The First Short GRB Millimeter Afterglow: The Wide-angled Jet of the Extremely Energetic SGRB 211106A

Prompt γ-rays from GRB 211106A were first discovered ¹⁹ by INTEGRAL/SPI-ACS (von Kienlin et al. 2003) on 2021 November 6 at 04:37:31.2 UT (Tohuvavohu et al. 2021); all times in this paper are given relative to this time. The INTEGRAL notice triggered the Gamma-ray Urgent Archiver for Novel Opportunities (GUANO; Tohuvavohu et al. 2020) operated by the Neil Gehrels Swift Observatory’s (Swift; Gehrels et al. 2004) Mission Operations Center. GUANO ordered the Swift Burst Alert Telescope (BAT; Barthelmy et al. 2005) to save 90 s of BAT event-mode data around the time of burst. Using the Non-Imaging Transient Reconstruction And TEmporal Search (NITRATES; DeLaunay & Tohuvavohu 2021), we find a strong detection with BAT in the time-domain. The BAT light curve exhibits two pulses, with duration, T₉₀ = 1.7 ± 0.1 s (50–300 keV, observer frame; Figure 1). The best-fit BAT position ²⁰ from NITRATES is R.A. = 22^h54^m3432 and decl. = −53^d14′09, with an uncertainty of 7′ (Tohuvavohu et al. 2021).

Zoom In Zoom Out Reset image size

GRB 211106A also triggered Konus-Wind (Aptekar et al. 1995) on 2021 November 6 at 04:37:32.485 UT. The observation revealed a light curve ²¹ with a single-pulse structure of ∼0.5 s (20 keV−2 MeV), consistent with the time of the second peak in the BAT light curve (Ridnaia et al. 2021).

The Gamma-ray Burst Monitor (GBM; Meegan et al. 2009) on board Fermi (GLAST Facility Science Team et al. 1999) did not trigger on this GRB. Fletcher & Fermi-GBM Team (2021) identified a significant event (signal-to-noise ratio (S/N) of 22) in the GBM data using the off-line targeted search pipeline (Goldstein et al. 2019), at a position consistent with the Swift/BAT-GUANO position. The Fermi/GBM light curve exhibits two pulses coincident with those in the BAT light curve, and with T₉₀ = 1.71 ± 0.18 s (50–300 keV, observer frame; Figure 1). Fitting the time-integrated GBM spectrum during the T₉₀ interval with RMfit ²² using a power-law model with an exponential cutoff (parameterized as the peak energy E_peak), we find a photon index, Γ_γ,CPL = −0.85 ± 0.20, E_peak = 306 ± 60 keV, and γ-ray fluence, . The isotropic-equivalent γ-ray energy (1–10⁴ keV, rest frame) corresponds to E_γ,iso = (1.1 ± 0.1) × 10⁵¹erg at z = 0.5 and E_γ,iso = (4.4 ± 0.4) × 10⁵¹erg at z = 1.0, two redshifts spanning the typical range for SGRBs as discussed in Section 1. Both E_γ,iso estimates are consistent with the E_peak–E_γ,iso distributions for SGRBs (Ghirlanda et al. 2009; Tsutsui et al. 2013; Minaev & Pozanenko 2020).

We compute the spectral lag between low-energy (25–50 keV) and high-energy (100–300 keV) GBM light curves using the same energy bands and procedure as described in Norris et al. (2000) and find . This is consistent with τ ≈ 0 as measured for SGRBs (Gehrels et al. 2006). According to the lag–luminosity relationship for long GRBs, L_peak ∝(τ/(1 + z))^−0.74 (Norris et al. 2000), where L_peak is the peak luminosity. Fitting the brightest 0.128 s time bin, we find a peak flux, F_peak ≈ 2.4 × 10⁻⁶ erg cm⁻² s⁻¹, yielding L_peak ≈ 1.5 × 10⁵¹ erg s⁻¹ and 6.2 × 10⁵¹ erg s⁻¹ at z = 0.5 and z = 1.0, respectively. If GRB 211106A were a long GRB, for the measured L_peak, the lag–luminosity relation would imply a lag τ ≈ 0.238 s in the more conservative z = 1.0 case. This is inconsistent with the measured lag at a 4.9σ level. We derive the hardness ratio (HR), defined as the photon flux above the background in a high-energy band divided by those in a low-energy band (Bhat et al. 2016; Goldstein et al. 2017), and find HR = 1.41 ± 0.36. Modeling the T₉₀–HR plane with a Gaussian mixture model ²³ following Rouco Escorial et al. (2021), we find that the probability that GRB 211106A belongs to the SGRB population is P(short) ≈ 92% (Figure 1).

