1000 Days of the Lowest-frequency Emission from the Low-luminosity GRB 171205A

We used the external synchrotron model for the GRB afterglow emission, which arises due to the interaction between the GRB outflow and the surrounding CBM (Granot & Sari 2002). As the outflow moves into the CBM, a "forward shock" or a "blast wave" shock moving into the CBM, and a "reverse shock" moving into the ejected outflow are created. These shocks have the ability to accelerate charged particles to relativistic speeds via Fermi acceleration (Longair 2011). Radio afterglow emission is expected to be synchrotron emission arising due to these relativistic charged particles in the shocks in the presence of magnetic fields.

The evolution of the blast wave is "self-similar" (Blandford & McKee 1976), and the dynamics depends only on the density of the CBM and the blast wave energy. The CBM is usually modeled to be one of the two forms, a constant density medium and a wind-like density medium (Chevalier & Li 2000). The number density profile of the ambient medium is usually modeled as a power law n ∝ r^−k. For the constant density case, the parameter k = 0 and n = n₀. For the wind-like case, the mass flows radially outwards at uniform speed and rate from the GRB progenitor giving k = 2; hence, for a mass-loss rate from the progenitor ${\dot{M}}_{W}$ and the progenitor wind velocity V_W, the density can be defined as (Chevalier et al. 2004; Gao et al. 2013)

$$\begin{eqnarray}&&n=\displaystyle \frac{{\dot{M}}_{W}}{4\pi {r}^{2}{m}_{p}{V}_{W}}=3\times {10}^{35}{A}_{* }{r}^{-2},\end{eqnarray} \tag{ 1 }$$

where m_p is the mass of the proton, A_* is in units of 3 × 10³⁵ cm⁻¹ (or 5 × 10¹¹ g cm⁻¹ for the mass density), corresponding to ${\dot{M}}_{W,-5}/{V}_{W,3}$. Here ${\dot{M}}_{W,-5}$ is the mass-loss rate in 10⁻⁵M_⊙ yr⁻¹ and V_W,3 = 10³ km s⁻¹.

The GRB wideband afterglow spectrum has several breaks characterized by various characteristic frequencies, namely, ν_a (the transition from the optically thick to the thin region, i.e., SSA peak), ν_c (synchrotron cooling frequency) and ν_m (frequency corresponding to the minimum injected Lorentz factor). In the fast cooling regime the frequency ordering is ν_m > ν_c, while in the slow cooling regime the ordering is the opposite. Generally, afterglow modeling is done in the slow cooling regime, where the most relevant ordering in radio frequencies in first few days are ν_a ≤ ν_m ≤ ν_c, and then ν_m ≤ ν_a ≤ ν_c at later times (Granot & van der Horst 2014). However, there has been evidence for fast cooling in some GRBs with high density environments (Chandra et al. 2008). The afterglow spectra evolves as F_ν ∝ ν² (ν < ν_a) and F_ν ∝ ν^1/3 (${\nu }_{a}\lt \nu \lt \min ({\nu }_{m},{\nu }_{c})$) for both the fast as well as the slow cooling regimes. In the regime of $\min ({\nu }_{m},{\nu }_{c})\lt \nu \,\lt \max ({\nu }_{m},{\nu }_{c})$, the evolution changes to F_ν ∝ ν^−1/2 and F_ν ∝ ν^−(p−1)/2 for the fast and slow cooling regimes, respectively, and then evolves as F_ν ∝ ν^−p/2 for $\nu \gt \max ({\nu }_{m},{\nu }_{c})$, where p is the usual power-law index showing particle number distribution with energy in the nonthermal emission case.

In addition to standard AG models, the SBO model also has been favored for low-luminosity GRBs, where the breakout of a shock traveling through the stellar envelope may be responsible for gamma-ray emission. Due to the decreasing density of the stellar matter outwards, the SBO velocity increases and may become relativistic. Nakar & Sari (2012) have defined a "relativistic breakout closure relation" between the breakout energy E_bo, temperature T_bo, and duration ${t}_{\mathrm{bo}}^{\mathrm{obs}}$, i.e., ${({t}_{\mathrm{bo}}^{\mathrm{obs}}/20{\rm{s}})\sim ({E}_{\mathrm{bo}}/{10}^{46}\mathrm{erg})}^{1/2}{({T}_{\mathrm{bo}}/50\mathrm{keV})}^{-2.68}$. This relation has been found to be followed by several low-luminosity GRBs. For GRB 171205A, the relation gives ∼80 s, which is roughly one-third of the observed duration. However, the large uncertainties in the E_p and E_iso (D'Elia et al. 2018) do not rule out this model.

The Swift-XRT light curve covers the epoch until day ∼902. In addition, Chandra observations are on day 71 and day 205 (Figure 2). We fit a power law to the X-ray data post day 1. This is to avoid possible energy injection due to central engine activities at ≤ 1 day. The light curve is fit with the power-law index α = 1.06 ± 0.06. D'Elia et al. (2018) also found a power-law fit with an index of 1.08 to the light curve post ∼1 day, consistent with our value. This is the typical value for the standard X-ray light-curve decay before jet break (Panaitescu & Kumar 2002), suggesting that no jet break was seen until the last Swift-XRT epoch. The jet break time is thus constrained to t_jet ≥ 71 days (Rhoads 1999), i.e., the last detected Chandra epoch.

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The photon index of the Swift-XRT data is a photon index ${\rm{\Gamma }}={1.94}_{-0.22}^{+0.23}$ (see footnote 2). This suggests $\beta ={0.94}_{-0.22}^{+0.23}$. The values of α and β are consistent with the X-ray frequency (ν_X) being above the cooling frequency (ν_X > ν_c), for both wind as well as the interstellar medium (ISM) density profiles. The X-ray temporal index is consistent with α = (3p − 2)/4 and spectral index β = p/2. These values make p = 2.08 ± 0.08 and 1.88 ± 0.46, respectively, which within the error bars, are consistent with each other. Within the error bars, this is also consistent with ν_X < ν_c for an ISM-like medium, where α = 3(p − 1)/4 and β = (p − 1)/2.

