Two Component Jets of GRB160623A as Shocked Jet cocoon afterglow

Two components of jets associated with the afterglow of the gamma-ray burst GRB 160623A were observed with multi-frequency observations including long-term monitoring in a sub-millimetre range (230 GHz) using the SMA. The observed light curves with temporal breaks suggests on the basis of the standard forward-shock synchrotron radiation model that the X-ray radiation is narrowly collimated with an opening angle $\theta_{n,j}<\sim6^{\circ}$ whereas the radio radiation originated from wider jets ($\sim27^{\circ}$). The temporal and spectral evolutions of the radio afterglow agree with those expected from a synchrotron radiation modelling with typical physical parameters except for the fact that the observed wide jet opening angle for the radio emission is significantly larger than the theoretical maximum opening angle. By contrast, the opening angle of the X-ray afterglow is consistent with the typical value of GRB jets. Since the theory of the relativistic cocoon afterglow emission is similar to that of a regular afterglow with an opening angle of $\sim30^{\circ}$, the observed radio emission can be interpreted as the shocked jet cocoon emission. This result therefore indicates that the two components of the jets observed in the GRB 160623A afterglow is caused by the jet and the shocked jet cocoon afterglows.


INTRODUCTION
The Gamma-ray burst (GRB) is believed to be a stellar explosion accompanied with relativistic outflows and narrowly-collimated jets (e.g. Piran 1999). Since direct imaging of GRB jets is impossible unlike AGN jets, the jet opening angles of GRBs have been measured by identifying a temporal break in the light curve in multi-frequency afterglow monitoring (Sari et al. 1999). The typical value of GRB jet opening-angles is ∼ 3 • .5 (e.g. Racusin et al. 2009), which is in the same order with that of AGN jets (median of 1 • .5 among 373 samples) measured with high-resolution imaging observations (Pushkarev et al. 2017). For both the two popula-tions of the GRBs, short and long GRBs, understanding of the jet and its structure is essential. There are several methods to constrain the GRB jet structure. An optical spectroscopic study of an associated supernova component has identified a cocoon structure (Izzo et al. 2019). Another method is to measure the detection ratio of off-axis GRB afterglows without prompt high-energy emissions (i.e. orphan GRB afterglow e.g. Nakar et al. 2002). However, systematic detection of orphan GRB afterglows has never been made (e.g. Huang et al. 2020). Continuous multi-frequency afterglow monitoring is another crucial method to constrain the jet structure. In the case of GRB030329, double-component jets (narrow and wide jets) were identified with optical and radio monitoring, including sub-millimetre (Berger et al. 2003). Sub-millimetre and millimetre afterglow observations have played an essential role in revealing new insights of the GRB afterglow (e.g. Urata et al. 2014; Figure 1. Light curves of (top 3 panels) counts of GRB 160623A in the prompt phase observed with CALET, Fermi/GBM, and Fermi/LAT and of (bottom panel) the photon energy distribution observed with Fermi/LAT. The grey shaded parts indicate the interval unobserved with Fermi due to Earth occultation. The inset shows a zoomed-up time-series at around the main peak in the top panel. Variability on a timescale of as short as 0.250 sec is visible. Huang et al. 2017;Urata et al. 2019). Here, we report the long-term monitoring of the GRB160623A afterglow using the Sub-millimeter Array (SMA) in conjunction with multi-frequency observations. We characterise the dependence of the afterglow flux on time and frequency as F (t, ν) ∝ t α ν β , where α is the decay index and β is the spectral energy index. We use the cosmological parameters of Ω M = 0.3, Ω Λ =0.7, and H 0 = 70 km s −1 Mpc −1 in this paper.