Owing to its short T₉₀, hard spectrum, and negligible spectral lag, we consider GRB 211106A to be a bona fide short-duration, spectrally hard GRB.

Swift/XRT began follow-up observations of the BAT/NITRATES position at ≈0.46 days, revealing a fading X-ray afterglow at R.A. = 22^h54^m2045 and decl. = −53^d 13′ 490, with an uncertainty of 34 (90% confidence; D’Elia et al. 2021). We downloaded time-sliced X-ray spectra per bin of the dynamically binned XRT light curve with the spectral extraction tool ²⁴ on the Swift website (Evans et al. 2009), which we later use together with all available X-ray data for a joint spectral analysis.

We observed the afterglow with Chandra/ACIS-S3 (Garmire et al. 2003) at ≈10.5 and 59.8 days with total effective exposure times of 19.8 ks and 37.9 ks, respectively, through target-of-opportunity and DDT programs #22500107 (PI: Berger, ObsID 23543) and #22408828 (PI: Rouco Escorial, ObsIDs 26249 and 26262). We used the CIAO software package (v. 4.12, Fruscione et al. 2006) and calibration files (caldb; v. 4.9.0) to reduce the data. We detect the X-ray afterglow in the first Chandra epoch at R.A. = 22^h54^m2051 and decl. = −53^d 13′ 5117 (1σ uncertainty of 062; including centroiding uncertainty of 018 and absolute astrometric uncertainty of 06). We refine this position by astrometric calibration against Gaia using HST imaging (Section 2.5) in Appendix C. We derive the X-ray count rate and spectrum from a 2″ aperture centered on the X-ray afterglow and report the results in Table 1.

Table 1. X-Ray Observations of GRB 211106A

Time	Count Rate	Unabsorbed Flux
(Days)	(10−3 counts s−1)	(10−14 erg s−1 cm−2)
Swift/XRT-PC
0.5	12 ± 3
0.6	7 ± 2
2.7	1.8 ± 0.4	11 ± 3
27	<5	<29
Chandra/ACIS-S3
10.5	1.7 ± 0.4
59.8	<0.3	<0.6
XMM-Newton/EPIC
14.9	2.6 ± 0.7, 1.6 ± 0.4, 1.1 ± 0.4	2.2 ± 0.3
33.0	1.0 ± 0.4, 0.3 ± 0.2	1.0 ± 0.2
Best-fit Spectral Parameters
z	ΓX	NH, int
		(1021 cm−2)
0.5	1.9 ± 0.3
1	1.9 ± 0.3

Notes. Time is log-centered. XMM-Newton count rates are listed by detector in order: pn, MOS1, and MOS2 (first epoch) and pn and MOS1 (second epoch). Fluxes are reported in the 0.3–10 keV band (observer frame).

Download table as:  ASCIITypeset image

We used XMM-Newton/EPIC (Strüder et al. 2001; Turner et al. 2001) to obtain two epochs of the afterglow at midtimes of ≈14.9 and 33.0 days after the burst, with total effective exposure times of 20.3 ks and 46.7 ks, respectively, through target-of-opportunity Program #086286 (PI: Fong, ObsIDs: 0862860301 and 0862860401). We reduced and analyzed the XMM-Newton data using SAS (v. 18.0.0; Gabriel et al. 2004). The afterglow was detected in both epochs. We derive the source flux and spectrum using a 20″ aperture (Table 1).

