A Short GRB "No-Host'' Problem? Investigating Large Progenitor Offsets for Short GRBs with Optical Afterglows
aa r X i v : . [ a s t r o - ph . H E ] J un D RAFT VERSION N OVEMBER
1, 2018
Preprint typeset using L A TEX style emulateapj v. 03/07/07
A S
HORT
GRB “N O -H OST ” P
ROBLEM ?I NVESTIGATING L ARGE P ROGENITOR O FFSETS FOR S HORT
GRB
S WITH O PTICAL A FTERGLOWS
E. B
ERGER Draft version November 1, 2018
ABSTRACTWe investigate the afterglow properties and large-scale environments of several short-duration gamma-raybursts (GRBs) with sub-arcsecond optical afterglow positions but no bright coincident host galaxies. The pur-pose of this joint study is to robustly assess the possibility of significant offsets, a hallmark of the compact objectbinary merger model. Five such events exist in the current sample of 20 short bursts with optical afterglows,and we find that their optical, X-ray, and γ -ray emission are systematically fainter. These differences may bedue to lower circumburst densities (by about an order of magnitude), to higher redshifts (by ∆ z ≈ . - γ -ray fluences cannotbe explained by lower densities. To study the large-scale environments we use deep optical observations toplace limits on underlying hosts and to determine probabilities of chance coincidence for galaxies near eachburst. In 4 of the 5 cases the lowest probabilities of chance coincidence ( P ( < δ R ) ∼ .
1) are associated withbright galaxies at separations of δ R ∼ ′′ , while somewhat higher probabilities of chance coincidence are asso-ciated with faint galaxies at separations of ∼ ′′ . By measuring redshifts for the brighter galaxies in three cases( z = 0 . , . , . ≈ -
75 kpc, while for the faint hosts the assumption of z & ∼
15 kpc. Alternatively, the limits at the burst positions ( &
26 mag) can be explainedby typical short GRB host galaxies ( L ≈ . - ∗ ) at z &
2. Thus, two possibilities exist: (i) ∼ / ∼
50 kpc or ∼
15 kpc from the centers of z ∼ . z & ∼ / z & z ∼ . z ∼
2. The large offset scenario leads to an offset distribution that is well-matched bytheoretical predictions of NS-NS/NS-BH binary kicks, or by a hybrid population with globular cluster NS-NSbinaries at large offsets and primordial binaries at offsets of .
10 kpc (indicative of negligible kicks). Deeperconstraints on any coincident galaxies to &
28 mag (using the
Hubble Space Telescope ) will allow us to betterexclude the high-redshift scenario.
Subject headings: gamma-rays:bursts INTRODUCTION
The bimodality of gamma-ray burst (GRB) durations(Kouveliotou et al. 1993) is indicative of separate progenitorpopulations for long- and short-duration GRBs. While di-rect observational support exists for the massive star originof long GRBs (e.g., Woosley & Bloom 2006), the most pop-ular progenitor model for short GRBs is the coalescence ofcompact object binaries with neutron star and/or black holeconstituents (NS-NS/NS-BH; Eichler et al. 1989; Paczynski1991; Narayan et al. 1992). One of the key predictions ofthis model is that some systems will experience large velocitykicks at birth, leading to eventual mergers well outside of thehost galaxies, in galactic halos and the intergalactic medium(Bloom et al. 1999; Fryer et al. 1999; Belczynski et al. 2006).These models predict that 10 -
20% of all mergers will occurat offsets of &
20 kpc for Milky Way mass galaxies. In suchenvironments the resulting afterglow emission is expected tobe fainter than for bursts occurring in coincidence with theirhost galaxies due to the low ambient density (Panaitescu et al.2001; Perna & Belczynski 2002).A subset of NS-NS binaries ( ∼ - Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cam-bridge, MA 02138 distribution of globular clusters, and initial predictions arethat 50 -
90% of these systems will have offsets of &
20 kpc(depending on the mass of the galaxy; Salvaterra et al. 2010).An additional expectation is that dynamically-formed bina-ries will be heavily skewed to lower redshifts due to the ad-ditional time delay between the formation and core-collapseof the globular clusters (Hopman et al. 2006; Salvaterra et al.2008).Other progenitor systems for short GRBs have also beenproposed, including young magnetars (Thompson & Duncan1995), accretion-induced collapse (AIC) of neutron stars(Qin et al. 1998), and delayed magnetar formation through bi-nary white dwarf mergers or white dwarf AIC (Levan et al.2006b; Metzger et al. 2008). These models are partially moti-vated by observations that cannot be easily accommodated inthe standard NS-NS merger model, such as extended soft γ -ray emission on timescales of ∼
100 s (e.g., Villasenor et al.2005; Metzger et al. 2008; Perley et al. 2009), or by phe-nomena such as short-duration giant flares from soft γ -ray repeaters (e.g., Hurley et al. 2005; Palmer et al. 2005;Tanvir et al. 2005; Nakar et al. 2006). The general expecta-tion is that these alternative progenitors will not experiencekicks, and will therefore lead to bursts in coincidence withhost galaxies.The detection of short GRB afterglows starting in mid-2005provided an opportunity to investigate the various progenitormodels through a range of observational tests: the redshiftdistribution (Berger et al. 2007; Gal-Yam et al. 2008), thehost galaxy demographics (Berger 2009), the afterglow prop-erties (Berger 2007; Gehrels et al. 2008; Kann et al. 2008;Nysewander et al. 2009), and perhaps most importantly, theirlocations relative to the host galaxies (Fong et al. 2010). Asof mid-2010, X-ray and optical afterglows have been de-tected from 40 and 20 short GRBs, respectively, with the lat-ter sample providing accurate sub-arcsecond positions. Ofthese 20 events, 15 directly coincide with host galaxies witha wide distribution of apparent magnitudes, and redshifts of z ≈ . - do not appear to coincide with galaxies, and therefore providean opportunity to assess the possibility of large progenitor off-sets, and to test the validity of the NS-NS merger models.Significant offsets have been claimed previously, in partic-ular for GRBs 050509b and 060502b with projected offsetsof 39 ±
13 and 73 ±
19 kpc, respectively (Bloom et al. 2006,2007). However, in both cases only X-ray positions are avail-able (3 . ′′ and 4 . ′′ radius, respectively), and the error circlescontain several galaxies consistent with a negligible offset(Berger et al. 2007; Bloom et al. 2007). Moreover, in the caseof GRB 050509b the X-ray error circle intersected the outerregions of the host, raising the possibility that the progeni-tor system was formed in, rather than kicked to, the outskirtsof the host. This possibility raises a crucial point, namelythat a substantial physical offset from the center of the hostdoes not necessarily point to a progenitor kick if the burst stillclosely coincides with the host light distribution (Fong et al.2010). An illustrative example of this point is GRB 071227whose optical afterglow position coincides with the outskirtsof edge-on disk galaxies, with an offsets of about 15 kpc fromthe host center (D’Avanzo et al. 2009; Fong et al. 2010).Large offsets have also been speculated in a few cases withprecise optical afterglow positions (GRBs 061201, 070809,and 080503; Stratta et al. 2007; Perley et al. 2008, 2009).However, these claims have not been investigated systemat-ically, mainly because they were treated on a case-by-casebasis, with probabilistic arguments that prevented conclusiveassociations. These cases, combined with the ambiguity in-herent to X-ray positions, demonstrate that bursts with opticalafterglows are essential for reaching any robust conclusionsabout progenitor offsets (due to kicks and/or a globular clus-ter origin).Here we present the first systematic study of short GRBswith optical afterglows and no coincident hosts, which com-bines their afterglow properties with the large-scale environ-ments. The purpose of this study is to statistically assess thepossibility of offsets and to compare this with alternative ex-planations (e.g., a high redshift origin). To achieve this goalwe set our study in the broader context of short GRBs thathave optical afterglows and coincident hosts, as well as shortGRBs with only X-ray positions. As we demonstrate through-out the paper, such a combined study is essential since offsetsor high redshifts are expected to jointly affect both the after-glow properties and the large-scale environments. Our studyalso provides a robust statistical assessment of a posteriori chance coincidence probabilities, and the expected number ofspurious associations, which cannot be properly assessed forindividual bursts. These are GRBs 061201: Berger (2006a); Stratta et al. (2007);Fong et al. (2010); 070809: Perley et al. (2007, 2008); 080503: Perley et al.(2009); 090305: Cenko et al. (2009); Berger & Kelson (2009); and 090515:Rowlinson et al. (2010).