We also plot early time 230 and 345 GHz light curves GRB 171205A, taken from Urata et al. (2019). We estimate the realistic error bars in the flux density values by adding 5% of the flux density in quadrature to the map rms to account for the systematic errors. The millimeter highest flux density is significantly higher than the peak flux densities at the uGMRT bands, indicating most likely the presence of a wind-like medium. The millimeter light curves are jointly fit with a broken power law with a common post-peak index. The data are best fit with post-break index of −1.37 ± 0.07 (bottom panel of Figure 2). For the above values of p, this is consistent with an evolution of (3p − 1)/4, for ν_m < ν_mm < ν_c for the wind density profile. The pre-break indices −0.17 ± 0.14 and −0.54 ± 0.31 for the 230 and 345 GHz bands, respectively. The breaks in 230 and 345 GHz are at 3.14 ± 0.28 day and 6.12 ± 1.17 day, respectively. At the epochs of the breaks, the flux density of the 230 and 345 GHz light curves are 43.83 ± 3.29 and 14.85 ± 2.86 mJy, respectively. We also fit the 345 GHz data with a single power-law model to determine the significance of the break. The single power-law model fits with an index of −1.05 ± 0.14, however, this results in a much larger reduced-χ² value of 2.47 as compared to 0.81 in the broken power-law case. For the broken power-law model, the characteristic frequency evolves with an index of +0.71 ± 0.12, hence, the breaks cannot be due to passage of ν_m, which decreases with time. The only possibility is the breaks are due to ν_c in the wind medium, where ν_c ∝ t^1/2. Thus, the data indicate ν_c ≈ 230 GHz on day 3.14 and ν_c ≈ 345 GHz on day 6.12. However, there is one concern. The pre-break evolution is rather flat. This could be reconciled if millimeter bands are close to the passage of ν_m. Another possibility is that there is a reverse shock component that is contributing to the millimeter band at the early epoch. The thick shell reverse shock model during the reverse shock crossing phase will evolve as − (p − 2)/2, for ν_mm > ν_c in the slow cooling phase and ν_mm > ν_m in the fast cooling phase. The characteristic frequency evolves with an index of +0.71 ± 0.12; this is in between the evolution of the ν_c ( ∝ t^1/2) in the forward shock and the evolution of ν_c ( ∝ t¹) in the reverse shock. This also suggests the possibility of reverse shock contributing to the AG model. If so, then the breaks at days 3.14 and 6.12 in 230 and 345 GHz are artificial breaks and may not reflect the cooling break.

We also combined the early epoch published centimeter and millimeter data from Urata et al. (2019), and late epoch Australian Telescope Compact Array data from Leung et al. (2020) with the uGMRT and the X-ray data, to obtain near-simultaneous spectra on around day 4, day 11, and day 909 (Figure 3). For the early epoch spectrum, the VLA data are on day 4.3 and the ALMA data are on day 5.2. We use the nearest epoch temporal evolution to derive the ALMA values on day 4.3. In the figure, we plot the values on day 5.2 as well as their derived values on day 4.3 along with the VLA data. We do not use optical data as SN signatures appeared by day 3 and hence the optical data are likely to be heavily contaminated by the underlying SN. We fit smooth single broken power-law (SBPL) and smooth double broken power-law (DBPL) fits to day 4.3 spectrum. We used the formalism of Granot & Sari (2002) for the treatment of smoothing of power laws at the break frequencies. We first fit only the centimeter and millimeter data. For day 4.3, the best-fit SBPL model peaks at 30.41 ± 4.08 GHz and afterwards evolves as −0.41 ± 0.25. Here we have fixed the pre-break spectral index to 2. However, even when we use this as a free parameter, the best-fit index is consistent with 2 within error bars. The DBPL model fits the data well and give the breaks at 7.25 ± 2.11 GHz and 44.41 ± 3.62 GHz with post-break indices 1.26 ± 0.12, and −0.41 ± 0.02, respectively. The peak flux density is 43.80 ± 1.12 mJy.

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We also fit the SBPL for the spectrum on day 11 and 909. The data indicates a fit −0.68 ± 0.02 with a peak of < 90 GHz, with the peak flux density of > 16.2 mJy. The pre-break index is 0.43 ± 0.46. The spectra on day 909 are fit with pre-break and post-break indices of 0.15 ± 0.13 and −0.90 ± 0.04, respectively, and a peak at 1.55 ± 0.48 GHz. The peak flux at day 909 is 1.15 ± 0.16 mJy.

Now we carry out the above fits including the X-ray data as well. The data to millimeter to X-ray data are fit by indices close to −1. These values are −1.01 ± 0.18 and −1.01 ± 0.02 for the first two spectra, respectively. For day 909, the X-ray upper limit does not constrain the model. The millimeter to X-ray indices consistent with the X-ray spectral indices are between 0.3 and 10 keV. This indicates that the cooling frequency (ν_c) is probably close to millimeter values if ν_X > ν_c. Due to lack of optical data, we were unable to constrain the cooling frequencies more precisely.

The peak flux density and the frequency of the peak in the three cases are 37.79 ± 3.95 mJy at 160.93 ± 35.31 GHz, > 16.2 mJy at < 90 GHz, and 1.15 ± 0.16 mJy at 1.55 ± 0.48 GHz, respectively. Our analysis indicates that the peak of the spectra on day 4 and day 909 are due to ν_m or ν_a. Between day 4 and 909, the peak flux density evolves as −0.63 ± 0.02. This clearly rules out an ISM model and supports the wind model.

Zhang et al. (2007) estimated kinetic energy in the synchrotron afterglow, E_K, from the X-ray data at the time of shallow to normal decay, which for GRB 171205A is 1.05 day. For ν_X > ν_c, E_K is independent of density and is only weakly depends on B and p, and therefore is an ideal regime to measure E_K. One can then derive E_K from the X-ray band using Equation (9) of Zhang et al. (2007), which in this case is ${E}_{K}\approx 1.4\times {10}^{50}{({\epsilon }_{B}/0.01)}^{2-p/2+p}{({\epsilon }_{e}/0.1)}^{4(1-p)/2+p}$ erg.

We plot uGMRT radio light curves and fit them jointly with an SBPL model. We allow the normalization to vary but fix the indices before and after the peak. We show the light curves in Figure 4. In the figure, the Band 4 and 5 values are scaled by factors of 10 and 100, respectively, for clarity. The indices before and after the peak are 1.37 ± 0.20 and −0.72 ± 0.06.