We use Xspec (v. 12.10.1f; Arnaud 1996) to perform a joint spectral fit of the Swift, Chandra, and XMM-Newton data in the 0.5–7 keV energy range sampled by all instruments. We use an absorbed power-law model with photon index (Γ_X ), intrinsic absorption (N_H,int), fixed Galactic absorption (N_H,Gal = 1.06 × 10²⁰ cm⁻²; Willingale et al. 2013), fixed normalization factors ²⁵ to account for cross-calibration between observatories, W-statistics (statistic cstat; Wachter et al. 1979) and WILM abundances (Wilms et al. 2000). We find no evidence for spectral evolution and derive Γ_X = 1.9 ± 0.3, at z = 0.5 and at z = 1. We derive unabsorbed X-ray fluxes (0.3–10 keV) using the cflux convolution model and convert count rate upper limits to flux limits using the associated instrumental response files and Poisson statistics with the spectral parameters fixed to the best-fit values. This appears to be one of the most luminous SGRB afterglows at the corresponding rest-frame time known to date (Figure 2). We discuss this X-ray light curve in the context of those from other SGRBs in Section 5.

Zoom In Zoom Out Reset image size

We observed GRB 211106A with ALMA at 97.5 GHz at a midtime of 12.9 days after the burst (project 2019.1.00863.T, PI: Fong). We utilized four 2 GHz spectral windows centered at 90.52, 92.42, 102.52, and 104.48 GHz and employed J2357–5311 as bandpass and flux density calibrator, J2239–5701 as complex gain calibrator, and J2207–5346 as a check source. We calibrated the data using the automated ALMA pipeline procedure_hifa_cal.xml in the Common Astronomy Software Applications (CASA; McMullin et al. 2007) v. 5.6.1–8 followed by imaging to the half-power point of the primary beam using one Taylor term and with Briggs weighting using a robust parameter of 0.5. We detect a single point source with flux density 148 ± 11 μJy in the image spanning 15 in diameter (Figure 3). We obtained four additional epochs of ALMA observations, and the mm-band point source is observed to fade to a flux density below detection by the time of the final epoch obtained 62.6 days postburst. The most precise position of the counterpart is afforded by the second epoch, which has the smallest synthesized beam area of 0346 × 0269, R.A. = 22^h54^m2053056 (±0.0012 s, 0011), decl. = −53^d13′50525 (±0010). The absolute systematic astrometric uncertainty on this position is given by beam_FWHM/(S/N)/0.9 ≈ 36 mas (Remjian et al. 2019), with negligible additional systematic uncertainty (≲2 mas) from the calibrator positions. The mm-band position is consistent with both the original and refined Chandra afterglow position (Section 2.2 and Appendix C). The positional coincidence and fading behavior confirm this source as the mm afterglow of GRB 211106A. We plot the ALMA light curve in Figure 4 and report the corresponding flux density values in Table 2.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We observed GRB 211106A with the Australia Telescope Compact Array (ATCA) at six epochs via DDT project CX493 (PIs: Laskar, Bhandari, Fong), with the first epoch taken at a midtime of 14.2 days after the burst. We used the dual-frequency, dual-polarization mode of the CABB correlator, with the two intermediate frequencies (IFs) tuned to different frequencies to maximize spectral coverage. We used the 4 cm (IFs tuned to 5.5 GHz and 9.0 GHz) receiver in each epoch and additionally observed at 15 mm (17 GHz/19 GHz) in four epochs and at 7 mm (33 GHz/35 GHz) in three epochs. We utilized PKS B1934−638 as bandpass and flux density calibrator and J2315−5018 as complex gain calibrator, except at 7 mm, where we utilized PKS B1921−238 as bandpass calibrator. The observations spanned multiple configurations.

We analyzed the data using standard reduction procedures in Miriad, treating each IF and each epoch separately, followed by imaging in CASA with two Taylor terms, employing Briggs weighting with a robust parameter of 0. To improve phase coherence in the data, we generated a deep image of the field by stacking the uv data from all epochs in each band separately and used the associated clean components as a model for self-calibrating the joint data set at each frequency (the target itself was not included in the model). After the second round of phase-only self-calibration, we subtracted the uv model from the visibilities to generate calibrated target-only data sets.

