Photometric and Spectroscopic Observations of GRB 190106A: Emission from Reverse and Forward Shocks with Late-time Energy Injection

Since their discovery in the 1960s, the understanding of gamma-ray bursts (GRBs) has been greatly advanced by various space satellites and ground-based telescopes (see Zhang, 2018, for a review). Based on statistics of their prompt emission, GRBs are divided into two categories defined by their $T_{90}$ duration and spectral hardness, i.e., short bursts with hard spectra (also called type I bursts) with $T_{90}<2$ s and long bursts with soft spectra (also called type II bursts) with $T_{90}>2$ s (Kouveliotou et al., 1993; Zhang et al., 2009). The association of the short GRB 170817A with the gravitational wave event GW170817 confirmed the longstanding prediction (Eichler et al., 1989) that neutron star mergers can indeed produce short bursts (Abbott et al., 2017a, b; Zhang et al., 2018). Long GRBs are generally believed to originate from massive star collapse (Woosley & Bloom, 2006). GRB 980425/SN 1998bw demonstrated that some stellar collapses produce long bursts and broad-lined Type Ic supernovae (Galama et al., 1999). The comparison between long-duration GRBs and broad-lined SN rates suggests the ratio GRBs/CC-SNe is a few $\sim 10^{-3}$ (Guetta & Della Valle, 2007).

Recent observations suggest that collapsing stars can also produce GRBs that last shorter than 2 s (Ahumada et al., 2021; Zhang et al., 2021; Rossi et al., 2022), compact star mergers seem to be also able to produce long GRBs (Rastinejad et al., 2022), indicating that classification of GRBs is more complex than the simple temporal division. Since its launch in 2004, the Neil Gehrels Swift Observatory (Swift hereafter) has detected more than 1700 GRBs with accurate position, enabling easy follow-up observations with ground-based telescopes (Gehrels et al., 2004). The typical isotropic equivalent energy (since it is the energy equivalent to the one that the GRB should have if the emission were isotropic) of GRBs ranges between $10^{50}-10^{54}$ ergs within a few seconds to minutes (Atteia et al., 2017). The jet break predicted by the collimated jet model has been observed in some GRBs, leading to the estimates of the true energy being $2-3$ orders of magnitude lower than the isotropic energy release (Frail et al., 2001).

Previous studies have shown that the X-ray light curves of GRB afterglows typically have several stages of power-law decay ($F\propto t^{-\alpha}$): a steep decay phase (typically $\alpha\sim 3$), a shallow decay phase also called a plateau (typically $\alpha\sim 0.5$), a normal decay phase (typically $\alpha\sim 1.2$), a post-jet-break phase (typically $\alpha\gtrsim 2$), with some bursts also accompanied by flares (Zhang et al., 2006). The typical optical light curve is an early rise followed by a normal decay, then sometimes followed by a re-brightening or a post-jet-break decay. Some long bursts, when at low enough redshift to allow a search, are found to be accompanied by a supernova bump (Zeh et al., 2004; Li et al., 2012).

In the standard model of GRBs, the afterglow is believed to involve a relativistically expanding fireball. Considering a relativistic thin shell with energy $E_{\rm K}$, initial Lorentz factor $\Gamma_{0}$, opening angle $\theta_{\rm j}$, and a width in laboratory frame $\Delta_{0}$ expanding into the interstellar medium (ISM) with density $n$. The interaction between the shell and ISM is described by two shocks: 1) a forward shock (FS) propagating into the ISM. The shell first undergoes a coasting phase, where it moves at a nearly constant speed $\Gamma(t)\simeq\Gamma_{0}$. It starts to decelerate and evolves into the second stage when the mass of the ISM swept by the forward shock is about $1/\Gamma_{0}$ of the rest mass of the shell. The third phase is the post-jet-break phase when the $1/\Gamma$ cone becomes larger than the geometric cone defined by $\theta_{\rm j}$. Finally, the blastwave enters the Newtonian phase (its velocity is much smaller than the speed of light) when it has swept up the ISM with the total rest mass energy comparable to the energy of the shell. During all these three phases, electrons are believed to be accelerated at the forward shock front to a power-law distribution $N(\gamma_{\rm e})\propto\gamma_{\rm e}^{-p_{\rm f}}$. A fraction $\epsilon_{\rm e,f}$ of the shock energy is distributed into electrons, and a fraction $\epsilon_{\rm B,f}$ is in the magnetic field generated behind the shock. Accounting for the radiative cooling and the continuous injection of new accelerated electrons at the shock front, one expects a broken power-law energy spectrum of them, which leads to a multi-segment broken power-law radiation spectrum at any epoch (Gao et al., 2013, for a review). The typical afterglow observations are successfully described by the synchrotron emission of electrons from the forward shocks. However, the information of the properties of the fireball is lost in the forward shock, especially when it has been decelerated by the ISM; 2) a reverse shock (RS) propagating into the shell, which occurs in the very early afterglow epoch. In the thin shell case, the reverse shock is too weak to decelerate the shell effectively. The Lorentz factor of the shocked shell material is almost constant while the shock propagates in the shell. The reverse shock crosses the shell at the fireball deceleration time. At this time, the reverse and forward shocked regions have the same Lorentz factor and internal energy density. However, the typical temperature of RS is lower since the mass density of the shell is higher. Consequently, the typical frequency of RS is lower, and RS may play a noticeable role in the low-frequency bands, e.g., optical or radio (Mészáros & Rees, 1997). After the RS crosses the shell, the Lorentz factor of the shocked shell may be assumed to have a general power-law decay behavior $\gamma_{3}\propto r^{-g}$. The shell expands adiabatically in the shell’s comoving frame. The emission from the RS is sensitive to the properties of the fireball. The observations of RS can thus provide important clues on the nature of the GRB source.