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The evolution before peak at uGMRT frequencies (ν_radio) is in rough agreement with the wind slow cooling phase for ν_radio < ν_a for ${\nu }_{a}\lt \min ({\nu }_{m},{\nu }_{c});$ the wind fast cooling phase for ν_a < ν_c < ν_m if the observing frequency is in the transition zone between ν_radio < ν_a to ν_a < ν_radio < ν_c, as well as the wind slow cooling phase for ν_m < ν_a < ν_c for the transition between ν_radio < ν_m to ν_m < ν_radio < ν_a. The post-peak index is rather shallow and is consistent only with the wind fast cooling phase in the regime of ν_a < ν_radio < ν_c. It is rather shallow for the post-jet break or nonrelativistic evolution. However, as we discuss in the next section, the shallow decline of the radio light curve is seen in other GRBs as well, and other emission components may contribute to it.

From our fits, the epochs of the peak flux densities are 5.19 ± 0.05 and 3.23 ± 0.15 mJy, respectively, in Bands 5 and 4 on day 101.08 ± 9.58 and day 153.71 ± 40.31, respectively. In Band 3, the data are optically thin, which constrains the peak to be <185.13 day and flux >2.81 mJy. The peak flux density evolves as −1.13 ± 0.76. While this value has a large error, it is consistent with the evolution in the stratified wind within 2σ and most likely rules out all the models involving ISM, where ${F}_{\max }\propto {t}^{0}$. This also rules out the 1 < p < 2 case for which ${F}_{\nu ,\max }$ is expected to remain constant (Gao et al. 2013).

In this section, we carry out detailed model fits to the uGMRT data. The simple closure relations seem to suggest that the GRB is in a slow cooling regime for the wind density medium. We fit the data with all three scenarios, i.e., the wind density slow cooling regime ν_a < ν_m < ν_c, ν_m < ν_a < ν_c , and the wind density fast cooling regime ν_a < ν_c < ν_m. We also account for the nonstandard wind profile, i.e., k ≠ 2. For this we keep k as a free parameter and adopt the expressions shown in van der Horst (2007).

Models are proposed for different stages of blast wave expansion. The precise coefficients associated with specified model parameters can be computed by numerical simulations. For the decelerating blast wave and the adiabatic wind-like case the parameter dependencies of the peak flux density and characteristic frequencies are given by Gao et al. (2013)

$$\begin{eqnarray}\begin{array}{rcl}{F}_{\nu ,\max } & = & 17.0\,\mathrm{mJy}{\left(\displaystyle \frac{1+z}{2}\right)}^{3/2}{\left(\displaystyle \frac{{E}_{\mathrm{KE}}}{{10}^{49}\mathrm{erg}}\right)}^{1/2}{\left(\displaystyle \frac{{\epsilon }_{B}}{0.01}\right)}^{1/2}\\ & & \left(\displaystyle \frac{{A}_{* }}{0.1{\dot{M}}_{W,-5}/{V}_{W,3}}\right){\left(\displaystyle \frac{D}{100\mathrm{Mpc}}\right)}^{-2}{\left(\displaystyle \frac{t}{10\mathrm{days}}\right)}^{-1/2},\end{array}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}\begin{array}{rcl}{\nu }_{c} & = & 1.7\times {10}^{17}\,\mathrm{Hz}{\left(\displaystyle \frac{1+z}{2}\right)}^{-3/2}{\left(\displaystyle \frac{{E}_{\mathrm{KE}}}{{10}^{49}\mathrm{erg}}\right)}^{1/2}\\ & & {\left(\displaystyle \frac{{A}_{* }}{0.1{\dot{M}}_{W,-5}/{V}_{W,3}}\right)}^{-2}{\left(\displaystyle \frac{{\epsilon }_{B}}{0.01}\right)}^{-3/2}{\left(\displaystyle \frac{t}{10\mathrm{days}}\right)}^{1/2},\end{array}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}\begin{array}{rcl}{\nu }_{m} & = & 2.7\times {10}^{7}\,\mathrm{Hz}\,G^{\prime} (p){\left(\displaystyle \frac{1+z}{2}\right)}^{1/2}{\left(\displaystyle \frac{{E}_{\mathrm{KE}}}{{10}^{49}\mathrm{erg}}\right)}^{1/2}\\ & & {\left(\displaystyle \frac{{\epsilon }_{e}}{0.1}\right)}^{2}{\left(\displaystyle \frac{{\epsilon }_{B}}{0.01}\right)}^{1/2}{\left(\displaystyle \frac{t}{10\mathrm{days}}\right)}^{-3/2},\end{array}\end{eqnarray} \tag{ 4 }$$

where the parameters _B and _e are microscopic parameters indicating the fraction of energy into the magnetic field and relativistic electrons, respectively, and E_KE is the afterglow kinetic energy, $G^{\prime} {(p)=0.053((p-2)/(p-1))}^{2}$.

The expression ν_a for the three regimes are

$$\begin{eqnarray}&&{\nu }_{a}\left\{\begin{array}{l}=4.3\times {10}^{9}\,\mathrm{Hz}\,g^{\prime} (p){\left(\tfrac{1+z}{2}\right)}^{-2/5}{\left(\tfrac{{E}_{\mathrm{KE}}}{{10}^{49}\mathrm{erg}}\right)}^{-2/5}\\ {\left(\tfrac{{A}_{* }}{0.1{\dot{M}}_{W,-5}/{V}_{W,3}}\right)}^{6/5}{\left(\tfrac{{\epsilon }_{B}}{0.01}\right)}^{1/5}{\left(\tfrac{{\epsilon }_{e}}{0.1}\right)}^{-1}{\left(\tfrac{t}{10\mathrm{days}}\right)}^{-3/5},\\ \mathrm{for}\ {\nu }_{a}\lt {\nu }_{m}\lt {\nu }_{c}.\\ =4.9\times {10}^{8}\,\mathrm{Hz}\,g^{\prime\prime} (p){\left(\tfrac{1+z}{2}\right)}^{\tfrac{p-2}{2(p+4)}}{\left(\tfrac{{E}_{\mathrm{KE}}}{{10}^{49}\mathrm{erg}}\right)}^{\tfrac{p-2}{2(p+4)}}\\ {\left(\tfrac{{A}_{* }}{0.1{\dot{M}}_{W,-5}/{V}_{W,3}}\right)}^{\tfrac{4}{p+4}}{\left(\tfrac{{\epsilon }_{B}}{0.01}\right)}^{\tfrac{p+2}{2(p+4)}}{\left(\tfrac{{\epsilon }_{e}}{0.1}\right)}^{\tfrac{2(p-1)}{p+4}}{\left(\tfrac{t}{10\mathrm{days}}\right)}^{-\tfrac{3(p+2)}{2(p+4)}},\\ \mathrm{for}\ {\nu }_{m}\lt {\nu }_{a}\lt {\nu }_{c}.\\ =6.0\times {10}^{4}\,\mathrm{Hz}\,g\prime\prime\prime (p){\left(\tfrac{1+z}{2}\right)}^{3/5}{\left(\tfrac{{E}_{\mathrm{KE}}}{{10}^{49}\mathrm{erg}}\right)}^{-2/5}\\ {\left(\tfrac{{A}_{* }}{0.1{\dot{M}}_{W,-5}/{V}_{W,3}}\right)}^{11/5}{\left(\tfrac{{\epsilon }_{B}}{0.01}\right)}^{6/5}{\left(\tfrac{t}{10\mathrm{days}}\right)}^{-8/5},\\ \mathrm{for}\ {\nu }_{a}\lt {\nu }_{c}\lt {\nu }_{m}.\end{array}\right.\end{eqnarray} \tag{ 5 }$$