We combine and image the two IFs at 15 mm and at 7 mm together for maximum S/N and report the results at the mean frequencies of 18 GHz and 34 GHz in these bands, respectively. We image 5.5 and 9.0 GHz separately due to the large fractional bandwidth covered by the 4 cm receiver. We detect a radio counterpart at 5.5, 9.0, and 18 GHz at a position consistent with the mm-band position (Figure 3). There is insufficient flux in the 34 GHz images for self-calibration, and we report upper limits in this band from imaging of the field per epoch. We verify our results by performing point-source fitting directly in the uv domain for each epoch and frequency band separately using uvmodelfit in CASA and recover fluxes consistent within 1σ of those obtained from imaging. We present our ATCA flux density measurements in Table 2.

Optical follow-up of GRB 211106A with the VLT yielded a deep nondetection at ≈2.9 days of R ≳ 26.4 mag (Malesani et al. 2021). We observed GRB 211106A with the Hubble Space Telescope (HST) over three epochs (at ≈19.1, 25.3, and 48.2 days after the burst, respectively) with the Wide Field Camera 3 (WFC3) in F110W (all epochs) and Advanced Camera for Surveys (ACS) in the F814W band (first and third epochs only) through program 16303 (PI: Berger). We aligned and drizzled each epoch using the Python-based code hst123 (Kilpatrick 2021) as described in Kilpatrick et al. (2022). In addition, we drizzled all F814W and F110W images into deeper combined images and determined their absolute world coordinate system in the Gaia eDR3 frame (with an rms astrometric uncertainty of 10 mas and 15 mas, respectively) using seven common astrometric standards in the HST imaging and Gaia catalog (Lindegren et al. 2021).

We perform image subtraction of the first two epochs relative to the final epoch to place a limit on the afterglow emission using hotpants (Becker 2015) with parameters identical to those used in Kilpatrick et al. (2022). We perform forced photometry at the location of the mm afterglow using an empirical point-spread function (PSF) constructed in the template image frames with photutils (Bradley et al. 2020) and list the resulting upper limits in Table 3.

The X-ray light curve can be fit as a single power law, ²⁷ with decline rate α_X = −0.97 ± 0.03 (Figure 2), which would imply p ≈ 1.9 if ν_c < ν_X and p ≈ 2.3 if ν_X < ν_c under the standard synchrotron framework (ignoring IC/KN effects). The expected spectral index in these cases is β ≈ −0.9 and β ≈ −0.6, respectively, both of which are consistent with the observed X-ray spectral index of β_X = −0.92 ± 0.30. The X-ray data then suggest p ≈ 1.9–2.3, but do not yield a definitive constraint on the location of ν_c.

The ALMA 97.5 GHz light curve appears flat (F_ν,3mm ≈ 0.15 mJy) from ≈13 to ≈20 days, after which it declines steeply as α_{3 mm}≈ −1.5 (Figure 4). The shallow light curve before the break indicates that the spectral peak (ν_m) passes through the 3 mm band at ≈13–20 days with a flux density, F_ν,m ≈ 0.15 mJy. The steepest decay at ν_m ≲ ν ≲ ν_c is expected to be α ≈ 3(1 − p)/4≈ −0.9 for p ≈ 2.2. Thus, unless there is a change in p, or it is much higher (i.e., p ≈ 3) than estimated from the X-ray light curve (p ≈ 2–2.3), the rapid postbreak decline suggests a jet break prior to the last ALMA detection at ≈43 days.

A broken power-law fit to the ATCA C-band (5.5 GHz) data yields a rise rate α_C,1 = 0.26 ± 0.10, a decline rate α_C,2 = −2.4 ± 0.8, break time 56 ± 4 days, and peak flux density, mJy. The fact that the 5.5 GHz light curve does not decline appreciably until ≳42 days, whereas the ALMA light curve starts declining much earlier at ≲28 days is consistent with the interpretation of a jet break at ≲43 days and with a light-curve turnover in the radio/mm bands arising from the cascading passage of ν_m through the mm/cm bands.

Interpolating the X-ray light curve to the time of the VLT upper limit at ≈2.9 days, we find an X-ray to optical spectral index of β_OX ≳ −0.39. This indicates that the optical flux is strongly suppressed relative to the expectation from the standard synchrotron model (β_OX > −0.5). Furthermore, the observed X-ray spectral index β_X ≈ −0.92 implies β_OX − β_X ≳ 0.52 and thus GRB 211106A satisfies the definition of a dark burst of both Jakobsson et al. (2004) and van der Horst et al. (2009). Several other SGRBs have been classified as dark (Berger et al. 2009; Fong et al. 2012; Berger et al. 2013), and we account for the dark nature by incorporating host extinction in our analysis using an SMC extinction model (Pei 1992).

