The Properties of GRB 120923A at a Spectroscopic Redshift of z ≈ 7.8

GRB 120923A triggered the Swift Burst Alert Telescope (BAT; Barthelmy et al. 2005) on 2012 September 23 at 05:16:06 UT (Yershov et al. 2012). The third BAT Catalog (Lien et al. 2016) gives the observed burst duration as T₉₀ = 26.1 ± 6.8 s, and fluence of $({3.2}_{-0.6}^{+0.9})\times {10}^{-7}$ erg cm⁻². The 1 s peak flux was ${F}_{15-150\mathrm{keV}}=4.1\times {10}^{-8}$ erg cm⁻² s⁻¹, close to the effective detection threshold of BAT. The time-averaged γ-ray spectrum is well fit by a power law with an exponential cut-off, with a photon index of ${\rm{\Gamma }}=-{0.30}_{-1.97}^{+1.38}$ and peak energy, E_peak = 44.5 ± 7.0 keV (errors at 90% confidence). Integrating the BAT (15–150 keV) spectral model taking z ≈ 8 (the evidence for a redshift of this order is presented in Section 3), and including the effect of statistical uncertainties in all measured quantities using a Monte Carlo analysis, we find that the isotropic equivalent γ-ray energy is ${E}_{\gamma ,\mathrm{iso}}=({4.9}_{-1.3}^{+3,3})\times {10}^{52}$ erg (1–10⁴ keV, rest frame).

The Swift X-ray telescope (XRT; Burrows et al. 2005) began observing the field at 05:18:26.0 UT, 140 s after the BAT trigger, leading to a detection of the X-ray afterglow. The source was localized to R.A. = 20^h15^m1073, decl. = +06°13'169 (J2000), with an uncertainty radius of 19 (90% containment). The XRT continued observing the afterglow for 3.6 days in photon-counting (PC) mode, with the last detection at ≈0.6 days.

We extracted XRT PC-mode spectra using the online tool on the Swift website (Evans et al. 2007, 2009).³² We used Xspec (v12.8.2) to fit the PC-mode spectrum between 1.7 × 10⁻³ and 0.67 days, assuming a photoelectrically absorbed power-law model (tbabs × pow) at the redshift of the GRB, and a Galactic neutral hydrogen column density of N_H,MW = 1.5 × 10²¹ cm⁻² (Willingale et al. 2013). Our best-fit model has a photon index of Γ = 1.77 ± 0.14 (68% confidence intervals, estimated using Markov Chain Monte Carlo (MCMC) in Xspec; C-stat = 84 for 105 degrees of freedom). The data do not constrain intrinsic absorption within the host galaxy (see also Starling et al. 2013). In the following analysis, we assume N_H,int = 0 and use the 0.3–10 keV count rate light curve from the Swift website, together with Γ = 1.77, to compute the 1 keV flux density (Table 1). We note that it is difficult to fully rule out the possibility of some contamination of the early X-ray light curve by residual prompt emission, given the limited photon counts, but the apparent evolution of photon index from the BAT to the XRT observations argues against this.

We obtained optical and near-infrared (NIR) imaging from Gemini-North using the Near Infrared Imager and Spectrometer (NIRI) and Gemini Multi-Object Spectrograph (GMOS), and the United Kingdom Infra-Red Telescope (UKIRT) using the Wide-Field Camera (WFCAM), beginning 80 min after the Swift trigger. Conditions in Hawaii were excellent with ≈05 full-width-half-maximum (FWHM) seeing, and the target was at low airmass for several hours. We detected a point source in the JHK bands at R.A. = 20^h15^m1078, decl. = +06°13'163 (J2000), accurate to ±03 in each dimension, which is consistent with the X-ray position. The source was absent in the rizY bands (Figure 1), and its blue color of H–K ≈ 0.1 mag, together with being a Y-band drop-out (Y − J ≳ 1 mag), suggested a very high redshift of z ≳ 7. The NIR counterpart faded in subsequent photometry obtained with the Very Large Telescope (VLT) Infrared Spectrometer and Array Camera (ISAAC), and the European Southern Observatory/Max Planck Gesellschaft (ESO/MPG) 2.2m GRB Optical and Near Infrared Detector (GROND; Greiner et al. 2008), in addition to UKIRT and Gemini-North over the next several nights, confirming it to be the GRB afterglow.

