GRB 210121A: A Typical Fireball Burst Detected by Two Small Missions

GRB 210121A almost simultaneously triggered HXMT (2021-01-21T18:41:48.750 UTC; Xue et al. 2021) and GECAM (2021-01-21T18:41:48.800 UTC; Peng et al. 2021). For simplicity, we take a unique T₀ = 2021-01-21T18:41:48.800 UTC and align all the data accordingly. The four-mission light curves, which are all binned with 0.2 s, barycenter corrected, and aligned to GECAM trigger time, are plotted together in Figure 1. The light curves are fully consistent with each other in the finest details, confirming the validation of the data of the four missions.

Zoom In Zoom Out Reset image size

Following Yang et al. (2020b) and Yang et al. (2020a), we calculate the burst duration, T₉₀, in the 8–800 keV energy band using the continuous time-tagged event (CTTE) data of the Fermi/GBM detector n0 with bin size = 0.064 s. The results are shown in Figure 2. With a T₉₀ value of ${13.31}_{-0.16}^{+0.22}$ s (also see Table 1), GRB 210121A definitely belongs to the long GRB population.

Zoom In Zoom Out Reset image size

Table 1. Observational Properties of GRB 210121A

Observed Properties	GRB 210121A
T90 (sharp peak only) (s)	${13.31}_{-0.16}^{+0.22}$ a
Total duration (s)	∼16.31
α at peak	$-{0.52}_{-0.05}^{+0.06}$
E p at peak (keV)	${1274.50}_{-118.34}^{+192.64}$
Time-integrated α b	$-{0.59}_{-0.02}^{+0.02}$
Time-integrated E p (keV)	${954.33}_{-38.62}^{+42.41}$
Total fluence c (10−4 erg cm−2)	${1.23}_{-0.07}^{+0.08}$
Peak flux (10−5 erg cm−2 s−1)	${2.19}_{-0.36}^{+0.48}$
z inferred by E p − Eγ,iso relation	0.3 − 3.0
Nearest host galaxy candidate	J010725.95–461928.8
	(z ∼ 0.319)

Notes.

^a All errors correspond to the 1σ credible intervals. ^b The time-integrated spectral parameters are measured over the total duration. ^c The total fluence and peak flux are calculated in the 10 keV–10 MeV energy band.

Download table as:  ASCIITypeset image

We notice that several substructures are clearly present in the light curve. Guided by the Bayesian block methodology (blue histogram in the top panel of Figure 2; Scargle et al. 2013), we divided the burst into five main emission episodes at 0.05 effective significance level, as listed in Table 2, and performed spectral analysis for each of them in Section 2.3.