Finally, our HST limits at ≳19 days cannot be used to place meaningful constraints on an AT2017gfo-like kilonova or previous SGRB kilonova candidates. The VLT limit at 2.9 days only probes to depths of comparable to ≈10 times the luminosity of AT 2017gfo for an assumed redshift of z = 0.5, while no meaningful constraints on kilonova emission can be derived from these optical/NIR observations at z = 1.0.

We now search the parameter space of p, E_K,iso, n₀, _e, _B, t_jet, and A_V for the best-fit synchrotron model to the afterglow observations using Markov Chain Monte Carlo (MCMC) with emcee (Foreman-Mackey et al. 2013). The details of our implementation are described in Laskar et al. (2013, 2014). We include the effects of KN corrections for the first time (G. A. McCarthy & T. Laskar 2022, in preparation) using the prescription of Nakar et al. (2009) as described by Jacovich et al. (2021). We run 512 walkers for 2000 steps, discarding an initial period of 30–200 steps (judged by stationarity in the resulting posterior density function) as burn in. We use a uniform prior on p from 2.001 to 2.99 and on the intrinsic extinction, A_V ≲ 8 mag. We restrict and to the range ∈ (−7, 0) with the additional constraint _e + _B < 1. We constrain (−10, 10) and E_K,iso ∈ (10⁴⁸, 5 × 10⁵⁴). We use Jeffreys (1946) priors for these last four parameters. We also perform the analysis without IC/KN corrections in each case for comparison, resulting in a total of four sets of parameters. We summarize the results of our MCMC analysis in Table 4.

Table 4. Afterglow Model Parameters from Multiwavelength Modeling of GRB 211106A

z	IC/KN	p					tjet	θjet	AV	EK
1.0	Y	2.47 ± 0.05						15.51 ± 1.43
0.5	Y	2.59 ± 0.04
1.0	N
0.5	N	2.63 ± 0.03								51.54 ± 0.58

Note. Units are as follows: n₀ is in cm⁻³, E_K,iso and E_K are in erg, t_jet is in days, θ_jet is in degrees, and A_V is in mag.

Download table as:  ASCIITypeset image

We find that some of the derived parameters are sensitive to the choice of redshift. The cooling frequency is between the optical and X-rays in the z = 1 models, above the X-rays in the z = 0.5 model without IC/KN, and ν_c ≈ ν_X in the z = 0.5 model when including IC/KN. In addition, the parameters derived from including IC/KN effects are quite different from those without. We note that the fits achieved by turning off IC effects yield Compton Y parameters at ν_c of Y_c < 1, where IC effects are indeed negligible (and vice versa), and thus all four sets of parameters are internally self-consistent. However, the fits without IC corrections are slightly systematically worse (maximum log-likelihood of and 100.39 for the z = 0.5 and z = 1.0 fits, respectively) compared to the fits including IC/KN effects ( and 108.22 for z = 0.5 and z = 1.0, respectively). Because the number of parameters in the models are the same, models with higher likelihoods are slightly statistically favored. Given the moderately high redshift of z ≈ 1 favored by the host SED, we focus the rest of the discussion on the z = 1.0 IC/KN model, with the understanding that some of the numerical results, in particular, are sensitive to these choices. We discuss the impact of the KN corrections in Appendix F. For completeness, we present the z = 1.0 model without IC/KN effects in Appendix E and include it in parameter comparisons below, where relevant.