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We performed photometry using Gaia,³³ with the target aperture placed at the location of the afterglow as determined from the high signal-to-noise ratio (S/N) J-band image and the aperture size set according to the seeing (≈1.3 × FWHM). We calibrated the WFCAM JHK-band images to the 2MASS photometric system³⁴ using several hundred stars on each frame, and tied the smaller field NIRI and ISAAC images to this using a secondary sequence of around 40 fainter stars close to the burst location. We obtained optical riz-band calibration using the wide-field GROND observations for the same secondary sequence. The Y-band calibration was achieved by interpolating the sequence star magnitudes between z and J according to $Y=J+0.534(z-J)-0.058$ (derived from GROND observations of photometric standard stars). Uncertainties introduced by these calibration steps are included in the error budget, but are negligible (zero-point errors <0.01 mag) compared to the random errors on the afterglow photometry. We summarize our NIR and optical observations and photometry in Table 2 (note: the GROND limits at the afterglow location are not reported since they are shallower than the corresponding VLT observations obtained at almost the same time), and present the resulting light curves in Figure 2. Constraints on the photometric redshift are outlined in Section 3.1.

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Our first spectrum of the afterglow was obtained with the VLT/X-shooter spectrograph (Vernet et al. 2011) together with the K-band blocking filter, beginning 0.78 days post-burst (Table 3). The slit width was fixed at 09, which is reasonably matched to the ≈10–11 seeing. The target was acquired by offsetting from a nearby bright star.

We nodded the target between two positions (A and B, separated by 5'') on the slit and took exposures in an "ABBA" sequence, as is usual for X-shooter. This was repeated at two different position angles of the slit, specifically 1576 and −1618 (defined from N through E), which maintained an approximately parallactic position. The data were reduced using the X-shooter pipeline (Goldoni 2011). The spectra were first rectified and re-sampled to produce linear spectra on a uniform 0.6 Å pix⁻¹ wavelength scale. Preliminary sky subtraction was done by differencing neighboring frames. No continuum trace was visible at this stage. We refined the sky subtraction by masking out the brightest sky lines, and subtracting any residual sky signal channel by channel. Atmospheric throughput variations were calibrated by reference to observations of two telluric standard stars (Hip094250, Hip094986) obtained close in time to the science data. Channels with the highest telluric absorption (>50%), bad pixels, and other image artefacts were all masked out. Finally, we co-added all the frames weighted by their respective S/Ns, and optimally binned the data in wavelength to produce wide, 30 Å, channels. This revealed a weak but clear trace at the expected position on the slit in the NIR arm (which covers the wavelength range ∼1.02–1.8 μm). We normalized the absolute flux scale of the spectrum to match the J-band photometry at the same epoch. No signal was detected in either the UVB (∼0.35–0.56 μm) or VIS (∼0.56–1.02 μm) arms. The spectroscopic redshift we deduce is presented in Section 3.2.

We triggered our cycle 19 Hubble Space Telescope (HST) program to acquire slit-less grism spectroscopy of the afterglow with the Wide-Field Camera 3-IR (WFC3-IR), in addition to further imaging in the NIR using the F140W filter (approximately a wide JH-band). We performed photometry of the afterglow in the F140W images using a ≈032 radius aperture, adopting the standard HST zero-point calibration and aperture correction for this filter. This sequence of observations, beginning at 4.3 days post-burst, revealed a marked steepening of the light curve compared to the previous J-band decline rate of α_J ≈ −0.25 (${F}_{\nu }\propto {t}^{\alpha }$) between ∼2 hr and ∼1 days (see Figure 2 and Section 4.2). As a consequence of this unexpectedly rapid fading of the afterglow, combined with challenges due to overlapping traces from faint sources in the crowded field, no usable grism spectrum could be extracted. We report our F140W photometry in Table 2 and do not consider the grism data further in our analysis.

We observed GRB 120923A with the Combined Array for Research in Millimeter Astronomy (CARMA) beginning on 2012 September 23.99 UT (0.77 days after the burst) at a mean frequency of 85 GHz. We found no significant millimeter emission at the position of the NIR counterpart or within the enhanced Swift/XRT error circle to a 3σ limit of 0.39 mJy.

We observed the afterglow in the C (4–7 GHz; mean frequency 6.05 GHz) and K (18–25 GHz; mean frequency of 21.8 GHz) radio bands using the Karl G. Jansky Very Large Array (VLA) starting 0.82 days after the burst. Depending on the start time of the observations, we used either 3C286 or 3C48 as the flux and bandpass calibrator. We used J1950+0807 as gain calibrator and carried out data reduction using the Common Astronomy Software Applications package (CASA³⁵ ).

A possible weak source was seen at 7.9 days in the C band with flux density 25 ± 8 μJy. We followed up this putative radio afterglow through a VLA Director's Discretionary Time proposal (12B-387, PI: Zauderer) over a period of 44 days (Figure 3). The C band observations at 11.8 days also show a marginally significant peak in the flux density map, but the position is offset from that of the previous epoch by ≈2σ. No significant source is detected in the subsequent C band epochs nor in the K band data within the Gemini-North error circle. Detailed examination and stacking analyses of the images suggests that the two possible detections in the C band are likely due to noise. We therefore consider the VLA observations to yield a non-detection of the radio afterglow, and report the upper limits and formal photometric point source fits derived from the maps and stacks in Table 4.