Table 2. The Spectral Fitting Results of GRB 210121A

ID	tstart	tstop	CPL					mBB
			Flux	α	Ep	$\displaystyle \frac{\mathrm{pgstat}}{\mathrm{dof}}$	BIC	Flux	m	${{kT}}_{\min }$	${{kT}}_{\max }$	$\displaystyle \frac{\mathrm{pgstat}}{\mathrm{dof}}$	BIC
			(10−6 erg		(keV)			(10−6 erg		(keV)	(keV)
			cm−2 s−1)					cm−2 s−1)
A1	−0.01	0.43	${21.9}_{-3.6}^{+4.8}$	$-{0.52}_{-0.05}^{+0.06}$	${1274.5}_{-118.3}^{+192.6}$	$\displaystyle \frac{294.6}{351}$	312.16	${22.5}_{-5.0}^{+4.6}$	${0.21}_{-0.11}^{+0.07}$	${8.51}_{-2.25}^{+4.36}$	${636.60}_{-90.27}^{+109.69}$	$\displaystyle \frac{296.5}{350}$	320.00
A2	0.43	0.87	${24.4}_{-2.8}^{+3.8}$	$-{0.22}_{-0.07}^{+0.07}$	${1040.3}_{-74.4}^{+98.1}$	$\displaystyle \frac{316.0}{351}$	333.56	${23.4}_{-3.3}^{+4.2}$	${0.67}_{-0.09}^{+0.01}$	${4.48}_{-0.08}^{+8.30}$	${401.66}_{-17.64}^{+76.74}$	$\displaystyle \frac{316.6}{350}$	340.10
A3	0.87	1.32	${21.5}_{-2.7}^{+3.1}$	$-{0.33}_{-0.05}^{+0.07}$	${880.1}_{-73.8}^{+85.1}$	$\displaystyle \frac{348.9}{351}$	366.52	${20.9}_{-2.7}^{+3.6}$	${0.42}_{-0.21}^{+0.05}$	${7.88}_{-1.51}^{+6.94}$	${384.38}_{-26.07}^{+79.34}$	$\displaystyle \frac{352.1}{351}$	375.57
A4	1.32	1.76	${13.1}_{-1.5}^{+2.1}$	$-{0.25}_{-0.08}^{+0.07}$	${627.3}_{-42.9}^{+69.7}$	$\displaystyle \frac{317.7}{351}$	335.35	${14.2}_{-2.3}^{+3.6}$	${0.11}_{-0.36}^{+0.14}$	${16.97}_{-3.08}^{+9.32}$	${357.37}_{-46.06}^{+133.04}$	$\displaystyle \frac{317.7}{350}$	341.18
A5	1.76	2.20	${10.8}_{-1.5}^{+2.1}$	$-{0.24}_{-0.10}^{+0.10}$	${581.1}_{-55.3}^{+76.1}$	$\displaystyle \frac{305.2}{351}$	322.80	${19.7}_{-9.7}^{+4.8}$	${0.47}_{-0.09}^{+0.19}$	${27.89}_{-5.52}^{+3.49}$	${1085.58}_{-443.50}^{+179.05}$	$\displaystyle \frac{301.1}{350}$	324.60
A	−0.01	2.20	${18.9}_{-1.3}^{+1.3}$	$-{0.38}_{-0.03}^{+0.03}$	${921.7}_{-43.2}^{+41.8}$	$\displaystyle \frac{449.7}{351}$	467.33	${18.9}_{-1.4}^{+1.8}$	${0.28}_{-0.08}^{+0.06}$	${10.98}_{-1.76}^{+2.47}$	${442.96}_{-28.59}^{+42.82}$	$\displaystyle \frac{459.9}{350}$	483.36
A+dip	−0.01	2.80	${15.6}_{-1.1}^{+1.3}$	$-{0.43}_{-0.03}^{+0.03}$	${950.4}_{-43.67}^{+56.70}$	$\displaystyle \frac{447.5}{351}$	465.15	${15.4}_{-1.3}^{+1.6}$	${0.29}_{-0.07}^{+0.05}$	${8.62}_{-1.68}^{+2.17}$	${438.45}_{-27.42}^{+39.98}$	$\displaystyle \frac{462.5}{350}$	458.62
B	2.80	3.30	${19.1}_{-2.7}^{+3.6}$	$-{0.42}_{-0.07}^{+0.05}$	${960.7}_{-80.8}^{+134.7}$	$\displaystyle \frac{293.7}{351}$	311.33	${23.2}_{-4.8}^{+5.7}$	$-{0.14}_{-0.12}^{+0.10}$	${22.29}_{-3.51}^{+4.24}$	${752.89}_{-116.45}^{+178.98}$	$\displaystyle \frac{283.1}{350}$	306.61
C	3.80	4.60	${13.4}_{-1.9}^{+2.3}$	$-{0.54}_{-0.05}^{+0.06}$	${905.2}_{-85.0}^{+117.4}$	$\displaystyle \frac{331.9}{351}$	349.50	${12.3}_{-1.5}^{+2.5}$	${0.31}_{-0.12}^{+0.01}$	${3.47}_{-0.43}^{+3.28}$	${366.94}_{-15.41}^{+76.85}$	$\displaystyle \frac{336.9}{350}$	360.37
D	4.60	10.40	${5.6}_{-0.6}^{+1.1}$	$-{0.65}_{-0.05}^{+0.03}$	${941.9}_{-51.2}^{+147.9}$	$\displaystyle \frac{599.8}{351}$	617.44	${5.0}_{-0.5}^{+0.8}$	${0.21}_{-0.08}^{+0.01}$	${2.99}_{-0.06}^{+2.42}$	${375.28}_{-16.80}^{+55.96}$	$\displaystyle \frac{609.4}{350}$	632.86
E	10.40	16.30	${3.8}_{-0.6}^{+0.9}$	$-{0.76}_{-0.05}^{+0.04}$	${960.9}_{-100.3}^{+186.5}$	$\displaystyle \frac{501.2}{351}$	518.84	${3.2}_{-0.5}^{+0.7}$	${0.13}_{-0.08}^{+0.01}$	${2.20}_{-0.25}^{+1.88}$	${362.27}_{-22.54}^{+67.79}$	$\displaystyle \frac{503.7}{350}$	527.23
	−0.01	16.30	${7.5}_{-0.4}^{+0.5}$	$-{0.59}_{-0.02}^{+0.02}$	${954.3}_{-38.6}^{+42.4}$	$\displaystyle \frac{1104.2}{351}$	1121.80	${6.7}_{-0.4}^{+0.4}$	${0.27}_{-0.03}^{+0.02}$	${3.10}_{-0.61}^{+1.21}$	${379.82}_{-11.84}^{+20.98}$	$\displaystyle \frac{1148.7}{350}$	1172.17