For our fiducial parameter set (z = 1 with IC/KN corrections), we plot the correlation contours and marginalized posterior density functions in Figure 6. The parameters of the highest-likelihood model are E_K,iso ≈ 1.9 × 10⁵³ erg, n₀ ≈0.5 cm⁻³, _e ≈ 0.97, _B ≈ 5 × 10⁻⁶, and p ≈ 2.4. For this model, ν_m passes through the ALMA 3 mm band at ≈18 days with a flux density at ν_m of F_ν,m ≈ 0.15 mJy, which is consistent with the constraints from the ALMA light curve. We also estimate a jet break time of t_jet ≈ 29 days, consistent with the steepening observed in the cm- and mm-band light curves. We note that whereas we have provided ranges for the parameter A_V, this parameter is unbounded above, because there was no detection of an optical transient associated with the event. However, we can establish a lower limit of A_V ≳ 2.6 mag, corresponding to the value above which 99.7% of the MCMC samples reside. Our derived values of A_V are consistent with the A_V–N_H,int correlations for dark GRBs (Zaninoni et al. 2013). We plot our model light curves and SEDs for the highest-likelihood parameter set in Figure 7.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Finally, we derive a very high value of _e for both models upon inclusion of IC/KN effects. We note that the allowed range of _e spans a factor of ≈2 and furthermore this (and indeed all derived parameters) is degenerate with respect to the unknown electron participation fraction, f_NT (Eichler & Waxman 2005). A value of f_NT ≈ 0.1, as estimated from particle-in-cell simulations, would alleviate this issue by a corresponding factor (Sironi & Spitkovsky 2011). Capturing emission or absorption from thermal electrons would resolve this degeneracy (Ressler & Laskar 2017).

The ALMA mm-band observations of GRB 211106A were vital for constraining the jet break time and to derive the beaming-corrected energy unencumbered by scintillation effects in the cm-band and complications from IC/KN corrections in the X-ray band. This contribution is especially important in this case due to the absence of detectable optical afterglow emission, and because the jet break occurs after the X-ray afterglow has faded beyond the sensitivity of Chandra. The identification of the jet break, in combination with measurements of the circumburst density and energy for this burst, allows us to constrain the jet opening angle to θ_jet ≈ 16°, and this value appears relatively robust to the modeling uncertainties discussed above. The one notable exception in the case of the z = 0.5 model without IC corrections is driven by the extremely low density and high E_K,iso, which itself arises from a strong degeneracy between these parameters for this model. ²⁸ We find that removing the mm-band data from the fit and rerunning the MCMC results in similar degeneracies, further highlighting the importance of securing mm-band detections.

Eight other SGRBs have robust opening angle measurements ²⁹ from identification of jet breaks in their light curves, with measured values of θ_jet spanning from 1° to 14° (Soderberg et al. 2006; Stratta et al. 2007; Nicuesa Guelbenzu et al. 2011; Fong et al. 2012, 2014; Troja et al. 2016; Lamb et al. 2019; Troja et al. 2019; O’Connor et al. 2021; Fong et al. 2021). Whereas an additional five events have robust lower limits on θ_jet (i.e., incorporating their E_K,iso and n₀), only one of these has a larger inferred lower limit than this (θ_jet ≳ 25° for GRB 050724A; Grupe et al. 2006). Thus, the opening angle for GRB 211106A is one of the widest inferred for SGRBs, and the resulting late jet break (t_jet ≈ 29 days) is the latest observed in any SGRB. This confirms the finding of Fong et al. (2015) that afterglow observations at ≳25 days are essential for obtaining strong constraints on θ_jet. This late jet break ensures that the mm-band afterglow remains detectable for longer. We discuss the detectability of mm-band afterglows further in Section 5.3.

We find that the afterglow of GRB 211106A has several superlative properties. In comparison with the population of Swift/XRT SGRB afterglows, the X-ray afterglow of GRB 211106A is one of the most luminous at a comparable rest-frame time (Figure 2). Similarly, the cm afterglow of GRB 211106A is extremely long lived, and, at z = 1.0, is more luminous than any other SGRB radio afterglow (second-most luminous if at z = 0.5). The luminosity of this mm-band afterglow rivals that of several LGRBs (Figure 4). These properties are reflected in the high E_K,iso ≈ 1.6 × 10⁵³ erg (median value from the MCMC) in our fiducial model (z = 1 with IC/KN corrections), which is two orders of magnitude larger than the median values of E_K,iso ≈ (1–3) × 10⁵¹ erg inferred for the SGRB population (Fong et al. 2015). This yields a prompt γ-ray efficiency of η_γ ≡ E_γ,iso/(E_K,iso + E_γ,iso) ≈ 0.03 for the z = 1.0 model (≈0.02 at z = 0.5). This is the second-lowest prompt efficiency inferred for SGRBs after GRB 150101B with η_γ ≈ 10⁻³ but consistent with the wide range spanned by this parameter for SGRBs (Fong et al. 2015).

