Ramírez et al. (2013). With a small spectral lag 10 ± 25 ms (Norris et al. 2010a), it is suggested to be a SGRB in Greiner's catalog. Considering its high SFR (Krühler et al. 2015) and possible interacting nature of the host galaxy (Tanvir et al. 2010b), we would suggest it to be still a Type II GRB. We still keep it in the consensus SGRB sample based on our sample selection criterion. Changing it to the consensus LGRB sample makes the median log(SFR) of SGRB to be 0.08, i.e., 1.2 M_☉ yr⁻¹, with a dispersion 0.71, and results in a lower ${P}_{\mathrm{KS}}$ 0.04 for this criterion.

For the bursts with both SFR and stellar mass ${M}_{* }$, specific SFR ($\mathrm{sSFR}=\mathrm{SFR}/{M}_{* }$) of the host galaxy is available. Since sSFR describes SFR per unit stellar mass, it is a more relevant parameter to describe the star formation status in the GRB location. The distributions of sSFRs are presented in Figure 1, row 11. sSFR shows a more significant difference between LGRBs and SGRBs than SFR. In general, the sSFR of LGRBs is 0.5 dex higher than SGRBs. The redshift evolution of the sSFR for the LGRB host is not significant, even though the redshift evolution of sSFR of the entire universe is apparent, with a peak at z = 2–3. This may indicate that sSFR is directly related to the LGRB rate. Another factor might be the selection effects. Since the massive hosts with less sSFRs are more easily detected, high redshift samples should on average show smaller sSFRs relative to the true distribution. The T₉₀-defined sample shows a 0.3 dex less difference than the consensus sample, again indicating the limitation of the T₉₀-only criterion.

In the consensus LGRB sample, the GRB with the lowest sSFR, 0.006 Gyr⁻¹, is GRB 050219A (Rossi et al. 2014). Its host was discovered by GROND and confirmed by VLT. No HST image is available. It is an elliptical galaxy 46 away from the GRB XRT location, with a 19 positional uncertainty. The estimated chance coincide probability is ${P}_{\mathrm{cc}}=0.8 \%$. If we exclude GRB 050219, the LGRB sSFR becomes 0.05 ± 0.62 Gyr⁻¹ and ${P}_{\mathrm{KS}}=0.01$. The overlap range becomes (−1.17, 1.05) and the overlapping fraction becomes 90% and 78% for the consensus LGRBs and SGRBs, respectively.

LGRB progenitor models prefer a low metallicity environment, since it would keep enough angular momentum in the core star to launch a jet. On the other hand, no metallicity limitation is required for SGRBs. The distributions of metallicity [X/H] of the consensus and T₉₀-defined LGRBs and SGRBs are presented in the left and right columns of Figure 1, row 12. If one event has double values, the average value is plotted. For the consensus samples, SGRBs show a 0.5 dex richer metallicity than LGRBs, and are consistent with the highest end of the consensus LGRBs. The ${P}_{\mathrm{KS}}$ value is 0.0007, indicating a relatively significant difference. The overlapping fractions are 47% and 100% for LGRBs and SGRBs, respectively, which is as low as that of the amplitude parameter f. However, the $z\lt 1.4$ LGRB sample is much more metal rich than the whole LGRB sample. In this redshift range, the difference between median LGRBs and SGRBs becomes 0.3 dex, and the overlapping fraction of LGRBs increases to 73%. Since the average redshift of low-z LGRBs is still higher than SGRBs, and metallicity from Berger (2009) may overestimate the SGRB metallicity, the difference between SGRBs and LGRBs in the same redshift bin may be even milder. This makes metallicity not a good indicator of the physical origin of individual GRBs.

Galaxy size is correlated with stellar mass, according to galaxy types (van der Wel et al. 2014). The R₅₀ distributions of the consensus and T₉₀-defined LGRB and SGRB samples are presented in Figure 1, row 13. The LGRB host size is typically 0.31 dex smaller than that of SGRBs in the consensus samples, with a small ${P}_{\mathrm{KS}}=4\times {10}^{-4}$. The overlapping fraction of LGRBs is ∼69%. For $z\lt 1.4$, the R₅₀ distribution of LGRB hosts is consistent with that of the whole sample, only 0.06 index larger. However, due to shrinkage of the sample size, the ${P}_{\mathrm{KS}}$ value is one order of magnitude larger. The T₉₀ defined SGRB sample includes more small size hosts, again indicating the limitation of the T₉₀ criterion.

SGRB offsets are expected to be larger than LGRBs, since the explosion of SNe that formed the NSs and BHs in the merger systems would have given the system two kicks, so that the system may have a large offset from the original birth location in the host galaxy. The cumulative offset distributions of SGRBs indeed differ from those of LGRBs (Fong et al. 2010; Fong & Berger 2013; Berger 2014). Our analysis shows that the typical physical offset of SGRBs, in units of kpc, is 0.77 dex larger than that of LGRBs. The KS test gives ${P}_{\mathrm{KS}}={10}^{-4}$. However, the overlapping fractions of both LGRBs and SGRBs are as large as 80%. Only five of the 28 SGRBs show offsets larger than all LGRBs. The redshift evolution of the offsets is not significant. At $z\lt 1.4$, LGRBs have the same median physical offset as the whole sample.

The offset normalized to the host size R₅₀ is a more physical parameter to delineate the location of an SGRB within the host galaxy. Also, normalized offset does not require measurements of the absolute values of the offset and host size, so one can include events without redshift measurements as well. The normalized offset distributions are presented in Figure 1, row 15. In general, SGRBs are 0.27 dex larger than LGRBs, and mildly different with ${P}_{\mathrm{KS}}=0.02$. No redshift evolution is seen. Only three SGRBs have normalized offset larger than all LGRBs, and only eight LGRBs have normalized offset smaller than all SGRBs. The overlapping fractions are as high as 90%.

The surface brightness fraction ${F}_{\mathrm{light}}$ is expected to be large for LGRBs since they are believed to be associated with the highest local SFR in the galaxy. The ${F}_{\mathrm{light}}$ of SGRBs is expected to be small since compact star mergers usually are expected to be kicked from the star-forming regions by the time the merger happens. It is also a parameter that does not require a redshift measurement. They are presented in the last row of Figure 1. It can be seen that SGRBs tend to be located in the faint regions of their hosts and LGRBs tend to be located in the bright regions of their hosts. An SGRB within the brightest region of its host is the ambiguous GRB 090426, which has ${F}_{\mathrm{light}}=0.82$. Although the numbers of both consensus SGRBs and LGRBs with ${F}_{\mathrm{light}}$ measurement are relatively small, ${F}_{\mathrm{light}}$ shows the most significant difference between the two types of GRBs in host galaxy properties, with ${P}_{\mathrm{KS}}=7\times {10}^{-5}$. The regions where LGRBs are located are 60% brighter than the regions where SGRBs reside. Excluding GRB 090426, the overlapping fractions become 48% and 100% for LGRBs and SGRBs. At $z\lt 1.4$, LGRBs are located in even brighter regions of their hosts, and SGRBs are located in even fainter regions due to the exclusion of ambiguous GRB 090426. It makes the difference between LGRBs and SGRBs even more significant, and the overlapping fractions are as low as 40%. It is one of the best physical origin indicator candidates. Similar to other parameters, T₉₀-defined samples show less difference between LGRBs and SGRBs.