Download table as:  ASCIITypeset image

Spectral lag, attributed to the fact that higher-energy gamma-ray photons always arrive earlier than the lower-energy gamma-ray photons, is a common phenomenon in GRBs during their prompt emission epochs (Norris et al. 1986, 2000; Band 1997; Chen et al. 2005). Several physical models, such as the curvature effect of a relativistic jet and rapidly expanding spherical shell, have been proposed to explain the spectral lags (Ioka & Nakamura 2001; Shen et al. 2005; Lu et al. 2006; Shenoy et al. 2013; Uhm & Zhang 2016). Statistically speaking, long GRBs are always characterized by obvious spectral lags, whereas lags of short GRBs are always negligible (Norris et al. 1996; Yi et al. 2006).

Table 3. Fitting Parameters of Photosphere versus Synchrotron Model

Photosphere Model		Synchrotron Model
Parameter	Range	Parameter	Range
η0	${789.82}_{-22.13}^{+331.91}$	logΓ	${3.94}_{-1.01}^{+0.04}$
p	${4.92}_{-1.26}^{+0.08}$	p	${5.99}_{-0.20}^{+0.00}$
θc,Γ	${0.02}_{-0.01}^{+0.001}$	logγinj	${5.94}_{-0.21}^{+0.01}$
θv	${0.02}_{-0.01}^{+0.002}$	log $\left(\displaystyle \frac{{R}_{\mathrm{inj}}^{0}}{{\rm{s}}}\right)$	${44.81}_{-0.55}^{+0.71}$
log $\left(\displaystyle \frac{{L}_{0}}{\mathrm{erg}\ {{\rm{s}}}^{-1}}\right)$	${51.94}_{-0.50}^{+0.84}$	log $\left(\displaystyle \frac{{B}_{0}}{{\rm{G}}}\right)$	${1.43}_{-0.37}^{+0.27}$
		q	${4.81}_{-0.50}^{+0.09}$
log $\left(\displaystyle \frac{{r}_{0}}{\mathrm{cm}}\right)$	${7.51}_{-0.46}^{+0.33}$	b	${0.90}_{-0.05}^{+0.32}$
z	${0.21}_{-0.07}^{+0.25}$	$\hat{t}$ (s)	${1.56}_{-0.17}^{+0.87}$
BIC	329.57	BIC	468.11
$\displaystyle \frac{\mathrm{PGSTAT}}{\mathrm{dof}}$	$\displaystyle \frac{291.1}{238}$	$\displaystyle \frac{\mathrm{PGSTAT}}{\mathrm{dof}}$	$\displaystyle \frac{424.1}{237}$

Download table as:  ASCIITypeset image

To calculate the spectral lags, we first extract the light curves in different energy ranges from Fermi/GBM Na i detector n0 and BGO detector b0. The multiwavelength light curves are shown in Figure 3 (top panel). After selecting the main emission range of 0–12 s, we calculate the lags between the lowest energy and any other bands following the method in Zhang et al. (2012b). The results are shown in Figure 3 (bottom panel). A turnover presents at the lag versus ΔE plot, which has been noticed in some other long GRBs (e.g., Wei et al. 2017; Du et al. 2021).