Catching very early (a few minutes after the trigger) optical emission from GRBs is not an easy task. There are only a few GRBs with optical observations during the prompt phase (Gao & Mészáros, 2015, for a review). Oganesyan et al. (2019) provided a sample of 21 GRBs with at least one observation during the prompt emission phase, and several GRBs in the sample are well observed (eg., GRB 070616, GRB 081008, GRB 121217A). Recently, Oganesyan et al. (2021) reported that they began to observe GRB 210619B $\sim$ 28s after the Swift trigger with D50 clear band during the prompt emission phase. However, our understanding of the earlier phases of GRBs continues to be quite incomplete compared to the later afterglow phases (occurring tens of minutes after the trigger).

In this paper, we report a special burst, GRB 190106A, for which optical observations began during the prompt emission phase, showing a double-peaked early optical light curve. We present optical photometric and spectroscopic observations of GRB 190106A with the NEXT (Ningbo Bureau Of Education And Xinjiang Observatory Telescope) and the Xinglong 2.16-m Telescopes. With the Xinglong 2.16-m/BFOSC spectroscopic observation, we present the redshift and calculate the equivalent widths of absorption lines in the afterglow spectrum. Combining our data with the Swift/XRT data and other observations from GRB Coordinates Network (GCN) reports, we constrain the parameters in an external shock model of the afterglow.

Our observations and data reduction are described in Section 2. The spectroscopic data analysis and redshift measurements are presented in Section 3. The optical and X-ray afterglow data analysis and the modeling of the afterglow light curve are reported in Section 4. We discuss possible models and present the conclusions in Section 5 and Section 6, respectively. A standard cosmology model is adopted with $H_{0}=67.3\ \rm{km\cdot s^{-1}Mpc^{-1}}$, $\Omega_{M}$=0.315, $\Omega_{\Lambda}$=0.685 (Planck Collaboration et al., 2014).

GRB 190106A triggered Neil Gehrels Swift Observatory (short as Swift) Burst Alert Telescope (BAT, Barthelmy et al. 2005) at 13:34:44 UT on 2019 Jan 06 (Sonbas et al., 2019). It is a long-duration burst with $T_{90}=76.8\pm 2.4$ s. Konus-Wind also detected the burst with $T_{90}=77.1^{+1.3}_{-4.2}$ s (Tsvetkova et al., 2019). The MASTER-Amur robotic telescope quickly slewed to the burst position, starting observations 36 s after the BAT trigger. An optical transient (with a magnitude of 15.23 in the P-band) was discovered within the Swift/BAT error circle in the second 10 s exposure image (Yurkov et al., 2019; Lipunov et al., 2019) located at equatorial coordinates (J2000.0): $RA=1^{h}59^{m}31.19^{s}$, $Dec.=+23^{\circ}50^{{}^{\prime}}44.79^{{}^{\prime\prime}}$, consistent with the Swift/UVOT position $RA=01^{h}59^{m}31.18^{s}$, $Dec.\ =\ +23^{\circ}50^{{}^{\prime}}44.0^{{}^{\prime\prime}}$ (Kuin & Sonbas, 2019). XRT and UVOT started observations at 81.8 s and 90 s after the BAT trigger, respectively. The BAT data files were downloaded from the Swift data archive¹¹1https://www.swift.ac.uk/swift_portal/. We extracted the BAT light curve and spectrum by the HEASoft software package (v6.27.2). The 15-150 keV spectra are analyzed in XSPEC (version 12.12) with power-law approximation over the time interval from 71 s to 81 s after the BAT trigger. We adopted the analysis results of the XRT repository products (Evans et al., 2007, 2009) and downloaded the 0.3-10 keV unabsorbed light curve from the UK Swift Science Data Centre²²2https://www.swift.ac.uk/xrt_curves/.