where the expressions for $g^{\prime} (p)$, g''(p), and g‴(p) are derived in Gao et al. (2013) and for p = 2.1. Using these expressions, the temporal and spectral evolution in different transitions regimes can be derived and are mentioned in Gao et al. (2013).

We also carry out modeling for the SBO cases, for which we adopt the methodology of Barniol Duran et al. (2015). In this model, due to decreasing outer ejecta density, the outer parts of the shock envelope are faster and less energetic, and the inner parts are slower and more energetic. As slower material catches up with the decelerating ejecta it reenergizes the forward shock and the blast wave energy continuously changes with time. Thus, this model can be treated as a series of successive shells that accelerate and catch up to the boundary and hence explain the increasing afterglow energy via continuous injection (Barniol Duran et al. 2015). If η is the ratio of the prompt to afterglow energy (η ≡ E_γ.iso/E_k,iso), then for the SBO case, we parameterize the model as ${\eta }_{\mathrm{eff}}{E}_{{\rm{k}},\mathrm{iso}}={E}_{\gamma .\mathrm{iso}}{\left(\tfrac{{{tA}}_{* }}{1+z}\right)}^{s}$, where s is a free parameter characterizing energy injection (Barniol Duran et al. 2015).

Using this expression along with the scalings for ν_a, ν_m, ν_c, and ${F}_{\max }$ for various regimes, provided by Barniol Duran et al. (2015), leads to the following closure relations for a wind-like medium:

Case 1 (ν_a < ν_m < ν_c):

$$\begin{eqnarray}{F}_{\nu }(t)\propto \left\{\begin{array}{ll}{\nu }^{2}{t}^{s+1}, & \mathrm{for}\ \nu \lt {\nu }_{a}\\ {\nu }^{1/3}{t}^{\tfrac{s}{3}}, & \mathrm{for}\ {\nu }_{a}\lt \nu \lt {\nu }_{m}\ \\ {\nu }^{-(p-1)/2}{t}^{-\tfrac{3p-1-s(p+1)}{4}}, & \mathrm{for}\ {\nu }_{m}\lt \nu \lt {\nu }_{c}\\ {\nu }^{-p/2}{t}^{-\tfrac{3p-2-s(p+2)}{4}}, & \mathrm{for}\ \nu \gt {\nu }_{c}\end{array}\right..\end{eqnarray} \tag{ 6 }$$

Case 2 (ν_m < ν_a < ν_c):

$$\begin{eqnarray}{F}_{\nu }(t)\propto \left\{\begin{array}{ll}{\nu }^{2}{t}^{s+1}, & \mathrm{for}\ \nu \lt {\nu }_{m}\\ {\nu }^{5/2}{t}^{\tfrac{7+3s}{4}}, & \mathrm{for}\ {\nu }_{m}\lt \nu \lt {\nu }_{a}\ \\ {\nu }^{-(p-1)/2}{t}^{-\tfrac{3p-1-s(p+1)}{4}}, & \mathrm{for}\ {\nu }_{a}\lt \nu \lt {\nu }_{c}\\ {\nu }^{-p/2}{t}^{-\tfrac{3p-2-s(p+2)}{4}}, & \mathrm{for}\ \nu \gt {\nu }_{c}\end{array}\right..\end{eqnarray} \tag{ 7 }$$

Case 3 (ν_a < ν_c < ν_m):

$$\begin{eqnarray}{F}_{\nu }(t)\propto \left\{\begin{array}{ll}{\nu }^{2}{t}^{2+s}, & \mathrm{for}\ \nu \lt {\nu }_{a}\\ {\nu }^{1/3}{t}^{-\tfrac{2(s+1)}{3}}, & \mathrm{for}\ {\nu }_{a}\lt \nu \lt {\nu }_{c}\ \\ {\nu }^{-1/2}{t}^{-\tfrac{s+1}{4}}, & \mathrm{for}\ {\nu }_{c}\lt \nu \lt {\nu }_{m}\\ {\nu }^{-p/2}{t}^{-\tfrac{3p-2+(p+2)s}{4}}, & \mathrm{for}\ \nu \gt {\nu }_{m}.\end{array}\right..\end{eqnarray} \tag{ 8 }$$

We now fit the uGMRT data with both the standard isotropic afterglow and SBO AG models. We use SBPL models for various regimes following the procedure in Granot & Sari (2002). We use z = 0.036 and D = 163 Mpc. We define E_KE = E_γ.iso/η, and keep η (η_eff for SBO) as the free parameter. The parameters p, A_*, _B, and _e are also free parameters.

With the inputs above, we carry out the detailed modeling using Markov chain Monte Carlo fitting using the Python package emcee (Foreman-Mackey et al. 2013). We choose 150 walkers and 2000 steps. Even though the analytical modeling suggests a wind-like medium, we start with fits to a constant density medium. The fit results in a high values of reduced χ² further ruling out the constant density model. We fit the standard wind model with k = 2 for all the cases. In addition, we also account for a nonstandard wind density medium keeping k as a free parameter.

Table 2 shows the fit statistics for different parameters using the above-mentioned models. For the ν_a < ν_m < ν_c case, we do not list the general k model as this model performed quite poorly for both afterglow as well as SBO. ν_a < ν_m < ν_c generally performs very poorly, with the SBO model performing slightly better than the isotropic AG model. In addition, the parameters obtained in this model are rather unphysical. While the fast cooling model gives best reduced ${\chi }_{\nu }^{2}$, this case is unlikely to be true. The analysis of millimeter and X-ray light published data have already revealed that ν_c lies between the millimeter and X-ray frequencies. Since ν_c ∝ t^1/2 in the wind model, uGMRT radio frequencies cannot be in the fast cooling regime.