The true (beaming-corrected) energy is also high, with median values from the MCMC (in units of erg) of and 50.3 for the z = 1 model with and without IC/KN corrections, respectively. To put this in context, we compute E_K for all SGRBs that have published values of E_K,iso and either measurements of or lower limits on θ_jet, resulting in a sample of 12 events from Fong et al. (2015) and 4 additional events published subsequently (Jin et al. 2018; Lamb et al. 2019; Troja et al. 2019; Fong et al. 2021; Rouco Escorial et al. 2021). We find that the highest value of E_K was obtained for GRB 180418A ( Rouco Escorial et al. 2021). Two additional events have values between those of the two z = 1 models (GRBs 120804 and 140930B, with and ≳50.3, respectively). The remaining 13 events all . This places GRB 211106A in the top ≳80% of SGRBs with measured beaming-corrected energy, making it one of the most energetic SGRBs to date. The mm-band detection was pivotal in this measurement, as it is the only band that samples both ν_m and F_ν,m prior to the jet break, thus breaking the E_K,iso–n₀ degeneracy.

It is reasonable to ask whether an unprecedented value of some physical property (e.g., high E_K,iso, large opening angle) for GRB 211106A places it in a position in parameter space that makes this event uniquely suitable for detection in the mm band, or whether the improvement in sensitivity in the mm band with the advent of ALMA would have soon yielded such a discovery for an SGRB afterglow anyway. Alternatively, perhaps we simply missed previous mm afterglows because we did not observe them at the right time, and the relatively late commencement of the mm-band follow-up in this case coincidentally yielded just the right temporal sampling of the light curve. We now address these questions, beginning by investigating the mm-band light curves of all SGRBs with published mm-band upper limits in the context of the synchrotron model.

A total of 11 SGRBs have been observed in the mm band so far (Figure 4). Of these, three events have no afterglow detection at any wavelength (020531, 051105A, 140606A), and an additional two (GRB 050509B and GRB 060801) do not have data ³⁰ of quality sufficient for constraining physical parameters. In Figure 8, we plot the mm-band observations for the remaining six SGRBs: GRB 080426 (de Ugarte Postigo et al. 2012), 130603B, 140622A, 140903A (Pandey et al. 2019), 131004A (Fong et al. 2015), and GRB 211106A (this work), along with model light curves corresponding to published values of the physical parameters for each event. Where multiple sets of physical parameters are available (e.g., for two different assumed values of _B), we plot the more optimistic model (except in the case of GRB 130603B, as discussed below), which is always the one with lower assumed _B and higher inferred density.

Zoom In Zoom Out Reset image size

In the case of GRBs 080426, 131004A, and 140622A, we find that the peak flux of the mm-band light curve is below the only published upper limits for these events by factors of ≈5.3, 3.7, and 147, respectively. Two of these events have extremely low values of density (n₀ ≈ 6.5 × 10⁻⁴ cm⁻³ for GRB 131004A and n₀ ≈ 3.2 × 10⁻⁴ cm⁻³ for 140622A). Although the third (GRB 080426) has a higher density (n₀ ≈ 1.2 cm⁻³), it also has one of the lowest inferred energies for SGRBs (E_K,iso ≈ 6 × 10⁵⁰ erg). For p ≈ 2.2 and at the typical SGRB redshift of z ≈ 0.5, the spectral peak flux density is given by μJy (Granot & Sari 2002). This implies that SGRBs with n₀ ≲ 10⁻² cm⁻³ or E_K,iso ≲ 10⁵⁰ erg are unlikely to be detectable with both past and present mm-band facilities and confirms that these three previous events evaded detection due to their lower density or energy.