Prompt emission
The Fermi Gamma-Ray Monitor (GBM) found a signal triggered by GRB 160623A at 05:00:34.23 UT on 2016 June 23 (Mailyan et al. 2016). The Fermi Large Area Telescope (LAT) also detected more than 15 photons above 1 GeV till approximately 2 ksec (0.02 days) after the trigger time and determined the centre position at (RA, Dec) = (315.24, +42.27 • ) (J2000) with an error radius of 0.1 • (Vianello et al. 2016). GRB160623A was detected also by CALET Gamma-ray Burst Monitor (CGBM) at 04:59:34.27 on 2016 June 23, which was 1 min earlier than the Fermi GBM trigger time (Yamaoka et al. 2016). Hereafter, we use the trigger time of the CGBM as the burst starting time, T 0 . All of the CGBM instruments detected the emission and the light curves exhibited a bright peak at T 0 +40 sec. By contrast, two of the Fermi instruments (GBM and LAT) missed to observe the main peak of the event. The Konus-Wind was also triggered at 04:59:37.594 and detected the emission up to ∼15 MeV (Tsvetkova et al. 2017). The time-averaged spectrum for the main burst in the 10 keV-10 MeV range was described by a Band function with low and high-energy photon indices of α = −0.76 +0.02 −0.02 of β = −2.80 +0.05 −0.06 , respectively, and a peak energy E obs p = 596 +15 −14 keV. The equivalent isotropic radiated energy in the prompt phase at the 10 keV-10MeV band E iso was estimated as (2.53 ± 0.03) × 10 53 erg (Tsvetkova et al. 2017).
We obtained the light-curve data with 0.125-sec time bins observed with the CALET from the CGBM Flight Trigger Alert Notices site 1 . We measured 5σ flux variations relative to the neighbouring data bins for a timescale of 0.250 sec ( Figure 1). The Fermi/GBM data were downloaded from the NASA HEASARC Fermi GBM Burst catalog. We used the Fermitools version 1.0.7 and HEASOFT for reducing the Fermi GBM/LAT data with gtsrcprob p > 0.9 and a GTI selection of "DATA QUAL>0, LAT CONFIG==1, and ABS(ROCK ANGLE)<52". The user contribution code "do gbm.py" by S. Holland was used for the GBM light-curve analysis. The Fermi/LAT photon data were downloaded from the Fermi Science Support Center. Using the likelihood and aperture photometry, we generated the light curve for an energy range of >100 MeV ( Figure 1). The highest-energy photon within the 2500 1 http://cgbm.calet.jp/cgbm trigger/flight/ sec time coverage was ∼3.4 GeV at 1315 sec after the burst, which was considerably after the main pulse observed with CALET and Konus-Wind. According to the Fermi/LAT GRB catalog (Ajello et al. 2019), the energetic photon at 18 GeV was also observed at 12038.53 sec after the burst. Figure 1 shows the light curves obtained by CALET/SGM (100-230 keV), Fermi/GBM (10-1000 keV), and Fermi/LAT (> 100 MeV) along with the photon energy distribution for an energy higher than 100 MeV.

X-ray and optical follow-ups
Neil Gehrels Swift Observatory started follow-up observations at ∼ 40 ksec after the burst. The XRT identified the X-ray afterglow at R.A. = 21 h 01 m 11 s .22, Decl.= +42 • 13 ′ 13 " .7 with an error radius of 3".5 (Mingo et al. 2016). The X-ray afterglow was observed with the XRT  We obtained reduced light curves and spectra in three periods of 0.47-0.60 days, 1.3-2.4 days, and 3.2-11.5 days of the Swift/XRT data from the UK Swift Science Data Centre (Evans et al. 2007(Evans et al. , 2009. The X-ray light curve is found to be described with a single power-law function with a decay index of α X = −1.92 ± 0.04 with a reduced χ 2 /dof=1.04/86 ( Figure 2). We rebinned the spectra so that each spectral bin contains more than 5 counts. Using the software XSPEC 12, we perform spectral fitting with a single power law modified with intrinsic and Galactic absorptions, the latter of which is fixed at N H = 7.17 × 10 21 cm −2 . For the first period, we perform spectral fitting, allowing the intrinsic absorption column density to vary. The derived bestfitting values of the intrinsic absorption column density and spectral index are N H =(2.7 ± 0.3) × 10 22 cm −2 and β X = −0.92 ± 0.10, respectively, with a reduced χ 2 /dof=0.88/276 (Figure 3). For the later periods, we fix the intrinsic absorption to the value obtained with the first period of spectrum. The derived spectral indices are β X = −1.0 ± 0.18 for the second period with a reduced χ 2 /dof=0.71/35 and β X = −0.89 ± 0.33 for third period with a reduced χ 2 /dof=0.63/12. We therefore find no spectral evolution after 0.47 days, comparing the spectra at three periods of 0.47-0.60 days, 1.3-2.4 days, 3.2-11.5 days.