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Table 4.  Millimeter and Radio Observations of GRB 120923A

Epoch	$t-{t}_{0}$	Observatory	Band	Frequency	Integration Time	3σ Upper Limit
	(days)			(GHz)	(minutes)	(μJy)
1	0.77	CARMA	3 mm	85.0	...	<390
1	0.824	VLA	K	21.8	17.7	<69.1
1	0.853	VLA	C	6.05	19.9	<29.7
2	3.90	VLA	K	21.8	18.1	<64.4
2	3.91	VLA	C	6.05	17.4	<31.0
3	7.91	VLA	C	6.05	27.8	<22.5
4	11.8	VLA	C	6.05	35.5	<20.1
5	23.9	VLA	C	6.05	37.9	<17.1
6	40.8	VLA	C	6.05	36.3	<18.4
7	43.8	VLA	C	6.05	49.5	<15.8
3 and 4a	10.1b	VLA	C	6.05	63.4	<15.5
6 and 7a	42.5b	VLA	C	6.05	85.8	<14.8

Notes.

^aStacks. ^bThe reported value of $t-{t}_{0}$ for stacks is weighted by the integration time of the individual observations used in the stack.

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We first investigate the redshift constraints from the optical–NIR spectral energy distribution (SED) of the afterglow, using techniques similar to those described in Laskar et al. (2014). For uniformity, we selected observations from a single telescope for this analysis, specifically the Gemini-North/GMOS riz measurements and the Gemini-North/NIRI YJHK measurements obtained within 5 hr post-burst. We corrected these data for Galactic extinction, using ${A}_{{\rm{V}},\mathrm{Gal}}=0.42$ mag (Schlafly & Finkbeiner 2011),³⁶ and the Milky Way extinction model of Pei (1992). The photometry was interpolated to a common time corresponding to the NIRI H-band observation, using a power-law fit to the J-band light curve between 0.06 and 1.0 days, the latter yielding ${\alpha }_{J}=-0.252\pm 0.022$. We added the interpolation uncertainty in quadrature with the photometric uncertainty to determine the total uncertainty at each point on the SED.

We assumed the intrinsic spectrum of the afterglow is a power law, ${F}_{\nu }\propto {\nu }^{\beta }$, and used the sight-line-averaged model for the optical depth of the IGM from Madau (1995), accounting for Lyα absorption by neutral hydrogen and photoelectric absorption by intervening systems. We also included Lyα absorption by the host galaxy interstellar medium (ISM), for which we assumed a column density of $\mathrm{log}({N}_{{\rm{H}}}/{\mathrm{cm}}^{-2})=21.1$, the mean value for GRBs at z ∼ 2–3 (Fynbo et al. 2009), although within the errors the photometric redshift is insensitive to the exact value chosen. The free parameters in our model are the redshift of the GRB, the extinction along the line of sight within the host galaxy (A_V), and the spectral index (β) of the afterglow SED. The Small Magellanic Cloud (SMC) dust extinction law of Pei (1992) was assumed to model the extinction in the host galaxy, ${A}_{{\rm{V}}}$ (this is likely to be appropriate for the expected low metallicity host galaxy, and has also been found to be a good approximation to the extinction laws in the majority of lower redshift GRB hosts, e.g., Schady et al. 2012; Perley et al. 2013). We took a flat prior for the redshift and the extinction, and employed the distribution of early (Δt < 4 hr) extinction-corrected optical–NIR spectral slopes, β_o, from Greiner et al. (2011) as a prior on β.

Fitting was performed using an MCMC algorithm to explore the parameter space, integrating the model over the filter bandpasses, and computing the likelihood of the model by comparing the resulting fluxes with the observed values using a Python implementation of the ensemble MCMC sampler emcee (Foreman-Mackey et al. 2013). The resulting median values and 68% credible intervals for the fitted parameters are z = 8.1 ± 0.4, $\beta =-{0.17}_{-0.25}^{+0.34}$, and ${A}_{{\rm{V}}}={0.07}_{-0.05}^{+0.09}$ mag, where the large errors on β reflect the limited lever arm obtained from the three JHK detections. The highest-likelihood model is z ≈ 7.79, β ≈ −0.39, and ${A}_{{\rm{V}}}\lesssim 0.1$ mag, and this is shown, along with a model with the median parameters, in Figure 4. The full posterior density function for the redshift is shown in Figure 5, and allows us to rule out a redshift of z ≲ 7.3 at 99.7% confidence.