Zoom In Zoom Out Reset image size

Both time-integrated and time-resolved spectral analyses are performed over the whole burst period, from –0.01 to 16.3 s. The five time-dependent slices, A to E, ¹⁵ are obtained by the Bayesian block method as mentioned in Section 2.1 and illustrated in Figure 2. The photon flux in slice A is so bright that we can further divide them into five slices (A1–A5), each containing enough photon counts for spectral fitting. The boundaries of each slice are listed in Table 2.

For each slice, we extract the corresponding source and background spectra and the corresponding instrumental response files following the procedures described in Zhang et al. (2018a). Since the energy range of Fermi/GBM is the broadest one among the four missions, for simplicity we only employ the GBM data in our spectral analysis. The spectral data are obtained from three detectors with relatively small viewing angles (i.e., the Na i detector n0 and n3, as well as the BGO detector b0). Nevertheless, we have confirmed that the joint-mission spectral fitting (e.g., in Figure 4) using all four missions yields results consistent with those with GBM data only.

Zoom In Zoom Out Reset image size

For each slice, we perform a detailed spectral fit using our self-developed Monte Carlo fitting tool McSpecFit (Zhang et al.2016, 2018a) with five frequently used empirical models, namely, the band function (Band), the blackbody (BB), the multicolor blackbody (mBB), ¹⁶ the single power-law (PL), and the cutoff power-law (CPL) models. ¹⁷ The ratio of Profile-Gaussian likelihood to the degree of freedom (PGSTAT/dof; Arnaud 1996) and the Bayesian information criterion (BIC; Schwarz 1978) are taken into account to test the goodness of fit.

Our results show that the CPL model is the preferred one for all the time-resolved slices. The best-fit parameters obtained by the CPL models are listed in Table 2. The corresponding spectral evolution is plotted in Figure 5. The peak energy constrained by the CPL model is typically around 1 MeV throughout the burst and exhibits strong spectral evolution from slices A1 to A5. Some previous studies on multipulse long GRBs (e.g., Lu et al. 2012) found that the E _p evolution displays two prevailing trends: (1) hard-to-soft then tracking, meaning E_p first shows a hard-to-soft evolution at the beginning of the burst then tracks the intensity level; (2) the intensity-tracking, meaning E_p tracking the intensity all the time during a burst. However, the E _p evolution of GRB 210121A is different from neither of the two above. The E _p follows the hard-to-soft pattern throughout the first pulse in slices A1–A5 and remains a high value until the final stage of the burst. The best-fit low-energy photon index, α, evolves rapidly and tracks the flux level. Moreover, α systematically exceeds the synchrotron "death line" (Preece et al. 1998) defined by α = −2/3 and reaches the highest value of ∼−0.2 in several slices, which indicates that the spectra are thermal-like (Meng et al. 2019).

Zoom In Zoom Out Reset image size

The hard low-energy photon index motivates us to reevaluate the fit using thermal-like spectral models. Although the single blackbody model was unacceptable in the time-resolved spectral fit, we found that the multicolor blackbody model (mBB), on the other hand, can well explain the time-resolved spectra with adequate goodness of fit (Table 2). The corresponding best-fit values of kT_min and kT_max are also plotted in Figure 5.

Based on above data analyses on GRB 210121A, we have obtained its temporal characteristic parameters such as T₉₀ of 11.78 s and some spectral properties including the spectral index α, the time-integrated peak energy being ${954.33}_{-38.62}^{+42.41}$ keV and the total fluence of ${1.23}_{-0.07}^{+0.08}\times {10}^{-4}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}$ calculated within the 10–10,000 keV energy range. The above properties are also listed in Table 1. To check how special GRB 210121A is, we mark the above values as red dashed lines (see Figure 6) within the distributions of some characteristic parameters of long GRBs from the Fermi/GBM burst catalog (Gruber et al. 2014; von Kienlin et al. 2014; Bhat et al. 2016; von Kienlin et al. 2020). As shown in Figure 6, GRB 210121A is relatively special compared to the majority of the bursts owing to its significantly high peak energy and fluence in the whole long GRB sample.