In our subsequent ground-based optical follow-up observations, the Xinglong 2.16-m obtained spectroscopic observations from which the redshift was determined (Xu et al., 2019), also confirmed by GMG (Mao et al., 2019) and X-shooter (Schady et al., 2019). We also collected observations from the GCNs reported by MASTER (Lipunov et al., 2019) and Sayan Observatory, Mondy (Belkin et al., 2019a, b). The MASTER data are converted to $R$-band by adding $\Delta R=0.51$ mag following Xin et al. (2018). The corrected MASTER magnitude and Mondy optical observations are shown in Fig. 2 in gray color.

As the blue end of the BFOSC spectrum has poor signal-to-noise ratio, our spectral analysis starts at $4300$ Å. After excluding the A and B band absorption and sky emission lines, we identified the metal absorption lines detected at more than $3\sigma$ significance. We detected lines from C IV, Al II, Al III, Fe II, and Mg II. Line centroids were determined by fitting a Gaussian function to the line profiles. We obtain a redshift of $z=1.861\pm 0.002$. The identified lines with the rest-frame equivalent widths ($\rm EW_{obs}$) are listed in Table 5 and also shown in Fig. 3.

With the redshift measurement in this work, we tested the GRB by using two well-known relations, namely the Amati (Amati et al., 2002; Amati, 2006) and Yonetoku (Yonetoku et al., 2004) relations, as show in Fig. 9 left and right panel, respectively. The positions of the burst lie within the $68\%$ prediction regions, consistent with both Amati and Yonetoku relations, which is also mentioned by Tsvetkova et al. (2019). The result suggests that GRB 190106A is a typical type II GRB.

The early double-peak optical light curve was expected by Zhang et al. (2003). We show that GRB 190106A is a good case with reverse-forward shocks, just like GRB 041219A (Fan et al., 2005) and GRB 110205A (Zheng et al., 2012). Such double-peak (“rebrightening”) light curve is typical for RS+FS emission combinations in a homogeneous ISM case (Zhang et al., 2003; Kobayashi & Zhang, 2003). The rising temporal index $\alpha_{O}=-1.88<-1/2$ favors the RS in thin-shell regime. Therefore, we adopted a thin-shell reverse-forward shock model in a constant ISM case to investigate GRB 190106A. In this scenario, the first optical peak (RS peak) gives the fireball deceleration time (Zhang et al., 2003), which can be used to estimate the initial Lorentz factor of the GRB, $\Gamma_{0}\simeq 300$. The second optical peak appears when $\nu_{\rm m}$ crosses the optical band. This peak flux can be used to constrain the values of jet isotropic kinetic energy $E_{\rm K,iso}$, ISM density $n_{1}$ and the microphysics parameter $\epsilon_{\rm B,f}$. Based on the fit with this scenario, we infer that the magnetic field strength ratio in RS and FS is $B_{\rm r}/B_{\rm f}\sim 9.5$, suggesting a magnetic flux carried by the ejecta from the central engine. Therefore, a magnetized central engine model, i.e., a BH central engine powered by the BZ process or a magnetar central engine, is preferred in GRB 190106A.

It is worth to note that the first optical peak, like GRB 041219A, can be interpreted with a reverse shock (Fan et al., 2005), internal shocks (Vestrand et al., 2005; Wei, 2007), or tail emission (Panaitescu, 2020). The last two models assume that the prompt optical and $\gamma$-ray emissions have a common origin. However, the radiation mechanism for the prompt $\gamma$-ray emission is still poorly understood (Kumar & McMahon, 2008).

The shallow decays in both X-ray and optical bands demand a nearly constant late-time energy injection with $L_{\rm inj}\simeq 4.5\times 10^{49}\ {\rm erg\ s^{-1}}$ and $q\sim 0.05$ lasting from $\sim 300$ s to $\sim 1500$ s. We investigated several energy injection sources, such as the spin-down of a magnetar, hyper-accreting BH powered by neutrino annihilation, and BH powered by BZ mechanism. The neutrino annihilation mechanism is less efficient for powering the jet at shallow decay phase. Both magnetar and BH central engine with BZ mechanism can give rise to the energy injection required. In general, the flat light curve feature favors the magnetar central engine model. A BH-accreting central engine can also makes a flat light curve, but requires a very small value of viscosity parameter (and thus a very slow accretion) (Lei et al., 2017). On the other hand, the disk will be dominated by advection and contains a strong wind at his afterglow phase. The light curve will then become steeper due to the suppression by the wind (Lei et al., 2017).