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The X-shooter spectrum (Figure 6) exhibits significant flux redward of 1.2 μm (below 2.5 × 10¹⁴ Hz), with a spectral slope of β = −0.6 ± 0.5, and a steep cut-off blueward of ≈1.1 μm. We model the spectrum as a power law with index β, and interpret the break as due to Lyα absorption by neutral hydrogen in the host galaxy followed by a Gunn–Peterson trough blueward of the host absorption. We proceed with the remainder of the analysis as for the photometric redshift, assuming a flat prior for the redshift and the extinction, and again using the distribution of β_o from Greiner et al. (2011) as a prior on β. We also fix the neutral hydrogen column density of the host galaxy to $\mathrm{log}({N}_{{\rm{H}}{\rm{I}},\mathrm{host}}/{\mathrm{cm}}^{-2})=21.1$ (Section 3.1); a significantly higher column than this is unlikely given the evidence for low extinction and the suggestion of a trend toward somewhat lower columns seen in GRBs at z ≳ 6 (Chornock et al. 2014), while assuming a lower value for ${N}_{{\rm{H}}{\rm{I}},\mathrm{host}}$ does not change the derived redshift within the errors.

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However, instead of integrating over filter bandpasses, we fitted the model directly to the observed X-shooter NIR spectrum. We found $z={7.84}_{-0.12}^{+0.06}$, β = −0.54 ± 0.40, and ${A}_{{\rm{V}}}={0.17}_{-0.12}^{+0.09}$, where the uncertainties reflect 68% credible intervals about the median. We plot our best-fit model in Figure 6. The best fit parameters are z ≈ 7.8, β ≈ −0.54, and ${A}_{{\rm{V}}}$ ≈ 0.17, all consistent with the median values, and with the photometric redshift of z = 8.1 ± 0.4 (Section 3.1).

At z ≈ 7.8, the BAT peak flux corresponds to a luminosity L_iso ≈ 3.2 × 10⁵² erg s⁻¹. In Figure 7 we show the peak luminosity for all the Swift GRBs with measured redshifts to 2015 March. The low energy cut-off imposed by the BAT selection function indicates that only GRBs at the bright end of the luminosity function can be detected at z > 6, despite Swift utilizing a variety of algorithms to try to recover even time-dilated bursts (e.g., Lien et al. 2014). It is clear that GRB 120923A was close to this detection limit, and the intrinsically faintest event found at z > 6.5 to date.

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In Figure 8, we compare the X-ray light curve of GRB 120923A to those of a large sample of Swift bursts (Evans et al. 2009). We find that GRB 120923A was among the faintest long-duration GRB afterglows seen by the XRT. Another view of these data is shown in Figure 9, in which each burst has been shifted to show how it would have appeared if it were at z = 8 (we also show the corresponding rest-frame axes). In this case we restrict the low-redshift sample to the events included in The Optically Unbiased GRB Host survey (TOUGH; Hjorth et al. 2012). The high-redshift completeness of that sample minimizes any optical selection biases. This shows that GRB 120923A was rather typical in terms of its intrinsic X-ray behavior.

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We present the GRB 120923A composite NIR light curve formed by the JHK and F140W photometry in Figure 2, scaling the JHK bands by small factors to match the F140W band. A fit to this overall light curve of a broken power-law model yields a shallow initial slope, α₁ ≈ −0.25, breaking at ≈35 hr to a steep decay with α₂ ≈ −1.9 (χ²/dof = 12.1/13). Note that the scaling factors for each filter were obtained as part of this light curve fitting procedure. We compare the light curve to other high-redshift GRBs in Figure 10. The afterglow of GRB 120923A is comparatively faint, and could easily have escaped detection in other circumstances; i.e., we were lucky in being able to observe the afterglow with an 8 m telescope in excellent seeing within 2 hr, and to continue observations for several hours before the source set.

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It is interesting to note that the SED of this afterglow is comparatively blue ($\beta =-{0.17}_{-0.25}^{+0.34}$ at ≈0.14 days; Figure 4 and Section 3.1), consistent with little line-of-sight dust extinction in the host, as has generally been found for other afterglows of the high-z GRBs (Zafar et al. 2011; Laskar et al. 2014). This may reflect the limited time to build up dust, particularly in the small galaxies that are likely dominating the total star formation budget at z > 6 (although see Watson et al. 2015 for an example of substantial dust in a galaxy at z ≈ 7.5). Of course, there is also an observational bias against discovering dusty afterglows at high redshift. We consider the quantitative constraints on dust extinction to GRB 120923A in Section 5.3.