Table 2.  Best-fit Parameters for the GRB 171205A uGMRT Data

Parameter	νa < νm < νc		νm < νa < νc				νa < νc < νm
	AG	SBO	AG		SBO		AG		SBO
	k = 2	k = 2	k = 2	General k	k = 2	General k	k = 2	General k	k = 2	General k
A*	${7.37}_{-0.80}^{+0.95}$	${2.82}_{-0.39}^{+0.46}$	${1.58}_{-0.75}^{+0.11}$	${1.11}_{-0.54}^{+1.03}$	${2.89}_{-1.26}^{+1.95}$	${3.54}_{-1.55}^{+2.46}$	${1.69}_{-0.51}^{+1.15}$	${0.17}_{-0.09}^{+0.19}$	${2.15}_{-0.78}^{+1.53}$	${0.22}_{-0.11}^{+0.16}$
η(ηeff for SBO)	${0.005}_{-0.0004}^{+0.0004}$	${0.30}_{-0.12}^{+0.13}$	${0.02}_{-0.01}^{+0.02}$	${0.02}_{-0.02}^{+0.03}$	${0.07}_{-0.05}^{+0.09}$	${0.13}_{-0.07}^{+0.12}$	${0.014}_{-0.002}^{+0.002}$	${0.03}_{-0.003}^{+0.003}$	${0.06}_{-0.03}^{+0.05}$	${0.03}_{-0.01}^{+0.02}$
B	${0.94}_{-0.09}^{+0.05}$	${0.70}_{-0.20}^{+0.20}$	${0.21}_{-0.13}^{+0.24}$	${0.11}_{-0.06}^{+0.17}$	${0.03}_{-0.02}^{+0.03}$	${0.01}_{-0.01}^{+0.01}$	${0.17}_{-0.10}^{+0.14}$	${0.02}_{-0.01}^{+0.01}$	${0.08}_{-0.05}^{+0.09}$	${0.01}_{-0.01}^{+0.01}$
e	${0.99}_{-0.02}^{+0.01}$	${0.78}_{-0.23}^{+0.16}$	${0.12}_{-0.06}^{+0.09}$	${0.13}_{-0.07}^{+0.11}$	${0.24}_{-0.11}^{+0.17}$	${0.12}_{-0.06}^{+0.07}$	⋯	⋯	⋯	⋯
p	${2.55}_{-0.06}^{+0.08}$	${3.87}_{-0.19}^{+0.10}$	${2.22}_{-0.04}^{+0.04}$	${2.18}_{-0.09}^{+0.14}$	${2.23}_{-0.05}^{+0.04}$	${2.22}_{-0.13}^{+0.16}$	⋯	⋯	⋯	⋯
k	⋯	⋯	⋯	${1.99}_{-0.02}^{+0.01}$	⋯	${1.99}_{-0.01}^{+0.01}$	⋯	${1.91}_{-0.01}^{+0.02}$	⋯	${1.92}_{-0.02}^{+0.02}$
s	⋯	${0.55}_{-0.04}^{+0.04}$	⋯	⋯	${0.13}_{-0.07}^{+0.08}$	${0.15}_{-0.08}^{+0.08}$	⋯	⋯	${0.35}_{-0.16}^{+0.13}$	${0.08}_{-0.18}^{+0.16}$
	${\chi }_{\nu }^{2}=7.55$	${\chi }_{\nu }^{2}=2.58$	${\chi }_{\nu }^{2}=1.74$	${\chi }_{\nu }^{2}=1.80$	${\chi }_{\nu }^{2}=1.72$	${\chi }_{\nu }^{2}=1.78$	${\chi }_{\nu }^{2}=1.60$	${\chi }_{\nu }^{2}=1.52$	${\chi }_{\nu }^{2}=1.58$	${\chi }_{\nu }^{2}=1.57$

Note. Here AG is the standard isotropic afterglow model and SBO is the shock breakout model. In the case of fast cooling, the data are only in the regime of ν_a to ν_c (2 to 1/3 transition of spectra), for which we do not have p dependencies in temporal or spectral slopes. The only p dependency is in the expression of ν_a via that ratio of G(p) parameter, which we have taken to be of order unity for p ∼ 2.1. The _e dependency is also not there as ν_m is unconstrained.

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The most viable model fits are obtained for the ν_m < ν_a < ν_c case. This is quite viable since in the wind density profile, ν_m evolves faster than ν_a and may reach the ν_m < ν_a regime at late epochs (Granot & van der Horst 2014). Here keeping k as free parameter also results in k ∼ 2. Our model fits are equally good for the standard AG model and the SBO model, and uGMRT data alone cannot differentiate between the two.

In Figure 5, we show the light curve for a standard wind k = 2 model for the ν_m < ν_a < ν_c case for both isotropic forward shock afterglow as well as the SBO AG model.

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The peak radio flux density of GRB 171205A at 1.3 GHz is ∼ 10²⁹ erg s⁻¹ Hz⁻¹. This is two orders of magnitude fainter than cosmological GRBs at this frequency (Figure 6). However, these values are comparable to other low-luminosity GRBs, e.g., GRB 031203 (Soderberg et al. 2004) and GRB 980425 (Kulkarni et al. 1998).

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The value of A_* in the standard afterglow and the SBO models are ${1.58}_{-0.75}^{+0.11}$ and ${2.89}_{-1.26}^{+1.95}$, respectively, which, assuming a wind velocity of 1000 km s⁻¹, translate to mass-loss rates of ${1.58}_{-0.75}^{+0.11}\times {10}^{-6}$ and ${2.89}_{-1.26}^{+1.95}\times {10}^{-6}$ M_⊙ yr⁻¹, respectively, for the two models. The nature of the surrounding ambient medium reflects on the progenitor nature of GRBs. It is expected that the progenitors of long GRBs are massive stars (Wolf–Rayet) and in most of the cases a long GRB is associated with an SN (Kulkarni et al. 1998; Woosley & Bloom 2006). Other evidence for massive star progenitors is that the long GRBs generally have star-forming host galaxies (Zhang 2019). In such a case, one expects the association with a wind-like CBM. However, several GRBs from massive stars collapse have shown homogeneous density (Panaitescu & Kumar 2001, 2002). A constant density medium can be produced around a massive star if the wind faces a shock termination (Chevalier et al. 2004). The low-frequency observations presented here provide a unique opportunity to determine the nature of the CBM of GRB 171205A and establish that GRB 171205A exploded in a wind-like environment. At uGMRT frequencies, the optically thick to thin transition peak arises after a long period of time (t > 100 days) after the burst, indicating a relatively high density medium. This may be created due to a large stellar mass-loss rate or a low wind velocity. Some previous works (Crowther 2003) have shown that the large mass-loss rate for Wolf–Rayet stars are associated with large metallicity of the medium. Thus GRBs in wind medium can be potential tools for studying metallicity variation at different redshifts.