In Section 4.1, we divided the X-ray light curve into three stages (steep decay, shallow decay, late decay). As a result, the break time between shallow decay and late decay in X-ray is significantly different with that in optical band ($1.6^{+0.7}_{-0.7}\times 10^{4}$ s vs $7.7^{+1.1}_{-1.1}\times 10^{4}$ s), as show in Table 1. However, the X-ray break time will be roughly consistent with optical if we fit the X-ray light curve with four segments (steep decay, plateau, normal decay, late decay). Considering this uncertainty, we attribute such break to the jet break, revealing an opening angle $\sim 4.2^{\circ}$. From the observations and modeling, we found that the total jet energy is $E_{\rm total}=E_{\gamma,\rm iso}+E_{\rm K,iso}\simeq 1.9\times 10^{53}$ erg. The opening angle-corrected jet energy will be $E_{\rm j}\sim 5\times 10^{50}$ erg, which is well below the maximum rotational energy of $3\times 10^{52}$ erg (Lattimer & Prakash, 2016) $-$ $7\times 10^{52}$ erg (Haensel et al., 2009) for a standard neutron star with mass $M\sim 1.4\,M_{\sun}$. Therefore, our data do not require a BH as the central engine of this GRB.

We present our optical observation of the afterglow of GRB 190106A with the NEXT telescope, and the Xinglong 2.16-m telescope equipped with BFOSC. With the spectrum obtained from BFOSC, we measured the redshift of the burst and calculated the Line Strength Parameter. The unusual optical light curve obtained by NEXT and Xinglong 2.16-m, combined with the MASTER observations, show a normal decay light curve with early double peak and late break. Therefore, the optical light curve can be divided into five stages: rapid rise in the early stage, followed by decay, then a slow rise reaching a second peak at around 200 s, followed by a shallow decay (plateau), and faster decay from about 1 d onward. The evolution of the X-ray light curve can be divided more simply into three stages: rapid decay, plateau and normal decay.

The multi-band observations, especially the early optical data of GRB 190106A, provide rich information to study the nature of GRB. It is found that GRB 190101A can be successfully explained by the reverse-forward shock model. Our conclusions are summarized as follows:

1. The redshift of the burst is $z=1.861\pm 0.002$. The Line Strength Parameter, which is very similar to the average value of the sample.

2. The studies with the Amati and Yonetoku diagrams indicate that GRB 190106A is a typical type II burst.

3. The early double-peak optical light curve can be well interpreted with combination of the RS and FS models.

4. The modeling with RS and FS models indicate that the magnetic field strength ratio in RS and FS is $B_{\rm r}/B_{\rm f}\sim 9.5$, suggesting a magnetic flux carried by the ejecta from the central engine. This favors a strongly magnetized central engine model, such as a magnetar central engine model or a BH central engine powered by the BZ process.

5. The initial Lorentz factor can be estimated with the first optical peak time (or deceleration time) as $\Gamma_{0}\sim 300$.

6. The multi-band afterglow data can be interpreted with external shock model. From the observations and modeling, we found that the total jet energy is $E_{\rm total}=E_{\gamma,\rm iso}+E_{\rm K,iso}\simeq 1.9\times 10^{53}$ erg.

7. The shallow decays in both X-ray and optical bands are explained by nearly constant late-time energy injection with $L_{\rm inj}\simeq 4.5\times 10^{49}\ {\rm erg\ s^{-1}}$ and $q\sim 0.05$ lasting for $\sim 1000$ s. Both magnetar and BH central engine models can give rise to such amount of injected energy, but the flat light curve feature favors a magnetar central engine.

8. The breaks at a few $\times 10^{4}$ s in both X-ray and optical bands are roughly consistent with the jet break, revealing an opening angle $\sim 4.2^{\circ}$. The opening angle-corrected jet energy will be $E_{\rm j}\sim 5\times 10^{50}$ erg.

We are very grateful to Yong Ma for the help with the NEXT observations. We acknowledge the support of the staff of the Xinglong 2.16-m telescope. This work was also partially supported by the Open Project Program of the Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences. This work is supported by the National Key R&D Program of China (Nos. 2020YFC2201400), the National Natural Science Foundation of China under grants U2038107, U1931203 and 12021003. D.X. acknowledges support by the science research grants from the China Manned Space Project with NO. CMS-CSST-2021-A13 and CMS-CSST-2021-B11. W. H. Lei and H. Gao acknowledge support by the science research grants from the China Manned Space Project with NO.CMS-CSST-2021-B11. W. Xie acknowledges support from the Guizhou Provincial Science and Technology Foundation (Grant No. QKHJC-ZK[2021] 027). H. Gao acknowledges support from the National SKA Program of China (grant No. 2022SKA0130101). J. Z. Liu acknowledges the science research grants from the China Manned Space Project with No. CMSCSST-2021-A08. Data resources are supported by the China National Astronomical Data Center (NADC) and the Chinese Virtual Observatory (China-VO). This work is supported by the Astronomical Big Data Joint Research Center, co-founded by the National Astronomical Observatories, the Chinese Academy of Sciences, and the Alibaba Cloud. We acknowledge the use of public data from the Swift data archive.