Zoom In Zoom Out Reset image size

The E _p –E_γ,iso relation (aka Amati relation; Amati et al. 2002) has been used as a powerful tool to diagnose GRB classifications. As shown in Figure 7, typical long and short GRBs follow two separate tracks. In addition, a third track was recently found for those short GRBs originating from magnetar giant flares (aka MGF GRBs; e.g., GRB 200415A, Yang et al. 2020a; Svinkin et al. 2021; Roberts et al. 2021; Zhang et al. 2020a). Since there is no redshift measurement for GRB 210121A, we assign its redshift as a free parameter ranging from 10⁻⁵ to 10 and overplot it with a dotted line in Figure 7. One can immediately infer from such a plot that the redshift of GRB 210121A should be within the range between 0.3 and 3.0 in order to be consistent with a long GRB. Other possibilities are almost ruled out, as it is certainly not a short GRB or a giant flare from a magnetar given the properties (e.g., nonnegligible lags, long duration) presented in Section 2. In addition, the absence of a nearby host galaxy at redshift ∼0.0001 further rules out its possibility of being an MGF GRB.

Zoom In Zoom Out Reset image size

As shown in Figure 7, GRB 210121A is a significantly extreme case among those GRBs with a redshift between 0.3 and 3. The large E _p value of GRB 210121A may be subject to the so-called "photosphere death line" constraints as discussed in Zhang et al. (2012a).

According to Zhang et al. (2012a), the photosphere emission model predicts an upper limit for the peak energy of a GRB in the form of

$$\begin{eqnarray}&&{E}_{{\rm{p}}}\leqslant \zeta {{kT}}_{0}\simeq 1.2\zeta {L}_{52}^{1/4}{r}_{0}^{-1/2}\,\mathrm{MeV},\end{eqnarray} \tag{ 1 }$$

where L₅₂ is the luminosity in units of 10⁵² erg s⁻¹, r₀ is the initial fireball radius in units of 10⁷ cm, and the factor ζ is taken as 2.82 in this study, which invokes a relativistic multicolor blackbody outflow. Accordingly, with a known E _p and E_γ,iso, one can calculate the lower limit of the initial fireball radius:

$$\begin{eqnarray}&&{r}_{0}\leqslant 1.44{\zeta }^{2}{\left(\displaystyle \frac{{E}_{{\rm{p}}}}{\mathrm{MeV}}\right)}^{-2}{\left(\displaystyle \frac{{E}_{\gamma ,\mathrm{iso},52}}{{\rm{\Delta }}t}\right)}^{1/2}\times {10}^{7}\,\mathrm{cm}.\end{eqnarray} \tag{ 2 }$$

By putting the observed E _p = 1274.5 keV, Δt = 0.44 s, and flux of ∼ 21.9 × 10⁻⁶ erg cm⁻² s ⁻¹ into Equation (2), we obtain an upper limit for r₀ of

$$\begin{eqnarray}&&{r}_{0}\leqslant [3.10,5.40]\times {10}^{7}\mathrm{cm}\end{eqnarray} \tag{ 3 }$$

for a redshift range of z ∼ [0.3, 3.0]. Such an upper limit is fully consistent with the prediction of the standard fireball model (e.g., Mészáros & Rees 2000; Mészáros et al. 2002), as well as the mean acceleration radius (∼10⁸ cm) of the fireball derived from observed data (Pe'er et al. 2015).

We apply a structured jet photosphere model (Lundman et al.2013; Meng et al. 2018, 2021) to fit the first-pulse spectra. The flux density of this model (in units of mJy) can be calculated numerically in the form

$$\begin{eqnarray}&&{F}_{\nu }(E)={F}_{\nu }(E;{\eta }_{0},p,{\theta }_{c,{\rm{\Gamma }}},{\theta }_{v},{L}_{0},{r}_{0},z).\end{eqnarray} \tag{ 4 }$$

Seven parameters are involved, namely, the baryon loading value η₀, the power-law decay index of the baryon loading p, the angular width for the isotropic core of the baryon loading θ_c,Γ, the viewing angle θ_v , the outflow luminosity L₀, the initial radius of the fireball r₀, and the redshift z. As shown in Figure 8, the model successfully fits the data with a PGSTAT/dof = 291.07/238.0 = 1.22. The best-fit parameters and their constraints as shown in Table 3 and Figure 9. The best-fitting value of the initial radius is ${r}_{0}={3.2}_{-2.1}^{+3.7}\times {10}^{7}$ cm, which is consistent with the constraints in Equation (3). Besides, the redshift is constrained to be 0.14 ≤ z ≤ 0.46.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The Lorentz factor at the photosphere can be discussed under two cases: saturated acceleration (Case I) and unsaturated acceleration (Case II). According to our results, the Lorentz factor is calculated to be

$$\begin{eqnarray}{\rm{\Gamma }}=\left\{\begin{array}{lll}{\eta }_{0} & =\,789.8, & \mathrm{CaseI},\\ {\left[\displaystyle \frac{{\sigma }_{T}}{6{m}_{p}c}\displaystyle \frac{L(\theta )}{4\pi {c}^{2}\eta (\theta ){r}_{0}}\right]}^{1/3} & =\,405.4, & \mathrm{CaseII},\end{array}\right.\end{eqnarray} \tag{ 5 }$$

where $\eta (\theta )=\tfrac{{\eta }_{0}}{{\left[{\left(\theta /{\theta }_{c,{\rm{\Gamma }}}\right)}^{2p}+1\right]}^{1/2}}+1.2$ is the structured baryon loading parameter and θ is the angle measured from the symmetry axis of the jet. Assuming that the fireball is saturated accelerated and θ = 0, the derived photosphere radius is ${R}_{\mathrm{ph}}=\frac{1}{(1+\beta )\beta {\eta }^{2}(\theta )}\tfrac{{\sigma }_{T}}{{m}_{p}c}\tfrac{L(\theta )}{4\pi {c}^{2}\eta (\theta )}$ = 1.0 × 10⁷ cm, compared with the saturated radius R_s = r₀ η(θ) = 2.6 × 10⁷ cm, the result of which is inconsistent with the condition that R_s < R_ph in Case I. On the other hand, the Lorentz factor Γ = 405.4 is obtained precisely in Case II, which is consistent with the average Γ ∼ 370 (Pe'er et al. 2015).

Similarly, we apply the synchrotron model (Uhm & Zhang 2014; Zhang et al. 2016) to fit the same spectrum used in Section 4.1. The redshift is assumed to be z = 0.319 based on the constraints in Sections 3.2, 4.1, and 5. The flux density of this model (in units of mJy) is in the form

$$\begin{eqnarray}&&{F}_{\nu }(E)={F}_{\nu }(E;{\rm{\Gamma }},p,{\gamma }_{\mathrm{inj}},{R}_{\mathrm{inj}}^{0},q,{B}_{0},b,\hat{t}).\end{eqnarray} \tag{ 6 }$$

Our fit can constrain eight parameters (Table 3, Figures 8 and 9): the Lorentz factor Γ, the power-law index of the electron spectrum p, the minimum Lorentz factor of electrons γ_inj, the normalized injection rate of electrons R_inj ⁰, the power-law index of the injection rate q, the initial magnetic filed B₀, the decaying factor of the magnetic field b, and the time at which electrons begin to radiate in the observer frame $\hat{t}$.

Compared to the photosphere model in Section 4.1, the model is underfitting with a PGSTAT/dof = 424.10/237.0 = 1.79. Besides, some of the parameters and the derived parameters are unreasonable:

• 1.  
  The bulk Lorentz factor in this model is as high as 10^3.94, which is greater than the upper limit constrained in various ways (Racusin et al. 2011).
• 2.  
  The photon index α = −(p − 1)/2 = −2.5. Not only is it inconsistent with the value in the CPL model, but also it is too soft compared to the typical values of the GRB sample (Poolakkil et al. 2021).
• 3.  
  The emission radius, ${R}_{0}=2{{\rm{\Gamma }}}^{2}c\hat{t}=7.09\times {10}^{18}$ cm, appears to be too large as a GRB emission radius.