The uGMRT light curve declines as ∼ t^−0.7. This indicates that there is no jet break until 3 yr. There are several explanations for the lack of jet breaks in some GRBs. In the cases of GRB 980326 and GRB 980519, Granot & van der Horst (2014) have argued that a wind medium can dilute the jet break even for highly collimated bursts. The jet break will be absent if the radio emission indeed arises from a quasi-spherical afterglow, such as that due to SBO (Nakar & Sari 2012) or a cocoon (Nakar 2015). In the case of GRB 030329, Berger et al. (2003) have argued that radio emission may arise from two components, a narrow jet, surrounded by a wider component (e.g., a cocoon) and the radio emission is being dominated by the wider component. However, the requirement of this model is that the contribution to the radio afterglow from the narrow jet may be negligible. X-ray observations cover the period of ∼200 days and show no indication of a jet break at least until the last detection on day ∼70. Using t_j > 71 days, gives a limit θ_j > 1.2 rad for the AG model and θ_j > 1.9 for SBO model (Nava et al. 2007; Wang et al. 2018).

Margutti et al. (2013, and references therein) have shown that ejecta kinetic energy profiles in stripped enveloped SNe vary based on different explosion mechanisms. While stripped-envelope SNe have a steep dependence E_K ∝ (Γβ)^−5.2 indicating no central engine activity, relativistic SNe, sub-energetic GRBs with SBO mechanisms are flatter with E_K ∝ (Γβ)^−2.4 showing weak activity from the central engine. Canonical GRBs, on the other hand, follow E_K ∝ (Γβ)^−0.4 typical of jet-driven explosions with long-lasting central engines. Our radio modeling and the relativistic treatment of Barniol Duran et al. (2013), results in E_K ≈ 1.1 × 10⁵¹ erg and Γβ ∼ 1. For the nonrelativistic SN component, we use values from Izzo et al. (2019), i.e., SN kinetic energy E_K = 2.4 × 10⁵² erg and ejecta velocity 55,000 km s⁻¹. Using these values, E_K ∼ (Γβ)^−1.9. While GRB 171205A is a sub-energetic GRB, it follows the energy-velocity profile somewhere between canonical GRBs and SBOs. These arguments suggest that the jet and SBO both may play an important role in the late-time afterglow emission in GRB 171205A.

Since we have radio light-curve peaks at two uGMRT frequencies, we could also estimate additional parameter evolutions. The relativistic energy under the equipartition assumption at the two epochs are E_Eq = 3.6 × 10⁴⁸ and 4.9 × 10⁴⁸ erg (Barniol Duran et al. 2013). Thus, there is an indication of the enhancement of energy E ∝ t^0.48. This along with flatter light-curve decays may also be explained if there is an energy injection from the central engine to the shock. For an injection luminosity $L{(t)={L}_{0}(t/{t}_{0})}^{-q}$, E ∝ t^1−q. This implies q = 0.52. However, our best fits result in a much larger value of q (s = 0.13, q = 1 − s ≡ 0.87. This may imply that if there is energy injection, it is not continuous and probably lasted for a small amount of time.

The equipartition size obtained from the above formulation (Barniol Duran et al. 2013) at the epochs of two peaks in Band 5 and Band 4 follow R(t) ∝t^0.49. We note that for the ISM and wind density profiles, R follows as R ∝ t^1/4 and R ∝ t^1/2, so it also points toward a wind-like medium surrounding GRB 171205A.

Our uGMRT observations cover a period of around 1000 days. However, our data does not suggest the GRB to be in the Newtonian regime yet (Figure 4). This is not uncommon for low-luminosity GRBs (e.g., GRB 060218, Irwin & Chevalier 2016). We note that the value of Γβ indicates a mildly relativistic outflow. Hence, it is likely that the GRB will make a transition into the Newtonian regime soon.

We note that the decay of the radio afterglow is much shallower than that of the X-ray afterglow. The shallowness of radio light curves was first pointed out by Panaitescu & Kumar (2004). For reasonable afterglow parameters, they estimated that the afterglow is supposed to cross ν_m at around 10 days for 10 GHz and follow a decay slope of (3p − 1)/4 for a wind medium, which was not the case for some GRBs, e.g., GRB 991216 and GRB 000926. They explored the difference between the radio and the optical decay indices, which could be caused by the fact that the injection frequency remains above the radio domain (∼10 GHz), or a different population of electrons, or variability in the microparameters. Finally, they concluded that a long-lived reverse shock in the radio regime could cause this flattening. However, this is unlikely in GRB 171205A as a strong persistent reverse shock requires a low wind density (Resmi & Zhang 2016). Here the late rising of the radio afterglow suggests a comparatively high density medium, which contradicts the previous statement. So, this scenario can be excluded.

Kangas & Fruchter (2019) noted that radio afterglows of some GRBs deviate at late times and low frequencies from the standard model, and attempted to explain it with the two-component jet model, a narrow jet core and a wider cocoon surrounding the jet. Granot & Sari (2002) have explained that this flattening is due to a counter-jet, which becomes visible when turning sub-relativistic. While such two components should result in a bump, for stratified wind medium, the evolution of a counter-jet is more gradual, causing mild flattening. An energy injection event or a different component dominating the radio emission can also produce this flattening. In the case of a slightly off-axis jet, the early radio emission could possibly be from the cocoon, the accelerated polar ejecta and at a late phase the contribution from the off-axis jet coming to the line of sight can increase the total radio flux (De Colle et al. 2018). The lack of X-ray data at such late times prevents us from directly distinguishing between these scenarios.

