DRAFT VERSION OCTOBER 1, 2013 Preprint typeset using LATEX style emulateapj v. 5/2/11

arXiv:1309.7479v1 [astro-ph.HE] 28 Sep 2013

SHORT GRB 130603B: DISCOVERY OF A JET BREAK IN THE OPTICAL AND RADIO AFTERGLOWS, AND A MYSTERIOUS LATE-TIME X-RAY EXCESS
W. FONG1, E. BERGER1, B. D. METZGER2, R. MARGUTTI1, R. CHORNOCK1, G. MIGLIORI1, R. J. FOLEY3,4 , B. A. ZAUDERER1, R. LUNNAN1, T. LASKAR1, S. J. DESCH5, K. J. MEECH6, S. SONNETT6, C. DICKEY7, A. HEDLUND7, P. HARDING8
Draft version October 1, 2013
ABSTRACT
We present radio, optical/NIR, and X-ray observations of the afterglow of the short-duration GRB 130603B, and uncover a break in the radio and optical bands at ≈ 0.5 d after the burst, best explained as a jet break with an inferred jet opening angle of ≈ 4 − 8◦. GRB 130603B is only the third short GRB with a radio afterglow detection to date, and the first time that a jet break is evident in the radio band. We model the temporal evolution of the spectral energy distribution to determine the burst explosion properties and find an isotropic-equivalent kinetic energy of ≈ (0.6 − 1.7) × 1051 erg and a circumburst density of ≈ 5 × 10−3 − 30 cm−3. From the inferred opening angle of GRB 130603B, we calculate beaming-corrected energies of Eγ ≈ (0.5 − 2) × 1049 erg and EK ≈ (0.1 − 1.6) × 1049 erg. Along with previous measurements and lower limits we find a median opening angle of ≈ 10◦. Using the all-sky observed rate of 10 Gpc−3 yr−1, this implies a true short GRB rate of ≈ 20 yr−1 within 200 Mpc, the Advanced LIGO/VIRGO sensitivity range for neutron star binary mergers. Finally, we uncover evidence for significant excess emission in the X-ray afterglow of GRB 130603B at 1 d and conclude that the additional energy component could be due to fall-back accretion or spin-down energy from a magnetar formed following the merger.

1. INTRODUCTION
The broad-band afterglows of short-duration gamma-ray bursts (GRBs; T90 < 2 sec; Kouveliotou et al. 1993) provide a unique opportunity to study the basic properties of these events: their energetics, circumburst densities, and jet opening angles. While the energy scales and densities provide fundamental insight to the explosion physics and progenitors, the geometry provides direct information on the population’s true energy scale and event rate. The most likely progenitors, neutron star-neutron star (NS-NS) and/or neutron star-black hole (NS-BH) mergers (Eichler et al. 1989; Narayan et al. 1992; Fong et al. 2010; Berger 2010; Fong & Berger 2013), are the premier candidates of gravitational waves for Advanced LIGO/VIRGO. Thus, an inference on the opening angle distribution will aid our expectations for coincident electromagnetic-gravitational wave detections.
Over the past ∼ 9 years, the Swift satellite (Gehrels et al. 2004) has discovered 77 short GRBs, with a median γ-ray fluence of ≈ 2 × 10−7 erg cm−2 (15 − 150 keV; Gehrels et al. 2008; Nysewander et al. 2009). Coupled with redshift measurements from their host galaxies, this has demonstrated a range of isotropic-equivalent γ-ray energies of Eγ,iso ≈ 1048 − 1052 erg (Berger 2007; Nysewander et al. 2009). Temporal
1 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
2 Department of Physics and Columbia Astrophysics Laboratory, Columbia University, New York, NY, 10027
3 Astronomy Department, University of Illinois at UrbanaChampaign, 1002 W. Green Street, Urbana, IL 61801 USA
4 Department of Physics, University of Illinois Urbana-Champaign, 1110 W. Green Street, Urbana, IL 61801 USA
5 School of Earth and Space Exploration, Arizona State University, P. O. Box 871404, Tempe, AZ, 85287-1404
6 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
7 Pomona College, 610 N. College Ave., Claremont, CA, 91711 8 Department of Astronomy, Case Western Reserve University, Cleveland, OH 44106-7215, USA

monitoring of their broad-band afterglows has led to a similarly broad range of inferred isotropic-equivalent kinetic energies, EK,iso ≈ 1048 − 1052 erg, circumburst densities of 1 cm−3 (Soderberg et al. 2006; Panaitescu 2006; Stratta et al.
2007; Perley et al. 2009; Berger 2010; Fong et al. 2011), and opening angles of 3 − 25◦ (Fox et al. 2005; Grupe et al. 2006; Soderberg et al. 2006; Fong et al. 2012; Margutti et al.
2012a; Nicuesa Guelbenzu et al. 2012; Berger et al. 2013;
Sakamoto et al. 2013). Collimation in GRBs is determined from temporal steep-
enings in afterglow light curves, termed “jet breaks”, which
are expected to be achromatic (Sari et al. 1999; Rhoads 1999; Panaitescu 2005). Jet breaks in the light curves of
long GRBs translate to an opening angle distribution with a range of θ j ≈ 2 − 25◦ and a median of ≈ 7◦, leading to beaming-corrected energies of Eγ = [1 − cos(θ j)]Eγ,iso ≈ 1051 erg (Bloom et al. 2003; Frail et al. 2001; Friedman & Bloom
2005; Kocevski & Butler 2008; Racusin et al. 2009). For short GRBs, the search for jet breaks has been more chal-
lenging, primarily due to the intrinsic faintness of their af-
terglows, a direct reflection of their low energy scales and circumburst densities. There are only three robust cases of
jet breaks for short GRBs based on well-sampled light curves
thus far (GRB 051221A: Soderberg et al. 2006, GRB 090426: Nicuesa Guelbenzu et al. 2011; GRB 111020A: Fong et al. 2012), with θ j ≈ 3 − 8◦. The non-detection of jet breaks to
1 day after the burst has also provided lower limits on the jet opening angles of 3 − 25◦ (Fox et al. 2005; Grupe et al. 2006; Fong et al. 2012; Coward et al. 2012; Margutti et al.
2012a; Berger et al. 2013), suggesting that short GRBs may have wider jets than their long-duration counterparts.
In addition to an inference on the opening angles, after-
glows can also provide unique constraints on the energy scales and circumburst densities through multi-wavelength detec-
tions and modeling of the spectral energy distributions. How-
ever, of the 77 Swift short GRBs detected to present, only two have been detected in the radio band (GRB 050724A:

2 Fong et. al.

Berger et al. 2005; GRB 051221A: Soderberg et al. 2006). Both of these events have inferred densities of ≈ 10−2 cm−3 and isotropic-equivalent energies of ≈ 1051 erg. The upgrade of the VLA with a ten-fold increase in sensitivity (Perley et al. 2011) provides a promising route to increased radio afterglow detections, and thus substantially tighter constraints on these properties.
Temporal afterglow information, particularly in the X-ray band, has also revealed cases of anomalous behavior that do not fit with the standard synchrotron picture of afterglows. For short GRBs, there have been observed cases of flares at 1000 s after the burst (Grupe et al. 2006; Margutti et al. 2011), shallow decays attributed to energy injection (e.g., Soderberg et al. 2006), putative early plateaus attributed to the spin-down power of a hyper-massive and highly-magnetized neutron star remnant (Rowlinson et al. 2010, 2013) and two cases of late-time X-ray re-brightenings on ∼ day timescales (GRB 050724A: Grupe et al. 2006; GRB 080503: Perley et al. 2009).
Recently, the short-duration GRB 130603B sparked much interest, because its bright optical afterglow enabled the first afterglow spectrum of a short GRB and thus an unambiguous redshift determination of z = 0.3565 ± 0.0002 (Cucchiara et al. 2013; de Ugarte Postigo et al. 2013). It also led to the first claimed detection of a “kilonova” associated with a short GRB (Berger et al. 2013; Tanvir et al. 2013), providing direct evidence for a compact object binary progenitor. Here, we present and model the broad-band afterglow of GRB 130603B. In Section 2, we present the X-ray, optical/NIR and radio data sets. In Section 3, we model the evolution of the spectral energy distribution (SED) and constrain the burst explosion properties. In Section 4, we discuss the steepening in the radio and optical light curves, best explained as a jet break. In Section 5, we investigate several possibilities to explain excess X-ray emission at 1 day. Finally in Section 6, we discuss GRB 130603B in the context of the short GRB population, and investigate implications for the energy scale and event rate.
Unless otherwise noted, all magnitudes in this paper are in the AB system and are corrected for Galactic extinction in the direction of the burst using E(B − V ) = 0.02 mag (Schlegel et al. 1998; Schlafly & Finkbeiner 2011). Reported uncertainties correspond to 68% confidence. We employ a standard ΛCDM cosmology with ΩM = 0.27, ΩΛ = 0.73, and H0 = 71 km s−1 Mpc−1.
2. OBSERVATIONS
GRB 130603B was detected on 2013 June 3 at 15:49:14 UT by the Burst Alert Telescope (BAT; Barthelmy et al. 2005) onboard the Swift satellite (Melandri et al. 2013), and by KonusWind (Golenetskii et al. 2013). Swift/BAT localized the burst to RA=11h28m53.2s and Dec=+17◦03′48.2′′ (J2000) with 1.0′ accuracy (90% containment; Barthelmy et al. 2013). The γray emission consists of a single pulse with a duration of T90 = 0.18 ± 0.02 s (15 − 150 keV; Barthelmy et al. 2013), a fluence of fγ = (6.6 ± 0.7) × 10−6 erg cm−2 (20 − 104 keV; Golenetskii et al. 2013), and a peak energy of Epk = 660 ± 100 keV (Golenetskii et al. 2013). The spectral lags are 0.6 ± 0.7 ms (15 − 25 keV to 50 − 100 keV) and −2.5 ± 0.7 ms (25 − 50 keV to 100−350 keV; Norris et al. 2013). The combination of the duration, high peak energy, and zero (or negative) lag unambiguously classifies GRB 130603B as a short-hard burst. At z = 0.3565 (Cucchiara et al. 2013; de Ugarte Postigo et al. 2013), the isotropic-equivalent gamma-ray energy is Eγ,iso ≈