We now interpret the multi-wavelength observations of GRB 120923A in the context of the standard synchrotron model, in which the afterglow radiation arises from the blast-wave shock set up by the expanding relativistic GRB ejecta interacting with their circumburst environment. This model assumes an idealized jet and ambient medium, and no late-time energy injection from the central engine (see Section 5.2). The resulting radiation is expected to exhibit characteristic power-law spectral segments connected at "break frequencies," namely the synchrotron cooling frequency (${\nu }_{{\rm{c}}}$), the characteristic synchrotron frequency (${\nu }_{{\rm{m}}}$), and the self-absorption frequency (${\nu }_{{\rm{a}}}$). The location of these frequencies depend on the physical parameters: the isotropic-equivalent kinetic energy (${E}_{{\rm{K}},\mathrm{iso}}$), the circumburst density (${n}_{0}$, or the normalized mass-loss rate in a wind-like environment, ${A}_{* }$), the fraction of the blast-wave energy imparted to non-thermal electrons (${\epsilon }_{{\rm{e}}}$), and the fraction converted into post-shock magnetic energy density (${\epsilon }_{B}$).

The different possible orderings of the break frequencies (e.g., ${\nu }_{{\rm{m}}}\lt {\nu }_{{\rm{c}}}$: "slow cooling," and ${\nu }_{{\rm{c}}}\lt {\nu }_{{\rm{m}}}$: "fast cooling") then give rise to five possible afterglow SED shapes (Granot & Sari 2002). As the radius and Lorentz factor of the blast-wave change with time, these break frequencies evolve and the afterglow SED may transition between these different spectral shapes. To preserve smooth light curves when break frequencies cross, we use the weighting schemes described in Laskar et al. (2014) to compute the afterglow SED as a function of time. As in Section 3.1, we adopt the SMC extinction curve (Pei 1992) to model the extinction in the host galaxy, ${A}_{{\rm{V}}}$, and include the possibility of an achromatic "jet-break" in the afterglow light curves due to spreading and edge-effects expected for a collimated outflow. To efficiently sample the available parameter space, we carry out an MCMC analysis using emcee. The details of our modeling scheme and MCMC implementation are described in Laskar et al. (2014).

The lack of any flattening in the late-time NIR light curve (Figure 10) indicates that any host contamination of the afterglow photometry is small, and we assume it to be negligible in what follows. The J-band light curve declines initially as ${\alpha }_{{\text{}}J}=-0.23\pm 0.04$ between 0.06 and 0.2 days. In the basic synchrotron model, such a shallow decline in the NIR is only possible if ${\nu }_{{\rm{c}}}\lesssim {\nu }_{\mathrm{NIR}}\lt {\nu }_{{\rm{m}}}$, where the light curves decline as t^−1/4 regardless of the density profile of the circumburst environment. This suggests that the afterglow radiation is in the fast cooling regime, and that the NIR bands are on segment F of Granot & Sari (2002). In this scenario, we would expect the light curve to steepen to $\alpha =(2\mbox{--}3p)/4$ when ${\nu }_{{\rm{m}}}\propto {t}^{-3/2}$ passes through the NIR band, where p is the power-law index of the electron energy distribution. Alternatively, in the particular case of a wind environment, ${\nu }_{{\rm{c}}}\propto {t}^{1/2}$ may pass through the NIR band first, and the NIR decay rate would steepen to α = −2/3.

The steepness of the late decay (α_J ≈ −1.8 ± 0.3 between 4.3 and 20 days), and marked change from the early behavior, provides evidence that a jet break occurred at ≲4.3 days, and also suggests the passage of ${\nu }_{{\rm{m}}}$ through the NIR band between 0.2 and 4.3 days, and indicates a uniform (ISM-like) environment. If we take the power law within this window, α_J = −1.2 ± 0.2, as indicative of the slope after ${\nu }_{{\rm{m}}}$ passage, but before the jet break, then using ${\alpha }_{J}=(2\mbox{--}3p)/4$ yields p = 2.3 ± 0.3.

The XRT PC-mode light curve is well-fit with a broken power law, with an initial flat segment, α_X,1 = 0.0 ± 0.2, breaking into³⁷ α_X,2 = −1.32 ± 0.05 at t_b = (6.3 ± 1.2) × 10⁻³ days. The initial flat portion of the X-ray light curve may be due to the X-rays being on the same segment (F) of the synchrotron SED as the NIR data. In this case, the X-ray decline rate is also expected to be t^−1/4. The break in the X-ray light curve would then correspond to the passage of ${\nu }_{{\rm{m}}}$ through the X-ray band. Since the X-ray band spans an order of magnitude in energy, while ${\nu }_{{\rm{m}}}$ evolves as t^−3/2, we would expect the break to be smoothed out over a factor of ≈10^−2/3 ≈ 5 in time. If we assumed ${\nu }_{{\rm{m}}}\approx {\nu }_{{\rm{J}}}\approx 2.2\times {10}^{14}$ Hz at ≈0.2 days, we would expect ${\nu }_{{\rm{m}}}\approx 1\,\mathrm{keV}$ at ≈2 × 10⁻³ days. This is consistent with the observed steepening in the X-ray lightcurve at ≈6 × 10⁻³ days. In this model, the post-break decline rate of ${\alpha }_{{\rm{X}}}=-1.32\pm 0.05$ yields p = 2.43 ± 0.07. The different decline rates in the X-ray and NIR bands between 0.06 and 0.2 days suggest that these bands are on different segments of the afterglow synchrotron spectrum, consistent with the spectral ordering, ${\nu }_{{\rm{c}}}\lesssim {\nu }_{\mathrm{NIR}}\lt {\nu }_{{\rm{m}}}\lt {\nu }_{{\rm{X}}}$, during this period.