A population of quasi-thermal electrons has also been argued as one of the reasons (Warren et al. 2017) that would mainly dominate at radio frequencies, as it would result in an increased ν_a and suppress radio emission below this. In GRB 171205A, this has been tentatively supported from polarization measurements. According to Urata et al. (2019), the millimeter data revealed 0.27% level linear-polarization, which is a factor of 4 smaller than the optical polarization measurements. This has been explained as Faraday depolarization by non-accelerated, cool electrons in the shocked region. However, one cannot rely on these results due to the dispute of the detection claimed by Laskar et al. (2020).

There have been suggestions that sub-energetic bursts are simply canonical GRBs viewed off-axis (Nakamura et al. 2001). However, such bursts will have two distinguishing characters, (a) low E_p and (b) a rise in the afterglow energy while the shocked ejecta gradually comes into the line of sight. In GRB 171205A, the afterglow energy increases slightly from 3.6 × 10⁴⁸ to 4.9 × 10⁴⁸ erg between ∼100 and ∼200 days. However, the E_p is comparable to that of canonical GRBs. Additionally, an off-axis jet is a geometric effect, which results in a frequency independent break in the light curve, which has not been seen for GRB 171205A, ruling out the off-axis model (D'Elia et al. 2018). Though a jet somewhat off-axis is not ruled out. D'Elia et al. (2018) found that GRB 171205A is an outlier of the Amati relation, as are some other low redshift GRBs, and its emission mechanism should be different from that of canonical, more distant GRBs.

There are two models to explain the electromagnetic emission in low-luminosity GRBs, central engine driven (Margutti et al. 2013; Irwin & Chevalier 2016) and SBO driven (Kulkarni et al. 1998; Nakar & Sari 2012; Barniol Duran et al. 2013; Suzuki & Maeda 2018). An issue with a purely SBO model is the requirement of high gamma-ray efficiency, for a quasi-spherical outflow. Another issue is the generation of such relativistic quasi-spherical outflow. One can envisage a situation where some fraction of the SN ejecta is accelerated to relativistic speeds to provide this quasi-spherical relativistic outflow. However, Tan et al. (2001) have shown that only a fraction ( ∼ 10⁻⁴) of SN energy goes into relativistic ejecta. Nakar (2015) has suggested an alternative scenario where a choked jet in a low-mass envelope can put significant energy into a quasi-spherical, relativistic flow.

Our uGMRT model fits are incapable of distinguishing between canonical afterglow versus SBO AG models. We check the applicability of this model for GRB 171205A. In this model, the expanding outflow is considered to harbor a series of successive shocks, which accelerate and catch up to the boundary and hence explain the increasing afterglow energy via continuous injection. In this model, eventually the total energy should reach around 2.4 × 10⁵² erg (Izzo et al. 2019), the kinetic energy of the associated SN. Generally one does not see such a large amount of energy as radio observations do not cover epochs that are late enough. However, our radio observations cover a period of nearly 1000 days. The SBO model fit gives E_K ≈ 3.4 × 10⁵⁰ erg, two orders of magnitude smaller than the one predicted in the pure SBO model. Suzuki et al. (2019) carried out multiwavelength hydrodynamical modeling of GRB 171205A in the framework of the post-SBO relativistic SN ejecta–CBM interaction scenario. While they claimed that this model worked well for GRB 171205A and favor the wind model, we note some problems with their model. They had to introduce a centrally concentrated CBM with a sudden density drop to explain the available radio and X-ray data; however, our work includes radio measurements up to 3 yr and do not show a sudden density drop.

The pure SBO model also has some other problems. An SBO model predicts a gamma-ray emission lasting ≥ 1000s, lower E_p (not exceeding 50 keV), a large absorption column density, a late-time soft X-ray emission, and comparable energy in the X-ray emission and the prompt gamma-ray flare. We note that the X-ray spectrum shows an intrinsic hydrogen column density of ${N}_{{\rm{H}}}={7.4}_{-3.6}^{+4.1}\times {10}^{20}$ cm⁻² (D'Elia et al. 2018). This intrinsic column density is at the low end of low-luminosity GRB distribution, even among low redshift Swift-XRT GRBs where the mean is N_H = 2.4 × 10²¹ cm⁻² at z < 0.2 (Arcodia et al. 2016). For the observations post day 1 onwards, there may be an indication of a slightly higher column density ${N}_{{\rm{H}}}={1.2}_{-1.7}^{+0.8}\times {10}^{21}$ cm⁻² (see footnote 2). But there is no particular indication of significant spectral softening, except a slight indication of Γ = 1.63 ± 0.30–1.94 ± 0.23. The total X-ray energy from the first observation onwards until the last detection is at least an order of magnitude smaller than the prompt energy.

D'Elia et al. (2018) have claimed the presence of a thermal component. While SBO from SNe is the most favorable model for a thermal component (Nakar & Sari 2012; Suzuki & Maeda 2018), late-time photospheric emission from jet (Friis & Watson 2013), or thermal emission from the cocoon (Suzuki & Shigeyama 2013) can also explain this component. If we assume the blackbody component to be significant, it comprises 20% flux and has a temperature of 89 eV (D'Elia et al. 2018). This corresponds to a radius of $R={({E}_{\mathrm{iso}}/{{aT}}_{{BB}}^{4})}^{1/3}\approx 1.4\times {10}^{13}$ cm (a is the radiation density constant). This is much larger than the typical Wolf–Rayet star radius, but can be explained if the shock expands in a non-spherical manner. Alternatively, Nakar (2015) has suggested the presence of an optically thick stellar envelope further away from the star, from where the breakout happens.

We have seen that our observations are inconsistent with a pure SBO due to the short duration, higher E_p, shallow E versus Γβ relation, low column density, and a much larger breakout radius predicted by the thermal component. It also cannot be explained as being merely a canonical GRB seen off-axis. We show below that both these components contribute toward the radio afterglow. GRB 171205A is the first GRB in which direct signatures of a cocoon have been seen (Izzo et al. 2019). This is rare because generally a line-of-sight jet is much brighter than the associated cocoon, hiding the cocoon signatures. An off-axis jet can reveal itself by the associated SN, but the cocoon signatures are long gone by the time an SN can be discovered. Ideally cocoon signatures are visible only in slightly off-axis GRBs. In GRB 171205A, the cocoon was identified by the broad absorption features overlapping the SN spectrum (Izzo et al. 2019) They also estimated, from the energy deposited in the cocoon, that the jet was quite energetic Izzo et al. (2019). This may imply that we may be seeing a slightly off-axis jet, which enabled us to reveal the cocoon, not overshadowed by the bright jet. With this knowledge, it is likely that radio afterglow arises from both components, the sub-relativistic wider cocoon and a slightly off-axis jet. The cocoon radio emission dominates the GRB emission at early times when the GRB jet is off-axis. Later the additional flux contribution comes when the jet spreads sideways and comes into the line of sight. In such a case, the total radio flux can also be large compared to an on-axis GRBs since the cocoon and the jet carry comparable energy (De Colle et al. 2018).