Submillimeter Array and radio follow-ups
We executed sub-millimetre (230 GHz) follow-up observations using the SMA. The first continuum observation was performed on 2016 June 24, about 1.1 days after the burst. The observation identified a bright (∼ 15 mJy) submm afterglow, which is one of the brightest GRB afterglows ever detected in the submillimetre range (Urata et al. 2015a). Continuous monitoring was then performed at the same frequency setting on 2016 June 25, 26, 27, 28, 29, and July 5 and 14 (Table 1). We reduced the SMA data, using the MIR data-reduction package and Miriad software. The data were flagged and calibrated with the MIR data-reduction package, using the standard procedure, and then images were constructed, using the Miriad software. The total flux was measured with the Common Astronomy Software Applications (CASA; McMullin et al. 2007).
We fit the SMA light-curve with a simple power-law function. The fitting using the time range from 1.3 to 12.4 days (i.e. all detections) yields a power-law index α = −0.65 ± 0.07 with a reduced χ 2 /dof=4.4/5. Note that the fitting would be significantly improved if we selected the period before 5 days. The temporal decay is described by the simple power-law with α = −0.54±0.05 (reduced χ 2 /dof = 1.3/2). In addition, the extrapolation of the above-mentioned steeper index (i.e. α = −0.65) is inconsistent with the upper limit of 21.4 day. Hence, these results indicate that there is a gradual temporal break after ∼12 days. We employ a smoothly-connected broken power-law function with a smoothness parameter of 1 and fixed decay indices before and after the break as −0.54 and −2, respectively. The fitting yields the temporal break at t R,j = 27 ± 14 days.
The AMI Large Array detected the radio afterglow at 15 GHz and measured the brightness to be 5.0±0.1 mJy at 2.0 days and 6.3 ± 0.1 mJy at 4.0 days, respectively (Mooley et al. 2016). These measurements indicate that the light curve at 15 GHz exhibited a brightening with α ∼ 0.33 between 2.0 and 4.0 days. The radio spectral indices between the AMI and SMA bands are also found to be β =∼ 0.27 at 2 days and β =∼ 0.05 at 4 days.

Radiation of Afterglow
The closure relation (e.g. summarized in Zhang, & Mészáros 2004) indicates that the X-ray afterglow after 0.46 days was consistent with the relation ν c < ν X during the post jet-break phase with the index of the electron energy distribution, p < 2 (i.e., α = (β − 3)/2). The observation with Swift/XRT started some time after the Fermi LAT trigger. Using them, we derive a lower limit of the jet break time to be t X,j < 0.46 days. Providing that the afterglow emission in the submm originated from the same synchrotron radiation with the X-ray afterglow, the closure relation requires the condition ν AMI < ν SMA < νa. Under this condition, the radio afterglow should show decaying with α =∼ −0.8 and steeper spectral index of β = 2. Although the SMA light curve exhibited decaying, the brightening in the 15 GHz band with the corresponding temporal index of α =∼ 0.33 is inconsistent with the relation. The radio spectral indices between the AMI and SMA bands (β =∼ 0.27 at 2 days and β =∼ 0.05 at 4 days) are too flat and hence are inconsistent with the expected result. Based on the closure relation, we also consider the two likely conditions ν a < ν AMI < ν SMA < ν m and ν AMI < ν a < ν SMA < ν m in the p > 2 case. The observed results in the AMI (brightening) and SMA (steepness) bands are, however, inconsistent with the temporal evolutions expected in either of the conditions. Therefore, we conclude that the radio emission originated from some different radiation processes or regions from the X-ray emission.
We characterize the SMA and AMI light curves and spectra in the forward-shock synchrotron-radiation framework. Since the optical light curve showed an unusual step decay (α opt =∼ −4.6 ± 0.3) in the first day, we excluded the optical data in the forward-shock modelling. Employing the boxfit code (van Eerten et al. 2012), which is applicable in the on-axis configuration with homogeneous circumburst medium (i.e. fixed observing angle as θ obs = 0), we obtain an optimal model with θ jet = 27.7 • , E = 7.7 × 10 52 erg, n = 70 cm −3 , p=2.6, ǫ B = 2.0 × 10 −5 , and ǫ e = 1.9 × 10 −1 . These values are consistent with those of a typical GRB afterglow (Panaitescu & Kumar 2002;van Eerten et al. 2012;Huang et al. 2017;Urata et al. 2015b), except for a wider jet opening angle in our result than that of a typical GRB afterglow. Note that the relatively higher circumburst density is consistent with a high intrinsic absorption obtained from the X-ray spectrum of GRB160623A (e.g. Fiore et al. 2007). Figure 4 shows the histogram of GRB jet opening angles. The jet opening angle of the GRB160623A radio afterglow is largest among all GRBs. Figure 2 demonstrates that the model functions well describe the observed radio light curves. With obtained physical parameters, we also derive the expected light curves and confirm that the emission from the wide jet in X-ray and optical bands should be negligible in observations.