2.1 × 1051 erg (20 − 104 keV, rest-frame).
2.1. X-rays
Observations with the X-ray Telescope (XRT; Burrows et al. 2005) on-board Swift commenced at δt = 59 s (where δt is the time after the BAT trigger) and revealed a fading, uncatalogued X-ray source with a UVOT-enhanced position of RA=11h28m48.15s and Dec=+17◦04′16.9′′ (J2000) and an uncertainty of 1.4′′ radius (90% containment; Goad et al. 2007; Evans et al. 2007, 2009). The source faded below the XRT detection threshold by δt ≈ 2 d. We analyze the XRT data using the HEASOFT package (v.6.13) and relevant calibration files. To generate a count-rate light curve, we apply standard filtering and screening criteria (see Margutti et al. 2012b), ensuring a minimum signal-to-noise ratio of 4 for each temporal bin.
We initiated a target-of-opportunity program on XMMNewton (ID: 072257, PI: Fong) with the European Photon Imaging Camera (EPIC-PN) and obtained observations at δt ≈ 2.7 d and ≈ 6.5 d with net exposure times of 18.5 ks and 30.2 ks, respectively. We analyze these data using standard routines in the Scientific Analysis System (SAS) and detect a fading source coincident with the XRT position. We find ≈ 60 counts (∼ 4σ) in the first observation in a 30′′-radius aperture, and ≈ 10 counts (3σ) in the second observation in a 15′′-radius aperture, where the aperture size is adjusted to maximize the signal-to-noise ratio.
To determine the flux calibration, we model the XRT data with an absorbed single power-law spectrum, using the Galactic neutral Hydrogen absorption column (NH,MW = 1.93 × 1020 cm−2; Kalberla et al. 2005). We fit for the photon index, Γ and the intrinsic Hydrogen absorption column (NH,int at z = 0.3565). Using all of the available XRT data, we find NH,int = (2.4 ± 0.4) × 1021 cm−2 and Γ = 2.2 ± 0.1. We apply these spectral parameters to the XRT and XMM data. The resulting fluxes from XMM are listed in Table 1.
2.2. Optical
Subsequent to the discovery of the X-ray afterglow (Melandri et al. 2013), ground-based optical/NIR observations began at δt ≈ 2.7 hr to search for an optical counterpart (Berger et al. 2013; Cucchiara et al. 2013; de Ugarte Postigo et al. 2013; Tanvir et al. 2013). We initiated four sets of r-band observations of GRB 130603B using instruments on the twin Magellan 6.5-m telescopes, spanning δt ≈ 8.1 hr to ≈ 37 d (Table 1). The description of these observations and the optical afterglow discovery are provided in Berger et al. (2013). In addition, we obtained a set of rband observations with MMTCam on the 6.5-m Multi-Mirror Telescope (MMT) and processed these data using standard procedures in IRAF. All of the published optical/NIR afterglow photometry (Berger et al. 2013; Cucchiara et al. 2013; de Ugarte Postigo et al. 2013; Tanvir et al. 2013), are listed in Table 1.
2.3. Radio
We observed the position of GRB 130603B with the Karl G. Jansky Very Large Array (VLA; Program 13A-046, PI: Berger) starting at δt ≈ 8.8 hr at a mean frequency of 5.8 GHz (upper and lower side-bands centered at 6.7 GHz and 4.9 GHz) using 3C286 and J1120-1420 for bandpass/flux and gain calibration, respectively. We follow standard procedures in the Astronomical Image Processing System (AIPS;

Short GRB 130603B

3

Table 1 GRB 130603B Afterglow Photometry

δt Exposure Time (d) (hr)

Telescope

2.69 5.14 XMM-Newton 6.50 8.38 XMM-Newton

Instrument

Band

X-rays

EPIC-pn EPIC-pn

1 keV 1 keV

Fν (µJy)

σν (µJy)

References

2.44 × 10−3 8.25 × 10−4

4.59 × 10−4 5.03 × 10−4

This work This work

Optical

0.008 0.089 0.24 0.25 0.27 0.28 0.29 0.29 0.33 0.34 0.37 0.60 0.60 0.61 0.61 0.62 0.62 1.30 1.30 1.34 1.59 1.60 1.61 1.61 1.62 2.32 3.26 4.26 7.30 8.23 8.25 8.41 9.37 a 9.41 21.26 21.29 21.52 29.57 37.34

0.05 1.42 0.50 0.25 0.25 0.50 0.008 0.25 0.40 0.17 0.40 0.14 0.19 0.14 0.19 0.14 0.14 0.15 0.15 0.33 0.17 0.17 0.17 0.39 0.17 0.37 0.17 0.17 0.37 0.33 0.33 0.33 0.62 0.73 0.67 0.67 0.28 0.73 0.75

Swift Swift NOT WHT WHT CAHA GTC WHT Gemini-South Magellan/Baade Gemini-South Gemini-North UKIRT Gemini-North UKIRT Gemini-North Gemini-North Gemini-South Gemini-South Magellan/Baade Gemini-North Gemini-North Gemini-North UKIRT Gemini-North VLT GTC GTC VLT TNG TNG Magellan/Baade HST HST TNG TNG MMT HST Magellan/Clay

UVOT UVOT MOS ACAM ACAM DLR-MKIII OSIRIS ACAM GMOS IMACS GMOS GMOS WFCAM GMOS WFCAM GMOS GMOS GMOS GMOS IMACS GMOS GMOS GMOS WFCAM GMOS HAWK-I OSIRIS OSIRIS HAWK-I DOLoRes DOLoRes IMACS ACS WFC3 DOLoRes DOLoRes MMTCam WFC3 LDSS3

V V r z i V r g g r i z K i J r g r i r g r i J z J r r J r i r F606W F160W r i r F160W r

Radio

< 199.5 < 53.95
12.59 25.35 16.44 8.32 10.96 6.31 5.30 8.64 12.25 6.54 13.68 4.53 9.29 2.88 1.60 < 0.30 < 0.58 < 0.46 < 0.19 0.21 < 0.48 < 1.25 < 1.00 < 1.25 < 0.33 < 0.23 < 1.45 < 1.15 < 0.52 < 0.40 < 0.03 0.17 < 1.49 < 0.93 < 1.91 < 0.10 < 0.40

1 1 0.23 2 1.36 1 0.88 1 0.73 1 0.20 2 0.34 2 0.19 3 0.14 4 1.18 3 0.18 2 1.32 2 0.12 2 1.12 2 0.08 2 0.06 2 3 3
4 2 0.05 2 2 2
2 2 2
2 2
1 1
This work 4
0.03 2, 4 1 1
This work 4
This work

0.37 0.37 1.43 1.43 1.44 4.32 4.32 84.31 84.31

2.00 2.00 1.00 1.00 1.00 2.00 2.00 1.00 1.00

VLA VLA VLA VLA VLA VLA VLA VLA VLA

4.9 GHz 6.7 GHz 4.9 GHz 6.7 GHz 21.8 GHz 4.9 GHz 6.7 GHz 4.9 GHz 6.7 GHz

125.1 118.6 < 56.7 64.9 < 50.0 < 51.0 < 25.8 < 68.6 < 33.7

14.4 This work 9.1 This work
This work 15.2 This work
This work This work This work This work This work

Note. — All upper limits correspond to 3σ confidence. Optical flux densities are corrected for Galactic extinction in
the direction of the burst, but are not corrected for extinction in the rest-frame of the burst. a The reported flux and uncertainty are of the claimed kilonova detection (Berger et al. 2013; Tanvir et al. 2013).
References: (1) de Ugarte Postigo et al. 2013; (2) Tanvir et al. 2013; (3) Cucchiara et al. 2013; (4) Berger et al. 2013

Greisen 2003) for data calibration and analysis. We detect a source located at RA=11h28m48.15s, Dec=+17◦04′18.0′′ (J2000; δRA= 0.21′′, δDec= 0.14′′), consistent with the optical and X-ray afterglow positions. We obtained three subsequent 5.8 GHz observations at δt ≈ 1.4 d, ≈ 4.3 d, and ≈ 84.3 d in which the source faded, indicating that it is the radio afterglow. We also obtained observations at a mean frequency of 21.8 Hz at δt ≈ 1.4 d (using J1118+1234 as the
phase calibrator), where the afterglow is not detected.
We measure flux densities for the upper and lower sidebands from each epoch using AIPS/JMFIT, and calculate 3σ

upper limits from source-free regions using AIPS/IMSTAT. The radio afterglow detections and upper limits are listed in Table 1.
3. BROAD-BAND AFTERGLOW PROPERTIES
We utilize the broad-band afterglow observations to constrain the explosion properties and circumburst environment of GRB 130603B. We emphasize that this is only the third radio afterglow detection of a short GRB, thereby enabling substantially tighter constraints on the physical properties than for the majority of short GRBs. We adopt the stan-

4
103
102
101

Fong et. al.
102 101

Flux Density (µJy) Flux Density (µJy)

100 100

10−1 δ t = 0.37 d

10−1 δ t = 0.60 d

10−2 108 109 1010 1011 1012 1013 1014 1015 1016 1017 1018 Frequency (Hz)

10−2 108 109 1010 1011 1012 1013 1014 1015 1016 1017 1018 Frequency (Hz)

Figure 1. Radio (red; 6.7 GHz), optical/NIR (green; griJ-band; Berger et al. 2013; Cucchiara et al. 2013; Tanvir et al. 2013) and X-ray (blue; 1 keV) afterglow spectral energy distributions of GRB 130603B at δt = 0.37 d (left) and 0.60 d (right). The grizJ afterglow observations are corrected for AVhost = 1 mag. Error bars correspond to 1σ confidence. A representative best-fit model (black line) is shown in each panel.

dard synchrotron model for a relativistic blastwave in a con-
stant density medium (ISM; Sari et al. 1999; Granot & Sari
2002). This model provides a mapping from the broad-band
afterglow flux densities to physical parameters of the explo-
sion and circumburst environment: isotropic-equivalent ki-
netic energy (EK,iso), circumburst density (n0), fractions of post-shock energy in radiating electrons (ǫe) and magnetic fields (ǫB), and the electron power-law distribution index (p), with N(γ) ∝ γ−p for γ γmin.
To determine the locations of the break frequencies with re-
spect to the X-ray, optical and radio bands, we first compare
the spectral indices from the afterglow observations. From the X-ray spectral fit, we find βX ≡ 1 − Γ = −1.2 ± 0.1 (Section 2.1), while from the optical griz-band afterglow photometry at δt ≈ 0.6 d (Table 1; Cucchiara et al. 2013; Tanvir et al. 2013), we measure an observed spectral index of βopt,obs = −2.0 ± 0.1. The NIR spectral index measured from the JKbands at the same epoch is substantially shallower, βNIR = −0.6 ± 0.2, indicating that the optical flux is suppressed by extinction in the host galaxy. To determine the amount of extinc-
tion, we apply a Milky Way extinction curve (Cardelli et al.
1989) to the grizJK photometry, fitting for the spectral index and rest-frame extinction (AVhost), and find best-fit values of βopt = −0.84 ± 0.10 and AVhost = 1.0 ± 0.1 mag, similar to the values found from other analyses (de Ugarte Postigo et al.
2013; Jin et al. 2013). Using standard Galactic relations be-
tween the intrinsic hydrogen column density and rest-frame
extinction (Predehl & Schmitt 1995; Watson 2011), we find an inferred extinction of AVhost = 0.9 − 1.6 mag from the NH,int value determined in Section 2.1, consistent with AVhost ≈ 1 mag. A comparison of βopt and βX indicates that the cooling frequency, νc, lies between the optical and X-ray bands, and that p = 2.55 ± 0.15.
To determine the location of the self-absorption and peak frequencies (νa and νm, respectively) with respect to the optical and radio bands, we compare the radio spectral slope determined from VLA observations at δt ≈ 0.37 d and 1.43 d (Table 1) to βopt. We find that βrad does not match the optical slope and furthermore is consistent with Fν ∝ ν1/3, as expected for νa < νrad < νm.

Knowing the relative locations of the break frequencies
with respect to our observing bands, we use the standard synchrotron model to determine allowable ranges for the phys-
ical parameters. We use the afterglow SED at two common epochs, δt = 0.37 d and 0.60 d, where the optical/NIR fluxes are corrected for AVhost = 1 mag (Figure 1). We also use the constraints ǫe, ǫB < 1/3 and determine:

3.3 × 108 < νa < 2.6 × 109 Hz 5.8 × 10−2 < ǫe < 1/3 2.0 × 10−3 < ǫB < 1/3
0.6 × 1051 erg < EK,iso < 1.7 × 1051 erg 4.9 × 10−3 cm−3 < n0 < 30 cm−3

(1) (2) (3) (4) (5)

where the ranges are set by the uncertainty in νa and the conditions that ǫe, ǫB < 1/3. We note that the inferred isotropicequivalent kinetic energy is comparable to Eγ,iso ≈ 2.1 × 1051 erg. We show representative model SEDs along with the broad-band afterglow observations in Figure 1.
4. AFTERGLOW EVOLUTION: JET BREAK
To investigate the temporal behavior of the optical/NIR afterglow, we interpolate all of the available afterglow data (Table 1) to the optical r-band using the observed spectral slope (Section 3) and then correct these fluxes for AVhost = 1 mag. The resulting temporal behavior of the optical afterglow flux is characterized by a broken power law (Figure 2). Invoking a broken power law model with two segments, we find pre- and post-break decay indices of α1 ≈ −1.26 ± 0.05 and α2 = −2.73 ± 0.08, with a break time of tb = 0.47−+00..0062 d. The required change in the temporal index is therefore ∆α ≈ 1.5. Although there are several possibilities that can explain breaks in GRB afterglow light curves, most of these cannot explain the large change in slope and the steep post-break decline seen here. For instance, the transition of the cooling frequency across the band predicts ∆α = 0.25 (Sari et al. 1998), while the cessation of energy injection observed in long GRBs typically leads to ∆α ≈ 0.7 with moderate decline rates of

Short GRB 130603B

5

103
NIR H−band 102 Ahost=1 mag
102 V

H−band Flux Density (µJy)

6.7 GHz Flux Density (µJy)

101

101 10−1
103
102
101

t
jet

100

Radio

100 101 Time after Burst (d)

102

Optical r−band AVhost=1 mag

10−1 10−2
102
101

1998bw 2006aj

100 10−1

t
jet

10−1

100

Time after Burst (d)

101

X−ray

1 keV Flux Density (µJy)

r−band Flux Density (µJy)

100 10−2
Swift/XRT

10−1

10−2

t
jet

10−1

100

Time after Burst (d)

101

10−3 10−3

XMM−Newton

t
jet

10−2

10−1

100

Time after burst (d)

101

Figure 2. Radio through X-ray afterglow light curves of GRB 130603B. Error bars correspond to 1σ confidence, and triangles denote 3σ upper limits. The afterglow model is shown as a black line, while the jet break time of tj ≈ 0.47 d is marked by a vertical grey dashed line. Also shown is a model with energy injection (dark grey dashed line) that fits the X-ray excess but violates the detections and limits in the optical, NIR, and radio bands. Top left: 6.7 GHz observations
with the VLA (red). Top right: H-band observations (green; Berger et al. 2013; de Ugarte Postigo et al. 2013; Tanvir et al. 2013), where JK-band observations
are extrapolated to H-band using βopt = −2. The observed values (open green squares) are corrected for AVhost = 1 mag (filled green symbols). The circled asterisk at δt ≈ 9 d is the “kilonova” associated with GRB 130603B (Berger et al. 2013; Tanvir et al. 2013). Bottom left: Optical r-band observations (orange; this work, Cucchiara et al. 2013; de Ugarte Postigo et al. 2013; Tanvir et al. 2013), where giz-band observations are extrapolated to r-band using βopt = −2. The
observed values (open orange squares) are corrected for AVhost = 1 mag (filled orange symbols). The displayed upper limits (orange triangles) are also corrected for extinction. Also shown are the optical light curves of GRB-SN 1998bw (Galama et al. 1998; Clocchiatti et al. 2011) and GRB-SN 2006aj (dot-dashed lines; Mirabal et al. 2006) corrected for extinction and redshifted to z = 0.3565. Bottom right: Observations from Swift/XRT (blue circles) and XMM-Newton (blue squares) at 1 keV.

α1 ≈ −0.5 and α2 ≈ −1.2 (Nousek et al. 2006; Zhang et al. 2006; Liang et al. 2007). A steep drop in the density is predicted to cause maximum changes of ∆α ≈ 0.4 for density contrasts of ∼ 10 (Nakar & Granot 2007), and would require a density contrast of 1000 to account for ∆α = 1.5.
We therefore conclude that the temporal steepening is in-
stead a jet break, when the edge of a relativistically-beamed
outflow becomes visible to the observer (Sari et al. 1999;
Rhoads 1999). In this scenario, the post-break flux declines as t−p (Sari et al. 1999). Indeed, we find good agreement between α2 = −2.7 ± 0.1 determined from the optical light curve and p = 2.55±0.15 independently determined from the broad-
band SED (Section 3). In addition, since the radio band lies between νa and νm

(Section 3), the radio flux density should increase as Fν ∝ t1/2 in the spherical regime (Granot & Sari 2002), while the flux will decrease as Fν ∝ t−1/3 in a post-jet break scenario (Sari et al. 1999). We find that the observed radio flux of GRB 130603B declines with α ≈ −0.45 between δt ≈ 0.4 d and 1.3 d, demonstrating that the evolution is not isotropic
(Figure 2). Thus, the temporal behavior of both the optical and radio afterglows support a jet break at t j ≈ 0.47 d, making this the first detection of a jet break in the radio afterglow
of a short GRB.
In conjunction with the energy, density, and redshift, the
time of the break can be converted to a jet opening angle
(Sari et al. 1999; Frail et al. 2001),

6 Fong et. al.

θ j = 9.51t3j,/d8(1 + z)−3/8EK−1,i/s8o,52n01/8 deg

(6)

where t j,d is in days, EK,iso,52 is in units of 1052 erg and n0 is in units of cm−3. For the ranges of EK,iso and n0 in Equations 4-5, we calculate θ j ≈ 4 − 14◦. However, given a NS-NS/NS-BH progenitor as indicated by the likely detection of a kilonova
(Berger et al. 2013; Tanvir et al. 2013), the circumburst density is likely more typical of ISM densities (n 1 cm−3), leading to θ j ≈ 4 − 8◦.

5. LATE-TIME X-RAY EXCESS
The synchrotron afterglow model with a jet break at t j ≈ 0.47 d provides a good match to the radio and optical light curves (Figure 2). However, unlike the optical afterglow behavior, we do not observe significant steepening in the X-ray light curve, and instead the afterglow flux at δt 0.03 d can be characterized by a single power law with αX = −1.88 ± 0.15. Thus, our afterglow model underpredicts the X-ray flux by a factor of ≈ 5 at δt 2 d (see Figure 2). We note that Tanvir et al. (2013) and de Ugarte Postigo et al. (2013) previ-
ously claimed that the same broken power-law fits both the optical and X-ray data, but this was based on the XRT data
alone. The XMM-Newton observations do not support these
claims. We are thus motivated to consider an additional energy source for this excess X-ray emission, which follows LX ≃ 4 × 1043td−1.88 erg s−1 (where td is in units of days).
One possible source of late-time excess X-ray emission is
continued energy injection into the blastwave from ongoing central engine activity (Zhang & Mészáros 2002; Zhang et al.
2006). We first consider continuous power law energy injection with L ∝ tq. We find that energy injection beginning at δt ≈ 1 d characterized by q = 0.3 (e.g., E ∝ t1.3) provides an adequate fit to the late-time X-ray light curve (Figure 2). Assuming that the injection extends to δt ≈ 10 d, the energy injection factor is ≈ 9.5. However, this energy injection model violates both the optical and radio light curves; in particular, the radio upper limits are a factor of ≈ 3 below the predicted flux with energy injection (Figure 2). Therefore, continuous energy injection is not a viable explanation for the excess X-
ray emission.
We are therefore motivated to consider a source of emission that predominantly contributes in the X-rays with neg-
ligible effects on the other bands. We focus on scenarios
in which this emission originates from the central engine, but which we now assume can be viewed directly through
the merger ejecta (we justify this assumption below). We
first consider ongoing accretion (“fall-back”) onto the newlyformed black hole following a compact object merger. By
extrapolating the matter trajectories from numerical simula-
tions of the merger process to late times, Rosswog (2007) predicts accretion luminosities of Lacc ∼ 1043 − 1045 erg s−1 on a timescale of ∼ 1 d, with a temporal decay of Lacc ∼ t−α similar to the canonical prediction of α = −5/3 for a tidally disrupted star (Rees 1988). Assuming a radiative efficiency of
10%, this scenario is well matched to the X-ray light curve
of GRB 130603B. However, such efficiencies are optimistic
and more detailed models of the fall-back process from compact object mergers (Rossi & Begelman 2009) predict much lower X-ray luminosities of LX 10−3Lacc, which would not be large enough to explain the observed excess.
Another possibility is that the X-ray emission is powered by
the spin-down of a massive magnetar remnant (Metzger et al.

2008; Bucciantini et al. 2012; Zhang 2013), a process that
has been used to explain putative plateaus in the X-ray after-
glows of short GRBs (Rowlinson et al. 2013). Such remnants
may be at least temporarily stable to gravitational collapse,
if they rotate with spin periods of few ms (e.g. Özel et al.
2010; Giacomazzo & Perna 2013). The remnant may also acquire strong magnetic fields of 1014 − 1015 G, similar to those of Galactic magnetars (Duncan & Thompson
1992; Zrake & MacFadyen 2013). The magnetar model pre-
dicts that the late-time spin-down luminosity should decay as Lsd ∝ t−2, consistent with the observed temporal decay of αX = −1.88 ± 0.15. The predicted spectrum is Fν ∝ ν−1 (Metzger et al. 2013), also consistent with the observed spectral index βX ≈ −1.2 ± 0.1. Fitting the entire X-ray light curve with a magnetar model characterized by the duration and lu-
minosity of the plateau (Zhang & Mészáros 2002), and assuming MNS = 1.4 − 2.5 M⊙ and RNS = 106 cm, we find bestfit parameters of B ≈ 2 × 1016 G and P ≈ 15 − 25 ms (where higher mass corresponds to slower spin periods). However,
such slow spin periods are likely unphysical in the merger
context due to the substantial angular momentum of the ini-
tial binary. Instead, assuming a more reasonable initial spin
period of 1 ms, the required magnetic field strength to pro-
duce the observed X-ray luminosity at 1 d assuming 10% radiative efficiency, is B ≈ 1015 G, but such a model would under-predict the light curve at δt 3000 s by a factor of a few. We thus conclude that the magnetar scenario could potentially explain the late-time X-ray excess for δt 3000 s.
To justify that we can observe the central engine directly,
as is required in either the fall-back or magnetar models, the
merger ejecta must be transparent to soft X-rays. Due to
the high bound-free X-ray opacity of neutral matter, this in
turn requires that the engine be sufficiently luminous to re-
ionize the merger ejecta (Metzger et al. 2013). The ejecta
becomes transparent to X-rays once two conditions are sat-
isfied: (1) the opacity becomes dominated by electron scattering (κbf/κes 1, where κbf and κes are the bound-free and electron scattering opacities, respectively) and (2) the electron scattering optical depth, τes, through the ejecta decreases to 1. Assuming ejecta mainly composed of hydrogen-like iron9 and an ejecta temperature of Tej = 104 K, we derive the following expressions (see Appendix for details):

κbf κes

≈

0.13

LX 4 × 1043erg s−1

−1

Mej 10−3M⊙

t

−1

vej

−1
,

1d c

(7)

τes = ρejκesRej ≃ 0.02

Mej 10−3M⊙

vej −2 t −2 c 1d

(8)

where Mej, Rej = vejt, and vej are the (effective) mass, radius, and velocity of the ejecta along the observer line of sight,
respectively. Using fiducial values for Mej and vej of the merger (Hotokezaka et al. 2013; Fernández & Metzger 2013), we find that both conditions are satisfied on timescales δt few hr given the observed X-ray luminosity. We thus conclude
that the ejecta are indeed transparent to the soft X-rays at late
times, supporting the idea that direct radiation from the cen-
tral engine could produce the observed X-ray excess emission

9 Outflows along the polar direction arise chiefly from the accretion disk and are expected to be composed of Fe-like nuclei (e.g. Metzger et al. 2008).

Short GRB 130603B

7

in GRB 130603B. We note that of the ≈ 10 short GRBs with X-ray obser-
vations to δt 1 d, two events, GRBs 050724 and 080503, also exhibited late-time X-ray excess emission on timescales of δt ∼ 1 − 2 d (Grupe et al. 2006; Perley et al. 2009). However, unlike GRB 130603B, these bursts both had corresponding behavior in the optical bands (Malesani et al. 2007; Perley et al. 2009), suggesting that the optical and X-ray emission were from the same emitting region.
6. COMPARISON TO PREVIOUS SHORT GRBS
The broad-band afterglow observations of GRB 130603B provide the second detection of a multi-wavelength jet break in a short GRB, and the first detection of a jet break in the radio band. Radio afterglow emission has thus far been detected in two short GRBs: GRB 050724A (Berger et al. 2005), GRB 051221A (Soderberg et al. 2006). The ability to monitor the radio afterglow of GRB 130603B at a flux density level of 0.1 mJy highlights the improved sensitivity of the VLA.
Indeed, the radio evolution can provide an important constraint on the progenitor. In the context of the compact object binary progenitor, the radioactive decay of rprocess elements in the sub-relativistic merger ejecta is predicted to produce transient emission, termed a “kilonova” (Li & Paczyn´ski 1998; Metzger et al. 2010; Goriely et al. 2011; Roberts et al. 2011; Rosswog et al. 2013), which is expected to peak in the NIR (Barnes & Kasen 2013; Kasen et al. 2013; Tanaka & Hotokezaka 2013). Late-time NIR emission in GRB 130603B detected with the Hubble Space Telescope (Figure 2; Berger et al. 2013; Tanvir et al. 2013) has been interpreted as the first detection of a r-process kilonova. An alternative scenario to explain the excess NIR emission of GRB 130603B may be a wide, mildly relativistic component of a structured jet (Jin et al. 2013) which has been used to explain the light curve behavior of a handful of long GRBs (e.g., Berger et al. 2003; Sheth et al. 2003; Peng et al. 2005; Racusin et al. 2008). In this scenario, the predicted radio emission is similarly boosted, and will be ≈ 80 µJy at δt ≈ 84 d, the time of our final radio observations (Jin et al. 2013). Instead, the non-detection of any radio emission to
34 µJy provides a strong constraint on the existence of a two component jet, and supports the kilonova interpretation of the NIR emission.
The detection of a jet break in GRB 130603B leads to an opening angle measurement of 4 − 14◦, with a more likely range of 4 − 8◦. This opening angle is the fourth10 such measurement for a short GRB after GRB 051221A (7◦; Soderberg et al. 2006), GRB 090426 (5 − 7◦; Nicuesa Guelbenzu et al. 2011), and GRB 111020A (3 − 8◦; Fong et al. 2012). From these four short GRB opening angle measurements, the median is θ j ≈ 6◦ (Figure 3).
The non-detections of jet breaks can provide lower limits on the opening angles, assuming on-axis orientation, as off-axis observing angles could disguise jet breaks (van Eerten & MacFadyen 2012, 2013). Indeed, such nondetections to timescales of ∼ 1 day with Swift/XRT have led to lower limits of θ j 2 − 6◦ (Fong et al. 2012), while monitoring with more sensitive instruments such as Chandra and XMM-Newton to timescales of ∼ 1 week has led to more meaningful limits of θ j 10 − 25◦ (Figure 3; Fox et al.
11 We note that Nicuesa Guelbenzu et al. (2012) claimed a jet break in the GRB 090305A afterglow but this is based on a single optical data point.

20

18
Long
16
Short
14

12

Number

10

8

6

4

2

0 0 5 10 15 20 25 30 35
Opening Angle θj (degrees)
Figure 3. Distribution of opening angles for long (red) and short (blue) GRBs, updated from Fong et al. (2012). Arrows represent upper and lower limits. The long GRB population includes pre-Swift (Frail et al. 2001; Berger et al. 2003; Bloom et al. 2003; Ghirlanda et al. 2004; Friedman & Bloom 2005), Swift (Racusin et al. 2009; Filgas et al. 2011), and Fermi (Cenko et al. 2010; Goldstein et al. 2011; Cenko et al. 2011) bursts. For short GRBs, the existing measurements are GRB 051221A (7◦; Soderberg et al. 2006), GRB 090426 (5 − 7◦, assigned 6◦ here; Nicuesa Guelbenzu et al. 2011), GRB 111020A (3 − 8◦, assigned 5.5◦ here; Fong et al. 2012) and GRB 130603B (4 − 8◦, assigned 6◦ here; this work). Short GRB lower limits are from the non-detection of jet breaks in Swift/XRT data (Fong et al. 2012), Chandra data for GRBs 050724A (Grupe et al. 2006), 101219A (Fong et al. 2013), 111117A (Margutti et al. 2012a; Sakamoto et al. 2013), and 120804A (Berger et al. 2013) and optical data for GRBs 050709 (Fox et al. 2005) and 081226A (Nicuesa Guelbenzu et al. 2012).

2005; Grupe et al. 2006; Berger et al. 2013). The search for

jet breaks has been less fruitful in the optical bands, pri-

marily due to the intrinsic faintness of the optical after-

glows and contamination from host galaxies. Indeed, the

sole lower limit from a well-sampled optical light curve is

from GRB 081226A, with θ j 3◦ (Nicuesa Guelbenzu et al. 2012), while we conservatively adopt a lower limit of θ j 15◦

for GRB 050709 based on a sparsely-sampled optical light

curve (Fox et al. 2005). Using the measured opening angles

and lower limits of 10 − 25◦, a likely median for short GRBs

is θ j ≈ 10◦. The opening angle distribution of short GRBs impacts

the true energy scale and event rate. The true energy is

lower than the isotropic-equivalent value by the beaming

factor, fb ( fb ≡ 1 − cos(θ j), E = fbEiso), while the actual

event rate an opening

is increased angle of ≈

by 4−

8f◦b−, 1t.he

For GRB resulting

130603B, with beaming factor

is fb ≈ (0.2 − 1) × 10−2. Therefore, the true energies are Eγ ≈ (0.5 − 2) × 1049 erg and EK ≈ (0.1 − 1.6) × 1049 erg.

The small population of short GRBs with well-constrained

opening angles have beaming-corrected energies of Eγ ≈

EK ≈ 1049 erg (Soderberg et al. 2006; Burrows et al. 2006; Grupe et al. 2006; Fong et al. 2012; Nicuesa Guelbenzu et al.

2012), roughly two orders of magnitude below the inferred

true energies for long GRBs (Frail et al. 2001; Bloom et al.

2003; Kocevski & Butler 2008; Racusin et al. 2009).

The true event rate is elevated compared to the observed

rate by fb−1. The current estimated observed short GRB volumetric rate is ≈ 10 Gpc−3 yr−1 (Nakar et al. 2006).

For a median opening angle of ≈ 10◦, the median in-

8 Fong et. al.

verse beaming factor is fb−1 ≈ 70, resulting in a true rate of ≈ 700 Gpc−3 yr−1. The observed all-sky event rate of ≈ 0.3 yr−1 within 200 Mpc (Guetta & Piran 2005) then becomes ≈ 20 yr−1. This rate is comparable to estimates for NS-NS merger detections with Advanced LIGO/VIRGO (LIGO Scientific Collaboration et al. 2013).
7. CONCLUSIONS
We presented broad-band observations of the afterglow of GRB 130603B, uncovering a jet break in the optical and radio light curves at δt ≈ 0.47 d. This comprehensive data set marks the first detection of a jet break in the radio band and the third radio afterglow detection in nearly a decade of follow-up. The inferred opening angle is θ j ≈ 4 − 8◦, leading to true energy releases of Eγ ≈ EK ≈ 1049 erg.
We observe excess X-ray emission at 1 day with no corresponding emission in the other bands. We rule out energy injection from ongoing activity from the central engine due to the non-detection of any radio or optical emission on a similar timescale. We find that fall-back accretion can explain the late-time excess only if the radiative efficiency is 10%. Finally, we consider that the emission is due to the spin-down of a massive magnetar and find that a model characterized by a spin period of ≈ 1 ms and magnetic field of ≈ 1015 G provides a good fit to the emission at δt 1 d, but underpredicts the X-ray emission at 3000 s. Furthermore, we show that

the merger ejecta are transparent to soft X-rays (also see Appendix), ensuring that the engine can be viewed in X-rays.
GRB 130603B highlights the importance of multiwavelength afterglow observations, which provide the only route to constraints on the basic explosion properties of GRBs. In particular, the radio band is advantageous because unlike the optical, it does not typically suffer from host galaxy contamination, and can provide an additional constraint on the circumburst density. Thus, continued target-of-opportunity efforts at the VLA will provide invaluable information on the sub-parsec explosion environments. In addition, the non-detection of late-time radio emission, coupled with the detection of NIR excess emission, can provide unambiguous support for the kilonova interpretation for future events, as it has for GRB 130603B.
The opening angle determination for GRB 130603B is the fourth robust jet break measurement for a short GRB. Using realistic assumptions for the opening angle distribution, this implies a conservative volumetric event rate of ≈ 700 Gpc−3 yr−1, and an all-sky event rate of ≈ 20 yr−1 within 200 Mpc, consistent with the predictions of NS-NS merger detections with Advanced LIGO/VIRGO. However, the opening angle distribution for wider jets of 5◦ is poorly constrained, and it is necessary to continue monitoring short GRB afterglows to late times to characterize this part of the distribution.

APPENDIX
RE-IONIZATION MODEL
The average density of the freely-expanding ejecta decreases with time as ρej ≃ Mej/(4π/3R3ej), where Mej, Rej = vejt is the ejecta radius, and vej is the ejecta velocity. The ionization state of the ejecta is determined by comparing the absorption rate of ionizing photons Rion = Cnγ,ν ν1σν1 c (per ion) to the rate of recombination Rrec = neαrec, where nγ,ν>ν1 = LX/4πhν1R2ejc is the number density of ionizing photons; C is a constant of order unity that depends on the spectrum of the ionizing radiation; Lν1 is the specific X-ray luminosity near the ionization threshold energy hν1 ∼ 10 keV; σν1 ≃ 8 × 10−21 cm2 is the photoionization cross section at ν = ν1 and ne ≃ ρej/2mp is the number density of electrons in the ejecta; αrec ≈ 2.0 × 10−10T4−0.8 cm3 s−1 is the [type 2] recombination coefficient (e.g. Osterbrock & Ferland 2006); and T4 ∼ 1 is the ejecta temperature in units of 104 K. The above results can be combined to determine the ratio of the bound-free κbf = fnσν1 /26mp and electron scattering κes = 0.2 cm2 g−1 opacities of the ejecta, where fn ≈ Rrec/Rion ≪ 1 is the neutral fraction (set by the balance between ionization and recombination rates). The resulting coefficient is in Equation 7, from which it is shown that the ejecta is sufficiently ionized for the observed X-rays to originate directly from the central engine interior to the ejecta.
One might be concerned that an X-ray source of sufficient luminosity to ionize the ejecta along the observer line of site (perpendicular to the merger plane) would also be sufficient to ionize matter ejected in the equator, the radioactive heating of which powers the optical/NIR kilonova emission. Indeed, the red colors of the kilonova result from the high line opacity of the lanthanides, which would vanish were the ejecta ionized by the central engine. However, equation (7) shows that κbf/κes ∝ L−X1t−1 is larger for the equatorial ejecta (due to its larger mass Mej and lower velocity vej), and that this ratio increases with time ∝ t (since LX ∝ t−2, approximately). The fact that κbf/κes may be sigificantly ≫ 1 for the equatorial kilonova ejecta implies that the latter may remain neutral, preserving the kilonova emission. However, more detailed calculations, including the different (and uncertain) recombination rates of the lanthanides, is necessary to verify this conclusion.

We thank Barry Madore for obtaining Magellan observations. We thank the VLA staff for rapid response capabilities, and especially Joan Wrobel for scheduling of VLA observations. The Berger GRB group is supported by the National Science Foundation under AST- 1107973. BAZ is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1302954. This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. This work is based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA). Observations were obtained with the VLA (program 13A-046) operated by the National Radio Astronomy Observatory, a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
Facilities: Swift (XRT), XMM-Newton (EPIC-PN), Magellan (IMACS), VLA

Short GRB 130603B
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