Izzo et al. (2019) could not distinguish between the cocoon along with a slightly off-axis jet versus only cocoon emission, where the faint gamma-rays are the predicted signal of the cocoon breaking out of the stellar envelope. However, our radio modeling rules out the pure SBO model in favor of the cocoon along with a slightly off-axis jet. According to theoretical models, the indicated speed of the ejecta is also consistent with the sub-relativistic speeds expected in this model.

With E_iso = 2.3 × 10⁴⁹ erg and z = 0.0368, GRB 171205A is one of the few low-z (z ≲ 0.1), low-luminosity GRBs. Other GRBs in this category are GRB 980425, (E_iso = 8.5 × 10⁴⁷ erg, z = 0.0083; Galama et al. 1998), GRB 031203, (E_iso = 4.0 × 10⁴⁹ erg, z = 0.105; Sazonov et al. 2004), GRB 060218 (E_iso = 2.6 × 10⁴⁹ erg, z = 0.033; Campana et al. 2006), and GRB 100316D (E_iso = 3.7 × 10⁴⁹ erg, z = 0.0590 ; Starling et al. 2011). Like other low-luminosity GRBs, the spectrum of GRB 171205A can be fit by a simple power-law model, however, the photon index Γ ∼ 1.94 is harder than these GRBs, except that of GRB 031203 (Γ = 1.63; Sazonov et al. 2004).

Even among the intrinsically sub-energetic bursts, GRB 171205A more closely resembles GRBs 980425 and 031203 and not GRBs 060218 and 100316D. GRBs 980425 and 031203 were difficult to realize in the SBO models due to their relatively hard spectra, shorter durations, and larger E_p, though a lack of thermal equilibrium may accommodate it (Katz et al. 2010). GRBs 060218 and 100316D stand out due to their large durations of a few thousand seconds and lower peak energies, E_p < 50 keV. The shorter T₉₀ and higher E_p for GRB 171205A are comparable to the respective values for GRBs 980425 and 031203.

A major difference between GRB 171205A and other low-luminosity GRBs is the absence of intrinsic absorption column density. All other GRBs in this class show significant neutral hydrogen column density N_H ∼ (6 − 7) × 10²¹ cm⁻², as opposed to an order of magnitude lower N_H for GRB 171205A (D'Elia et al. 2018). The higher column density is considered an essential feature for SN SBO models in low-luminosity GRBs.

The peak radio flux density of GRB 171205A at 1.3 GHz is ∼ 10²⁹ erg s⁻¹ Hz⁻¹. This value is comparable to other low-luminosity GRBs, e.g., GRB 031203 (Soderberg et al. 2004). However, the X-ray luminosity at 10 hr is L_x ≈ 2 × 10⁴² erg s⁻¹, which is four times smaller than that of GRB 031203 (L_x = 9 × 10⁴² erg s⁻¹; Soderberg et al. 2004). This discrepancy is even more significant for a wind-like medium, since the measured peak radio luminosities are at the 1.3 and 8.5 GHz bands for GRB 171205A and GRB 031203, respectively.

It has been found that the X-ray afterglow decays slowly in low-luminosity GRBs. For example, the X-ray emission in GRB 031203 followed F_X‐ray(t) ∝ ν^−0.8t^−0.4 (Soderberg et al. 2004), and for GRB 980425 F_X‐ray(t) ∝ ν⁻¹t^−0.2 (Kulkarni et al. 1998). This is opposed to the canonical GRBs with F_X‐ray(t) ∝ ν^−1.3t⁻¹. Barniol Duran et al. (2015) have shown that a flat temporal decay of the X-ray light curve can be explained by the SBO model, although the dominance of an underlying SN has also been suggested as a possible reason for this flatness (Soderberg et al. 2004). With F_X‐ray(t) ∝ ν^−0.94t^−1.1, GRB 171205A is more like canonical GRBs. On the contrary, the X-ray spectral index was very soft for GRB 060218A with F_X‐ray(t) ∝ ν^−2.2t^−1.1, which softened even further at later epochs (Soderberg et al. 2006). GRB 171205A did not have that much spectral softening. In addition, contrary to smooth light curves of low-luminosity GRBs, the X-ray light curve of GRB 171205A revealed three temporal breaks (D'Elia et al. 2018).

The lack of jet break seems to be a common feature of low-luminosity GRBs. This may either indicate a much wider angle ejecta responsible for afterglow emission, or a stratified medium that can dilute the jet break in GRBs and hide its signatures.

Another defining feature of these GRBs is the presence of a thermal component, which has also been seen in GRB 171205A (D'Elia et al. 2018). Though this feature is quite common in GRBs associated with SNe (Campana et al. 2006; Starling et al. 2011), their origin is still a matter of debate. SBO from the relativistic SN shell is the most favorable model (Suzuki & Maeda 2018), however, late-time photospheric emission from a jet (Friis & Watson 2013), or a thermal emission from a cocoon (Suzuki & Shigeyama 2013) could also explain this component. However, it appears that the presence of a thermal component is not a unique feature of low-luminosity GRBs. Starling et al. (2012) and Sparre & Starling (2012) analyzed a sample of canonical GRBs and found evidence of a thermal component in a significant number of GRBs, though large radii associated with the blackbody emission argue against the SBO model.

Finally, while low-luminosity GRBs are considered to be a different class, Nakar (2015) has provided a unified picture of low-luminosity GRBs and cosmological GRBs, in terms of a key difference, namely, the existence of an extended low-mass envelope. In the unified model, the envelope is present in low-luminosity GRBs, but absent in cosmological GRBs. The lack of an envelope allows a jet to launch without any resistance in cosmological GRBs, but the extended envelope in low-luminosity GRBs smothers the jet and deposits a large amount of energy in the stellar envelope, driving a mildly relativistic shock producing low-luminosity GRBs via SBO. Our model does not support this picture.