Afterglow Observations of Fermi-LAT Gamma-Ray Bursts and the Emerging Class of Hyper-Energetic Events
S. B. Cenko, D. A. Frail, F. A. Harrison, J. B. Haislip, D. E. Reichart, N. R. Butler, B. E. Cobb, A. Cucchiara, E. Berger, J. S. Bloom, P. Chandra, D. B. Fox, D. A. Perley, J. X. Prochaska, A. V. Filippenko, K. Glazebrook, K. M. Ivarsen, M. M. Kasliwal, S. R. Kulkarni, A. P. LaCluyze, S. Lopez, A. N. Morgan, M. Pettini, V. R. Rana
aa r X i v : . [ a s t r o - ph . H E ] A p r Submitted to ApJ
Preprint typeset using L A TEX style emulateapj v. 2/16/10
AFTERGLOW OBSERVATIONS OF
Fermi -LAT GAMMA-RAY BURSTS AND THE EMERGING CLASS OFHYPER-ENERGETIC EVENTS
S. B. Cenko , D. A. Frail , F. A. Harrison , J. B. Haislip , D. E. Reichart , N. R. Butler , B. E. Cobb ,A. Cucchiara , E. Berger , J. S. Bloom , P. Chandra , D. B. Fox , D. A. Perley , J. X. Prochaska ,A. V. Filippenko , K. Glazebrook , K. M. Ivarsen , M. M. Kasliwal , S. R. Kulkarni , A. P. LaCluyze S. Lopez , A. N. Morgan , M. Pettini , and V. R. Rana Submitted to ApJ
ABSTRACTWe present broadband (radio, optical, and X-ray) light curves and spectra of the afterglows offour long-duration gamma-ray bursts (GRBs 090323, 090328, 090902B, and 090926A) detected bythe Gamma-Ray Burst Monitor (GBM) and Large Area Telescope (LAT) instruments on the
Fermi satellite. With its wide spectral bandpass, extending to GeV energies,
Fermi is sensitive to GRBs withvery large isotropic energy releases (10 erg). Although rare, these events are particularly importantfor testing GRB central-engine models. When combined with spectroscopic redshifts, our afterglowdata for these four events are able to constrain jet collimation angles, the density structure of thecircumburst medium, and both the true radiated energy release and the kinetic energy of the outflows.In agreement with our earlier work, we find that the relativistic energy budget of at least one of theseevents (GRB 090926A) exceeds the canonical value of 10 erg by an order of magnitude. Such energiespose a severe challenge for models in which the GRB is powered by a magnetar or neutrino-drivencollapsar, but remain compatible with theoretical expectations for magneto-hydrodynamical collapsarmodels (e.g., the Blandford-Znajek mechanism). Our jet opening angles ( θ ) are similar to those foundfor pre- Fermi
GRBs, but the large initial Lorentz factors (Γ ) inferred from the detection of GeVphotons imply θ Γ ≈ Fermi -LAT events preferentially occur in a low-densitycircumburst environment, and we speculate that this might result from the lower mass-loss rates oftheir lower-metallicity progenitor stars. Future studies of
Fermi -LAT afterglows in the radio withthe order-of-magnitude improvement in sensitivity offered by the Extended Very Large Array shoulddefinitively establish the relativistic energy budgets of these events.
Subject headings: cosmology: observations - gamma rays: bursts - radio continuum: general INTRODUCTION Department of Astronomy, University of California, Berke-ley, CA 94720-3411, USA. National Radio Astronomy Observatory, 1003 LopezvilleRoad, Socorro, NM 87801, USA. Space Radiation Laboratory, California Institute of Technol-ogy, MS 105-24, Pasadena, CA 91125, USA. Department of Physics and Astronomy, University of NorthCarolina, Chapel Hill, NC 27599, USA. Einstein Fellow. Department of Astronomy and Astrophysics, PennsylvaniaState University, 525 Davey Laboratory, University Park, PA16802, USA. Harvard-Smithsonian Center for Astrophysics, 60 GardenStreet, Cambridge, MA 02138, USA. Department of Physics, Royal Military College of Canada,Kingston, ON, Canada. Department of Astronomy and Astrophysics, UCO/Lick Ob-servatory, University of California, 1156 High Street, Santa Cruz,CA 95064, USA. Centre for Astrophysics and Supercomputing, SwinburneUniversity of Technology, 1 Alfred St, Hawthorn, Victoria 3122,Australia. Department of Astronomy, California Institute of Technol-ogy, MS 105-24, Pasadena, CA 91125, USA. Departamento de Astronom´ıa, Universidad de Chile, Casilla36-D, Santiago, Chile. Institute of Astronomy, Madingley Road, Cambridge CB30HA, UK. International Center for Radio Astronomy Research, Uni-versity of Western Australia, 35 Stirling Hwy, Crawley, WA 6009,Australia.
Long-duration gamma-ray bursts (GRBs ), likehydrogen-deficient Type Ib/c supernovae (SNe Ib/c), re-sult from the gravitational collapse of the evolved core ofa massive star. The main characteristic that sets GRBsapart from other SNe is that a substantial fraction of theenergy of the explosion is coupled to relativistic ejecta.A compact central engine is responsible for acceleratingand collimating these jet-like outflows and driving the SNexplosions (Woosley & Bloom 2006; Gehrels et al. 2009;Soderberg et al. 2010). The precise nature of the cen-tral engine which powers GRB-SNe, however, remainsan open question.Motivated by empirical constraints, all viable central-engine models for long-duration GRBs share some com-mon characteristics (e.g., Piran 2005). They must pro-duce a collimated outflow with an initial Lorentz factor(Γ ) of a few hundred on observed time scales of 10–100 s,with luminosities and kinetic energies of order 10 ergs − and 10 erg, respectively. Leading models includethe “collapsar” model in which a relativistic jet is pro-duced from a rotating black hole/accretion disk system(Woosley 1993; MacFadyen & Woosley 1999), and the“magnetar” model in which the rapid energy loss from anewly born millisecond neutron star (formed either from Throughout this work, we shall refer exclusively to long-duration GRBs (i.e., those apparently with massive-star progen-itors) unless explicitly stated otherwise.
Cenko et al.the gravitational collapse of a massive star or from ac-creting or coalescing white dwarfs) with a 10 G mag-netic field drives a Poynting flux-dominated relativisticoutflow (Usov 1992).These and other more exotic models for GRB cen-tral engines are highly constrained by their energet-ics. The prompt high-energy emission, when com-bined with a spectroscopically determined redshift (andhence distance measurement), yields the isotropic ra-diated gamma-ray energy ( E γ, iso ). Well-sampled af-terglow observations allow both a measurement of thedegree of collimation (and hence the true beaming-corrected energy release in the prompt emission, E γ )and the kinetic energy remaining in the shock thatpowers the broadband afterglow emission ( E KE ). Suchmeasurements, made nearly a decade ago, pointed toa total relativistic energy yield ( E rel ≈ E γ + E KE )of ∼ erg (Frail et al. 2001; Panaitescu & Kumar2001a; Freedman & Waxman 2001; Bloom et al. 2003;Berger et al. 2003a).Since that time, there has been growing evidence fora considerable range in the relativistic energy scale E rel ,suggesting either a diversity in central engines or theirproperties. Most notably, a population of nearby (red-shift z . .
1) subenergetic long-duration GRBs havebeen identified (Bloom et al. 2003; Soderberg et al. 2004,2006). They too are associated with SNe Ib/c, but theirrelativistic energy release is a factor of 100 less than thatof typical cosmological GRBs and their outflows are sig-nificantly less collimated (quasi-spherical). Since theycan only be detected at low redshifts where the com-parative volume for discovery is low, they are small intotal number. But their volumetric rate is inferred to be10–100 times larger than that of the more distant long-duration GRBs (Soderberg et al. 2006; Cobb et al. 2006;Liang et al. 2007).More recently, evidence has been growing for a class ofGRBs whose total relativistic energy release is at least anorder of magnitude above the canonical value of 10 erg(e.g., Cenko et al. 2010 and references therein). Unlikesubluminous events, the total energy budget of thesehyper-energetic events poses a significant challenge forsome progenitor models. In particular, models in whichthe GRB is powered by a magnetar or a neutrino-drivencollapsar are strongly disfavored. On the other hand,collapsars driven by magneto-hydrodynamical (MHD)processes, such as the Blandford-Znajek mechanism(Blandford & Znajek 1977), can naturally accomodateenergy budgets as large as 10 erg.Unfortunately, it has been rather difficult to con-strain the beaming-corrected energetics for the hundredsof GRBs detected by the Swift satellite (Gehrels et al.2004). The reasons for this difficulty are nowlargely understood. First, the relatively narrow en-ergy bandpass (15–150 keV) can miss entirely thepeak of the gamma-ray spectrum, making estimatesof E γ, iso highly uncertain. Second, there has beena dearth of measurements of jet opening angles (e.g.,Panaitescu 2007; Kocevski & Butler 2008; Liang et al.2008; Racusin et al. 2009) and well-sampled multi-wavelength GRB afterglows (used to derived the after-glow kinetic energy E KE ). Swift
GRBs are on averagemore than twice as distant (Jakobsson et al. 2006) and Redshift E γ ( i s o ) [ e r g ] Pre−SwiftSwiftFermi−LAT
Sun c Fig. 1.—
Prompt isotropic gamma-ray energy release ( E γ, iso ) ofGRBs. With its soft, narrow bandpass (15–150 keV), Swift typi-cally selects events with smaller isotropic energy release but largeropening angles than previous missions, which triggered predomi-nantly in the MeV bandpass (Perna et al. 2003). GRBs detectedat GeV energies with the
Fermi -LAT all fall at the brightest endof the isotropic energy distribution, and must therefore be highlycollimated to achieve a canonical beaming-corrected energy re-lease of ∼ erg. References: pre- Swift : Amati (2006);
Swift :Butler et al. (2007);
Fermi -LAT: Greiner et al. (2009), this work. therefore significantly fainter ( ∼ . Swift has preferentially selected the faint end of the lu-minosity function — GRBs with low isotropic energy re-lease but large opening angles (Perna et al. 2003).With its nearly seven decades in energy coverage(10 keV – 100 GeV),
Fermi can provide unparalleled con-straints on this subsample of the most luminous events.In light of the empirical relation between the peakenergy of the gamma-ray spectrum and the isotropicgamma-ray energy release (the E p – E γ, iso , or “Amati”relation; Amati 2006), MeV/GeV events detected byeither the Gamma-Ray Burst Monitor (GBM, 8 keV –40 MeV; Meegan et al. 2009) or the Large Area Telescope(LAT, 20 MeV – 300 GeV; Atwood et al. 2009) onboard Fermi preferentially select a sample of GRBs with largeisotropic energy release (Figure 1). High- E γ, iso eventsalso have brighter X-ray and optical afterglows on aver-age (Nysewander et al. 2009). Follow-up afterglow ob-servations can then determine whether these GRBs arehighly beamed events ( θ . ◦ ) with a typical energy re-lease or true hyper-energetic GRBs.The Fermi -LAT offers a further advantage over previ-ous GRB missions sensitive only at MeV and keV ener-gies by providing strict constraints on the initial Lorentzfactor of the relativistic outflow. To avoid e + − e − pair production (and the accompanying thermal spec-trum), the GRB jet must be moving towards the ob-server with ultra-relativistic speeds (the “compactness”problem; Cavallo & Rees 1978). The higher the energyof the most energetic photon detected from a GRB, themore strict the lower limit on the outflow Lorentz fac-tor will be. Combining the Lorentz factor limits for themost relativistic GRBs with inferred jet opening anglesfrom broadband afterglow models can provide critical di-agnostics of the jet acceleration mechanism.Here we report on broadband (radio, optical, andfterglow Observations of Fermi -LAT GRBs 3
Time Since Burst (d) F l u x D en s i t y ( µ Jy ) −4 −3 −2 −1 X−ray (1 keV)Optical (R/r’)Radio (8 GHz)
Fig. 2.—
The broadband radio (blue), optical (red), and X-ray (black) light curve of GRB 090323. The best-fit model is plotted in solidlines (see Table 4 for parameters). The identical model parameters for an isotropic explosion are plotted as the dashed lines. The strengthof the possible modulation of the radio afterglow caused by interstellar scintillation (e.g., Frail et al. 2000a) is indicated by the light-blueshaded region. The model provides a reasonable fit in all bandpasses. It is clear that any jet break must occur at t >
10 days, althoughthe upper bound on the jet break time is only weakly constrained.
X-ray) observations of four long-duration GRBs de-tected by the
Fermi -LAT at GeV energies: GRBs 090323,090328, 090902B, and 090926A. For each event we con-struct afterglow models to constrain the collimationand beaming-corrected energetics, and we compare theseLAT events with previous GRBs detected at other en-ergies (i.e., keV energies from
Swift , and MeV energiesfrom pre-
Swift satellites). For three of these GRBs, wealso present the optical spectra used to determine the af-terglow redshift. A more thorough analysis of the host-galaxy properties of these events will be presented in aforthcoming work.Throughout this paper, we adopt a standard ΛCDMcosmology with H = 71 km s − Mpc − , Ω m = 0 .
27, andΩ Λ = 1 − Ω m = 0 .
73 (Spergel et al. 2007). We definethe flux-density power-law temporal and spectral decayindices α and β as f ν ∝ t − α ν − β (e.g., Sari et al. 1998).All quoted uncertainties are 1 σ (68%) confidence inter-vals unless otherwise noted. OBSERVATIONS
GRB 090323
High-Energy Properties
GRB 090323 was detected by the
Fermi
GBM at00:02:42.63 on 23 March 2009 (Ohno et al. 2009; UTdates are used throughout this work). In the 8 keV to40 MeV bandpass of the GBM, the light curve was mul-tipeaked with a duration of t ≈
150 s. GRB 090323was also detected at MeV energies by several of thesatellites comprising the Inter-Planetary Network (IPN;Hurley et al. 1999), including the Konus instrument on It is customary to report GRB durations measured as the timebetween the arrival of 5% and 95% of the background-subtractedfluence. This quantity is referred to as t . the Wind satellite (Hurley et al. 2009; Golenetskii et al.2009c).Examining only the first 70 s of GBM data ,van der Horst & Xin (2009) find that the prompt spec-trum is well described by a power law having an expo-nential cutoff at high energies with α = − . ± .
03 and E p = 697 ±
51 keV. The resulting fluence in the 8–10 keV(observer frame) bandpass is f γ = (1 . ± . × − ergcm − . The Konus- Wind instrument was able to mea-sure the high-energy spectrum over the entire durationof the MeV emission. Fitting a Band model (Band et al.1993) to their spectrum, Golenetskii et al. (2009c) finda reasonable fit with α = − . +0 . − . , β = − . +0 . − . , E p = 416 +76 − keV, and f γ = 2 . +0 . − . × − erg cm − (20–10 keV observer-frame bandpass).In order to facilitate direct comparisons betweenevents, we must transform this high-energy fluence toa common (rest-frame) bandpass (i.e., a “k”-correction;Bloom et al. 2001). Here we adopt the rest-frame 1–10 keV bandpass, as this encompasses the full range ofpeak energies observed from GRBs (Band et al. 1993)without (for most pre- Fermi satellites) requiring largeextrapolations outside the observed bandpass. At z =3 .
568 ( § Wind measurement corre-sponds to a prompt fluence of f γ = (1 . ± . × − erg cm − in the 1–10 keV rest-frame bandpass.Given the limited temporal coverage of the GBM spec-trum, we shall adopt this value for the prompt fluence ofGRB 090323 for the remainder of this work.In addition to the detection at MeV energies by theGBM, GRB 090323 was also detected at GeV energies After this point, the
Fermi spacecraft slewed to position theGRB at the center of the LAT field of view, causing rapid changesin the GBM background level.
Cenko et al. −17
Observed Wavelength (A) F λ ( e r g c m − s − A − ) M g II M g II A l II C I V C I V S i II * S i II C I V C I V S i I V S i I V F e II F e II F e II C II * N i II S i II * S i II O I S i II * S i II N V N V L y α L y β A l III A l III C II z = 3.568z = 3.379z = 2.101 Fig. 3.—
GMOS-S optical spectrum of the afterglow of GRB 090323. The broad absorption feature at λ ≈ α in the GRB host galaxy. We identify a number of strong, narrow absorption features redward of Ly α from the GRB host galaxy at acommon redshift of 3 . ± .
004 (black annotations). The emission blueward of Ly α is strongly affected by the Ly α forest. We identifytwo additional intervening absorbers, based on Mg II λλ z = 2 . IV λλ z = 3 . λ = 9000 ˚A. by the Fermi
LAT. Like several previous GRBs observedat GeV energies (e.g., Hurley et al. 1994; Gonz´alez et al.2003; Giuliani et al. 2008; Abdo et al. 2009b), the GeVemission began several seconds after the MeV emissionis detected, and remains significant long ( ∼ E ≈ . t measurement had an energy of E ≈
500 keV (at t ≈
90 s; Piron et al. 2009).
Afterglow Observations
The
Swift satellite began observations of the field ofGRB 090323 with the onboard X-ray Telescope (XRT;Burrows et al. 2005b) at 19:27 on 23 March 2009 ( ∼ . α =12 h m . s δ = +17 ◦ ′ . ′′
2, with a 90% contain-ment radius of 2 . ′′ ; the re-sulting evolution is plotted in Figure 2.The optical afterglow of GRB 090323 was discoveredshortly thereafter by GROND (Updike et al. 2009b).The optical/NIR spectral energy distribution, con-structed from simultaneous imaging in the g ′ r ′ i ′ z ′ JHK http://astro.berkeley.edu/ ∼ nat/swift ; seeButler & Kocevski (2007) for details. filters, implied a spectral steepening around the observed g ′ band. Associating this break with absorption fromLy α in the GRB host galaxy, Updike et al. (2009b) de-rive a photometric redshift of 4 . ± . r ′ and i ′ filters and individual frames were au-tomatically reduced using our custom IRAF softwarepipeline. To increase the signal-to-noise ratio (S/N), in-dividual frames were astrometrically aligned using theScamp software package and coadded using Swarp . Weused aperture photometry to extract the flux of the af-terglow from these coadded frames with the aperture ra-dius roughly matched to the full width at half-maximumintensity (FWHM) of the point-spread function (PSF).Aperture magnitudes were then calibrated relative tofield sources from the Sloan Digital Sky Survey DataRelease 7 (Abazajian et al. 2009). Imaging continued onsubsequent nights with P60 until the afterglow was belowour detection threshold. The results of this monitoringcampaign, uncorrected for foreground Galactic extinc-tion ( E [ B − V ] = 0 .
025 mag; Schlegel et al. 1998), arepresented in Table 9.We obtained additional imaging of the field ofGRB 090323 with the two Gemini Multi-Object Spectro-graphs (GMOS-N and GMOS-S; Hook et al. 2004). Im-ages were taken at both Gemini North and Gemini Southin the Sloan r ′ and i ′ filters, and they were reduced using IRAF is distributed by the National Optical Astronomy Ob-servatory, which is operated by the Association for Research inAstronomy, Inc., under cooperative agreement with the NationalScience Foundation. See http://astromatic.iap.fr . fterglow Observations of Fermi -LAT GRBs 5
TABLE 1Radio Observations of GRB 090323
Date ∆ t ν f ν Facility(UT) (days) (GHz) ( µ Jy)Mar 26.38 3.38 8.46 27 ±
38 VLAMar 27.38 4.38 8.46 225 ±
35 VLAMar 27.99 4.99 4.9 105 ±
24 WSRT a Mar 28.43 5.43 8.46 100 ±
40 VLAMar 29.16 6.16 8.46 157 ±
31 VLAMar 30.18 7.18 8.46 219 ±
39 VLAMar 31.32 8.32 8.46 281 ±
38 VLAApr 1.30 9.30 8.46 164 ±
35 VLAApr 3.29 11.29 8.46 166 ±
27 VLAApr 3.28 11.28 4.86 110 ±
45 VLAApr 4.41 12.41 8.46 183 ±
35 VLAApr 5.14 13.14 8.46 123 ±
29 VLAApr 6.28 14.28 8.46 312 ±
27 VLAApr 7.42 15.42 8.46 43 ±
27 VLAApr 9.44 17.44 8.46 127 ±
30 VLAApr 10.42 18.42 8.46 295 ±
27 VLAApr 14.09 22.09 8.46 178 ±
56 VLAApr 17.04 25.04 8.46 167 ±
33 VLAApr 25.46 33.46 8.46 78 ±
32 VLAMay 3.41 41.41 8.46 77 ±
31 VLAMay 11.35 49.35 8.46 61 ±
29 VLAAug 1.18 131.18 8.46 − ±
27 VLA a Reference: van der Horst (2009). the IRAF gemini package. Photometry was performedwith the same methodology used for the P60 imaging ofthe field, and the resulting measurements are shown inTable 9.Additionally, we have compiled optical and NIR mea-surements of the afterglow of GRB 090323 from theGCN Circulars and included these in Table 9. Themajority of the late-time measurements (of most inter-est to us for modeling purposes) were obtained in the R band. We note that most of these measurements werecalibrated with respect to a single object (1070-0238439)from the USNO-B1 catalog (Monet et al. 2003), follow-ing Kann et al. (2009b). Using the SDSS observationsof this field and the filter transformations of Jordi et al.(2006), we find an R -band magnitude for this sourceof R = 17 .
31 mag (compared to an assumed value of17.15 mag from Kann et al. 2009b). We therefore offsetall reported R -band magnitudes from the GCN Circularsby +0 .
16 mag.Finally, we observed the afterglow of GRB 090323 withthe Very Large Array (VLA) beginning a few days af-ter the initial burst trigger. The flux-density scale wastied to 3C 286 or 3C 147 and the phase was measured byswitching between the GRB and a nearby bright point-source calibrator. To maximize sensitivity, the full VLAcontinuum bandwidth (100 MHz) was recorded in two50 MHz bands. Data reduction was carried out followingstandard practice in the AIPS software package.Our initial VLA detection of GRB 090323 was reportedby Harrison et al. (2009). GRB 090323 was also detectedat radio wavelengths by the Westerbork Synthesis RadioTelescope (WSRT; van der Horst 2009). The full set ofVLA measurements is listed in Table 1. In order to im-prove the S/N and to reduce the modulation of the light See http://gcn.gsfc.nasa.gov/gcn3 archive.html. The Very Large Array is operated by the National Radio As-tronomy Observatory, a facility of the National Science Foundationoperated under cooperative agreement by Associated Universities,Inc. curve caused by interstellar scintillation (e.g., Frail et al.2000a), we binned the data from adjacent epochs. Thesebinned points were used for our afterglow modeling ( § Optical Spectroscopy
We began spectroscopic observations of the optical af-terglow of GRB 090323 with GMOS-S on 24 March 2009( ∼ .
93 hours after the GBM trigger; Chornock et al.2009). We first obtained 2 ×
600 s spectra with the B600grating and a central wavelength of 6000 ˚A, providingcoverage over the range ∼ ×
600 s spectra with the R400 grating anda central wavelength of 8000 ˚A, providing coverage of ∼ gemini and specred packages(see, e.g., Cenko et al. 2008 and references therein for de-tails). Wavelength calibration was performed relative toCuAr lamps and then adjusted based on measured night-sky emission lines. The resulting root-mean square wave-length uncertainty was . .
25 ˚A for the spectra with theB600 grating and . .
40 ˚A for the spectra taken with theR400 grating. Telluric features were removed using thecontinuum from well-exposed spectrophotometric stan-dard stars (e.g., Wade & Horne 1988; Matheson et al.2000).Flux calibration was performed relative tothe spectrophotometric standard star LTT 7379(Stone & Baldwin 1983; Baldwin & Stone 1984).We caution, however, that the standard-star observa-tions were conducted on different nights from the GRBobservations (31 August 2009 for the B600 grating; 4August 2009 for the R400 grating), so the absoluteflux calibration is somewhat uncertain (estimated to be ∼ λ ≈ α at z ≈ .
6. The spectrumblueward of this wavelength is dominated by absorptionfrom the Ly α forest, while the lack of Ly α forest featuresredward of this transition indicates that it correspondsto the redshift of the GRB host galaxy. Unfortunately,the GMOS CCD chip gap over the range 5500–5525 ˚Aprecludes an accurate measurement of the Ly α profileand hence a determination of the H I column density.Redward of Ly α , we find a series of strong (rest-frameequivalent width W ≥ II λ II ∗ λ I λ II λ II ∗ λ II λ II ∗ λ IV λλ II λ II ∗ λ IV λλ z = 3 . ± . IV λλ z = 3 .
379 and Mg II λλ z = 2 . Time Since Burst (d) F l u x D en s i t y ( µ Jy ) −3 −2 −1 UV (U−band)X−ray (1 keV)Radio (8 GHz)
Fig. 4.—
The broadband radio (blue), UV (red), and X-ray (black) light curve of GRB 090328. The best-fit model is plotted in solidlines (see Table 5 for parameters). The identical model parameters for an isotropic explosion are plotted as the dashed lines. The radiolight curve is not very well fit at early times, although it likely suffers from strong interstellar scintillation (light-blue shaded region). Inthis case a jet break is required by the data to fall at t &
10 days. At z = 3 . keV bandpassis E γ, iso = (3 . ± . × erg. Using the formulationof Lithwick & Sari (2001), the lower limit on the outflowLorentz factor (assuming a nonthermal spectrum up to E obs ≈
500 keV) is Γ & GRB 090328
High-Energy Properties
GRB 090328 triggered the
Fermi
GBM at 09:36:46 on28 March 2009 (McEnery et al. 2009). In the GBMbandpass, the light curve is multipeaked with a durationof t ≈
70 s. GRB 090328 was also detected at MeV en-ergies by several IPN satellites (Golenetskii et al. 2009a),including Konus-
Wind (Golenetskii et al. 2009d).A spectrum consisting of the first ∼
30 s of GBM data(containing the brightest part of the high-energy lightcurve) is well fit by a Band function with α = − . ± . β = − . ± . E p = 653 ±
45 keV (Rau et al. 2009).The resulting fluence in the 8 keV to 40 MeV (observerframe) bandpass is f γ = (9 . ± . × − erg cm − .These results are all consistent with the analogous val-ues derived by the Konus- Wind instrument, which in-clude data out to t + 73 s. Given the wider bandpassof the GBM and the higher precision of its fluence mea-surement, we adopt this value for remainder of this work.Using the observed redshift of 0.736 ( § f γ = (7 . ± . × − erg cm − in the1–10 keV rest-frame bandpass.GRB 090328 was also detected at GeV energies by the Fermi -LAT. Much like GRB 090323, flux in the LATband from GRB 090328 is detected out to ∼
900 s af-ter the GBM trigger (Cutini et al. 2009). Many pho-tons with energies above 1 GeV are detected from thedirection of GRB 090328; however, they are all detectedwell after the end of the MeV emission (Cutini et al. 2009; Piron et al. 2009). The highest energy photon de-tected from the direction of GRB 090328 was measuredat ∼ t + 798 s), while the most energetic photondetected during the prompt emission had E ≈
700 keVat t + 60 s (Piron et al. 2009). Afterglow Observations
The
Swift
XRT began target-of-opportunity observa-tions of GRB 090328 at 01:26 on 29 March 2009 ( ∼ . α = 6 h m . s δ = − ◦ ′ . ′′ . ′′ Swift began settledobservations of the field of GRB 090328 approximately16 hours after the
Fermi trigger. The optical afterglow,detected in both the U -band and white filters, wasidentified shortly thereafter (Oates 2009). UVOT obser-vations of the afterglow continued for ∼ U -band data from the HEASARC archive andconducted photometry with the images following thetechnique described by Li et al. (2006). Given the largeuncertainty associated with flux calibration for the whitefilter, we have not included data taken in this band. Theresults of this analysis, not including a correction forforeground Galactic extinction ( E [ B − V ] = 0 .
057 mag;Schlegel et al. 1998), are shown in Table 10.We obtained a single i ′ image of the afterglow ofGRB 090328 with GMOS-S on 29 April 2009. This im-age was reduced in an identical manner to our observa- See http://heasarc.gsfc.nasa.gov . fterglow Observations of Fermi -LAT GRBs 7 −17
Observed Wavelength (A) F λ ( e r g c m − s − A − ) F e II F e II M g II M g II M g I C a II C a II [ O II ] [ O III ] [ O III ] Fig. 5.—
GMOS-S optical spectrum of the afterglow of GRB 090328. We identify a series of forbidden O emission lines and Fe, Mg, andCa absorption features at a common redshift of 0 . ± . TABLE 2VLA Radio Observations ofGRB 090328
Date ∆ t ν f ν (UT) (days) (GHz) ( µ Jy)Mar 30.02 1.62 8.46 172 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± tions of GRB 090323, and the zero point was calculatedusing predetermined values from the Gemini website .We have also included the simultaneous GROND opti-cal and NIR measurements from Updike et al. (2009a)in our modeling, and therefore display them in Table 10as well.Finally, we began observing the afterglow ofGRB 090328 with the VLA on 30 March 2009 (Frail et al.2009) and continued for nearly two months. The datawere reduced in a manner identical to that described in § Optical Spectroscopy
We began spectroscopic observations of GRB 090328with GMOS-S at 00:05 on 30 April 2009 ( ∼ . × ∼ . ∼ § II ] λ III ] λλ II λ II λ II λλ I λ II λλ z = 0 . ± . keV bandpassis E γ, iso = (1 . ± . × erg. Using the formulationof Lithwick & Sari (2001), the lower limit on the outflowLorentz factor (assuming a nonthermal spectrum up to E obs ≈
700 keV) is Γ & GRB 090902B
High-Energy Properties
At 11:05:08.31 on 2 September 2009, the
Fermi -GBM triggered and located GRB 090902B(Bissaldi & Connaughton 2009). In the GBM bandpass,the light curve consisted of a bright, multipeakedpulse with a duration t ≈
21 s. GRB 090902B wasalso detected in a similar bandpass by
Suzaku -WAM(Terada et al. 2009).Furthermore, GRB 090902B was bright enough tobe detected at GeV energies by the
Fermi -LAT(de Palma et al. 2009). Like the other events in our sam-ple, LAT emission was seen out to t + 1000 s, at latetimes decaying like a power law with temporal index α LAT ≈ . E = 33 . +3 . − . GeV at t +82 s. Withinthe MeV prompt emission phase, the highest energy pho-ton was measured at E = 11 . +1 . − . GeV (Abdo et al.2009a).Unlike the other events considered here, the prompthigh-energy spectrum of GRB 090902B is not adequately Cenko et al.
Time Since Burst (d) F l u x D en s i t y ( µ Jy ) −1 −2 X−ray (1 keV)Radio (8.5 GHz)UV (U−band)Optical (R−band)
Fig. 6.—
The broadband radio (blue), optical (red), UV (cyan), and X-ray (black) light curves of GRB 090902B. The best-fit model isplotted in solid lines (see Table 6 for parameters). The identical model parameters for an isotropic explosion are plotted as the dashedlines. The strength of the possible modulation of the radio afterglow caused by interstellar scintillation (e.g., Frail et al. 2000a) is indicatedby the light-blue shaded region. As suggested by Pandey et al. (2010), the early ( t . . t ≈ described by a single Band function. While the 100–1000 keV bandpass is reasonably well fit by such a model,the spectrum exhibits excess emission at both low ( .
100 keV) and high ( &
10 MeV) energies. Abdo et al.(2009a) have suggested that the high-energy spectrumof GRB 090902B can be reproduced as the sum of twocomponents: a Band function peaking at ∼
700 keV,and a single power-law (photon index Γ ≡ β + 1 =1 .
93) extending over the entire GBM+LAT bandpass.In this model, the power-law component accounts for ∼
24% of the total 10 keV to 10 GeV fluence. The phys-ical mechanism responsible for this complex spectrum isstill not entirely understood; possible explanations in-clude a hadronic origin [either proton synchrotron ra-diation (Razzaque et al. 2009) or photohadronic inter-actions (Asano et al. 2009)] or thermal emission fromthe jet photosphere (M´esz´aros & Rees 2000; Ryde 2004;Ryde et al. 2010).Using their two-component spectrum, Abdo et al.(2009a) report a total fluence of f γ = (4 . ± . × − erg cm − in the 8 keV to 30 GeV (observer frame)bandpass. At a redshift of 1.8229 ( § . ± . × − erg cm − in the 1–10 keV rest-frame bandpass. Afterglow Observations
The
Swift
XRT began target-of-opportunity observa-tions of the field of GRB 090902B at 23:36 on 2 Septem-ber 2009 ( ∼ . α = 17 h m . s δ = +27 ◦ ′ . ′′ . ′′ Swift
UVOT began concurrently observing thefield of GRB 090902B and first reported the detection of acandidate optical afterglow consistent with the X-ray po-sition (Swenson & Siegel 2009). Subsequent observationsrevealed that the candidate had faded, confirming its as-sociation with GRB 090902B (Swenson & Stratta 2009).In Table 11 we present UVOT U -band observations ofGRB 090902B, reduced in an identical manner to thosedescribed in § r ′ image of the afterglow ofGRB 090902B with GMOS-N on 3 September 2009. Thisimage was reduced in the same manner as those of theother events, and the resulting photometry is presentedin Table 11. We have included optical and NIR pho-tometry of GRB 090902B from Pandey et al. (2010) inour modeling, and therefore display them in Table 11 aswell.Finally, we began observing the afterglow ofGRB 090902B with the VLA on 3 September 2009(Chandra & Frail 2009) and continued for ∼ § Optical Spectroscopy
We began spectroscopic observations of GRB 090902Bwith GMOS-N at 06:29 on 3 September 2009 ( ∼ . ×
900 s exposures, both with the R400grating and a central wavelength of 6000 ˚A, providingcoverage of ∼ § § Fermi -LAT GRBs 9 −17
Observed Wavelength (A) F λ ( e r g c m − s − A − ) M g I M g II M g II M n II F e II M g II F e II M n II F e I F e II F e II F e I C r II C r II Zn II F e II Fig. 7.—
GMOS-N optical spectrum of the afterglow of GRB 090902B. We identify a series of absorption features from neutral and singlyionized Mg, Mn, Fe, and Cr at a common redshift of 1 . ± . TABLE 3Radio Observations of GRB 090902B
Date ∆ t ν f ν Facility(UT) (days) (GHz) ( µ Jy)2009 Sep 3.77 1.31 4.8 111 ±
28 WSRT a ±
39 VLA2009 Sep 7.05 4.59 8.46 13 ±
31 VLA2009 Sep 8.05 5.59 8.46 130 ±
34 VLA2009 Sep 10.15 7.69 8.46 10 ±
32 VLA2009 Sep 11.05 8.59 8.46 80 ±
32 VLA2009 Sep 13.10 10.64 8.46 99 ±
31 VLA2009 Sep 14.14 11.60 8.46 71 ±
33 VLA2009 Sep 18.04 15.50 8.46 52 ±
32 VLA2009 Sep 19.00 16.46 8.46 89 ±
36 VLA2009 Sep 25.09 22.51 8.46 26 ±
29 VLA2009 Sep 27.08 24.50 8.46 67 ±
29 VLA2009 Oct 7.01 34.43 8.46 38 ±
28 VLA2009 Oct 9.01 36.43 8.46 66 ±
27 VLA2009 Oct 11.81 39.23 8.46 21 ±
31 VLA2009 Nov 6.90 65.44 8.46 9 ±
20 VLA2009 Nov 7.77 66.31 8.46 22 ±
19 VLA2009 Nov 9.00 67.54 8.46 48 ±
19 VLA2009 Nov 14.88 73.42 8.46 31 ±
21 VLA2010 Mar 20.62 199.16 8.46 18 ±
16 VLA a Reference: van der Horst et al. (2009). formed relative to spectra of the standard star Feige 34(Oke 1990) taken with the same instrumental setup ason 1 May 2008.The resulting spectrum of GRB 090902B is shown inFigure 7. Super-imposed on a smooth power-law contin-uum, we identify strong absorption features correspond-ing to Mg I λ II λλ II λ II λ II λ II λ II λ I λ II λ II λ II λ I λ II λλ I λ . ± . α absorption down to λ . z . .
3. Together with thestrength of the above features (in particular Fe I λ z = 1 . keV rest-frame bandpass is E γ, iso = (3 . ± . × erg. Assuming a nonthermalspectrum up to E obs = 11 GeV, Abdo et al. (2009a) havedetermined a lower limit to the initial outflow Lorentzfactor of Γ & GRB 090926A
High-Energy Properties
GRB 090926A triggered the GBM on
Fermi at04:20:26.99 on 26 September 2009 (Bissaldi 2009). Thelight curve consists of a single pulse with duration t ≈
20 s in the GBM bandpass. The prompt emission wassufficiently bright to trigger several additional satelliteinstruments, including
Suzaku -WAM (Noda et al. 2009),Konus-
Wind (Golenetskii et al. 2009b), and RT-2 onCORONAS-PHOTON (Chakrabarti et al. 2009).Simultaneously fitting both the GBM and LAT (seebelow) data from t to t + 21 s, Bissaldi et al. (2009)report that the spectrum is reasonably well modeled bya Band function with α = − . ± . β = − . ± . E p = 268 ± f γ = (2 . ± . × − erg cm − . These results differ only slightly fromthe values reported from other satellites. At z = 2 . keV bandpass is (1 . ± . × − erg cm − .GRB 090926A was also detected by the Fermi -LAT.The emission in the LAT bandpass lasted at least 400 s,with possible indications of significant flux out to ∼ E > t + 26 s(Uehara et al. 2009). Afterglow Observations
The
Swift
XRT began observing the field ofGRB 090926A at 17:17 on 26 September 2009 ( ∼ Time Since Burst (d) S c a l ed F l u x D en s i t y ( µ Jy ) UB (x 1.5)V (x 1.5)R (x 1.5)I (x 2.0)X−ray (x 100)
Fig. 8.—
Early optical and X-ray afterglow of GRB 090926A.After an initial decline in the U and V filters, the afterglow experi-ences a prominent rebrightening in all filters, peaking at t ≈ t ≫ ∆ t GRB ) injection of energyfrom the central engine (Rees & Meszaros 1998).
13 hours after the GBM trigger). A fading X-ray coun-terpart at α = 23 h m . s δ = − ◦ ′ . ′′ . ′′ Fermi -LAT localization of GRB 090926A beginning 19.0hours after the GBM trigger in the B -, V -, R -, and I -band filters. Within the Swift -XRT localization, we iden-tified an uncatalogued and fading source as the opticalafterglow of GRB 090926A (Haislip et al. 2009b,a). In-dividual images were automatically reduced using ourcustom, IRAF-based reduction pipeline and then astro-metrically aligned and stacked. We subsequently mea-sured the afterglow flux with aperture photometry, wherethe inclusion radius was approximately matched to theFWHM of the PSF. PROMPT continued to observe thefield for ten more nights (Haislip et al. 2009e,c,d).We also obtained 3 epochs of I - and J -band imagingof the afterglow of GRB 090926A using the ANDICAM(A Novel Dual Imaging CAMera) instrument mountedon the 1.3 m telescope at CTIO . This telescope is op-erated as part of the Small and Moderate Aperture Re-search Telescope System (SMARTS) consortium . Eachepoch consisted of 6 individual 360 s I -band observationsand 30 individual 60 s J -band observations. Between op-tical exposures, the telescope was slightly offset and theindividual J -band exposures were additionally ditheredvia an internal tilting mirror system. Standard data re-duction was performed on these images, including cosmicray rejection, overscan bias subtraction, zero subtraction,flat fielding and sky subtraction to correct for the NIR . . −1 Time Since Burst (d) S c a l ed F l u x D en s i t y ( µ Jy ) V/g’ (x 100)R/r’ (x 10)I/i’ X−ray (x 100)
Fig. 9.—
Late-time afterglow and model of GRB 090926A. Boththe X-ray and optical ( g ′ r ′ i ′ ) bandpasses exhibit a steepening de-cline at t ≈
10 days, strongly indicative of a jet break. background and the I -band fringing. For each epoch, theindividual images were then aligned and averaged to pro-duce a single frame in each band with summed exposuretimes of 36 minutes in I and 30 minutes in J .Relative aperture photometry was performed on theSMARTS data, in comparison with a number of nonva-riable sources in the field of GRB 090926A. The I -bandfield was photometrically calibrated by comparison (onphotometric nights) with Landolt standard stars in thefield of T Phe (Landolt 1992). J -band photometric cal-ibration was performed using 2MASS (Skrutskie et al.2006) field stars.SMARTS BV RI observations of the field ofGRB 090926A were also obtained on two photo-metric nights a few months after the GRB occurred (16and 18 December 2009). For these observations, totalsummed exposure times amounted to 180 s in
BRI and120 s in V . The absolute photometry of the field wasagain established based on same-night observations ofthe T Phe Landolt standard stars. These observationswere then used to provide absolute calibration for thePROMPT observations of GRB 090926A.We obtained additional late-time imaging of the fieldof GRB 090926A on 19 October 2009 with GMOS-S onGemini South. A total of 600 s of exposure time wasobtained in the Sloan g ′ -, r ′ -, and i ′ -band filters. Thedata were reduced in the manner described in § E ( B − V ) =0 .
024 mag; Schlegel et al. 1998], are shown in Table 12and Figures 8 and 9.Finally, the field of GRB 090926A was observed in theradio (5.5 GHz) on 1 October 2009 with the AustraliaTelescope Compact Array (ATCA). No source was de-tected at the afterglow location to a 2 σ limit of f ν < . Fermi -LAT GRBs 11
Spectroscopy
Malesani et al. (2009) obtained a spectrum of the af-terglow of GRB 090926A with the X-Shooter instrumentmounted on the 8 m Very Large Telescope UT2. Based onthe detection of a damped-Ly α system and many strong,narrow absorption features, these authors derive a red-shift of 2.1062 for the host galaxy of GRB 090926A.At this redshift, the prompt isotropic gamma-ray en-ergy release in the 1–10 keV bandpass is E γ, iso = (1 . ± . × erg. Assuming a nonthermal spectrum upto E obs = 20 GeV, we infer a lower limit for the initialLorentz factor of Γ &
700 (Lithwick & Sari 2001). AFTERGLOW MODELING AND RESULTS
In the standard “fireball” model of GRBs (e.g., Piran2005), a compact central engine (likely either a black holeor a rapidly spinning proto-neutron star) drives a colli-mated ( θ . ◦ ), ultrarelativistic (Γ & η γ ≡ E γ, iso / ( E γ, iso + E KE , iso ) of the total relativisticenergy to high-energy radiation.The outflow is ultimately slowed as it sweeps up andshock heats the circumburst medium, and synchrotronradiation from electrons accelerated at the shock frontresults in the broadband afterglow. The resulting spec-trum is well described as a series of broken power lawswith three characteristic frequencies: ν a , the frequencybelow which the radiation is self-absorbed; ν m , the char-acteristic frequency of the emitting electrons; and ν c ,the frequency above which electrons are able to cool ef-ficiently through radiation (e.g., Granot & Sari 2002).The temporal evolution of the afterglow depends on thedensity profile of the circumburst medium. We considerhere two possibilities: a constant-density circumburstmedium [ ρ ( r ) ∝ r ], as would be expected in an environ-ment similar to the interstellar medium (ISM: Sari et al.1998), and a wind-like environment [ ρ ( r ) ∝ r − ], aswould be the case for a massive-star progenitor thatshed its outer envelope at a constant rate (Chevalier & Li2000).At early times, the afterglow emission appears isotropicto distant observers due to the effects of relativisticbeaming. However, the outflow slows as it sweeps upmore and more circumburst material. When Γ( t ) ≈ /θ ,lateral spreading of the jet becomes important and ob-servers will notice “missing” emission from wide angles(Rhoads 1999; Sari et al. 1999). This hydrodynamictransition manifests itself as an achromatic steepeningin the afterglow light curve. Measuring the time of thisjet break ( t j ) allows us to infer the opening angle of theoutflow.In order to ascertain the total relativistic energy out-put from a GRB, we require three measurements: (1) E γ, iso , the isotropic energy release in the prompt gamma-ray emission, which is inferred from the high-energy flu-ence and the associated afterglow or host redshift; (2) θ , the half-opening angle of the beamed emission, in-ferred from the detection of a jet break; and (3) E KE ,the kinetic energy of the blast wave that is powering thebroadband afterglow, which can be inferred either via af-terglow modeling or, more accurately, from late-time ra- dio calorimetry in the nonrelativistic phase (Berger et al.2004; Frail et al. 2005; van der Horst et al. 2008). Westress here that we are neglecting contributions from non-electromagnetic phenomena (neutrinos, gravity waves,etc.) and slower-moving material (i.e., supernova emis-sion), and so are providing only lower limits on the totalenergy budget.Unfortunately, none of the radio afterglows in oursample of LAT events are sufficiently bright to performcalorimetry in the nonrelativistic phase. Instead, we con-struct afterglow models (including both the standard for-mulation and corrections for radiative losses and inverse-Compton emission; Sari & Esin 2001) and compare thesewith our observations using the multi-parameter fittingprogram of Yost et al. (2003). Our objective is to trans-late the observed three critical frequencies, together withthe peak flux density, F ν, max , and the jet break time, t j , into a physical description of the outflow. In par-ticular, we shall attempt to estimate seven parameters: E KE , the kinetic energy of the blast wave; n , the par-ticle density of the circumburst medium (or, alterna-tively for a wind-like circumburst medium, A ∗ , where ρ = 5 × A ∗ r − g cm − ) ; ǫ e , the fraction of the to-tal energy apportioned to electrons; ǫ B , the fraction ofthe total energy apportioned to the magnetic field; p ,the electron power-law index; A V , the host-galaxy ex-tinction ; and θ , the jet half-opening angle.Optical magnitudes have been converted to flux den-sities after correcting for Galactic extinction using zeropoints from Fukugita et al. (1995). To account for differ-ences in instrumental configurations, we have applied a7% cross-calibration uncertainty to all data points beforecalculating the models. All reported uncertainties havebeen determined using a Monte-Carlo bootstrap analysiswith 1000 trials and represent only statistical errors as-sociated with the fit. Systematic errors associated withmodel uncertainties are potentially larger and difficult toestimate. GRB 090323
Preliminary Considerations
Before proceeding to a detailed model, we derive someinitial constraints by looking at the spectral and tem-poral behavior of the afterglow. Considering first theX-ray afterglow, we fit the flux density to a power-law decay and find a best-fit index of α X = 1 . ± . χ = 28 . β X = 1 . +0 . − . ( χ = 8 . r ′ , R , and i ′ filters), forcing the decay index to be identical in all fil-ters and ignoring the points at t >
10 days due to hostgalaxy contamination (see below). Though the fit quality For a wind-like medium, the circumburst density is normalizedfor a progenitor mass-loss rate of ˙ M = 10 − M ⊙ yr − and a windspeed of v w = 1000 km s − (Chevalier & Li 1999). The units of A ∗ are thus g cm − , and the conversion to a particle density (as afunction of radius) is given by n = 30 A ∗ r − cm − . We have assumed an SMC-like extinction curve for all eventshere (Pei 1992; Kann et al. 2006). Given the relatively modestamounts of dust inferred for these host galaxies, this choice doesnot affect any of our primary conclusions.
TABLE 4GRB 090323 Afterglow Best-Fit Parameters E KE , iso A ∗ ǫ e ǫ B θ p A V (host) χ ν (d.o.f.)(10 erg) (g cm − ) (%) (%) ( ◦ ) (mag)200 +90 − . +0 . − . . ± . . ± .
12 2 . +0 . − . . ± .
06 0 . ± .
03 1.39 (70) is much worse ( χ = 178 . α O = 1 . ± . t = 1 .
12 days results in a spectral index of β O = 0 . ± . t ≈ α and β in different circumburst me-dia and spectral regimes (e.g., Price et al. 2002), we findthat we can rule out a low cooling frequency at large sig-nificance, as this would require α = (3 β − / ≈ . t ≈
20 days has twoimportant implications. First, it suggests a wind-like cir-cumburst medium, as the flux would be expected to risein proportion to t / for ν a < ν < ν m in a constant-density environment. From this and our previous X-ray and optical spectral and temporal decay indices, wecan infer that the electron spectral index is relativelysteep, p ≈ . t &
20 days. (Another possibility for thedecay could be the peak frequency ν m passing throughthe radio bands.)Finally, the relatively bright r ′ -band detection at t =130 days is almost certainly dominated by flux from thehost galaxy and not the afterglow of GRB 090323. If weassume this flux is due entirely to host light, the hostwill contribute a significant fraction of the flux in someof the late-time points of our optical light curve ( ∼ t = 14 days in r ′ ). We assume a flat spectrum andsubtract a host contribution of f ν = 0 . µ Jy from alloptical data points for our afterglow modeling.
Modeling Results
With the above constraints in hand, we have modeledthe afterglow of GRB 090323 with the software describedabove. The resulting best-fit wind model is plotted inFigure 2 and the derived parameters are provided in Ta-ble 4. The overall fit quality is reasonable ( χ = 97 . ν c lies at or abovethe X-ray bandpass for the duration of our observa-tions ( t & E KE , iso to A ∗ is required to be larger than inferred for previ- ous GRBs (e.g., Panaitescu & Kumar 2001b; Yost et al.2003). While the isotropic blast-wave kinetic energyis relatively large compared to that of previously mod-eled GRBs ( E KE , iso = 2 . × erg), it is in fact com-parable to the prompt gamma-ray energy release, aswould be expected for reasonable values of the gamma-ray efficiency η γ . The inferred density is slightly lowerthan usual ( A ∗ = 0 .
12 g cm − ), though smaller valueshave been reported in the literature (e.g., GRB 020405;Chevalier et al. 2004).The models result in a jet break time of t j =17 . +19 . − . days. This occurs after the X-ray and opticalobservations have stopped (except for the host detectionin the optical), and is therefore most directly constrainedby the radio light curve. In Figure 2 we also plot the samemodel parameters but for an isotropic explosion, wherethe turnover in the radio at late times is due to the peakfrequency ν m passing through the radio bandpass. Thecurrent radio data provide only weak constraints on thejet break time upper bound, although the models sug-gest a much smaller uncertainty in the opening angle.We return to the robustness of our determination of θ in § θ = 2 . ◦ ) is still relatively small compared with pre-vious samples. Though the dependence is not strong( θ ∝ ( E KE , iso /A ∗ ) − / ), the large ratio of E KE , iso to A ∗ effectively lowers the opening angle for a given jet breaktime.After applying the collimation correction, we find thatthe true energy release of GRB 090323 is E γ = 4 . +2 . − . × erg, E KE = 2 . +2 . − . × erg. We compare theseresults with a larger sample of events in § GRB 090328
Preliminary Considerations
Following the results of § α X = 1 . ± .
09 ( χ = 24 . β X = 1 . +0 . − . ( χ = 6 . N H = 4 . +3 . − . × cm − at z = 0 . U -band light curve to a single power-law decayresults in an index of α O = 1 . ± .
1; however, the qual-ity of the fit is extremely poor ( χ = 24 . Fermi -LAT GRBs 13
TABLE 5GRB 090328 Afterglow Best-Fit Parameters E KE , iso A ∗ ǫ e ǫ B θ p A V (host) χ ν (d.o.f.)(10 erg) (g cm − ) (%) (%) ( ◦ ) (mag)11 +5 − . +0 . − . ± . +0 . − . . +1 . − . . +0 . − . . ± .
04 1.63 (43) white filter (Marshall et al. 2009). This result suggeststhe presence of host-galaxy contamination at late times.The best-fit spectral index assuming a power-lawmodel for the simultaneous multi-color GROND data is β O = 1 . ± .
04, although the fit quality is extremelypoor ( χ = 85 . J band),however, and the relatively steep spectral index (com-pared to β OX ≈ .
8) appears to be robust. This is con-sistent with the presence of dust indicated by the X-rayspectral fits.In the case of GRB 090328, examining the α – β clo-sure relations yields little insight. Because of the poorfit quality in the optical and the large uncertainty in theX-ray spectral index, we are unable to rule out much ofthe available parameter space. We note, however, thatwith the exception of the excess absorption, the X-ray af-terglow light curve and spectrum of GRB 090328 closelyresemble those of GRB 090323. Similarly, if we assumethat the late-time optical data are dominated by host-galaxy light, the optical light curve is also compatiblewith that seen from GRB 090323. Modeling Results
The results of our best-fit model for the afterglow ofGRB 090328 are shown in Figure 4 and the parametersare provided in Table 5. The overall fit quality is rea-sonable ( χ = 70 . ǫ e → ǫ B → U -bandpoints are not predominantly due to host light, the fitquality of our models decreases somewhat ( χ ν & . t j = 6 . +12 . − . days and θ = (5 . +1 . − . ) ◦ . Primarily be-cause of the relatively sparse optical data, we find severalunique models with similar though slightly worse overallfit statistics. We note, however, that all these solutionsresult in comparable opening angles, the most importantparameter for our energetics calculations.Correcting for the effects of beaming, we find an energyrelease of E γ = 5 . +4 . − . × erg and E KE = 4 . +6 . − . × erg. The total relativistic energy release, E tot ≈ erg, is somewhat less than the value we derive forGRB 090323. GRB 090902B
Preliminary Considerations
A single power-law model with α X = 1 . ± .
03 pro-vides a good fit to the X-ray light curve of GRB 090902Bover the entire span of the XRT observations ( χ = 94 . β X = 0 . ± .
13 ( χ = 42 . z = 1 .
82, the best-fit host column densityis N H = (6 . +2 . − . ) × cm − .The decline inferred from the early-time ROTSE-III R -band observations is significantly steeper than the late-time ( t & f ν ∝ t − α ν − β , we find α O = 0 . ± .
05 and β O = 0 . ± . χ = 36 . ν O < ν c < ν X ). Furthermore, the relatively shallowoptical decline strongly rules out a wind-like circum-burst medium. We find that both the X-ray and op-tical bandpasses are broadly consistent with expansioninto a constant-density medium and an electron index p ≈ .
2. The observed X-ray temporal decline is some-what steeper than what is predicted, but this could be ac-counted for by synchrotron radiative losses at later times.The radio light curve appears to decay from the earliestobservations at t +1 . t & TABLE 6GRB 090902B Afterglow Best-Fit Parameters E KE , iso n ǫ e ǫ B θ p A V (host) χ ν (d.o.f.)(10 erg) (cm − ) (%) (%) ( ◦ ) (mag)68 +14 − (5 . +1 . − . ) × − +4 − . +2 . − . . +0 . − . . +0 . − . . +0 . − . The radio light curve of GRB 090902B most closely re-sembles that of GRB 991216 in which the early power-lawdecline is due to the overlap of emission from the reverseand forward shocks (Frail et al. 2000b). Since we areconcerned here with the modeling of the behavior of theforward shock, we will exclude the early radio point andpostpone a full discussion to a subsequent paper dealingwith a compilation all known GRBs with prompt radioemission (Chandra et al. 2010).
Modeling Results
Using the constraints derived above, our best-fit modelfor GRB 090902B assuming a constant-density circum-burst medium is shown in Figure 6, and the derivedmodel parameters are presented in Table 6. The over-all fit quality is quite reasonable ( χ = 145 . R -banddata points and the first VLA detection in our fitting,as we believe the flux at these points is dominated byreverse-shock emission.Much like the other events considered here, our inferredparameters for GRB 090902B suggest a large afterglowkinetic energy ( E KE , iso = 6 . +1 . − . × erg; a factor offive less than the prompt gamma-ray energy release) anda low circumburst density ( n = 5 . +1 . − . × − cm − ).In fact, we are unable to find any acceptable solutions( χ ν <
2) with n > − cm − . The inferred circumburstdensity for many long-duration GRBs is lower than typ-ical values observed in dense molecular clouds (wherepresumably their massive-star progenitors have formed).Yet the value we have derived for GRB 090902B is closerin fact to what one might find in the ambient ISM or eventhe intergalactic medium (IGM), as has been found forthe few short-hard GRBs with sufficient afterglow data(e.g., Panaitescu 2006; Perley et al. 2009b). We returnto this issue in more detail in § ν m , will not fall to theradio bandpass until t &
40 days. The declining radiolight curve at late times therefore requires a jet breakat t j = 6 . +2 . − . days. Again, because of the large ratioof E KE , iso to n , this corresponds to a relatively narrowopening angle: θ = (3 . +0 . − . ) ◦ .Correcting for collimation, we find the true energy re-lease from GRB 090902B to be E γ = (5 . ± . × erg, E KE = 1 . +0 . − . × erg. GRB 090926A
Preliminary Considerations
Fitting a single power-law decay to the X-ray lightcurve, we find a reasonable quality fit ( χ = 120 . α X = 1 . ± .
03. The fit quality improvessomewhat if we allow for a steeper decay at late times,although the post-break decay index is not particularlywell constrained: α X, = 1 . ± . α X, = 2 . +0 . − . , t b = 9 . +2 . − . days, χ = 111 . χ = 41 . β X = 1 . ± .
13 and does not requireany absorption in addition to the Galactic component.The behavior in the optical bandpass, however, is sig-nificantly more complex (Fig. 8). The flux in the ini-tial UVOT U - and V -band observations declines until t ≈ . U BV RI ).The optical light curve of GRB 090926A is reminiscentof the rebrightening seen at t ≈ t ≈ BV RI data at t > α O = 1 . ± .
02 ( χ = 181 . t ≈
23 days greatly overestimates the observed flux(Fig. 9). Much like the X-ray data, this strongly suggestsa steepening of the optical light curve at t & β O . We include only the V -, R -, and I -band data,as both the U and B bands are likely affected by Ly α absorption at z = 2 .
11. We then find a best-fit opticalspectral index of β O = 1 . ± .
05. The formal fit qualityis relatively poor, however ( χ = 183 . t & β OX ≈ . α X, = 1 . α O, = 1 .
38) and spectral ( β X = 1 . β O = 1 .
03) indicesin the X-ray and optical for t ≈ β OX , is comparableto both the optical and X-ray spectral indices. Thesefacts strongly suggest that both the X-ray and opticalbandpasses fall in the same synchrotron spectral regime.Considering the various synchrotron closure relations,the best fit appears to occur when both bandpasses fallabove the cooling frequency, ν c . The afterglow decay infterglow Observations of Fermi -LAT GRBs 15
TABLE 7GRB 090926A Afterglow Best-Fit Parameters E KE , iso A ∗ ǫ e ǫ B θ p A V (host) χ ν (d.o.f.)(10 erg) (g cm − ) (%) (%) ( ◦ ) (mag)24 . +1 . − . . +0 . − . +2 − . +0 . − . . ± . . ± .
02 0 . ± .
01 1.18 (149) this regime is independent of circumburst medium. Sucha low cooling frequency is somewhat unusual, though notunprecedented (e.g., GRB 050904; Frail et al. 2006) inGRB afterglows. The implied electron index in this casewould be p ≈ . t ≈ Modeling Results
Unfortunately, without a radio light curve we cannotuniquely solve for the physical parameters of the after-glow of GRB 090926A. We can, however, at the very leastmore robustly constrain the jet break time and openingangle of this event, as well as identify broad trends inthe parameters associated with acceptable solutions. Asdiscussed previously, we consider only data at t ≥ χ = 175 . t ≈ ± θ ≈ ◦ . Based onthe observed spread of E KE and A ∗ in our wind mod-els, we adopt an approximate uncertainty in this valueof θ ≈ (7 +3 − ) ◦ .Correcting for collimation, we find a prompt energyrelease of E γ = 1 . +1 . − . × erg. Assuming a reason-able value for the gamma-ray efficiency ( η γ & E KE , iso & erg. We then find a collimation-correctedafterglow energy of E KE & × erg. DISCUSSION
Central-Engine Constraints I: Energetics andRemnants
In Table 8, we summarize the primary results fromthis work, including the redshift, initial Lorentz factor,beaming angle, density, and collimation-corrected energyrelease for each of the four LAT GRBs considered here. Before the launch of the
Swift satellite in 2004,the majority of all well-observed afterglows wereinferred to be highly collimated, with opening an-gles θ . ◦ (Zeh et al. 2006). The most notableexceptions were the handful of the most nearbyevents, including GRB 980425 (Galama et al. 1998;Kulkarni et al. 1998), GRB 031203 (Soderberg et al.2004; Sazonov et al. 2004; Thomsen et al. 2004;Cobb et al. 2004; Malesani et al. 2004; Gal-Yam et al.2004), and (post- Swift ) GRB 060218 (Mirabal et al.2006; Campana et al. 2006; Soderberg et al. 2006;Modjaz et al. 2006; Sollerman et al. 2006; Pian et al.2006; Ferrero et al. 2006; Maeda et al. 2007), all ofwhich appear to be isotropic explosions that wereenergetically dominated by their nonrelativistic ejecta(i.e., their associated supernovae).The typical GRB afterglows discovered by
Swift , how-ever, did not fit neatly into this simple bimodal pic-ture. The afterglows of most
Swift
GRBs, including thelarge fraction at cosmological distances, exhibit a muchbroader range of opening angles (Kocevski & Butler2008; Racusin et al. 2009), with some extreme eventslacking a detectable jet break signature in the X-rays outto hundreds of days after the burst (e.g., GRB 060729;Grupe et al. 2007, 2010).All four of the LAT-detected events we have studiedhere are consistent with a relatively high degree of colli-mation ( θ . ◦ ). In this respect, then, the afterglows ofLAT-detected GRBs more closely resemble the pre- Swift sample. This in and of itself is not entirely surprising,given the tremendous high- E γ, iso bias for events detectedby the LAT (Figure 1).In Figure 10, we plot the two-dimensional (prompt+ afterglow) collimation-corrected relativistic energy re-lease for the four LAT events in this work, compared withseveral additional samples. Shown in red are 11 pre- Swift
GRBs at cosmological distances ( z > .
5) for which suf-ficient broadband (X-ray, optical, and radio) data existto constrain both E γ and E KE . We find the logarithmicmean for the sum of these two values, E rel ≈ E γ + E KE , to be h E rel i = 2 . × erg, with an error in the mean of0.17 dex. The solid black line indicates a constant valueof E rel corresponding to this mean, while the gray shadedregions indicate 1 σ , 2 σ , and 3 σ confidence intervals.The gray dotted line in Figure 10 represents a con-stant gamma-ray efficiency of η γ = 50%. Most eventsare roughly consistent (or even exceed) this value. Thisresult presents a problem for most internal shock mod-els of the prompt emission, which predict a maximalgamma-ray efficiency of η γ .
10% (Kobayashi et al.1997; Daigne & Mochkovitch 1998). Alternatively, if the Assuming an approximately log-normal distribution, we calcu-late the weighted mean of h log ( E tot ) i , where σ = δE tot / (ln(10) × E tot ). TABLE 8Summary of GRB Parameters
GRB z f γ a E γ, isoa Γ θ E γ E KE n/A ∗ (10 − erg cm − ) (10 erg) ( ◦ ) (10 erg) (10 erg) (cm − / g cm − )090323 3.568 1 . ± .
20 3 . ± . &
600 2 . +0 . − . . +2 . − . . +2 . − . . +0 . − . . ± .
08 0 . ± . &
200 5 . +1 . − . . +0 . − . . +0 . − . . +0 . − . . ± .
05 3 . ± . & . +0 . − . . ± . . +0 . − . (5 . +1 . − . ) × − . ± .
03 1 . ± . &
700 7 +3 − +15 − & . · · · ba keV observer frame bandpass. b We have not included an estimate for the density of GRB 090926A, as this parameter was not well constrained due to thelack of radio data. early afterglow undergoes a relatively long-lived radia-tive phase, we may be significantly underestimating theblastwave kinetic energy (Ghisellini et al. 2010).As discussed previously, the three most nearby GRBsare clearly subenergetic outliers. The energy releasefrom the supernovae associated with these events, E SN ∼ –10 erg (Iwamoto et al. 1998; Mazzali et al. 2006),is several orders of magnitude larger than the energy ap-portioned to the relativistic ejecta. To further distinguishthese events, the rate of such subluminous GRBs suggeststhey are many times more common (per unit volume)than the typical cosmological GRBs (Soderberg et al.2006; Cobb et al. 2006; Guetta & Valle 2007), althoughButler et al. (2010) have suggested that both samplesmay be described by a single luminosity function — thatis, subluminous GRBs may simply extend continuouslyfrom the higher-energy population.Of the LAT events studied here, the total relativisticenergy output from only a single one (GRB 090328) isconsistent with the pre- Swift mean at the 3 σ level. Thisis not entirely surprising, however, as the E rel distribu-tion of pre- Swift
GRBs exhibits a reasonable dispersion( ∼ .
55 dex, or a factor of 3.5). It is clear, however, thatGRB 090323, GRB 090902B, and GRB 090926A all fallat the very high end of the pre-
Swift distribution. Inparticular, the only event comparable to GRB 090926A,with E γ ≈ erg and E KE relatively unconstrained,is GRB 970508 ( E rel ≈ . × erg, dominated bythe large afterglow kinetic energy; Yost et al. 2003;Berger et al. 2004).GRBs 090323, 090902B, and 090926A appear consis-tent instead with a subsample of the brightest Swift events from Cenko et al. (2010) (see also Frail et al.2006; Chandra et al. 2008). This, too, is not unexpected,as these
Swift events were chosen on the basis of large E γ, iso values, and therefore should in large part mimic atleast this component of the LAT selection effects.Much like several events in the bright Swift sample,GRB 090926A appears to exceed the canonical GRB rel-ativistic energy release of 10 erg by roughly an orderof magnitude. We stress that our methodology providesa relatively conservative estimate for the prompt energyrelease of GRB 090926A, for a number of reasons. First,we consider only the rest-frame 1–10 keV bandpass for all events considered in Figure 10. Extrapolating mea-surements from previous instruments, with bandpassestypically extending only to ∼ Swift ), up to the GeV range would introduce sig-nificant uncertainties in E γ, iso . While allowing for a morerobust burst-to-burst comparison, we have not included a significant fraction of the detected high-energy fluencein our energy calculations for these LAT events ( ∼ E rel we derive forGRB 090902B is a factor of several lower than that re-ported by other authors ( § ∼
75% larger, corre-sponding to a beaming-corrected prompt energy releaseof E γ ≈ × erg.Together with the discovery of several comparableevents to GRB 090926A in the past few years, includ-ing GRB 050904 ( E rel ≈ × erg; Frail et al. 2006),GRB 070125 ( E rel ≈ × erg; Chandra et al. 2008),GRB 050820A ( E rel ≈ × erg; Cenko et al. 2010),and GRB 090423 ( E rel & × erg; Chandra et al.2010), we now believe there is substantial evidence infavor of a subpopulation of GRBs with relativistic en-ergy outputs either very near or above 10 erg. We referto such events as hyper-energetic GRBs in what follows,and outline some of the implications of this particularenergy threshold.Much as was argued by Starling et al. (2009) for thecase of GRB 080721, the total energy budget is an im-portant diagnostic for any central-engine model. In par-ticular, models for which the outflow is powered by thespin-down of a highly magnetized ( B & G) proto-neutron star are subject to strict constraints on the totalenergy budget of E total < × erg (the rotational en-ergy of a maximally spinning 1.4 M ⊙ neutron star; e.g.,Thompson et al. 2004; Metzger et al. 2007).Only accounting for the relativistic energy output,GRB 090926A seems to approach within at least a factorof a few of this limit. While we caution that there are stillsignificant uncertainties associated with the models usedto infer the afterglow parameters (and hence E rel ), wehave not yet accounted for additional sources of energy,including (nonrelativistic) SN emission, radiative lossesat early times due to bright X-ray flares (Burrows et al.2005a; Falcone et al. 2007), and synchrotron losses dur-ing the later phases of afterglow evolution (Yost et al.2003). Even if we have overestimated the relativistic en-ergy output for these events by a factor of several andthe magnetar energy limit is not strictly violated, thefterglow Observations of Fermi -LAT GRBs 17tremendous efficiency required by this process strainscredulity.
Central-Engine Constraints II: Lorentz Factor,Opening Angle, and Acceleration Mechanisms
Unlike magnetar models that are powered by the spin-down of a highly magnetized proto-neutron star, GRBmodels in which the core of an evolved massive starcollapses promptly to form a black hole and accretiondisk system (“Type I collapsars” following the nomen-clature of MacFadyen et al. 2001) have significantly re-laxed constraints on the total energy budget that arein at least some cases capable of accommodating hyper-energetic events. For instance, the initial models ofMacFadyen & Woosley (1999) that begin with a 35 M ⊙ He star with a 10 M ⊙ evolved core lead to accretion ratesof ∼ . ⊙ s − onto a 3 M ⊙ rotating black hole. Assum-ing approximately continuous feeding over the fallbacktime of the stellar envelope ( ∼
10 s), this corresponds toa total accreted mass ∼ ⊙ . In addition to the accre-tion process, an even larger reserve lies in the rotationalenergy of the black hole: E rot = M BH c ( − (cid:20)(cid:16) p − a (cid:17) + a (cid:21) / ) , (1)where M BH is the black hole mass and a is the dimen-sionless rotation parameter ( a ≡ Jc/M G ).At least two competing theories exist, however, to ex-plain how the system can channel this energy to pro-duce the collimated, relativistic jets we observe fromGRBs. First, the energy may be extracted from theaccretion process via ν ¯ ν annihilation (e.g, Woosley1993; MacFadyen & Woosley 1999; Popham et al. 1999;Ruffert & Janka 1999; Narayan et al. 2001). At thehyper-Eddington rates expected for collapsars, the ac-cretion disk formed around the rotating black hole willbe optically thick and photons are unable to escape. Theviscous heat is instead balanced by cooling via neutrinoemission. Annihilation of ν ¯ ν pairs will produce a gas ofhot electron-positron pairs, which, assuming sufficientlylow baryon loading, can then rapidly expand in the low-density regions along the axis of rotation (a “fireball”,e.g., Zhang et al. 2003).Alternatively, if the black hole is rotating and the ac-cretion disk is threaded by sufficiently large magneticfields ( B ≈ G for a 3 M ⊙ black hole), energy can beextracted directly from the rotating black hole via theBlandford-Znajek mechanism (e.g, Blandford & Znajek1977; Lee et al. 2000). The accretion disk serves primar-ily to anchor the large magnetic field (which would oth-erwise disperse), and the energy is emitted as a largelyPoynting flux-dominated outflow.The efficiency of converting the potential energy ofthe rotating black hole plus accretion disk system intoa form suitable to launch a collimated, relativistic out-flow has been intensively studied in the last decade.In the case of ν ¯ ν annihilation, the overall efficiencyof converting the neutrino luminosity of the coolingdisk ( L ν ) into e + – e − pairs ( L ν ¯ ν ) depends sensitively onthe mass accretion rate, the disk geometry, and (per-haps) the effects of general relativity on neutrino physics(e.g., Popham et al. 1999; MacFadyen & Woosley 1999; Ruffert & Janka 1999). But the majority of recent sim-ulations suggest at most a modest efficiency ( η ν ¯ ν ≡ L ν ¯ ν /L ν . . L ν ≈ –10 erg s − , this would require an extremelylong-lived phase of continuous accretion to explain hyper-energetic GRBs.Jets powered by MHD processes, on the other hand,can more easily accommodate large energy releases. Tobegin with, by extracting energy directly from the ro-tation of the black hole, the Blandford-Znajek pro-cess begins with a significantly larger energy reservoir: E rot ≈ × erg for a rapidly spinning ( a = 0 . ⊙ (Eqn. 1). Both analytic mod-els (e.g., Lee et al. 2000) and numerical simulations (e.g.,McKinney 2005) suggest that as much as 5–10% of thisrotational energy can be made available to power a colli-mated outflow, easily within the requirements of hyper-energetic events. We caution, however, that the jet ef-ficiency is a strong function of the black hole spin, andslowly spinning black holes have significantly lower effi-ciencies.Setting energetics considerations aside for the moment,there still remains the question of whether either the ν ¯ ν annihilation mechanism or MHD processes are capableof producing jets with the Lorentz factors and degree ofcollimation inferred from GRB observations. Here oursample of Fermi -LAT events, with their extreme initialLorentz factors, offers a distinct advantage over previousGRB studies. Combining the Lorentz-factor limits forthe most relativistic GRBs with the inferred jet openingangles from our broadband afterglow models can providecritical diagnostics of the jet acceleration mechanism.The results from MHD simulations of jet accelerationappear to depend sensitively on the nature of the mediuminto which the jet propagates. Tchekhovskoy et al.(2009b) have recently conducted fully relativistic MHDsimulations in which a mildly magnetized (magnetiza-tion parameter σ .
1) jet is initially confined by thepressure of a stellar envelope out to some radius, andthen allowed to propagate freely in all directions (seealso Komissarov et al. 2009). Both authors find that thejet accelerates rapidly in this transition region (“rarefac-tion” acceleration) and can reach Lorentz factors Γ of afew hundred, yet still remains highly collimated ( θ . ◦ )even after leaving the region of confinement. Further-more, the deconfinement radii required to produce theseoutflows agree well with the expected value for Wolf-Rayet stars ( r ≈ –10 cm).Based on both results from these simulations and ana-lytical arguments, Tchekhovskoy et al. (2009b) demon-strate a relationship between the initial Lorentz fac-tor and jet opening angle: Γ θ ≈ θ ≈
70) and GRB 090926A (Γ θ ≈
90) appear in-consistent with this result.One way to circumvent this requirement is if the jetshave extremely high magnetization parameters ( σ ≫
1; Tchekhovskoy et al. 2009a), as such Poynting flux-8 Cenko et al.
Afterglow Kinetic Energy (E KE ; erg) P r o m p t E ne r g y ( E γ ; e r g ) Pre−
Swift
GRBsBright
Swift
GRBsSubluminous GRBs
Fermi −LAT GRBsMagnetar Limit
Fig. 10.—
Two-dimensional relativistic energy release ( E rel ≈ E γ + E KE ) from GRBs. Cosmologically distant ( z & .
5) events fromthe pre-
Swift era are shown in red. The logarithmic mean for these events, h E rel i = 2 × erg, is indicated by the solid black line.Shaded regions correspond to 1 σ , 2 σ , and 3 σ errors on this mean value. The three most nearby events (GRBs 980425, 031203, and060218) are plotted in green and are underluminous by several orders of magnitude. The four LAT events from this work are plottedin blue; all but GRB 090328 fall at the high end of the pre- Swift distribution (note that we have not plotted horizontal errors bars forGRB 090926A due to the large uncertainty in E KE ). Instead, they are more consistent with some of the brightest events from the Swift era (black squares). The total relativistic energy release from GRB 090926A appears to exceed 10 erg. Such hyper-energetic events posea severe challenge to the magnetar models, where the total energy release cannot exceed 3 × erg (dashed black line). References —Panaitescu & Kumar (2002): GRBs 990123, 990510, 991208, 991216, 000301C, 010222; Yost et al. (2003): GRBs 970508, 980703, 000926;Berger et al. (2004): GRBs 970508, 980703; Chevalier et al. (2004): GRB 020405; Berger et al. (2001): GRB 000418; Li & Chevalier (1999):GRB 980425; Soderberg et al. (2004): GRB 031203; Soderberg et al. (2006): GRB 060218; Frail et al. (2006): GRB 050904; Chandra et al.(2008): GRB 070125; Cenko et al. (2010): GRBs 050820A, 060418, 080319B. dominated jets can be accelerated to extreme Lorentzfactors over relatively large angles. However, it is unclearhow such outflows can convert sufficient electromagneticenergy to accelerate electrons and produce the observedprompt gamma-ray emission. Other particle-accelerationmechanisms besides MHD shocks may be required in thiscase (e.g., Beloborodov 2009). Alternatively, the gamma-ray emission may be patchy (e.g., Kumar & Piran 2000)or the jet may be structured (see, e.g., Granot 2007 andreferences therein), so that we are measuring only theextrema of Γ and not the true bulk of the relativisticflow carrying most of the energy. Comparison with Other Work
In this section, we attempt to place this work in con-text, both by comparing our results with those of otherauthors who have studied these same events, and by high-lighting additional differences between our LAT sampleand GRBs detected by satellites at lower energies.McBreen et al. (2010) present optical and NIR obser-vations of three events from this work (GRBs 090323,090328, and 090902B), taken primarily with the GRONDinstrument (Greiner et al. 2008). In the case ofGRB 090323, these authors find an optical spectral in- dex of α O = 1 . ± .
01, consistent with the value de-rived here, and our measurements of the host-galaxy fluxagree nicely. We derive a slightly steeper optical spectralindex, but our results are consistent at the 2.5 σ level.Most importantly, McBreen et al. (2010) infer from thesteep optical decay that a jet break occurred before thefirst optical observations began ( t j . θ . ◦ ) and a correspond-ingly small collimation-corrected prompt energy release[ E γ . × erg for a constant-density (wind-like)circumburst medium]. We consider this possibility un-likely, however, as it is difficult to explain both the flatradio light curve and the more slowly fading X-ray after-glow ( α X ≈ .
5) through post jet-break evolution (seealso § α o ≈ .
3) derived at early times requires a jet break be-fore the commencement of observations ( t j . . Fermi -LAT GRBs 19reconcile the shallower X-ray decay ( α X ≈ .
65) and inparticular the rising radio light curve at this time withmodels of post-jet break evolution (see also § t ≈
23 days) optical observa-tion with the VLT provides strong confirmation that theradio decline at t & t j ≈ E γ are roughly a factor of 4 less (note that part of this dif-ference is also due to the wider bandpass McBreen et al.2010 use to calculate E γ, iso ).Pandey et al. (2010) also present optical and X-ray ob-servations of GRB 090902B, most of which were includedin our broadband modeling here. It is not surprising,then, that we derive similar values for the optical tem-poral and spectral indices (the same also holds for theX-ray bandpass). The afterglow model derived by theseauthors is broadly similar to ours, but we favor a some-what steeper electron index ( p = 2 . . θ > ◦ (based on a lower limit to the jetbreak time of t j > E &
100 MeV)component observed from several LAT events is in factdue to the same source as the late-time afterglow emis-sion: synchrotron radiation from accelerated electronsin the circumburst medium shock-heated by the outgo-ing blast wave (i.e., external shock emission; see alsoGhisellini et al. 2010).The afterglow parameters derived by these authors forGRB 090902B differ somewhat from ours, largely dueto the fact that they assume the X-ray bandpass at t ≈ ν X < ν c ). While the observed X-ray spectral andtemporal indices at t ≈ and optical data if ν X > ν c at t ≈ ν = 100 MeV and t = 50 s. Wefind f ν ≈
30 nJy, roughly a factor of 7 below the observedvalue (Abdo et al. 2009a). The discrepancy between ourresults and those of Kumar & Duran (2009a) is largelydue to the lower kinetic energy we have inferred for theblast wave ( E KE , iso ≈ × , a factor of 18 lower thanthat used by Kumar & Duran 2009a). This would sug-gest that the delayed high-energy component is not dueto afterglow emission. We caution, however, that our −4 −2 Circumburst Density (n or A*) I s o t r op i c A ft e r g l o w E n e r g y ( E K E ,i s o ) Fig. 11.—
Circumburst density and isotropic afterglow energy re-lease from cosmological ( z > .
5) GRBs. Constant-density modelsare shown as squares, while wind-like models are plotted as circles.The GRBs detected by the
Fermi -LAT (red) clearly have prefer-entially larger isotropic energy releases and smaller circumburstdensities than the rest of the sample. See the caption of Figure 10for references. flux calculation does not incorporate the reduced cross-section for inverse Compton emission due to the Klein-Nishina effect at very high energies, and this will affectour flux calculation to some extent.A further interesting claim from the work ofKumar & Duran (2009a) is that the inferred value ofthe magnetic field for GRB 090902B (along with severalother LAT-detected events) is consistent with shock com-pression of a modest circumstellar field ( B & µ G). Inother words, no dynamo process is necessary to gener-ate the magnetic field strengths needed to produce theobserved synchrotron afterglow emission. For a constant-density circumburst medium, the preshock magnetic fieldis given by B = (2 πm p ǫ B n ) / c. (2)We also find that the product ǫ B × n (and hence the de-rived B field) is smaller for LAT events than for otherGRBs detected at lower energies, primarily due to thelower inferred circumburst densities (see below). How-ever, using our best-fit parameters for GRB 090902B, wefind B ≈ µ G, broadly consistent with the results ofPiran & Nakar (2010) and Li (2010). While this value issmaller than the preshock magnetic fields previously in-ferred for GRBs ( B ≈
10 mG for ǫ B = 0 . n = 1 cm − ),it suggests that at least some magnetic field amplificationmay still be required.Finally, we return to the issue of the relatively lowcircumburst densities derived in §
3. Given the strongevidence for a connection between long-duration GRBsand broad-lined SNe Ib/c, it would be natural to expectthe massive-star progenitors of GRBs to explode in thedense molecular cloud environments where we observestars forming in our own Galaxy.Past modeling of broadband GRB afterglows, how-ever, has not always revealed this to be the case. Ofthe past GRBs with sufficient radio observations toestimate the circumburst density, the derived valuesspan a large range from 1 . × − cm − (GRB 990123;Panaitescu & Kumar 2002) to 680 cm − (GRB 050904;Frail et al. 2006). We plot in Figure 11 the derived cir-0 Cenko et al.cumburst densities for these previous events (either n or A ∗ , depending on the circumburst density profile) as afunction of isotropic afterglow kinetic energy, along withthree events from our LAT sample (we have not includedGRB 090926A as lack of radio coverage makes densityestimates highly degenerate). It is clear that the eventsdetected by the LAT have on average larger isotropicenergies and smaller densities than the previous sample.The larger isotropic kinetic energy is not hard to un-derstand, as the LAT is less sensitive than, for example,the Burst Alert Telescope (BAT; Barthelmy et al. 2005)onboard Swift and should therefore select brighter events(in terms of the high-energy fluence). Unless E γ, iso and E KE , iso were anticorrelated, we would expect LAT eventsto have larger isotropic blast-wave energies as well. Butthe lower densities require an additional explanation. Wespeculate on possible reasons for this difference in § E KE , iso /n (or, alternatively E KE , iso /A ∗ ) we have derived for these events has twoimportant implications. First, the opening angle derivedfor a given jet break time scales inversely as E KE , iso andproportionally to n/A ∗ ( § n = 0 . − fromFrail et al. 2001; n = 10 cm − from Bloom et al. 2003).In this manner, LAT events can have relatively late jetbreaks but still be narrowly collimated ( θ . ◦ ).Secondly, a large E KE , iso /n ratio will act to delay thedeceleration time of the outflow. Assuming the “thinshell” case, the outgoing relativistic blast wave will de-celerate when (Sari & Piran 1999; Molinari et al. 2007) t dec (ISM) = (cid:18) E KE , iso (1 + z ) πm p c n Γ (cid:19) / , (3) t dec (Wind) = E KE , iso (1 + z )8 πc A Γ . (4)(Note that we have corrected Eqn. 2 from Molinari et al.2007 to remove the erroneous factor of m p .) To someextent, the large ratio of E KE , iso /n will offset the ef-fect of the larger initial Lorentz factors for Fermi -LATevents. Using the parameters we have derived fromthe LAT events in our sample, we find t dec ≈ t dec ≈ t dec ≈
33 sfor GRB 090902B. If the late-time GeV emission is in-deed due to external shock emission, the delay betweenthe MeV and GeV photons should correspond roughlyto the blast-wave deceleration time. This may be prob-lematic for GRB 090902B, for which the observed delay( ∼ E KE , iso , n , and particularly Γ ( § Limitations and Future Work
To better understand our results in § § § θ can be written as (e.g., Chevalier & Li2000) θ (Wind) =0 . (cid:18) z (cid:19) − / (cid:18) E KE , iso erg (cid:19) − / (cid:18) A ∗ . − (cid:19) / (cid:18) t j (cid:19) / [rad] . (5)This result assumes only that the shock is ul-trarelativistic and undergoes a self-similar evolution(Blandford & McKee 1976), and is therefore relativelyrobust.Only in the case of GRB 090926A (and also forGRB 090902B if we include the late-time VLT observa-tion from McBreen et al. 2010) do we find clear evidencefor a jet break in multiple bandpasses. For GRB 090323,the lack of a steepening in the X-ray and optical lightcurves apparently limits t j &
10 days. If we simply ig-nore our modeling results and assume that the shockenergy is comparable to the prompt gamma-ray energy( E KE , iso ≈ × erg) and that the progenitor windspeed and mass-loss rate are comparable to those ob-served from Galactic Wolf-Rayet stars ( A ∗ ≈ − ),then we find a lower limit on the opening angle of θ (Wind) & ◦ . The resulting limit on the prompt en-ergy release is therefore E γ & × erg, similar towhat we derived from our broadband models.If we were instead to assume the GRB exploded ina constant-density medium, the opening angle then be-comes (e.g., Sari et al. 1999) θ (ISM) =0 . (cid:18) z (cid:19) − / (cid:18) E KE , iso erg (cid:19) − / (cid:16) n − (cid:17) / (cid:18) t j (cid:19) / [rad] . (6)Under similar assumptions as above, the limit on theopening angle would be θ (ISM) & ◦ , corresponding toa prompt energy release of E γ & × erg. Clearlya constant-density circumburst medium only makes theenergy requirements more strict.An alternative possibility for GRB 090323(McBreen et al. 2010; also suggested by Schady et al.2007 to explain the afterglow of GRB 061007) is ajet break before the beginning X-ray and opticalobservations ( t . α X ≈ .
5) is too shallow to accom-modate a typical electron spectral index p (for ν > ν m , f ν ∝ t − p post jet-break; Sari et al. 1999). The observedbehavior would therefore require late-time energy inputto flatten the X-ray and optical decay. Furthermore,the relatively flat radio light curve for t .
20 days wouldrequire that the synchrotron self-absorption frequencyfell above the radio bandpass during this phase; oth-erwise the radio bandpass would be required to decay,either as t − / ( ν < ν m ) or t − p ( ν > ν m ) . We consider We note that the above results are independent of circumburstmedium, as the expansion of the outflow is predominantly lateralafter the jet break (Chevalier & Li 2000). fterglow Observations of
Fermi -LAT GRBs 21this somewhat contrived picture unlikely in the case ofGRB 090323, particularly given the reasonable qualityof our fits using only standard afterglow theory.A similar analysis of GRB 090328 suggests that thejet-break time cannot occur any earlier than t ≈ θ (Wind) & ◦ , θ (ISM) & ◦ . Both values result in a prompt energy release E γ & erg, broadly consistent with our modeling results.In the end, all of these estimates of energy, den-sity, and jet geometry rest on the relativistic syn-chrotron model. While the standard afterglow modelhas undergone continuous improvements and it hasbeen well tested (Meszaros & Rees 1997; Sari et al.1998, 1999; Wijers & Galama 1999; Chevalier & Li2000; Panaitescu & Kumar 2000; Yost et al. 2003;Willingale et al. 2007), it still must make several simpli-fying assumptions about the shock dynamics, magneticfield generation, particle acceleration, energy injection,and the circumburst density structure. Of particular con-cern are the recent results of relativistic simulations byZhang & MacFadyen (2009), which suggest that viewingangle can dramatically alter the observed afterglow emis-sion at early times.If we are to verify this class of hyper-energetic bursts,we need independent estimates of the relativistic energycontent. Waxman et al. (1998) first suggested that late-time (radio) calorimetry could be used for this purposein order to sidestep early-time complications such as theoutflow geometry, the density structure, and ongoing ac-tivity from the central engine. Recent relativistic hy-drodynamic simulations show that the earlier analyticmodels which used spherical geometry and Sedov-Taylordynamics to explain the late-time behavior were approxi-mately correct and produce a robust estimate of the totalkinetic energy (Zhang & MacFadyen 2009). In the past,the method has been limited to only a small number ofradio-bright events (e.g., van der Horst et al. 2008 andreferences therein). But it is somewhat encouraging thatboth early- and late-time estimates for the most ener-getic pre- Fermi event (GRB 970508; E KE ≈ erg) arein close agreement (Yost et al. 2003; Berger et al. 2004).With the advent of radio facilities having greatly in-creased sensitivity such as LOFAR (van Haarlem 2005)and the EVLA (Perley et al. 2009c), it should soon bepossible to verify candidate hyper-energetic events bysearching for long-lived ( t &
100 days) radio afterglows.Finally, we add a further note of caution that thederivation of the initial Lorentz factor Γ is alsosubject to significant systematic uncertainties (e.g.,Boˇsnjak et al. 2009). In order to calculate the opticaldepth to pair production, it is necessary to determinethe effective blast-wave radius as well as the instanta-neous spectral parameters. The former is typically in-ferred from the variability time scale, while the latter isusually averaged over the entire duration of the promptemission, and it is not always clear how large an effectthis will have on the calculation of Γ . The calculationsare further complicated if the spectrum is not a purepower law, as would be the case for thermal emission aris-ing from the jet photosphere (Ryde et al. 2010). Here we have attempted to calculate the initial Lorentz factors ina consistent manner, and it is not unreasonable to believethat the relative ordering of Γ is robust. However, smallchanges in Γ can have a large effect on some of the pa-rameters derived here (e.g., t dec ; Eqns. 3 and 4). Futureearly afterglow observations of Fermi -LAT GRBs to di-rectly measure the deceleration time and hence constrainΓ (e.g., Molinari et al. 2007) could provide valuable in-sight in this area. CONCLUSIONS
We have undertaken extensive broadband continuum(radio, optical, and X-ray) and spectroscopic observa-tions of four long-duration GRBs (GRBs 090323, 090328,090902B, and 090926A) detected by the LAT instru-ment on the
Fermi satellite at GeV energies. This workwas motivated by the realization that
Fermi is espe-cially sensitive to GRBs with large isotropic energy re-lease, and hence provides an interesting sample of eventsto test GRB central-engine models and their relativis-tic outflows. Our afterglow models constrain the jetbreak times and the density of the circumburst medium,from which we derive the collimation angle and hencebeaming-corrected energy release for each event. We findthree GRBs with a total relativistic content about anorder of magnitude in excess of the canonical 10 erg,with GRB 090926A almost certainly in excess of 10 erg.This analysis provides support for our earlier claim of aclass of hyper-energetic GRBs. The discovery of moreGRBs with total energy release & erg is troublingfor central engines in which the energy to drive the jetis derived either from a rotating magnetar or collapsarspowered by neutrino annihilation. For this reason, we areled to believe that, at least for hyper-energetic GRBs, themassive star progenitor collapses directly to a black holeand the rotational energy of this system is extracted viathe Blandford-Znajek process.Although we find relatively narrow opening angles forall four events ( θ . ◦ ), the extreme initial Lorentz fac-tors inferred for these LAT events imply that the product θ Γ can be a factor of 5–10 larger than estimates of previ-ous GRBs detected at MeV energies. These values are in-consistent with recent simulations of low-magnetizationMHD jets, suggesting that the outflow may be at leastinitially Poynting-flux dominated. If this is indeed thecase, it is unclear how the initial kinetic energy of theoutflow is converted to prompt gamma-ray emission.Interestingly, for the three events having sufficient ra-dio coverage to derive a circumburst density, we findanomalously large values of E KE , iso /n (or, for a wind-like medium, E KE , iso /A ∗ ). While the large E KE , iso valuesare simple to understand, the low circumburst densitiesrequire a more complex explanation.One possibility is that the progenitor stars of LATGRBs are somehow different from the progenitors of mostprevious GRBs detected at MeV or keV energies. Itis currently thought that GRB progenitors are distin-guished from the progenitors of ordinary SNe Ib/c bytheir low metallicities (e.g., MacFadyen & Woosley 1999;Woosley & Heger 2006; Modjaz et al. 2008): the lowermass-loss rates allow the progenitors of GRBs to keepmore angular momentum. The increased rotation evac-uates a cavity through which a relativistic jet can prop-agate. If LAT events have larger initial Lorentz factors,2 Cenko et al.it may be that they come from lower metallicity progeni-tors with minimal pre-explosion mass loss. Observationsof the host galaxies of these events, both through absorp-tion and emission spectroscopy, may help shed light onthis matter.It is also possible that the low density preference is theresult of other, more subtle, selection effects. In particu-lar, if the GeV emission arises in the external shock, the Fermi -LAT could be biased towards events in low-densityenvironments. If the circumburst density is too high, theblastwave will decelerate at small radii (Equations 3 and4), where the outflow may be opaque to GeV photons.More observations of LAT GRBs, particularly at veryearly times, would help to investigate this hypothesis.We end by emphasizing the importance of afterglowobservations of high- E γ, iso events in the Fermi era toprovide further confirmation of this picture. Such GRBsare either highly collimated outflows ( θ . ◦ ) with a typ-ical energy release, or truly hyper-energetic events; bothrepresent extreme tests of jet collimation and central-engine models, respectively. Current efforts suffer fromdelays in LAT localizations and limited ground-based af-terglow follow-up efforts. The latter can be improved byfocusing rare follow-up resources on Fermi -LAT GRBs;as Nysewander et al. (2009) and McBreen et al. (2010)have shown, these events have brighter X-ray and op-tical afterglows on average, and are therefore accessibleeven for moderate-aperture optical facilities. Targetingthese bright afterglows will make it easier to measure thejet breaks, which have proven almost impossible to ob-tain in the
Swift era. Finally, we note that one testableconsequence of hyper-energetic GRBs is long-lived after-glow emission ( & Swift grants NNX09AL08G andNNX10AI21G, and National Science Foundation (NSF)grants AST–0607485 and AST–0908886. B.E.C. grate-fully acknowledges support from an NSF Astronomy& Astrophysics Postdoctoral Fellowship (AST-0802333).N.R.B. is supported through the Einstein Fellowship Pro-gram (NASA Cooperative Agreement NNG06DO90A).J. S. B. and his group were partially supported byNASA/
Swift
Guest Investigator grant NNX09AQ66Gand a grant from DOE SciDAC.P60 operations are funded in part by NASA throughthe
Swift
Guest Investigator Program (grant numberNNG06GH61G). Based in part on observations obtainedat the Gemini Observatory (Programs GS-2009A-Q-23,GS-2009B-Q-5, GN-2009A-Q-26, and GN-2009B-Q-28),which is operated by the Association of Universities forResearch in Astronomy, Inc., under a cooperative agree-ment with the NSF on behalf of the Gemini partner-ship: the National Science Foundation (US), the Par-ticle Physics and Astronomy Research Council (UK),the National Research Council (Canada), CONICYT(Chile), the Australian Research Council (Australia),CNPq (Brazil) and CONICET (Argentina). We wishto thank the entire staff at Gemini for assistance withthese observations. SMARTS is supported by NSF grantAST–0707627.
Facilities:
Fermi (LAT, GBM), VLA, PO:1.5m,Gemini:South (GMOS), Gemini:North (GMOS),CTIO:2MASS (ANDICAM), Swift (XRT, UVOT)
REFERENCESAbazajian, K. N., et al. 2009, ApJS, 182, 543Abdo, A. A., et al. 2009a, ApJ, 706, L138—. 2009b, Science, 323, 1688Amati, L. 2006, MNRAS, 372, 233Asano, K., Guiriec, S., & M´esz´aros, P. 2009, ApJ, 705, L191Atwood, W. B., et al. 2009, ApJ, 697, 1071Baldwin, J. A., & Stone, R. P. S. 1984, MNRAS, 206, 241Band, D., et al. 1993, ApJ, 413, 281Barthelmy, S. D., et al. 2005, Space Science Reviews, 120, 143Beloborodov, A. M. 2009, eprint arXiv, (astro.ph/0907.0732)Berger, E., Kulkarni, S. R., & Frail, D. A. 2003a, ApJ, 590, 379—. 2004, ApJ, 612, 966Berger, E., Soderberg, A. M., Frail, D. A., & Kulkarni, S. R.2003b, ApJ, 587, L5Berger, E., et al. 2001, ApJ, 556, 556—. 2005, ApJ, 634, 501Birkl, R., Aloy, M. A., Janka, H.-T., & M¨uller, E. 2007, A&A,463, 51Bissaldi, E. 2009, GRB Coordinates Network, 9933, 1Bissaldi, E., Briggs, M. S., Piron, F., Takahashi, H., & Uehara, T.2009, GRB Coordinates Network, 9972, 1Bissaldi, E., & Connaughton, V. 2009, GRB CoordinatesNetwork, 9866, 1Blandford, R. D., & McKee, C. F. 1976, Physics of Fluids, 19,1130Blandford, R. D., & Znajek, R. L. 1977, MNRAS, 179, 433Bloom, J. S., Frail, D. A., & Kulkarni, S. R. 2003, ApJ, 594, 674Bloom, J. S., Frail, D. A., & Sari, R. 2001, The AstronomicalJournal, 121, 2879Boˇsnjak, ˇZ., Daigne, F., & Dubus, G. 2009, A&A, 498, 677Burenin, R., et al. 2009, GRB Coordinates Network, 9037, 1 Burrows, D. N., et al. 2005a, Science, 309, 1833—. 2005b, Space Science Reviews, 120, 165Butler, N. R., Bloom, J. S., & Poznanski, D. 2010, ApJ, 711, 495Butler, N. R., & Kocevski, D. 2007, ApJ, 663, 407Butler, N. R., Kocevski, D., Bloom, J. S., & Curtis, J. L. 2007,ApJ, 671, 656Campana, S., et al. 2006, Nature, 442, 1008Cavallo, G., & Rees, M. J. 1978, MNRAS, 183, 359Cenko, S. B., Bloom, J. S., Morgan, A. N., & Perley, D. A. 2009,GRB Coordinates Network, 9053, 1Cenko, S. B., & Perley, D. A. 2009, GRB Coordinates Network,9027, 1Cenko, S. B., et al. 2006, PASP, 118, 1396—. 2008, ApJ, 677, 441—. 2010, ApJ, 711, 641Chakrabarti, S. K., et al. 2009, GRB Coordinates Network,10009, 1Chandra, P., & Frail, D. A. 2009, GRB Coordinates Network,9889, 1Chandra, P., et al. 2008, ApJ, 683, 924—. 2010, ApJ, 712, L31Chandra, P., et al. 2010, in preparationChevalier, R. A., & Li, Z.-Y. 1999, The Astrophysical Journal,520, L29—. 2000, ApJ, 536, 195Chevalier, R. A., Li, Z.-Y., & Fransson, C. 2004, ApJ, 606, 369Chornock, R., Perley, D. A., Cenko, S. B., & Bloom, J. S. 2009,GRB Coordinates Network, 9028, 1Cobb, B. E., Bailyn, C. D., van Dokkum, P. G., Buxton, M. M.,& Bloom, J. S. 2004, ApJ, 608, L93 fterglow Observations of
Fermi -LAT GRBs 23
Cobb, B. E., Bailyn, C. D., van Dokkum, P. G., & Natarajan, P.2006, ApJ, 645, L113Cucchiara, A., Fox, D. B., Tanvir, N., & Berger, E. 2009, GRBCoordinates Network, 9873, 1Curran, P. A., Starling, R. L. C., van der Horst, A. J., & Wijers,R. A. M. J. 2009, MNRAS, 395, 580Cutini, S., Vasileiou, V., & Chiang, J. 2009, GRB CoordinatesNetwork, 9077, 1Daigne, F., & Mochkovitch, R. 1998, MNRAS, 296, 275de Palma, F., Bregeon, J., & Tajima, H. 2009, GRB CoordinatesNetwork, 9867, 1de Ugarte Postigo, A., Xu, D., Malesani, D., Hjorth, J., Fynbo, J.P. U., Jakobsson, P., & Adamo, A. 2009, GRB CoordinatesNetwork, 9051, 1Djorgovski, S. G., et al. 1997, Nature, 387, 876Evans, P. A. 2009, GRB Coordinates Network, 9871, 1Falcone, A. D., et al. 2007, ApJ, 671, 1921Ferrero, P., et al. 2006, A&A, 457, 857Frail, D. A., Chandra, P., & Cenko, B. 2009, GRB CoordinatesNetwork, 9060, 1Frail, D. A., Soderberg, A. M., Kulkarni, S. R., Berger, E., Yost,S., Fox, D. W., & Harrison, F. A. 2005, ApJ, 619, 994Frail, D. A., Waxman, E., & Kulkarni, S. R. 2000a, ApJ, 537, 191Frail, D. A., et al. 2000b, ApJ, 538, L129—. 2001, ApJ, 562, L55—. 2006, ApJ, 646, L99Freedman, D. L., & Waxman, E. 2001, ApJ, 547, 922Fukugita, M., Shimasaku, K., & Ichikawa, T. 1995, PASP, 107,945Gal-Yam, A., et al. 2004, ApJ, 609, L59Galama, T. J., et al. 1998, Nature, 395, 670Gehrels, N., Ramirez-Ruiz, E., & Fox, D. B. 2009, ARA&A, 47,567Gehrels, N., et al. 2004, ApJ, 611, 1005Ghisellini, G., Ghirlanda, G., Nava, L., & Celotti, A. 2010,Monthly Notices of the Royal Astronomical Society, 403, 926,(c) Journal compilation c (cid:13)
Panaitescu, A., & Kumar, P. 2000, ApJ, 543, 66—. 2001a, ApJ, 560, L49—. 2001b, ApJ, 554, 667—. 2002, ApJ, 571, 779Pandey, S. B., et al. 2010, eprint arXiv, (astro-ph/1003.4250)Pei, Y. C. 1992, The Astrophysical Journal, 395, 130Perley, D. A. 2009, GRB Coordinates Network, 9042, 1Perley, D. A., Klein, C. R., Morgan, A. N., & Petigura, E. 2009a,GRB Coordinates Network, 9036, 1Perley, D. A., et al. 2008, ApJ, 688, 470—. 2009b, ApJ, 696, 1871Perley, R., et al. 2009c, Proceedings of the IEEE (ISSN:0018-9219), 97, 1448Perna, R., Sari, R., & Frail, D. 2003, ApJ, 594, 379Pian, E., et al. 2006, Nature, 442, 1011Piran, T. 2005, Reviews of Modern Physics, 76, 1143Piran, T., & Nakar, E. 2010, eprint arXiv, (astro-ph/1003.5919)Piron, F., et al. 2009, in 2009
Fermi
Symposium, ed. eConfProceedings C0911022Popham, R., Woosley, S. E., & Fryer, C. 1999, ApJ, 518, 356Price, P. A., et al. 2002, ApJ, 572, L51Racusin, J. L., et al. 2009, ApJ, 698, 43Rau, A., Connaughton, V., & Briggs, M. 2009, GRB CoordinatesNetwork, 9057, 1Razzaque, S., Dermer, C. D., & Finke, J. D. 2009, eprint arXiv,(astro-ph/0908.0513)Rees, M. J., & Meszaros, P. 1998, ApJ, 496, L1Reichart, D., et al. 2005, Il Nuovo Cimento C, 28, 767Rhoads, J. E. 1999, ApJ, 525, 737Roming, P. W. A., et al. 2005, Space Science Reviews, 120, 95Rosswog, S., Ramirez-Ruiz, E., & Davies, M. B. 2003, MNRAS,345, 1077Ruffert, M., & Janka, H.-T. 1999, A&A, 344, 573Rumyantsev, V., & Pozanenko, A. 2009, GRB CoordinatesNetwork, 9324, 1Ryde, F. 2004, ApJ, 614, 827Ryde, F., et al. 2010, ApJ, 709, L172Sari, R., & Esin, A. A. 2001, ApJ, 548, 787Sari, R., & Piran, T. 1999, ApJ, 517, L109Sari, R., Piran, T., & Halpern, J. P. 1999, ApJ, 519, L17Sari, R., Piran, T., & Narayan, R. 1998, ApJ, 497, L17Sazonov, S. Y., Lutovinov, A. A., & Sunyaev, R. A. 2004, Nature,430, 646Schady, P., et al. 2007, MNRAS, 380, 1041Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500,525Shen, R., Kumar, P., & Robinson, E. L. 2006, MNRAS, 371, 1441Skrutskie, M. F., et al. 2006, AJ, 131, 1163Soderberg, A. M., & Ramirez-Ruiz, E. 2003, MNRAS, 345, 854Soderberg, A. M., et al. 2004, Nature, 430, 648—. 2006, Nature, 442, 1014—. 2010, Nature, 463, 513Sollerman, J., et al. 2006, A&A, 454, 503Spergel, D. N., et al. 2007, ApJS, 170, 377 Starling, R. L. C., van der Horst, A. J., Rol, E., Wijers, R. A.M. J., Kouveliotou, C., Wiersema, K., Curran, P. A., &Weltevrede, P. 2008, ApJ, 672, 433Starling, R. L. C., et al. 2009, MNRAS, 400, 90Stone, R. P. S., & Baldwin, J. A. 1983, MNRAS, 204, 347Stratta, G., D’Elia, V., & Perri, M. 2009, GRB CoordinatesNetwork, 9876, 1Swenson, C. A., & Siegel, M. H. 2009, GRB CoordinatesNetwork, 9869, 1Swenson, C. A., & Stratta, G. 2009, GRB Coordinates Network,9877, 1Tam, P. H., Pun, C. S. J., Huang, Y. F., & Cheng, K. S. 2005,New Astronomy, 10, 535Tchekhovskoy, A., McKinney, J. C., & Narayan, R. 2009a, ApJ,699, 1789Tchekhovskoy, A., Narayan, R., & McKinney, J. C. 2009b, eprintarXiv, (astro-ph/0909.0011)Terada, Y., et al. 2009, GRB Coordinates Network, 9897, 1Thompson, T. A., Chang, P., & Quataert, E. 2004, ApJ, 611, 380Thomsen, B., et al. 2004, A&A, 419, L21Uehara, T., Takahashi, H., & McEnery, J. 2009, GRBCoordinates Network, 9934, 1Updike, A., Klose, S., Clemens, C., & Greiner, J. 2009a, GRBCoordinates Network, 9054, 1Updike, A. C., Filgas, R., Kruehler, T., Greiner, J., & McBreen,S. 2009b, GRB Coordinates Network, 9026, 1Usov, V. V. 1992, Nature, 357, 472van der Horst, A. J. 2009, GRB Coordinates Network, 9047, 1van der Horst, A. J., Kamble, A. P., Wijers, R. A. M. J., &Kouveliotou, C. 2009, GRB Coordinates Network, 9883, 1van der Horst, A. J., & Xin, L. P. 2009, GRB CoordinatesNetwork, 9035, 1van der Horst, A. J., et al. 2008, A&A, 480, 35van Haarlem, M. P. 2005, EAS Publications Series, 15, 431Vetere, L. 2009, GRB Coordinates Network, 9961, 1Vetere, L., Evans, P. A., & Goad, M. R. 2009, GRB CoordinatesNetwork, 9936, 1Wade, R. A., & Horne, K. 1988, ApJ, 324, 411Wang, X. F., Xin, L. P., Zheng, W. K., Qiu, Y. L., Wei, J. Y.,Deng, J. S., & Hu, J. Y. 2009, GRB Coordinates Network,9034, 1Waxman, E., Kulkarni, S. R., & Frail, D. A. 1998, ApJ, 497, 288Wijers, R. A. M. J., & Galama, T. J. 1999, ApJ, 523, 177Willingale, R., et al. 2007, ApJ, 662, 1093Woosley, S. E. 1993, ApJ, 405, 273Woosley, S. E., & Bloom, J. S. 2006, ARA&A, 44, 507Woosley, S. E., & Heger, A. 2006, ApJ, 637, 914Yost, S. A., Harrison, F. A., Sari, R., & Frail, D. A. 2003, ApJ,597, 459Zeh, A., Klose, S., & Kann, D. A. 2006, ApJ, 637, 889Zhang, W., & MacFadyen, A. 2009, ApJ, 698, 1261Zhang, W., Woosley, S. E., & MacFadyen, A. I. 2003, ApJ, 586,356 fterglow Observations of
Fermi -LAT GRBs 25
TABLE 9Optical/NIR Observations of GRB 090323
Date a Time Since Burst b Telescope/Instrument Filter Exposure Time Magnitude c Reference d (UT) (days) (s)2009 Mar 24.12 1.12 GROND g ′ . ± .
07 12009 Mar 24.12 1.12 GROND r ′ . ± .
03 12009 Mar 24.12 1.12 GROND i ′ . ± .
02 12009 Mar 24.12 1.12 GROND z ′ . ± .
02 12009 Mar 24.12 1.12 GROND J . ± .
02 12009 Mar 24.12 1.12 GROND H . ± .
02 12009 Mar 24.12 1.12 GROND K s . ± .
03 12009 Mar 24.19 1.20 P60 r ′ . ± .
07 *2009 Mar 24.20 1.21 P60 i ′ . ± .
04 *2009 Mar 24.23 1.23 Gemini-S/GMOS i ′ . ± .
03 *2009 Mar 24.32 1.32 P60 r ′ . ± .
04 *2009 Mar 24.33 1.33 P60 i ′ . ± .
04 *2009 Mar 24.34 1.35 P60 r ′ . ± .
04 *2009 Mar 24.36 1.36 P60 i ′ . ± .
04 *2009 Mar 24.42 1.42 P60 r ′ . ± .
05 *2009 Mar 24.43 1.43 P60 i ′ . ± .
05 *2009 Mar 24.44 1.44 P60 r ′ . ± .
04 *2009 Mar 24.45 1.46 P60 i ′ . ± .
06 *2009 Mar 24.65 1.65 Xinglong/TNT R R . ± .
04 32009 Mar 25.06 2.06 RTT150 R . ± .
04 42009 Mar 25.21 2.21 P60 r ′ . ± .
10 *2009 Mar 25.22 2.22 P60 i ′ . ± .
09 *2009 Mar 25.23 2.24 P60 r ′ . ± .
11 *2009 Mar 25.24 2.25 P60 i ′ . ± .
09 *2009 Mar 25.26 2.26 P60 r ′ . ± .
09 *2009 Mar 25.27 2.27 P60 i ′ . ± .
08 *2009 Mar 25.28 2.28 P60 r ′ . ± .
08 *2009 Mar 25.29 2.29 P60 i ′ . ± .
08 *2009 Mar 25.30 2.30 Nickel R . ± . r ′ . ± .
07 *2009 Mar 25.31 2.32 P60 i ′ . ± .
07 *2009 Mar 25.50 2.50 Faulkes South i ′ . ± . R . ± . r ′ . ± .
14 *2009 Mar 26.24 3.26 P60 i ′ . ± .
19 *2009 Mar 27.31 4.31 P60 i ′ > .
60 *2009 Mar 27.36 4.36 Nickel R . ± .
18 72009 Mar 28.11 5.10 TLS Tautenberg R . ± .
20 82009 Mar 28.25 5.28 P60 i ′ . ± .
14 *2009 Mar 28.89 5.89 TLS Tautenberg R . ± .
50 92009 Mar 29.00 5.99 Shajn R . ± . R . ± .
06 112009 Mar 31.91 8.90 TLS Tautenberg R . ± .
36 92009 Apr 6.40 14.41 Gemini-N/GMOS r ′ . ± .
10 *2009 Jul 29.96 129.97 Gemini-S/GMOS r ′ . ± .
15 * a UT at beginning of exposure. b Time from midpoint of exposure to
Fermi -GBM trigger. c Reported magnitudes have not been corrected for Galactic extinction ( E ( B − V ) = 0 .
025 mag; Schlegel et al. 1998). Obser-vations in the R band are referenced to Vega, while all other filters are reported on the AB magnitude system (Oke & Gunn1983). d * – This work; 1 – Updike et al. (2009b); 2 – Wang et al. (2009); 3 – Kann et al. (2009b); 4 – Burenin et al. (2009); 5 –Perley et al. (2009a); 6 – Guidorzi et al. (2009); 7 – Perley (2009); 8 – Kann et al. (2009c); 9 – Kann et al. (2009a); 10 –Rumyantsev & Pozanenko (2009); 11 – de Ugarte Postigo et al. (2009). TABLE 10Optical/NIR Observations of GRB 090328
Date a Time Since Burst b Telescope/Instrument Filter Exposure Time Magnitude c Reference d (UT) (days) (s)2009 Mar 29.06 0.67 UVOT U . ± .
10 *2009 Mar 29.13 0.73 UVOT U . ± .
16 *2009 Mar 29.98 1.58 Gemini-S/GMOS i ′ . ± .
10 *2009 Mar 29.98 1.60 GROND g ′ . ± .
05 12009 Mar 29.98 1.60 GROND r ′ . ± .
03 12009 Mar 29.98 1.60 GROND i ′ . ± .
04 12009 Mar 29.98 1.60 GROND z ′ . ± .
03 12009 Mar 29.98 1.60 GROND J . ± .
06 12009 Mar 29.98 1.60 GROND H . ± .
06 12009 Mar 29.98 1.60 GROND K . ± .
08 12009 Mar 30.06 1.69 UVOT U . ± .
11 *2009 Mar 31.42 3.04 UVOT U . ± .
20 *2009 Apr 3.79 6.40 UVOT U . ± .
24 *2009 Apr 4.79 7.40 UVOT U . ± .
23 *2009 Apr 9.68 12.33 UVOT U . ± .
24 * a UT at beginning of exposure. b Time from midpoint of exposure to
Fermi -GBM trigger. c Reported magnitudes have not been corrected for Galactic extinction ( E ( B − V ) = 0 .
057 mag; Schlegel et al. 1998). Obser-vations in the U band are referenced to Vega, while all other filters are reported on the AB magnitude system (Oke & Gunn1983). d * – This work; 1 – Updike et al. (2009a). TABLE 11Optical Observations of GRB 090902B
Date a Time Since Burst b Telescope/Instrument Filter Exposure Time Magnitude c Reference d (UT) (days) (s)2009 Sep 2.51 0.06 ROTSE-IIIa R . ± . R > . U . ± .
15 *2009 Sep 3.08 0.64 UVOT U . ± .
09 *2009 Sep 3.19 0.74 Nickel R . ± .
10 12009 Sep 3.24 0.79 Gemini-N/GMOS r ′ . ± .
15 *2009 Sep 3.24 0.82 UVOT U . ± .
08 *2009 Sep 3.33 0.88 Liverpool R . ± .
11 12009 Sep 3.74 1.30 UVOT U . ± .
26 *2009 Sep 3.87 1.42 WHT-LIRIS J . ± .
15 12009 Sep 3.89 1.44 Liverpool R . ± .
10 12009 Sep 3.92 1.47 WHT-LIRIS K . ± .
20 12009 Sep 3.99 1.54 GROND r ′ . ± .
05 12009 Sep 4.00 1.55 NOT V . ± .
11 12009 Sep 4.01 1.56 NOT R . ± .
11 12009 Sep 4.02 1.57 NOT I . ± .
11 12009 Sep 4.36 1.91 UKIRT-WFCAM J . ± .
20 12009 Sep 4.36 1.91 UKIRT-WFCAM K . ± .
25 12009 Sep 4.98 2.53 GROND r ′ . ± .
07 12009 Sep 5.93 3.48 Liverpool R . ± .
25 12009 Sep 6.37 3.97 UVOT U . ± .
21 *2009 Sep 8.98 6.53 GROND r ′ . ± .
17 12009 Sep 10.37 7.97 UVOT U > .
56 * a UT at beginning of exposure. b Time from midpoint of exposure to
Fermi -GBM trigger. c Reported magnitudes have not been corrected for Galactic extinction ( E ( B − V ) = 0 .
042 mag; Schlegel et al. 1998).Observations in the the r ′ filter are reported on the AB magnitude system (Oke & Gunn 1983), while all other filters arereferenced to Vega. d * – This work; 1 – Pandey et al. (2010). fterglow Observations of Fermi -LAT GRBs 27
TABLE 12Optical/NIR observations of GRB 090926A
Date a Time Since Burst b Telescope/Instrument Filter Exposure Time Magnitude c (UT) (d) (s)2009 Sep 26.72 0.5415 UVOT U . ± . V . ± . U . ± . V . ± . U . ± . V . ± . U . ± . V . ± . R . ± . I . ± . U . ± . V . ± . I . ± . R . ± . V . ± . I . ± . R . ± . R . ± . I . ± . I . ± . J . ± . V . ± . B . ± . R . ± . I . ± . U . ± . R . ± . I . ± . V . ± . B . ± . V . ± . I . ± . R . ± . I . ± . R . ± . B . ± . V . ± . I . ± . R . ± . R . ± . I . ± . B . ± . V . ± . R . ± . I . ± . U . ± . R . ± . I . ± . B . ± . V . ± . R . ± . I . ± . V . ± . B . ± . I . ± . V . ± . R . ± . U . ± . I . ± . R . ± . B . ± . V . ± . R . ± . I . ± . R . ± . I . ± . V . ± . B . ± . I . ± . R . ± . I . ± . R . ± . V . ± . B . ± . TABLE 12 — Continued
Date a Time Since Burst b Telescope/Instrument Filter Exposure Time Magnitude c (UT) (d) (s)2009 Sep 27.21 1.0653 PROMPT-4 R . ± . I . ± . U . ± . R . ± . I . ± . B . ± . V . ± . R . ± . I . ± . I . ± . R . ± . B . ± . V . ± . R . ± . I . ± . I . ± . R . ± . B . ± . V . ± . I . ± . R . ± . R . ± . I . ± . V . ± . B . ± . R . ± . I . ± . R . ± . I . ± . B . ± . V . ± . R . ± . I . ± . B . ± . R . ± . I . ± . V . ± . U . ± . U . ± . V . ± . U . ± . U . ± . U . ± . U . ± . U . ± . U . ± . V . ± . U . ± . V . ± . I . ± . R . ± . I . ± . R . ± . I . ± . J . ± . I . ± . B > . R . ± . V > . V . ± . U . ± . I . ± . R . ± . I . ± . R . ± . B . ± . V . ± . I . ± . R . ± . I . ± . R . ± . V . ± . U . ± . R . ± . I . ± . fterglow Observations of Fermi -LAT GRBs 29
TABLE 12 — Continued
Date a Time Since Burst b Telescope/Instrument Filter Exposure Time Magnitude c (UT) (d) (s)2009 Oct 1.11 4.9658 SMARTS / ANDICAM I . ± . J . ± . V > . B . ± . I . ± . R . ± . U . ± . R . ± . V > . B > . R . ± . I . ± . R > . I > . B > . U . ± . I > . R > . B > . U . ± . R > . I > . U . ± . U . ± . R . ± . I > . U . ± . U . ± . g ′ . ± . r ′ . ± . i ′ . ± . a UT at beginning of exposure.b Time from midpoint of exposure to Fermi -GBM trigger.c Reported magnitudes have not been corrected for Galactic extinction ( E ( B − V ) = 0 .
024 mag; Schlegel et al. 1998). Observations in the g ′ -, r ′ -, and i ′′