The spectral index in segment F is expected to be β = −0.5, independent of p. When the X-rays are on this segment, we would expect Γ_X = 1 − β_X = 1.5, which is consistent with the value of Γ_X = 1.61 ± 0.14 derived in Section 2.1. We would also expect spectral evolution from Γ_X = 1.5 to Γ_X = 1 + p/2 after ${\nu }_{{\rm{m}}}$ crosses the X-ray band. Unfortunately, paucity of data following the orbital gap in the X-ray light curve precludes confirmation of this behavior.

Interpolating the X-ray lightcurve using the best-fit broken power-law model, we find a flux density of (3.5 ± 0.4) × 10⁻² μJy at the time of the Gemini/NIRI J-band observation at 0.064 days. The spectral index between the NIR and X-ray band is then ${\beta }_{\mathrm{NIR}-{\rm{X}}}\approx -0.65\pm 0.01$. This is significantly different from −0.5, suggesting that at least one spectral break frequency lies between the NIR and X-ray band. Assuming a spectral slope of β = −0.5 and β = −p/2 = −1.22 below and above this break, respectively, and using the measured J-band flux density and extrapolated X-ray flux density, we can locate the break to be at ≈5.9 × 10¹⁶ Hz at this epoch. However, extrapolating ${\nu }_{{\rm{m}}}\propto {t}^{-3/2}$ from ≈2.2 × 10¹⁴ Hz at ≈0.2 days to 0.064 days yields ${\nu }_{{\rm{m}}}\approx 1.2\times {10}^{15}$ Hz, which is more than an order of magnitude lower. Here we have neglected the possibility of dust extinction in the host galaxy. A small amount of extinction would produce a shallower spectral slope, ${\beta }_{\mathrm{NIR}-{\rm{X}}}$, and hence lead us to overestimate ${\nu }_{{\rm{m}}}$, so in principle could help explain this discrepancy. However, we estimate that requiring ${\beta }_{\mathrm{NIR}-{\rm{X}}}\approx {\beta }_{{\rm{X}}}$ would necessitate A_V ≳ 0.2, which is disfavored from our analysis of the NIR photometry in Section 3.1. We return to the question of host extinction in Section 5.3.

In the synchrotron model, we can use the observed X-ray flux density at 1 keV at a time that is dominated by afterglow radiation to estimate the burst kinetic energy (e.g., Granot et al. 2006). This requires the X-ray band to be located above the peak and cooling frequencies. Since ${\nu }_{{\rm{c}}},{\nu }_{{\rm{m}}}\lt {\nu }_{{\rm{X}}}$ after the break in the X-ray light curve, this condition is satisfied. We use the last point preceding the Swift orbital gap with f_X ≈ 0.22 μJy at ≈0.36 hr, together with fiducial values of p = 2.2 (e.g., Curran et al. 2010) and ${\epsilon }_{{\rm{e}}}={\epsilon }_{B}=1/3$ to estimate ${E}_{{\rm{K}},\mathrm{iso}}\approx 3\times {10}^{51}$ erg. We verify this result in the next section.

An alternative possibility for the shallow J-band light curve between 0.06 and 0.22 days is energy injection into the blast wave, either due to late-time central engine activity, or due to additional energy imparted by undecelerated ejecta at lower Lorentz factors (Sari & Mészáros 2000; Laskar et al. 2015). Since α_X < α_J ≈ −0.23 over this period, this scenario would require ν_m < ν_J < ν_c < ν_X and an ISM environment. However, we would then expect the X-ray light curve to exhibit a similar signature of energy injection, tracking the optical light curve with ${\alpha }_{{\rm{X}}}={\alpha }_{J}+\tfrac{{\alpha }_{J}+p}{3+p}$. There is no positive value of p for which this expression gives the observed steep X-ray decline of α_X ≈ −1.3, and therefore the energy injection scenario is disfavored.

Thus, in summary, the X-ray light curve, X-ray spectrum, and NIR J-band light curve suggest that the observed synchrotron radiation from the blast-wave shock is in the fast cooling regime with ${\nu }_{{\rm{c}}}\lesssim {\nu }_{\mathrm{NIR}}\lt {\nu }_{{\rm{m}}}\lt {\nu }_{{\rm{X}}}$ at ≈0.2 days; ${\nu }_{{\rm{m}}}$ passes through the X-ray band at about a few ×10⁻³ days, and through the J-band between ≈0.2 days and 4.3 days, while the steep decline in the HST F140W data indicates a jet break before ≈4.3 days.

We now describe the full multi-wavelength modeling of all available afterglow data for GRB 120923A using the techniques presented in Laskar et al. (2014), which include accommodating upper limits. We adopted weak, flat priors based on plausible ranges: 2.01 < p < 3.45, ${\epsilon }_{{\rm{e}}},{\epsilon }_{B}\lt 1/3$, $-10\lt \mathrm{log}({n}_{0}/{\mathrm{cm}}^{-3})\lt 10$, $-4\lt \mathrm{log}({E}_{{\rm{K}},\mathrm{iso}}/{10}^{52}\,\mathrm{erg})\lt 2.7$, ${A}_{{\rm{B}}}\lt 20$ mag, and $-5\lt \mathrm{log}({t}_{\mathrm{jet}}/\mathrm{day})\lt 5$. For the sake of generality, we did not fix the redshift, but based on our analysis of the NIR SED (Section 3.2) restricted the redshift range to 7.0 < z < 8.5.

We find that an ISM-like model with a jet break adequately explains the full set of afterglow observations. Our highest likelihood model (Figure 11) has the parameters p ≈ 2.5, z ≈ 8.1, ${\epsilon }_{{\rm{e}}}\approx 0.33$, ${\epsilon }_{B}\approx 0.32$, ${n}_{0}\approx 4.0\times {10}^{-2}\,{\mathrm{cm}}^{-3}$, and ${E}_{{\rm{K}},\mathrm{iso}}\approx 2.9\times {10}^{51}$ erg, with a jet break at ${t}_{\mathrm{jet}}\approx 3.0$ days (χ²/dof = 1.1). We note that the derived value of ${E}_{{\rm{K}},\mathrm{iso}}$ confirms the estimate made using the X-ray data (Section 5.2). An implication of this is a very high value for the radiative efficiency $\eta ={E}_{\gamma ,\mathrm{iso}}/({E}_{\gamma ,\mathrm{iso}}+{E}_{{\rm{K}},\mathrm{iso}})\approx 0.92$. Such high values for η have also been inferred for the prompt emission of some other GRBs (e.g., Zhang et al. 2007), although they remain a challenge to explain theoretically.

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The redshift derived by this approach is completely consistent with the photometric redshift found in Section 3.1. This model requires a small amount of extinction in the host galaxy, ${A}_{{\rm{V}}}\approx 0.06$ mag (Figure 12). Using the relation,

$$\begin{eqnarray}&&{\theta }_{\mathrm{jet}}=0.1{\left(\displaystyle \frac{{n}_{0}}{{E}_{{\rm{K}},\mathrm{iso}}/{10}^{52}}\right)}^{1/8}{\left(\displaystyle \frac{{t}_{\mathrm{jet}}/(1+z)}{6.2\mathrm{hr}}\right)}^{3/8}\end{eqnarray} \tag{ 1 }$$

for the jet opening angle (Sari et al. 1999) we find ${\theta }_{\mathrm{jet}}\approx 4\buildrel{\circ}\over{.} 9$ and beaming-corrected kinetic energy, ${E}_{{\rm{K}}}\approx 1.1\times {10}^{49}$ erg.

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The break frequencies³⁸ are located at ${\nu }_{\mathrm{ac}}\approx 3\times {10}^{7}$ Hz, ${\nu }_{\mathrm{sa}}\approx 7\times {10}^{7}$ Hz, ${\nu }_{{\rm{c}}}\approx 6\times {10}^{14}$ Hz, and ${\nu }_{{\rm{m}}}\approx 3\times {10}^{15}$ Hz at 0.1 days and the peak flux density is ≈13 μJy at ${\nu }_{{\rm{c}}}$ for the highest-likelihood model. In this model, ${\nu }_{{\rm{m}}}$ passes through 1 keV at ≈5 × 10⁻³ days, which is precisely the time of the observed break in the X-ray light curve, t_b = (6.3 ± 1.2)× 10⁻³ days (Section 5.2). The shallow-to-steep transition in the X-ray light curve is therefore consistent with the passage of ${\nu }_{{\rm{m}}}$.

We note that the spectrum peaks at ${\nu }_{{\rm{c}}}$ in the fast cooling regime, and the proximity of the cooling break to the NIR J-band at ≈0.1 days results in a spectrum near the J-band that is flatter than ν^−0.5. This explains the lower value of ${\nu }_{{\rm{m}}}$ (which lies between ${\nu }_{{\rm{c}}}$ and ${\nu }_{{\rm{X}}}$) inferred from the NIR and X-ray light curves, compared with the value required in a broken power-law fit to match the NIR J-band and interpolated X-ray flux density at this time. The location of ${\nu }_{{\rm{c}}}\gtrsim {\nu }_{J}$ at 0.1 day rules out the wind model, since in that case we would expect the NIR light curve to decline as t^−2/3 after ≈0.1 day (Section 5.2). The passage of ${\nu }_{{\rm{m}}}$ through the NIR J-band occurs at ≈0.5 days, at which point both ${\nu }_{{\rm{c}}}$ and ${\nu }_{{\rm{m}}}$ are below ν_J and the light curve steepens to α ≈ −1.4, consistent with the limited observations at this time. Finally, the best-fit model requires a jet break at ≈3 days.