This leaves two events: GRBs 130603B and 140903A. Both the energy and density of GRB 130603B are higher than the above thresholds. For GRB 140903A, while the inferred density is low (n₀ ≈ 3.4 × 10⁻³ cm⁻³), the energy (which has a stronger impact on F_ν,m) is high (E_K,iso ≈ 3 × 10⁵² erg), and thus both events should have been detectable by the metric of peak flux density. For these two events, the reason for mm-band nondetections appears to be their narrow collimation angles, θ_jet ≈ 6° and θ_jet ≈ 4°, respectively. Physically, narrower collimation corresponds to a lower true energy, E_K. Observationally, the earlier jet break limits the peak flux of the mm-band light curve. In the case of GRB 140903A, the mm model light curve peaks at ≈0.24 mJy, which is lower than the spectral peak flux prior to the jet break (F_ν,m ≈ 0.5 mJy) and below the PdBI upper limit of ≈0.4 mJy, thus explaining the mm-band nondetection. Two models are available for GRB 130603B with different values of _B (Pandey et al. 2019). The model with lower _B and higher density actually overpredicts the existing mm-band observations (even upon including the jet break), and we can rule this model out. While the lower-density model does produce fluxes higher than the deepest upper limits for this event, the timing and depth of the epochs unfortunately do not probe the underlying light curve. The early observations were not deep enough, and by the time deeper observations were taken, the light curve would have faded below detectability due to the early jet break. This suggests that early, deep observations are essential to capture the mm counterparts of narrowly collimated/low-E_K outflows.

The inferred energy and density for GRB 211106A (in all models) are higher than the thresholds discussed above. The wide opening angle and resulting late jet break (t_jet ≈ 29 days) further drive the long-lived mm-band afterglow. Finally, the factor of 5–10 higher sensitivity of ALMA compared to CARMA and PdBI has further broadened the detectability window. To illustrate this, we plot model light curves for all 17 SGRBs at known redshifts with published E_K,iso and n₀ values (but without mm observations) as gray lines in the left panel of Figure 8. We find that the mm-band afterglows of 9/23 (39%) SGRBs (solid lines) would have been detectable for at least ≳2 days (observer frame) with ALMA, while only one event (GRB 150101B) satisfies this condition at pre-ALMA sensitivity levels.

To further quantify this, we compute the duration for which SGRB mm-band afterglows are detectable with ALMA at 3σ in 30 minutes of on-source integration time (F_ν ≳ 50 μJy) at 90 GHz for different values of n₀, E_K,iso, and θ_jet and compare the results with the inferred parameters for a sample of 38 events from Table 3 of Fong et al. (2015), which forms an X-ray-complete parent sample spanning 10 yr. We plot the results, divided into three redshift bins, in the right panel of Figure 8. The mm-band afterglows of the events to the right of the lines (drawn for four different jet opening angles) are detectable with ALMA for more than 2 days. We find that, independent of the opening angle, GRB 211106A would have been detectable owing to its position in the n₀–E_K,iso space alone. Its wide jet (and hence, high E_K) further ensured a high likelihood of discovery upon triggering of mm-band observations.

The detectability of the other events is contingent on their unknown opening angle (or, equivalently, their unknown true E_K), although some events (especially at high redshift) simply cannot be detected owing to a combination of low density and/or energy, as previously suggested. Nine events fall to the right of the θ_jet = 5° line, and these events, even if narrowly collimated (i.e., with low E_K), would have been detectable with ALMA. On the other hand, 22 events (58%) would not have been detectable for any value of their intrinsic θ_jet or E_K.

If we assume that the sample of 38 events in Fong et al. (2015) is representative of the SGRB population, then if SGRBs with X-ray afterglows were to be uniformly followed up in the mm band, we might expect a conservative success rate of (corresponding to the nine events that fall to the right of the θ_jet ≲ 5° lines) and a detection rate of r_mm ≈ 9/10 ≈ 0.9 mm afterglows per year (as the sample spans 10 yr). For events with wider jets θ_jet ≳ 30°, the corresponding rates are and r_mm ≈ 1.6 per year. These rates are even better than the discovery rates (≈7%) of SGRB afterglows in the cm-band (Fong et al. 2015). At pre-ALMA sensitivity levels, the mm-band detection rate is poorer by a factor of ≈3 with . We conclude that all three aspects (high density, wide opening angle/higher E_K, and improved sensitivity) have contributed to the discovery of the mm-band afterglow of GRB 211106A. Systematic ALMA follow-up of SGRBs should yield a significant (24%–40%) discovery rate of mm-band afterglows, potentially outpacing cm-band detections.