The paper is organized as follows. In §2 we present deepoptical observations of the environments of GRBs 061201,070809, 080503, 090305, and 090515, as well as spectro-scopic observations of bright galaxies near the burst positionsfor GRBs 061201, 070809, and 090515. We study trends inthe afterglow and prompt emission properties of bursts withand without coincident hosts in §3, and determine a posteri-ori probabilities of chance coincidence as a function of pro-jected angular offset for galaxies near the position of eachburst in §4. We also determine projected physical and host-normalized offsets, and use these in conjunction with the af-terglow and prompt emission properties to address two sce-narios for the short bursts with optical emission and no coinci-dent bright hosts: (i) an origin in faint galaxies at z & z ∼ . - . z & SHORT GRB SAMPLE AND OBSERVATIONS
We include in this investigation all 20 short GRBs with op-tical afterglow detections as of June 2010. This is the fullsubset of events for which sub-arcsecond positions are avail-able. We stress that this sample represents only about 1/3 ofall short GRBs discovered to date, and about 1/2 of the sam-ple with X-ray afterglow detections. Thus, it is not a completesample of short GRBs, but it is the only subset for which wecan investigate the possibility of large offsets with meaningfulstatistical significance. As we demonstrate in §5, we do notexpect this sample to be strongly biased with respect to cir-cumburst density, at least for n & - cm - . The propertiesof the 20 short GRBs, as well as events with deep optical lim-its, are summarized in Table 1. As can be inferred from theTable, some of the 20 events with only X-ray detections donot have optical follow-up observations, suggesting that thesample with optical afterglows may be largely representative.For the purpose of our investigation we define three sub-samples that will be used throughout the paper: (i) Sample1 : short GRBs with detected afterglows and coincident hostgalaxies (15 bursts); (ii)
Sample 2 : the 5 short bursts with de-tected optical afterglows and no bright coincident hosts; and(iii)
Sample 3 : short GRBs with detected X-ray afterglows(from the
Swift
X-ray Telescope) but no optical detections de-spite rapid follow-up observations (11 bursts).
Optical Imaging
For the bursts in
Sample 2 we use deep space- and ground-based optical observations to place limits on the brightness ofunderlying galaxies, and to assess the probability of chancecoincidence for nearby galaxies. For GRB 061201 we use
Hubble Space Telescope (HST) observations obtained withthe Advanced Camera for Surveys (ACS) in the F814W fil-ter, with a total exposure time of 2244 s (Fong et al. 2010).For GRB 070809 we use r -band observations obtained on2008 January 14 UT with the Low Dispersion Survey Spec-trograph (LDSS3) mounted on the Magellan/Clay 6.5-m tele-scope, with a total exposure time of 1500 s. For GRB 080503we use HST Wide-Field Planetary Camera 2 (WFPC2) ob-servations in the F606W filter from 2009 January 30 UT,with a total exposure time of 4000 s (Perley et al. 2009).We also use the limits on a coincident host inferred from adeeper stack of HST observations by Perley et al. (2009), with m AB (F606W) & . r -band observations obtained on 2010 May 8 UT with a total ex-posure time of 2400 s. Finally, for GRB 090515 we use r -bandobservations obtained with the Gemini Multi-Object Spectro-graph (GMOS) mounted on the Gemini-North 8-m telescopefrom 2009 May 15 UT with a total exposure time of 1800 s.The ground-based observations were reduced and analyzedusing standard routines in IRAF. The analysis of the HST ob-servations is detailed in (Fong et al. 2010). The limiting mag-nitudes for all five observations are listed in Table 2, and im-ages of the five fields are shown in Figures 1–5. Optical Spectroscopy
In addition to the imaging observations, we obtained spec-troscopic observations of galaxies near the positions of GRBs061201, 070809, and 090515. Our observations of a galaxylocated 16 . ′′ from the afterglow position of GRB 061201(marked “S4” in Figure 1) revealed a star forming galaxy at z = 0 .
111 (Stratta et al. 2007; Fong et al. 2010); see Figure 6.For GRB 070809 we obtained spectra of two galaxies lo-cated 5 . ′′ and 6 . ′′ from the optical afterglow position(marked “S2” and “S3”, respectively in Figure 2) usingLDSS3 on 2008 January 14 UT. The galaxy at a separationof 5 . ′′ was previously identified as a star forming galaxy at z = 0 .
218 by Perley et al. (2008). Here we find that the objectat a separation of 6 . ′′ is an early-type galaxy at z = 0 . ′ × ′ field centered on the GRB position. These ob-servations provide redshifts for several galaxies near the hostposition, including a star forming galaxy at z = 0 .
626 (5 . ′′ offset; “S1” in Figure 5), an early-type galaxy at z = 0 . . ′′ offset; ”S5”), and a star forming galaxy at z = 0 . . ′′ offset; “S6”); see Figure 8. In an upcoming paper wewill demonstrate that the galaxy at z = 0 .
403 is a member of acluster. AFTERGLOW PROPERTIES
We begin our investigation by assessing the distributionof optical afterglow magnitudes for the three samples de-fined in §2. The observed magnitudes and limits as a func-tion of time after the burst are shown in Figure 9. The me-dian observation time for the sample is about 8.5 hr after theburst. The distribution of detected optical afterglow magni-tudes is broad, ranging from r AB ≈
21 to ≈
26 mag. The lim-its range from r AB &
23 to &
25 mag (with the exception ofGRB 080702 which only has a shallow limit of about 21 ABmag: Greco et al. 2008).The mean brightness and standard deviation for
Sample 1 are h r AB i = 23 . ± . R ≈ t ≈
10 hr by (Panaitescu et al. 2001). Since the avail-able limits are at least &
23 mag, we conclude that the bursts These numbers remain essentially unchanged if we extrapolate all mea-sured magnitudes to the fiducial time of 8.5 hr with a typical afterglow decayindex of α = - . lacking optical detections are drawn from a population withfainter afterglows. For the 5 bursts in Sample 2 we find a me-dian and standard deviation of h r AB i = 24 . ± . . Sample 1 and
Sample 2 are drawn from the same underlying distribution of optical af-terglow brightnesses. Similarly, the probability that
Sample1 and
Sample 3 are drawn from the same underlying distri-bution is .
5% (an upper limit since the bursts in
Sample 3 are not detected in the optical). On the other hand, the prob-ability that
Sample 2 and
Sample 3 are drawn from the sameunderlying distribution is high, ≈ Sample 2 and
Sample 3 can be explained in two primary ways. First,they could result from systematically lower circumburst den-sities. In the standard afterglow model with ν m < ν opt < ν c ,the afterglow flux scales as F ν ∝ n / for a uniform medium(Sari et al. 1998). Thus, a difference of about + . Sample 1 .Alternatively, the fainter fluxes may be due to higher red-shifts for
Sample 2 and
Sample 3 compared to
Sample 1 sincethe optical flux also scales as F ν ∝ (1 + z ) (3 + p ) / d - L , where d L is the luminosity distance. The + . ∆ z ≈ + . +
1) for a
Sample 1 mean redshift of z = 0 . z = 1). Similarly, the flux also depends on the totalenergy, with F ν ∝ E (3 + p ) / , and therefore a difference of + . γ -ray emission, and the relation betweenthe optical and X-ray afterglow brightness. In the frameworkof the standard GRB model we do not expect lower densitiesto impact the prompt emission since it is expected to be pro-duced by internal processes (shocks or magnetic dissipation)that do not depend on the external medium. On the other hand,lower energies or higher redshifts will tend to systematicallyaffect the prompt and afterglow emission.In Figure 11 we plot the distributions of γ -ray fluence ( F γ ),afterglow X-ray flux at the fiducial time of 8 hr ( F X , ), andduration ( T ) for the three samples. These distributions allowus to explore the underlying reason for the difference in opti-cal afterglow brightness between the three samples. First, wefind that the distribution of F γ values for Sample 1 has a meanvalue that is about a factor of 5 times larger than for
Sample2 and
Sample 3 . This is indicative of higher redshifts for thelatter two samples if the isotropic-equivalent energies of allshort GRBs are similar, or alternatively a lower energy scaleif the redshifts are similar.In the same vein, we find that the distributions of F X , val-ues for Sample 2 and
Sample 3 have lower means than for
Sample 1 . This result is indicative of overall fainter afterglowemission for the former two samples, and this can again beexplained in the context of lower energies or higher redshifts. We use the standard synchrotron spectrum definitions: ν m is the charac-teristic synchrotron frequency corresponding to electrons with the minimumLorentz factor ( γ m ) of the electron distribution, N ( γ ) ∝ γ - p ; p usually has avalue of ≈ . - .
5; and ν c is the synchrotron cooling frequency (Sari et al.1998). Unlike in the case of the γ -ray emission, a lower circum-burst density would also account for the fainter X-ray fluxesif ν X < ν c . Finally, we find that the durations of the burstsin Sample 2 and
Sample 3 are shorter by about a factor of 2compared to the events with optical afterglows and coincidenthosts, although there is substantial scatter in all three samples.The shorter durations are not trivially explained in the contextof lower energies, higher redshifts, or lower densities.To explore this result in more detail we plot the observedfluence as a function of duration for the events in all threesamples (Figure 12). We find that there is a mild positivecorrelation between the two quantities, but that the events in
Sample 1 appear to have larger fluences at a given durationcompared to the events in
Sample 2 and
Sample 3 . This isindicative of lower γ -ray fluxes for the latter two samples,possibly as a result of higher redshifts. Higher redshifts willalso shift the intrinsic durations of the bursts in Sample 2 and
Sample 3 into better agreement with the bursts in
Sample 1 .We therefore conclude that the differences in prompt emis-sion and optical/X-ray afterglow properties are consistentwith a higher redshift origin for the bursts in
Sample 2 and
Sample 3 . The fainter afterglow emission is also consistentwith lower density environments for these two samples, al-though this does not clearly explain the differences in promptemission (at least in the framework of the standard GRBmodel). We return to the discussion of low density versus ahigh redshift origin in §4 when we investigate the host galaxyproperties.In addition to the overall faintness of the optical and X-rayafterglows, a substantial difference in density may also be im-printed on the ratio of optical to X-ray brightness. This is be-cause the synchrotron cooling frequency depends on densityas ν c ∝ n - , and is therefore expected to transition across theX-ray band as the density decreases. For ν c > ν X the X-rayand optical bands occupy the same portion of the synchrotronspectrum, with a resulting spectral index of β = - ( p - / ≈ - . ≈ - .
75 while for ν c < ν X (i.e., high density), thespectrum between the two bands will be steeper, reaching amaximum value of ≈ - .
25 when ν c ≈ ν opt . In Figure 13we plot the X-ray flux versus optical magnitude for all threesamples. For each burst the fluxes in the optical and X-raysare taken at similar times after the burst, or extrapolated toa common time. The correction factors due these extrapola-tions are generally . Sample1 and
Sample 2 we find a clear correlation between the fluxesin the two bands, leading to a mean optical to X-ray spectralindex of h β OX i = - . ± .
17. This is essentially indistin-guishable from the ratio for long GRBs, h β OX i = - . ± . ν c & ν X , but exhibit dispersion that is likely due to scat-ter in the values of p and/or the location of ν c relative to theX-ray band.The similarity of β OX for long and short GRBs does notnecessarily indicate that the densities are similar for the twosamples. In particular, if ν c is located close to the X-rayband for long GRBs, while for short GRBs ν c ≫ ν X (due to alower density), the effect on β OX will be marginal, particularlywithin the overall observed scatter. For example, with p = 2 . β OX between a model with ν c exactly inter-mediate between the optical and X-ray bands, and a modelwith ν c > ν X , is ∆ β OX ≈ .
25. On the other hand, the scatterresulting from a range of p = 2 . - . We do not extrapolate X-ray upper limits. ∆ β OX = 0 .
15. Similarly, the nearly equivalent median β OX values may indicate that for both GRB populations ν c > ν X .In this case, the resulting lower limits on ν c therefore preventthe use of β OX as an indicator of density.Comparing Sample 1 and
Sample 2 , we find no clear dif-ference in β OX (Figure 13). The same is true for the burstsin Sample 3 , which are all consistent with the same relationgiven the optical upper limits and a mix of X-ray detectionsand upper limits. Thus, the ratio of optical to X-ray flux doesnot allow us to distinguish redshift/energy and density effectsbetween the three samples.To summarize, the optical afterglows of short GRB withoutcoincident hosts (or with only optical limits) are systemati-cally fainter than those of short GRBs with coincident hosts.The same is true for their X-ray fluxes and γ -ray fluences.The fainter afterglows may reflect lower densities (by an orderof magnitude), but this does not naturally explain the lower γ -ray fluences. Alternatively, the fainter afterglows and γ -ray fluences can be explained as a result of higher redshifts( ∆ z ≈ . -
1) or lower energies (by about a factor of 3). LARGE-SCALE ENVIRONMENTS
We next turn to an analysis of the large-scale environmentsof the bursts in
Sample 2 , partly in comparison to the hostsof bursts in
Sample 1 . As indicated in §2, we place limits of r AB ≈ . - . z . Sample 1 ). Probabilities of Chance Coincidence
To assess the potential that galaxies near each of the 5 burstsare the hosts, we calculate their probability of chance coinci-dence. We follow the methodology of Bloom et al. (2002),namely, we determine the expected number density of galax-ies brighter than a measured magnitude, m , using the results ofdeep optical galaxy surveys (Hogg et al. 1997; Beckwith et al.2006): σ ( ≤ m ) = 10 . × ln(10) × . m - - . arcsec - . (1)The probability for a given separation, P ( < δ R ), is then givenby P ( < δ R ) = 1 - e - π ( δ R ) σ ( ≤ m ) , (2)where we use the fact that for offsets substantially larger thanthe galaxy size, δ R is the appropriate radius in Equation 2(Bloom et al. 2002).The resulting distributions for each field are shown in Fig-ure 14. We include all galaxies that have probabilities of . .
95. We find that for 4 of the 5 bursts, faint galaxies( ∼ -
26 mag) can be identified within ≈ . - ′′ of theafterglow positions, with associated chance coincidence prob-abilities of ≈ . - .
2; in the case of GRB 090515 we do notdetect any such faint galaxies within ≈ ′′ of the afterglowposition. For GRB 080503 we also include the galaxy at anoffset of 0 . ′′ and m AB (F606W) = 27 . ± . ≈ . - .
15, are brighter objects with offsetsof about 6 - ′′ from the burst positions; only in the case ofGRB 080503 the lowest chance coincidence is associated withthe nearest galaxy (see Perley et al. 2009).For comparison we repeat the same analysis for shortGRBs from Sample 1 which have faint coincident hosts(GRB 060121: 26.0 AB mag; GRB 060313: 26.6 AB mag;and GRB 070707: 27.3 AB mag). The results of the prob-ability analysis are shown in Figure 15. We find that in allthree cases, the coincident hosts exhibit the lowest probabil-ity of chance coincidence, ≈ . - .
05. Only in the caseof GRB 070707 do we find galaxies with δ R & few arcsecthat have P ( < δ R ) . .
1. Thus, these three bursts are con-sistent with negligible offsets from faint galaxies, presumablyat z & a posteriori probabilities to assign unique galaxyassociations is fraught with difficulties. First, for a givenapparent brightness, galaxies located further away from theGRB position, potentially due to larger kicks and/or longermerger timescales in the NS-NS merger framework, havehigher probabilities of chance coincidence. Since we have no a priori model-independent knowledge of the range of possi-ble kicks and merger timescales, we cannot rule out galaxiesat very large offsets for which P ( < δ R ) ∼
1. Indeed, a rea-sonable constraint of v kick . km s - and τ merger .
10 Gyrleads to only a weak constraint on the offset of .
10 Mpc. At z = 0 . z = 1) this corresponds to about 1 . ◦ (0 . ◦ ), a pro-jected distance at which nearly all galaxies will have a chancecoincidence probability of order unity.A second difficulty is that we are using angular offsets,which ignore the potential wide range of redshifts (and byextension also luminosities) of the various galaxies. For ex-ample, if the faint galaxies with small offsets are located at z &
1, the corresponding physical offsets are ∼
15 kpc, whileif the galaxies at ∼ ′′ offsets are located at z ∼ . ∼
30 kpc. A galaxy atan even lower redshift, z ∼ .
1, with an offset of 50 kpc willbe located about 30 ′′ from the GRB position and incur a largepenalty in terms of chance coincidence probability. It is im-portant to note, however, that galaxies at lower redshift willgenerally have brighter apparent magnitudes, partially com-pensating for the larger angular separations (Equations 1 and2). In only a single case (GRB 070809) we find a galaxy with P ( < δ R ) . . δ R & ′ (which at z = 0 .
043 for this galaxycorresponds to a physical offset of about 100 kpc).A final complication, which is not unique to this subset ofevents, is that we can only measure projected offsets, δ R = δ R × cos( θ ). The measured offsets can be used as lowerlimits on the actual offsets, while for the overall distributionwe can apply an average correction factor of π/
2, based onthe expectation value for the projection factor, cos( θ ).Despite these caveats we can address the probability that all of the associations are spurious. This joint probability is sim-ply the product of the individual probabilities (Bloom et al.2002). For the faint galaxies at small angular separations theprobability that all are spurious associations is P all ≈ × - ,while for the galaxies with the lowest probability of chancecoincidence the joint probability is nearly 30 times lower, P all ≈ × - . Conversely, the probabilities that none ofthe associations are spurious are ≈ .
42 and ≈ .
59, respec-tively. These values indicate the some spurious coincidencesmay be present for
Sample 2 . Indeed, the probabilities that1, 2, or 3 associations are spurious are [0 . , . , . . , . , . - - a posteriori probabilities, we conclude that there is strongerstatistical support for an association of at least some of the5 bursts in Sample 2 with bright galaxies at separations of ∼ ′′ , than for an association with the faint galaxies at sepa-rations of ∼ ′′ . Clearly, we cannot rule out the possibility thatin reality the hosts are a mix of faint and bright galaxies with arange of angular offsets of & ′′ . We note that if deeper obser-vations eventually lead to the detection of underlying galax-ies ( . . ′′ ) at the level of ≈
27 mag, the associated chancecoincidence probabilities will be ≈ .
05 per object, and thejoint probabilities will be only slightly higher than for thebright galaxies with ∼ ′′ offsets. On the other hand, if wecan achieve magnitude limits of &
28 mag on any coincidenthosts, the resulting probabilities of chance coincidence willbe larger than for the offset bright galaxies. Thus, eliminatingthe possibility of underlying hosts at the level of &
28 magis of the utmost importance. So far, only GRB 080503 hasbeen observed to such a depth with no detected coincidenthost (Perley et al. 2009), but observations of the full sampleare required for a robust statistical comparison. As we discussin §4.2 below, such deep limits will also reduce the probabil-ity of underlying hosts based on redshift arguments.Beyond the use of projected angular offsets, we note thatthe faint galaxies near the burst positions are likely to haveprojected physical offsets of about
15 kpc. To assess the pro-jected physical offsets for the galaxies with the lowest proba-bility of chance coincidence we measured spectroscopic red-shifts in three cases (GRBs 061201, 070809, and 090515; §2).In the case of GRB 061201, the galaxy redshift of z = 0 . . at z = 0 .
218 identified by Perley et al. (2008), butinstead belongs to the early-type galaxy identified here, whichhas a redshift of z = 0 . . z = 0 . r AB &
26 mag);or (ii) the bursts have substantial offsets of at least ≈ - z ∼ . - .
5; for the ensemble of 5 events the larger offsetsare statistically more likely than the ∼
15 kpc offsets. In thecontext of large offsets, even larger values may be possible ifthe bursts originated in galaxies with larger separations and P ( < δ R ) ∼ Although the redshifts of these galaxies are not known, the angular di-ameter distance is nearly independent of redshift beyond z ∼
1, which is ap-propriate for these faint host galaxies. We note that even if the burst was associated with this galaxy, the corre-sponding offset would be 20 . globular cluster origin) and hence NS-NS/NS-BH progenitorsfor at least some short GRBs. Scenario 1: Undetected Faint Hosts at High Redshift
We can place upper limits on the redshifts of the GRBsin
Sample 2 based on their detections in the optical (i.e.,the lack of complete suppression by the Ly α forest). Theafterglow of GRB 061201 was detected in the ultravioletby the Swift /UVOT and it is therefore located at z . . g - or r -band, and can therefore be placedat z . r -band magnitudes as afunction of redshift for the all available short GRB hosts from Sample 1 . For the faint hosts without known redshifts (GRBs060121, 060313, and 070707), we place upper limits on theredshift using optical detections of the afterglows (Table 1).A wide range of host magnitudes, r AB ∼ . - . r -band magnitudes of long GRBhosts (Savaglio et al. 2009), as well as the r - z phase spacethat is traced by galaxies with luminosities of L = 0 . - ∗ .We use the appropriate value of L ∗ as a function of redshift,taking into account the evolving galaxy luminosity function(Steidel et al. 1999; Blanton et al. 2003; Willmer et al. 2006;Reddy & Steidel 2009). We find excellent correspondence be-tween the hosts of long and short GRBs, and the phase-spacetraced by 0 . - ∗ galaxies, at least to z ∼
4. In the contextof these distributions, the available limits for the short GRBsin
Sample 2 translate to redshifts of z & . ∗ galaxies, or z & ∗ galaxies. The latter lower lim-its are comparable to the redshift upper limits inferred fromthe afterglow detections. We note that for GRB 080503, thelimit of & . . - ∗ galaxy.The redshifts of z & . ∗ hosts areconsistent with the faintness of the optical afterglows, fromwhich we inferred ∆ z ≈ . - Sample 1 (§3).We note, however, that the one known short GRB at z & ∼ ∗ , which may suggest that the appropriate red-shift lower limits are z & z & Sample 1 with a known redshift (9/10) have z ≈ . -
1, with a median of h z i ≈ .
5; the sole exceptionis GRB 090426 at z = 2 .
61. The three bursts with faint coin-cident hosts have upper limits of z . z & . - L & . ∗ . Adding the Sample 2 burstswith the assumption that they have z & z ∼
3, andleave a substantial gap at z ∼ - . ∗ galaxies, the inferred lower limitson the redshifts ( z & .
5) lead to a potentially more uniformredshift distribution.It is difficult to explain a bimodal redshift distribution with asingle progenitor population such as NS-NS binaries, withoutappealing to, for example, a bimodal distribution of mergertimescales. Another possibility is two distinct progenitor pop-ulations, producing bursts of similar observed properties butwith distinct redshift ranges. While these possibilities are dif- ficult to exclude, they do not provide a natural explanation forthe short GRB population.A final alternative explanation is that any underlying hostsreside at similar redshifts to the known hosts in
Sample 1 ( z ∼ . . .
01 L ∗ .This scenario would not naturally explain why the bursts in Sample 2 have fainter optical and X-ray afterglows, as wellas lower γ -ray fluences. We therefore do not consider thispossibility to be the likely explanation. Scenario 2: Large Offsets
While higher redshifts may explain the lack of detectedhosts, the fainter afterglows, and the weaker γ -ray fluencesof the bursts in Sample 2 , this scenario suffers from severaldifficulties outlined above. The alternative explanation is thatthe bursts occurred at significant offsets relative to their hosts,and hence in lower density environments that would explainthe faint afterglow emission (though possibly not the lower γ -ray fluences). As we demonstrated in §4.1, the offsets may be ∼ ′′ ( ∼
15 kpc) if the bursts originated in the faint galaxies atthe smallest angular separations, or ∼ ′′ ( ∼ -
75 kpc) ifthey originated in the brighter galaxies with the lowest prob-ability of chance coincidence. Below we address the implica-tions of these two possible offset groups through a compari-son to the offsets measured for the bursts in
Sample 1 (e.g.,Fong et al. 2010).We plot the distributions of projected angular offsets for theshort GRBs with and without coincident hosts in Figure 17.The offsets for
Sample 1 have a mean and standard deviationof about 0 . ± . ′′ and a range of about 0 . - ′′ . Modeledwith a log-normal distribution, the resulting mean and widthin units of arcseconds are log( δ R ) ≈ - . σ log( δ R ) ≈ . Sample 2 with the galax-ies that have the lowest probability of chance coincidence,the resulting distribution has h δ R i = 9 ± Sample 1 . The ef-fect is less pronounced if we associate the bursts with thegalaxies located at the smallest angular offsets (Figure 17).Even for these separations the mean and standard deviationare log( δ R ) ≈ . ± . Sample 1 have a mean and standard de-viation of about 1 ± . R e , and a range of about 0 . - R e . Alog-normal fit results in a mean of log( δ R / R e ) ≈ σ log( δ R / R e ) ≈ .
2. The bursts in
Sample 2 have much largerhost-normalized offsets, with ( δ R / R e ) = 7 . ± . R e , reflecting thefact that the effective radii of the faint galaxies are smallerthan those of the brighter ones.Finally, we plot the projected physical offsets in Figure 19.The mean and standard deviation for Sample 1 are δ R = 4 . ± . δ R ) ≈ . σ log( δ R ) ≈ .
3. On the other hand, the bursts in
Sample 2 have a mean offset of about 19 kpc if they arise inthe faint galaxies with small angular separation, or about 40kpc if they arise in the brighter galaxies, again pointing todistinct distributions.The distributions of angular, physical, and host-normalizedoffsets exhibit a clear bimodality if we associate the bursts in
Sample 2 with the galaxies at z ∼ . - .
5. This is particularlyapparent in the more meaningful quantities, namely physicaland host-normalized offsets (Figures 18 and 19). The effectis still apparent, though less pronounced in the case of asso-ciation with the faint galaxies at z &
1. Thus, if the offsetscenario is correct, the resulting distributions point to a possi-ble bimodality rather than a single continuous distribution ofoffsets.The cumulative distributions of physical offsets for
Sample1 alone, and in conjunction with the two possible offset groupsfor
Sample 2 are shown in Figure 20. The combined distribu-tions have a median of about 4 kpc, driven by the bursts withcoincident hosts. However, there is a clear extension to largerphysical offsets in the case of association with the brightergalaxies, with about 20% of all objects having δ R &
30 kpc.The cumulative distributions are particularly useful for com-parison with NS-NS merger models since predictions exist forboth the kick scenario and the globular cluster origin model.We turn to this discussion below. DISCUSSION AND IMPLICATIONS
We have shown that the lack of host galaxy detections incoincidence with the bursts in
Sample 2 indicates either ahigh redshift ( z &
2) origin, or substantial projected offsets of ∼ -
75 kpc ( ≈ - R e ). Both scenarios can account for thelack of underlying galaxy detections and the fainter optical/X-ray afterglows (either due to redshift or density effect); thepossibility of large offsets from galaxies at z ∼ . - .
5, how-ever, does not naturally explain the lower γ -ray fluences andsomewhat shorter durations of the bursts in Sample 2 . Indeed,the lower fluences can be more easily accommodated in thecase of undetected high redshift coincident hosts, or in thecase of faint hosts with offsets of ∼
15 kpc.Below we test the results of the offset scenario against pre-dictions for NS-NS merger models and dynamically-formedNS-NS binaries in globular clusters. We also investigatewhether the densities expected at offsets of ∼ -
75 kpc (i.e.,galaxy halos or the intergalactic medium) can accommodatethe observed optical magnitudes. Finally, we discuss the im-plications of the various scenarios for short GRB energetics.
Comparison to NS-NS Merger Models
The sample of short GRBs with optical afterglows repre-sents about 1 / Sample 2 is indeed largeoffsets, despite their detection in the optical band .The bursts with only X-ray afterglow detections(
Swift /XRT) have typical positional uncertainties of σ X ≈ - ′′ and therefore lead to a deeper ambiguityabout the identity of the hosts. We have previously arguedthat most of these bursts are associated with galaxies con-sistent with a negligible offset (or as large as tens of kpc;Berger et al. 2007; Fong et al. 2010). In some cases largeroffsets have been advocated based on a posteriori chancecoincidence probabilities (e.g., GRB 050509b: Bloom et al.2006; GRB 060502b: Bloom et al. 2007). However, from the analysis in §4.1 it is clear that while the inferred probabilitiesare only weakly dependent on the positional accuracy when δ R & σ X (i.e., galaxies at large offsets), a large penalty isincurred for faint galaxies located within the X-ray errorcircles since in that case the appropriate value in Equation 2is δ R = σ X . As a result, the faint galaxies will have chancecoincidence probabilities of P ( < δ R ) ∼
1. To avoid thiscomplication in our comparison to NS-NS model predictionswe restrict the analysis to the sample with optical afterglowpositions.In recent work by Fong et al. (2010) we have shown thatthe offset distribution for short GRBs with optical and/orX-ray positions, and accounting for incompleteness due tobursts with only γ -ray positions, is broadly consistent withthe predictions of NS-NS merger models (Bloom et al. 1999;Fryer et al. 1999; Belczynski et al. 2006). In particular, weconcluded that &
25% of all short bursts have δ R .
10 kpc,while &
5% have offsets of &
20 kpc. We repeat the anal-ysis here using the offsets inferred in §4.3 for both the faintgalaxies at small angular separations and the brighter galaxiesat larger separations. As shown in Figure 20, the model pre-dictions have a median of about 6 kpc, compared to about 4kpc for the observed sample. On the other hand, the modelspredict 10 -
20% of offsets to be &
30 kpc, in good agree-ment with the observed distribution in both the ∼
15 kpc and ∼
40 kpc scenarios. We note that the overall smaller offsetsmeasured from the data may be due to projections effects. In-deed, the mean correction factor of π/ Sample 1 and
Sample2 (Figures 18 and 19). In the framework of NS-NS bi-nary kicks this bimodality may indicate that the binaries gen-erally remain bound to their host galaxies, thereby spend-ing most of their time at the maximal distance defined by d max = 2 GM host / v (i.e., with their kinetic energy stored aspotential energy; Bloom et al. 2007). This would require typ-ical kick velocities of less than a few hundred km s - .We further compare the observed offset distribution to pre-dictions for dynamically-formed NS-NS binaries in globu-lar clusters, with a range of host galaxy virial masses of5 × - M ⊙ (Salvaterra et al. 2010). These modelspredict a range of only ≈ -
40% of all NS-NS mergers tooccur within 10 kpc of the host center, in contrast to the ob-served distribution with about 70% with δ R .
10 kpc. Westress that this result is independent of what offsets we assignto the bursts in
Sample 2 since they account for only 1/4 of thebursts with optical afterglows. On the other hand, the globu-lar cluster origin may account for the bimodality in the physi-cal and host-normalized offsets (Figures 18 and 19), with theobjects in
Sample 2 arising in globular clusters and the ob-jects with coincident hosts arising from primordial NS-NS bi-naries. This possibility also agrees with the predicted frac-tion of dynamically-formed NS-NS binaries of ∼ - Sample 2 alone (assuming the hosts are the galaxies with thelowest probability of chance coincidence) is well-matched bythe range of predictions for dynamically-formed NS-NS bina-ries in globular clusters (Figure 20). In this scenario, however,the implication is that short GRBs outside of globular clustersdo not experience kicks as expected for NS-NS binaries sincethe largest measured offset is only 15 kpc.Unless the populations of short GRBs with only X-ray or γ -ray positions have fundamentally different offset distribu-tions, we conclude that the measured offsets of short GRBsand the predicted offsets for NS-NS kicks are in good agree-ment, if we treat all short GRBs with optical afterglows asa single population . Alternatively, it is possible that the bi-modal distributions of physical and host-normalized offsetspoint to a progenitor bimodality, with the bursts in Sample 2 originating in globular clusters.
Circumburst Densities
Large offsets are expected to result in low circumburst den-sities, and we now investigate whether the observed opticalmagnitudes for
Sample 2 can be used to place meaningfulconstraints on the offsets. The optical afterglow magnitudesdo not provide a direct measure of the circumburst densitysince they depend on a complex combination of density, en-ergy, and fractions of the burst energy imparted to the radiat-ing electrons ( ǫ e ) and magnetic fields ( ǫ B ). From our compar-ison of the X-ray and optical afterglows (§3) we were unableto clearly locate the cooling frequency, which in principle canprovide additional constraints on the density. However, wecan still gain some insight into the required circumburst den-sities using a few basic assumptions. We assume that the γ -ray energy ( E γ , iso ) is a reasonable proxy for the total energy,that ǫ e , ǫ B < /
3, and that p = 2 .
2. We further use a fiducialredshift of z = 0 . E γ , iso we use the 15 -
150 keV fluences mea-sured by
Swift (Table 1), and determine a correction factorto account for the incomplete energy coverage using burststhat have also been detected by satellites with a broader en-ergy range (Figure 12). We find a typical correction factor of ≈ ≈ - keV range. For the fiducial redshift of z = 0 .
5, the mean energy for short GRBs with optical after-glows is E γ , iso ≈ × erg, when we include the correctionfactor (Figure 21).With these assumptions we find the following relation be-tween the optical brightness and the circumburst density(Granot & Sari 2002): F ν , opt < × n / . (3)Given the typical observed fluxes of about 2 µ Jy for
Sam-ple 1 , and about 0.6 µ Jy for
Sample 2 , we infer typical min-imum densities of & × - and & × - cm - , respec-tively. Thus, the observed optical brightnesses can be pro-duced even at very low densities that are typical of the IGM.This indicates that we cannot rule out the large offset sce-nario based on density arguments. Indeed, even if we allowfor more typical values of ǫ e ≈ ǫ B ≈ .
1, the resulting densitiesare ≈ × - and 4 × - cm - , respectively. These resultscompare favorably with predictions for NS-NS kicks, whichsuggest that most mergers will occur at densities of & - cm - (Perna & Belczynski 2002; Belczynski et al. 2006). Thedistribution of densities in globular clusters is not well known,preventing a meaningful comparison to our inferred minimumdensities (Salvaterra et al. 2010). Energetics
Finally, we investigate the energetics of the bursts in
Sam-ple 2 in the context of a high-redshift origin ( z & ≈ ′′ separations ( z ∼ z ≈ . - . E γ , iso are shown in Figure 21. For the lowest redshift origin, the inferred values are ≈ (1 - × erg, for a z ∼ ≈ × - erg, and for a z & ≈ × - × erg.For comparison, the mean value for the bursts in Sample 1 is h E γ , iso i ≈ × erg, with a range of ≈ - × erg. However, there is a clear redshift dependence for themeasured E γ , iso values (Figure 21), with ≈ × erg at z . . ≈ × erg at z & .
5. Thus, the bursts in
Sample2 generally fit within the known range of isotropic energiesregardless of their actual redshift. Indeed, at z ∼ E γ , iso to that of GRB 090426. As a result, wecannot use the inferred energy release as a clear discriminantof the redshift range for Sample 2 .If the bursts in
Sample 2 indeed originated at high redshifts,the resulting isotropic-equivalent energies suggest that thereis either a large spread in the energy release of short GRBs (atleast 2 orders of magnitude) or a large variations in the ejectageometry. If the typical energy for short GRBs is about 5 × erg, as indicated by the nearest events , then the inferredvalues of E γ , iso ≈ × at z ∼ ≈ - ◦ . This is similar to the opening angle of about7 ◦ that was inferred for GRB 051221 (Burrows et al. 2006;Soderberg et al. 2006). CONCLUSIONS
We undertook the first systematic study of short GRBs withdetected optical afterglows (and hence sub-arcsecond posi-tion) but no coincident host galaxies to limits of r AB & γ -ray fluencesand slightly shorter durations. Both samples have similar ra-tios of X-ray to optical flux, which are moreover similar tothe ratios measured for long GRBs. The fainter afterglows ofthe bursts lacking coincident hosts may be due to lower den-sities, lower energies, or higher redshifts. However, we notethat only the scenarios with lower energies or higher redshiftsnaturally explain the faintness of the prompt emission in thecontext of the standard GRB model . This is because in thecontext of internal processes (shocks or magnetic dissipation)the external density should not play a role.We further use deep optical imaging to determine the prob-ability of chance coincidence for galaxies in the field aroundeach burst, and to place redshift limits for underlying hostsunder the assumption that they are drawn from the same dis-tribution of the detected short GRB hosts ( L ≈ . - ∗ ).This analysis leads to the following possible scenarios: (i) theunderlying hosts are fainter than ∼
26 mag, indicative of red-shifts of z & . L ∼ . ∗ ) or z & L ∼ L ∗ ); or (ii)the hosts are galaxies with substantial offsets — either faintgalaxies at separations of ≈ ′′ ( ≈
15 kpc for z &
1) or brightergalaxies, which we find to be located at z ∼ . - .
5, withoffsets of ≈ - ′′ ( ≈ -
75 kpc). In the former scenario,unless the galaxies have L ∼ . ∗ , the resulting redshift dis-tribution is bimodal with peaks at z ∼ . ∼
3. Such ascenario most likely requires a bimodal age distribution in thecontext of NS-NS mergers, or two distinct progenitor systemsdominating at low and high redshifts. While this cannot be We ignore the factor of ∼ Swift . ruled out by present data, the lack of overlap at z ∼ - L . . ∗ ) at similar redshifts to the detected hosts, since this doesnot naturally explain the difference in afterglow and promptemission properties.In the context of the large offsets scenario, the probabilityof chance coincidence (both individually and for the sample)is lower for the brighter galaxies at offsets of ≈ - ′′ thanfor the faint galaxies at offsets of ≈ ′′ . However, it is notunlikely that the true associations are a mix of both popula-tions, since in each case there is a non-negligible probabilitythat 1 - a poste-riori ) against associations with faint galaxies inside the errorcircle, despite the fact that they are consistent with no offset.From spectroscopic observations for 3 of the 5 burstswe find that the galaxies with the lowest probability ofchance coincidence are a star forming galaxy at z =0 .
111 (GRB 061201), an early-type galaxy at z = 0 . z = 0 .
403 (GRB 090515). If these associations are indeed cor-rect, they only slightly alter the host demographics, which aredominated by star forming galaxies (Berger 2009). However,this does suggest that our present understanding of the relativeratios of star forming and elliptical hosts may be incomplete.The resulting distributions of angular, physical, and host-normalized offsets for the bursts with and without coincidenthosts appear to be distinct, rather than continuous. How-ever, the joint distribution of projected physical offsets is ingood agreement with theoretical predictions for NS-NS bi-nary mergers. On the other hand, the predicted distribution fordynamically-formed NS-NS binaries in globular clusters pro-vides a much poorer fit to the entire data set, unless they ac-count for only the bursts with large offsets (
Sample 2 ). In thecase of a hybrid population of primordial and dynamically-formed binaries, with the latter accounting for only the largeoffsets, the fact that all the remaining offsets (
Sample 1 ) are .
10 kpc, is indicative of no significant kicks. The large phys-ical offsets also naturally explain the fainter afterglow emis-sion as a result of lower circumburst densities. The resultingisotropic γ -ray energies match the observed distribution forshort GRBs with coincident hosts, either at z ∼ . z & ∼ -
70 kpc (corre-sponding to ≈ -
10 galactic effective radii) are a likely ex-planation for the bursts with optical afterglows and no coin- cident hosts is of fundamental importance. The only progen-itor model that naturally explains this result in the merger ofNS-NS/NS-BH binaries, most likely due to kicks, or possiblywith a minor contribution from a globular cluster population(accounting specifically for the events in
Sample 2 ). Whilea conclusive demonstration of a large offset requires an ab-sorption redshift measurement that matches an offset galaxyredshift, the distribution of optical afterglow magnitudes in-dicates that this will be difficult to achieve. Indeed, an ab-sorption redshift is available for only one likely short GRB(Levesque et al. 2010).We end with several important observations. First, rapid op-tical follow-up of short GRBs with 8-meter class telescopes isessential since observations to a depth of about 25 mag withina few hours after the burst may recover nearly all optical after-glows, regardless of circumburst density (Figure 9). Second,short GRBs with only X-ray positions are unlikely to providestrong support for either negligible or large offsets due to theappreciable size of the error circles and the fact that the sam-ple with optical afterglows exhibits wide host galaxy diversity,i.e., events with coincident bright hosts at z ∼ . -
1, eventswith coincident faint hosts likely at z &
1, and events withno coincident hosts likely due to offsets. Third, a meaningfulstudy of short GRB offsets requires a statistical approach tomitigate the shortcomings of a posteriori chance coincidenceprobabilities, as well as to incorporate the relevant informa-tion from afterglow and prompt emission observations.Finally, we note that from a wide range of observations ofboth the afterglows and host galaxies it appears that the casefor NS-NS mergers as the progenitors of short GRBs is gain-ing observational support. Our main result here is that shortGRBs with optical afterglows and no detected host galaxiesare somewhat less likely to be explained with high redshifts orwith dwarf galaxy hosts at low redshift. Instead, these burstslikely exploded ∼
15 kpc from galaxies at z ∼ z ∼ .
3. With larger samples, these possibil-ities will allow us to improve our understanding of the shortGRB redshift distribution, the host galaxy demographics, andpredictions for gravitational wave detections. If high redshiftsindeed turn out to be prevalent, this will have a significanteffect on the possibility of multiple progenitor populations.We acknowledge helpful discussions with Alicia Soder-berg, Ryan Chornock, and Josh Grindlay. This work waspartially supported by Swift AO5 grant number 5080010, andmade use of data supplied by the UK Swift Science Data Cen-tre at the University of Leicester.
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ROPERTIES OF S HORT
GRB
S WITH O PTICAL A FTERGLOWS OR L IMITS
GRB T z a F γ b t X F X c t opt F ν , opt Refs.(s) (erg cm - ) (hr) (erg cm - s - ) (hr) ( µ Jy)
Short GRBs with Optical Detections (
Samples 1 & ) . × - . × -
34 2.3 1–3050724 3.0 0.257 3 . × - . × -
12 8.4 4–6051221A 1.4 0.546 1 . × - . × - < . . × - . × - < . × - . × - . × - . × - d < .
7, 0.111? 3 . × - . × - < . . × - . × -
11 1.9 16070714B 3.0 0.923 7 . × - . × - . × - . × - d <
3, 0.473? 1 . × - . × -
11 0.8 20–21071227 1.8 0.381 2 . × - . × - d < · · · . × - < . × - . × - < . × - d < . · · · . × - < . × - . × - . × - . × - . × - d < .
3, 0.403? 2 . × - < . × - · · · . × - . × - . × - < . × - Short GRBs with Optical Limits (
Sample 3 ) . × - < . × - · · · . × - < . × - · · · . × - < . × - · · · . × - < . × - . × - < . × - . × - < . × - . × - < . × - . × - < . × - · · · . × - . × - · · · . × - < . × - · · · . × - < . × - · · · . × - < . × - N OTE . — Prompt emission and afterglow data for short GRBs with detected optical afterglows (top section) anddeep optical afterglow limits (bottom section). a Redshifts include spectroscopic measurements, limits from afterglow detections in the UV/optical, and for thebursts in
Sample 2 , redshifts for galaxies with the lowest probability of chance coincidence (marked by ?). b The fluences are in the observed 15 -
150 keV band, with the exception of GRB 050709 (2 -
400 keV) andGRB 060121 (2 -
400 keV). c All XRT data are from Evans et al. (2007) and Evans et al. (2009). d Short GRBs in
Sample 2 .References: [1] Villasenor et al. (2005); [2] Fox et al. (2005); [3] Hjorth et al. (2005); [4] Barthelmy et al.(2005); [5] Berger et al. (2005); [6] Grupe et al. (2006); [7] Burrows et al. (2006); [8] Soderberg et al. (2006);[9] de Ugarte Postigo et al. (2006); [10] Levan et al. (2006a); [11] Berger et al. (2007); [12] Roming et al. (2006);[13] D’Avanzo et al. (2009); [14] Stratta et al. (2007); [15] Fong et al. (2010); [16] Piranomonte et al. (2008);[17] Graham et al. (2009); [18] Berger et al. (2009); [19] Kocevski et al. (2010); [20] Perley et al. (2007);[21] Perley et al. (2008); [22] Perley et al. (2009); [23] Rowlinson et al. (2010); [24] Cenko et al. (2009); [25]Berger & Kelson (2009); [26] Antonelli et al. (2009); [27] Levesque et al. (2010); [28] McBreen et al. (2010);[29] Rowlinson et al. (2010); [30] Malesani et al. (2009); [31] Fong et al. in prep.; [32] Gehrels et al. (2005);[33] Bloom et al. (2006); [34] Ferrero et al. (2007); [35] Berger (2006b); [36] Prochaska et al. (2006); [37]La Parola et al. (2006); [38] Bloom et al. (2007); [39] Cenko et al. (2008); [40] de Ugarte Postigo et al. (2008);[41] Greco et al. (2008); [42] Berger et al. (2008); [43] Berger et al. (2010) TABLE 2O
BSERVATIONS OF S HORT
GRB
S WITH O PTICAL A FTERGLOWS AND NO C OINCIDENT H OST G ALAXIES ( Sample 2 )GRB Instrument Filter t exp m lim a (s) (AB mag)061201 HST/ACS F814W 2224 26.0070809 Magellan/LDSS3 r r r N OTE . — a Limits are 3 σ . F IG . 1.— HST /ACS/F814W image of the location of GRB 061201. Galaxies near the position of the optical afterglow (cross-hairs) are marked. F IG . 2.— Magellan/LDSS3 r -band images of the location of GRB 070809. Galaxies near the position of the optical afterglow (cross-hairs) are marked. F IG . 3.— HST /WFPC2/F606W image of the location of GRB 080503. Galaxies near the position of the optical afterglow (cross-hairs) are marked. A faintgalaxy at a separation of only 0 . ′′ was found by Perley et al. (2009) based on a deeper stack of HST/WFPC2 observations. These authors also find that thegalaxy marked “S5” is located at z = 0 . F IG . 4.— Magellan/LDSS3 r -band images of the location of GRB 090305. Galaxies near the position of the optical afterglow (cross-hairs) are marked. F IG . 5.— Gemini-North/GMOS r -band images of the location of GRB 090515. Galaxies near the position of the optical afterglow (cross-hairs) are marked.Note that the object coincident with the cross-hairs is the optical afterglow. GRB 061201z = 0.111
Wavelength (Ang) F l u x ( − e r g / c m / s / A ng ) [OIII]H b H a [NII][SII] F IG . 6.— Magellan/LDSS3 spectrum of the galaxy with the lowest probability of chance coincidence near the position of GRB 061201. This galaxy is marked“S4” in Figure 1. It has a redshift of z = 0 .
111 and it is undergoing active star formation (Berger 2006a; Stratta et al. 2007; Fong et al. 2010). GRB 070809z = 0.473
Wavelength (Ang) F l u x ( − e r g / c m / s / A ng ) CaII H&K[OII] G band Na I [OII] F IG . 7.— Magellan/LDSS3 spectrum of the galaxy with the lowest probability of chance coincidence near the position of GRB 070809. This galaxy is marked“S3” in Figure 2. It has a redshift of z = 0 .
473 and is an early-type galaxy with no evidence for on-going star formation activity (see inset). [OII] S1: z = 0.626 C oun t s CaII H&K G band
S5: z = 0.403 [OII]
GRB 090515
S6: z = 0.657 F IG . 8.— Magellan/LDSS3 spectra of three galaxies with a low probability of chance coincidence near the position of GRB 090515. The galaxy with the lowestprobability of chance coincidence is marked “S5” in Figure 5. It has a redshift of z = 0 .
403 and is an early-type galaxy which is part of a galaxy cluster (Fong etal. in prep.) Sample 1Sample 2Sample 3 t −1/2 t −1 O p t i c a l AB M agn i t ude Time after the burst (hrs) 0 2 4 6 8 10Number F IG . 9.— Optical afterglow brightness on timescales of a few hours after the burst for short GRBs with detected afterglows ( Sample 1 : black squares;
Sample2 : red squares) or upper limits (gray triangles). The lines at the top right indicate the fading tracks for afterglow decay rates of α = - . -
1. The right panelshows the projected histogram for the bursts with detected afterglows (hatched) and upper limits (open). The symbols mark the mean for each sample, and thevertical bar marks the standard deviation for
Sample 1 .
28 27 26 25 24 23 22 2100.10.20.30.40.50.60.70.80.91
Sample 1Sample 2 (KS=0.08)
Sample 3 (KS=0.05)
Optical AB Magnitude at t=8 hr C u m u l a t i v e F r a c t i on F IG . 10.— Cumulative afterglow brightness distributions for the bursts in Figure 9, extrapolated to a common fiducial time of 8 hr after the burst with a fadingrate of α = - .
75. The K-S probabilities relative to the sample with detected afterglows and coincident hosts are noted in the figure. It appears unlikely that thebursts with no coincident hosts, and those with deep upper limits, are drawn from the same distribution as the bursts with detected hosts. −8.5 −8 −7.5 −7 −6.5 −6 −5.5 −502468 Sample 1Sample 2Sample 3 N u m be r log [F g ] (erg/cm )−14.5 −14 −13.5 −13 −12.5 −12 −11.5 −110246 N u m be r log [F X,8 ] (erg/s/cm )−1.5 −1 −0.5 0 0.50246 N u m be r log [T ] (s) F IG . 11.— Histograms of γ -ray fluence (top), afterglow X-ray flux at 8 hr (middle), and duration (bottom) for the three short GRB samples discussed in thispaper. The arrows mark the mean for each sample, indicating that the bursts in Sample 2 and
Sample 3 have lower γ -ray fluences, fainter X-ray fluxes, and shorterdurations, than the bursts with detected afterglows and coincident hosts. −1 −8 −7 −6 −5 −4 Sample 1Sample 2Sample 3 T (s) F g ( e r g / c m ) F IG . 12.— Short GRB γ -ray fluence as a function of duration for the three samples discussed in this paper. An overall correlation is apparent in the data. Thebursts in Sample 2 and
Sample 3 appear to lie below the mean correlation for the bursts in
Sample 1 , i.e., they have lower fluences for their durations, or longerdurations for their fluences.
26 25 24 23 22 2110 −14 −13 −12 Short: b OX = −0.72 – b OX = −0.65 – Optical AB Magnitude F X ( e r g c m − s − ) F IG . 13.— X-ray versus optical flux for the bursts from Figure 9. The cross-hatched region marks the median and standard deviation assuming the expectedpower-law correlation with an index β OX . The light shaded region marks the region occupied by long GRBs (Jakobsson et al. 2004). The distributions for longand short GRBs are largely indistinguishable, as are the distributions for short GRBs with an without coincident hosts. We note that a large fraction of the burstswith optical upper limits also have undetected X-ray afterglows on timescales of a few hours after the burst. The overall similarity between the ratio of optical toX-ray flux for long and short GRBs does not allow us to clearly locate the synchrotron cooling frequency ( ν c ) in relation to the X-ray band. If ν c > nu X for shortGRBs, the faintness of the optical afterglows for bursts with no coincident hosts cannot be used to distinguish density and redshift effects. −2 −1 −2 −1 P r obab ili t y , P ( < d R ) −2 −1 d R = Distance from GRB (arcsec) F IG . 14.— Probability of chance coincidence as a function of distance from a short GRB optical afterglow position for galaxies near the location of each burst.These are the galaxies marked in Figures 1-5. In each panel we mark the galaxy with the lowest probability of chance detection with a circle. In 4 of the 5 cases,the lowest probability is associated with galaxies that are offset by ∼ - ′′ . Moreover, even the nearest galaxies are offset by ≈ . - . ′′ . −2 −1 d R = Distance from GRB (arcsec) P r obab ili t y , P ( < d R ) −2 −1 F IG . 15.— Same as Figure 14, but for short GRBs with coincident faint hosts. In this case, the lowest probability of chance coincidence is associated with theunderlying faint host. Sample 1Sample 2 (limits)
Sample 2 (offsets)Long GRBs0.1−1 · L* Redshift H o s t R − band M agn i t ude N u m be r F IG . 16.— Host galaxy optical magnitude as a function of redshift for short GRB hosts (black squares), long GRB hosts (gray circles), and galaxies with aluminosity of 0 . - ∗ (shaded region). The dashed lines mark the upper limits at the GRB positions for the short GRBs with no coincident hosts. The arrowsmark the upper limits on the redshifts of three bursts with faint hosts, based on the detection of the afterglows in the optical band (i.e., lack of a strong Lymanbreak). If underlying host galaxies exist for Sample 2 , their non-detection indicates z & . . ∗ ) or & ∗ ). The alternative possibility that they arelocated at similar redshifts to the detected hosts, requires . .
01 L ∗ , but this does not naturally explain their fainter afterglows. −1 −0.5 0 0.5 1 1.500.511.522.533.54 Sample 1Sample 2 ( z ~ Sample 2 ( z ~ log [ d R] (arcsec) N u m be r F IG . 17.— Histogram of projected angular offsets relative to the host galaxy center for short GRBs with coincident hosts (hatched black), and bursts with nocoincident hosts if the galaxies with lowest chance coincidence probability are the hosts (hatched red), or if the faint galaxies with smallest angular separation arehosts (open red); see Figure 14. The dashed line is a log-normal fit to the bursts with coincident hosts. −0.5 0 0.5 1012345 Sample 1Sample 2 ( z ~ Sample 2 ( z ~ N u m be r log [ d R / R e ] F IG . 18.— Same as Figure 17 but normalized relative to the host effective radii, R e . The dashed line is a log-normal fit to the bursts with coincident hosts. −0.5 0 0.5 1 1.5 200.511.522.533.54 Sample 1Sample 2 ( z ~ Sample 2 ( z ~ log [ d R] (kpc) N u m be r F IG . 19.— Same as Figure 17 but projected physical offsets in units of kpc. The dashed line is a log-normal fit to the bursts with coincident hosts. Sample 1Sample 1+2 ( z ~ Sample 1+2 ( z ~ Sample 2 ( z ~ NS−NS: Bloom et al. 1999NS−NS: Fryer et al. 1999NS−NS: Belczynski et al. 2006GCs: Salvaterra et al. 2010 d R (kpc) C u m u l a t i v e F r a c t i on F IG . 20.— Cumulative distributions of projected physical offsets for short GRBs with coincident hosts (black line), and combined with offsets for the hostswith the lowest probabilities of chance coincidence (thick red line) or the faint hosts with smallest angular offsets (thin red line). Also shown are predicteddistributions for NS-NS kicks from several models (Bloom et al. 1999; Fryer et al. 1999; Belczynski et al. 2006), and for dynamically-formed NS-NS binariesfrom globular clusters (shaded region marks a range of predictions for host galaxy masses of 5 × - M ⊙ ; Salvaterra et al. 2010). The models with kickvelocities are in good agreement with the measured offset distribution for either set of galaxy associations, while the globular clusters model provides a poormatch to the data. Sample 1Sample 2 ( z ~ Sample 2 ( z = 1) Sample 2 ( z = 3) Redshift E g , i s o ( e r g ) F IG . 21.— Isotropic-equivalent γ -ray energy as a function of redshift for the bursts with detected optical afterglows. We plot the inferred energies for Sample2 at the redshifts corresponding to the galaxies with the lowest probability of chance coincidence (red squares); at z ∼ z ∼ ∗ (thinopen squares). The bursts in Sample 2 match the distribution for the