In broad agreement with the basic analysis presented in Section 5.2, the model afterglow SED remains in fast cooling until ≈0.34 days (approximately 1 hr in the rest-frame). This conclusion is driven in the fit by the apparent change in NIR spectral slope between the early data, particularly the Gemini photometry at ∼0.14 days and the VLT epoch at ∼0.8 days, as illustrated in Figure 13.

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From our MCMC simulations, we constrain the fitting parameters to $p={2.7}_{-0.2}^{+0.3}$, $z={8.1}_{-0.3}^{+0.2}$, ${\epsilon }_{{\rm{e}}}={0.31}_{-0.04}^{+0.02}$, ${\epsilon }_{B}\,={0.23}_{-0.11}^{+0.07}$, ${n}_{0}=({4.1}_{-1.4}^{+2.2})\times {10}^{-2}\,{\mathrm{cm}}^{-3}$, ${E}_{{\rm{K}},\mathrm{iso}}=({3.2}_{-0.5}^{+0.8})\,\times {10}^{51}$ erg, ${t}_{\mathrm{jet}}={3.4}_{-0.5}^{+1.1}$ days (68% credible intervals), and ${A}_{{\rm{V}}}\lesssim 0.08$ mag (90% confidence upper limit). Thus, although the best-fit model has a small amount of extinction (Figure 12), our MCMC results indicate that evidence for dust along the line of sight is statistically marginal.

Applying the expression for ${\theta }_{\mathrm{jet}}$ above to our MCMC chains with their individual values of ${E}_{{\rm{K}},\mathrm{iso}}$, ${n}_{0}$, z, and ${t}_{\mathrm{jet}}$, we find ${\theta }_{\mathrm{jet}}={5.0}_{-0.8}^{+1.3}$ degrees and ${E}_{{\rm{K}}}=({1.2}_{-0.2}^{+0.5})\times {10}^{49}$ erg. Correcting ${E}_{\gamma ,\mathrm{iso}}$ for beaming using this measurement of ${\theta }_{\mathrm{jet}}$, we find ${E}_{\gamma }=(1.8\pm 0.7)\times {10}^{50}$ erg. We present histograms of the marginalized posterior density for each parameter in Figure 14 and correlation contours between the physical parameters and expected relations between the parameters in the absence of constraints on one of the spectral break frequencies in Figure 15. We summarize the results of our MCMC analysis in Table 5.

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Table 5.  Parameters from Multi-wavelength Modeling of GRB 120923A

Parameter	Best-fit Value	MCMC Result
z	8.1	${8.1}_{-0.3}^{+0.2}$
p	2.5	${2.7}_{-0.2}^{+0.3}$
${\epsilon }_{{\rm{e}}}$	0.33	${0.31}_{-0.04}^{+0.02}$
${\epsilon }_{B}$	0.32	${0.23}_{-0.11}^{+0.07}$
${n}_{0}$(cm−3)	$4.0\times {10}^{-2}$	$({4.1}_{-1.4}^{+2.2})\times {10}^{-2}$
${E}_{{\rm{K}},\mathrm{iso}}$ (1051 erg)	2.9	${3.2}_{-0.5}^{+0.8}$
${t}_{\mathrm{jet}}$(day)	3.0	${3.4}_{-0.5}^{+1.1}$
${\theta }_{\mathrm{jet}}$(degrees)	4.9	${5.0}_{-0.8}^{+1.3}$
${A}_{{\rm{V}}}$(mag)	0.06	≲0.08a
${E}_{\gamma ,\mathrm{iso}}$ b (1052 erg)	${4.8}_{-1.6}^{+6.1}$
Eγ (1050 erg)	1.8	1.8 ± 0.8c
EK (1049 erg)	1.1	${1.2}_{-0.2}^{+0.5}$

Notes.

^a90% confidence upper limit. The median value of the host extinction in our MCMC analysis is ${A}_{{\rm{V}}}=3.8\times {10}^{-5}$ mag with a 68% credible interval ${A}_{{\rm{V}}}\in (0.00,0.06)$. ^b1–10⁴ keV, rest frame. ^cUsing symmetrized uncertainties (one-half positive error minus negative error) for both ${E}_{\gamma ,\mathrm{iso}}$ and ${\theta }_{\mathrm{jet}}$, followed by an MC calculation.

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