Jet Opening angle and Cocoon radiation
We further evaluate the jet opening angles on the basis of equation (1) of Frail et al. (2001), using the observed isolated equivalent energy and assuming η = 0.2, where η is the radiative efficiency. The jet opening angle for the radio afterglow is estimated, using the temporal break in 230 GHz, to be θ R,j =13 • .0±2 • .8 for the circumburst density n = 1 cm −3 and 22 • .2±5 • .3 for n = 70 cm −3 , where n = 1 and n = 70 cm −3 are for the typical value and for the estimated one from the radio afterglow modelling, respectively. Alternatively, using the explosion energy derived on the basis of the afterglow modelling, we estimate the jet opening angle of GRB160623A to be 26 • .3. These values are more than twice larger than the are also highlighted with cyan diamond marks. We collected the jet opening angles of other GRBs from literature (Racusin et al. 2009;Berger et al. 2003;Frail et al. 2001;Bloom et al. 2003;Ghirlanda et al. 2004;Friedman, & Bloom 2005;Cenko et al. 2010Cenko et al. , 2011Filgas et al. 2011). The measurement methods of their jet opening angles are described in individual references. Basically, the methods are identical to one another, as described in Sari et al. (1999) and according to afterglow modelling within the framework of the forward-shock synchrotron radiation.
typical jet opening angle of the GRB. In the same manner, we also estimate the upper limits of the jet opening angle for the X-ray afterglow to be θ X,j < 2.8 • for n=1 cm −3 , θ X,j < 4.7 • for n = 70 cm −3 , and θ X,j < 5.6 • for n = 70 cm −3 from the explosion energy. These upper limits are consistent with the typical value of GRB jet opening angles (Figure 4).
The origin of the wide jet emission may require an additional component to those common for regular GRB afterglows. Mizuta, & Ioka (2013) constrained the maximum opening angle θ j,max to be 1/5Γ 0 , where Γ 0 is the initial Lorentz factor (i.e. θ j,max <∼12 • for Γ 0 > 100). We estimate the initial Lorentz factor of GRB160623A to be Γ 0 > 220 from the prompt time variability of 0.250 sec (Lithwick, & Sari 2001;Golkhou et al. 2015) and ac-cordingly the maximum opening angle of this event to be θ j,max < 5 • .5. In consequence, the radio afterglow jet angle of GRB160623A does not agree with the theoretical maximum opening angle, whereas the upper limit of the X-ray afterglow jet angle does. According to Nakar, & Piran (2017), the typical opening angle of the relativistic cocoon afterglow is ∼ 30 • . Since the theory of the relativistic cocoon afterglow emission is similar to that of the regular afterglow (Nakar, & Piran 2017), the parameters estimated above characterize the shocked jet cocoon emission. Assuming the energy ratio of wide to narrow components as E wide /E narrow ∼ 0.1 (i.e. the collapsar jet case; Peng et al. (2005)) and the identical micro-physical parameters (n, ǫ B , and ǫ e ) to the wide jet (Nakar, & Piran 2017) with the synchrotron slope of p ∼ 2 (based on the X-ray spectrum) and the narrow jet opening angle of 5.5 • , we confirmed that the expected narrow jet components in X-ray and radio bands can describe the observed light curves (Figure 2). Considering the prompt phase of GRB160623A missed by Fermi/LAT (Figure 1), the huge total energy (∼ 8.5 × 10 53 erg) is likely reasonable as same as other energitic (> 10 54 erg) Fermi/LAT events (e.g., Abdo et al. 2009;Urata et al. 2012;Ajello et al. 2019). In fact, even the late phase radiation in 100MeV-10GeV reached (2.4 ± 0.3) × 10 52 erg (Ajello et al. 2019). This result therefore implies that the GRB160623A radio afterglow originated from a relativistic cocoon afterglow.
The afterglows with double jet components are rarely observed. There are only five events (shown in Figure 4) and one of the notable event is GRB030329 with θ n,j = 5 • .2 and θ w,j = 17 • .2 (Berger et al. 2003). Since afterglows of GRB030329 and GRB160623A were densely monitored in the mm/submm ranges, further mm/submm observations would address the wide jet and shocked cocoon radiation. This work is supported by the Ministry of Science and Technology of Taiwan grants MOST 105-2112-M-008-013-MY3 (Y.U.). This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester.