Lowly Polarized Light from a Highly Magnetized Jet of GRB 190114C

We use aperture photometry to compute the source flux; in particular, we employ the Astropy Photutils package (Bradley et al. 2016). The brightness of the optical transient (OT) during the RINGO3 observations provides a high signal-to-noise ratio even at high temporal resolution; the source is detected at a signal-to-noise ratio of ≳60 in each of the first ∼10 × 2.34 s frames. Due to the fading nature of the afterglow, the signal-to-noise ratio of the detection rapidly drops for the following observations (e.g., 200 s later, the signal-to-noise ratio of each 2.34 s frame decreases to ∼30). By ∼T₀ + 2000 s, the source is detected in the 1 minute frames at a signal-to-noise ratio of ∼25. Consequently, our data choice is to use the 2.34 s RINGO3 frames for the first 30 minutes of observations to allow high temporal resolution, then the 1 minute exposures for the succeeding 1.3 hr.

At later times, when the OT has faded, we dynamically coadd frames and accept measurements with a ≥20 signal-to-noise ratio detection. With these signal-to-noise ratio criteria, ≳T₀ + 700 s measurements are the result of coadding frames. Integrating at different signal-to-noise ratios does not change the light-curve general features: ≪20 signal-to-noise ratio integrations show additional internal structure that is not statistically significant at the 3σ level, and ≫20 signal-to-noise ratios further smooth minor features and reject fainter OT detections at later times.

To test for instrument stability during the RINGO3 observations, we study the flux variability of the only star in the field (CD-27 1309; ∼11 mag star). Using the OT binning, CD-27 1309 photometry presents an ∼0.01 mag deviation from the mean in all bands (or ∼1% in flux).

The IO:O observations started 34.7 minutes postburst with the r filter. Given that the OT signal-to-noise ratio is ∼40 for each of the 10 s frames, we derive its flux from the six exposures individually. The IO:O r magnitudes are standardized using five ∼14–15 mag stars from the Pan-STARRS DR1 catalog (Chambers et al. 2016). In Table 1 and Figure 1, we present the IO:O r-filter photometry. The IO:O light curve is corrected for the mean Galactic extinction A_r = 0.034 ± 0.001 mag (E${}_{B\mbox{--}V,{\rm{MW}}}=0.0124\pm 0.0005$ is derived¹² from a 5' × 5' field statistic; Schlegel et al. 1998) but not for host galaxy extinction (see Section 3.3.3).

Table 1.  GRB 190114C LT Observations with RINGO3 BV/R/I, IO:O r Bands, and MASTER VWF/MASTER II Observations in an r-equivalent Band

Band	t${}_{\mathrm{mid}}$	t${}_{\exp }/2$	mag	mag${}_{\mathrm{err}}$	F${}_{\nu }$	F${}_{\nu \mathrm{err}}$
	(s)	(s)			(Jy)	(Jy)
BV	202.5	1.2	14.33	0.06	6.64e-03	3.8e-04
BV	204.8	1.2	14.36	0.06	6.49e-03	3.7e-04
BV	207.2	1.2	14.32	0.06	6.70e-03	3.9e-04
BV	209.5	1.2	14.36	0.06	6.49e-03	3.7e-04
BV	211.9	1.2	14.38	0.06	6.37e-03	3.7e-04
BV	...	...	...	...	...	...

Note. Here t${}_{\mathrm{mid}}$ corresponds to the mean observing time and ${t}_{\exp }$ to the length of the observation window. Magnitudes and flux density values are corrected for atmospheric and Galactic extinction.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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After the RINGO3 polaroid, the light is split by two dichroic mirrors into three beams that are simultaneously recorded by three EMCCD cameras (Arnold et al. 2012). In Figure 2, we derive the photonic response function of the RINGO3 instrument, which accounts for atmospheric extinction of the site¹³ , telescope optics,¹⁴ instrument dichroics,¹⁵ lenses (Arnold 2017), filters,^{16 ,17} transmission, and the quantum efficiency of the EMCCDs (Arnold 2017). The total throughput results in three broad bandpasses with mean photonic wavelengths ${\lambda }_{0,\{{\rm{BV}},{\rm{R}},{\rm{I}}\}}=5385,7030,8245\,\mathring{{\rm{A}}}\,$ and FWHMs${}_{\{{BV},R,I\}}=2232,1130,835\,\mathring{{\rm{A}}}$.

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Because of the different spectral coverage of RINGO3 bandpasses relative to other photometric systems and the ∼0.02–0.05 mag photometric precision, we standardize RINGO3 magnitudes in the Vega system following Johnson & Morgan's (1953) procedure. Observations of four unreddened A0-type stars (HD 24083, HD 27166, HD 50188, and HD 92573) and the GRB 190114C field were submitted via LT phase2UI¹⁸ using the same instrumental setup as the night of the burst and autonomously dispatched on the nights of 2019 January 30–31. We standardize the magnitudes in the RINGO3 system using the CD-27 1309 star, which adds ∼0.05 mag uncertainty to the photometry.

Taking into account the notation m = −2.5 log(F_ν) + C_ν, with F_ν in erg cm⁻² s⁻¹ Hz⁻¹ (e.g., Bessell & Murphy 2012), we compute the magnitude–to–flux density conversion C_ν by deriving the mean flux density F_ν of the Vega star (α Lyr) composite spectrum¹⁹ through each RINGO3 band (Bohlin et al. 2014). We set m = 0 for all bandpasses, and we obtain ${C}_{\nu ,\{{BV},R,I\}}=-48.60,-48.90,-49.05$.

In Table 1 and Figure 1, we present the GRB 190114C absolute flux-calibrated photometry of the RINGO3 BV/R/I bands. All three light curves start at a mean time T₀ + 202.5 s. The R- and I-band photometry ends at ∼7000 s postburst. For the BV band, the stacking does not reach the signal-to-noise ratio ≥20 threshold for the last ∼800 s of observations; therefore, the photometry is discarded. Magnitudes and flux density are corrected for atmospheric extinction with ${M}_{c,\{{BV},R,I\}}=0.14\,$, 0.04, 0.02 mag and ${F}_{c,\{{BV},R,I\}}=0.89,0.96,0.98$, respectively, which we compute from a weighted mean of the bandpass throughput and the theoretical atmospheric extinction of the site¹³. We also correct for the mean Galactic extinction, ${A}_{\{{BV},R,I\}}/$E${}_{B\mbox{--}V}\,=3.12,2.19,1.73$, with ${E}_{B\mbox{--}V,{\rm{MW}}}=0.0124\,\pm 0.0005$ (Schlegel et al. 1998), which we derive using the Pei (1992) Milky Way dust extinction profile. The light curves are not corrected for host galaxy extinction (see Section 3.3.3).

To derive the polarization of a source with RINGO3 instrumental configuration, we first compute the OT flux at each rotor position of the polaroid with aperture photometry using the Astropy Photutils package (Bradley et al. 2016). The flux values are converted to Stokes parameters q–u following the Clarke & Neumayer (2002) procedure and then to polarization degree and angle. Following Słowikowska et al.'s (2016) methodology to correct for RINGO3 polarization instrumental effects, we use 44 observations of BD +32 3739, BD +28 4211, and HD 212311 unpolarized stars and 41 observations of HILT 960 and BD +64 106 polarized stars for each band. Due to the positive nature of polarization,²⁰ measurements are not normally distributed in the low signal-to-noise ratio and low-polarization regime (Simmons & Stewart 1985). Consequently, to derive the confidence levels in the Stokes parameters and polarization, we perform a Monte Carlo error propagation starting with 10⁵ simulated flux values for each rotor position.

Following Mundell et al. (2013), we initially infer the polarization of the source with a single measurement with a maximum signal-to-noise ratio. By coadding the 2.34 s frames of the first 10 minute epoch, we obtain a signal-to-noise ratio detection of ∼130 corresponding to a mean time of ∼321 ± 120 s. From this estimate, we derive a polarization degree at the 2σ confidence level of ${P}_{\{{BV},R,I\}}={2.2}_{-0.8}^{+0.9} \%$, ${2.9}_{-0.8}^{+0.9} \%$, ${2.4}_{-0.8}^{+0.9} \%$; angle ${\theta }_{\{{BV},R,I\}}=81^\circ \pm 12^\circ$, 70° ± 9°, 71° ± 11°; and Stokes parameters ${q}_{\{{BV},R,I\}}=-0.021\pm 0.006$, −0.022 ± 0.006, −0.019 ± 0.006, and ${u}_{\{{BV},R,I\}}=0.007\pm 0.006$, 0.019 ± 0.006, 0.015 ± 0.006. In this paper, we quote a 2σ confidence level for the polarization degree P and angle θ because it better reflects the non-Gaussian behavior of polarization in the low-degree regime.

Polarization is a vector quantity; variation in either or both degree/angle on timescales shorter than Δt ∼ 240 s can result in a polarization detection of lower degree. To check for variability in polarization on timescales Δt < 240 s, we dynamically coadd the 2.34 s frames at a lower signal-to-noise ratio such that they reach a threshold of ∼70. With this choice, we can claim polarization variability at a 3σ confidence level if we measure a change in the polarization degree of ≳3%. Integrations at higher and lower signal-to-noise ratios reproduce the results within 1σ; however, because we estimate polarization to be ∼2%–3%, ≪50 signal-to-noise integrations are dominated by instrumental noise and are essentially upper limits. The remaining frames of the first 10 minute epoch and the following 2 × 10 minutes are coadded as individual measurements to ensure a maximal signal-to-noise ratio. We do not use the next 8 × 10 minute epochs because the signal-to-noise ratio declines below ∼10 and falls within the instrument sensitivity; the instrumental noise is dominating polarization detections of ≲6%.

In Table 2, we present the Stokes parameters and the polarization degree and angle for the three RINGO3 bandpasses. To check for instrument stability, we calculate the star CD-27 1309 polarization using the OT binning choice. The star CD-27 1309 manifests deviations of ∼0.15% from the mean. Due to the sensitivity of polarization with the photometric aperture employed, we check that apertures within 1.5–3 FWHM yield polarization measurements compatible within 1σ for both CD-27 1309 and the OT.

Table 2.  GRB 190114C Polarization Observations with LT RINGO3 BV/R/I Bands and MASTER II White Band

Band	t${}_{\mathrm{mid}}$	t${}_{\exp }/2$	S/N	q	q${}_{\mathrm{err}}$	u	u${}_{\mathrm{err}}$	P	P${}_{\mathrm{err}}$	θ	${\theta }_{\mathrm{err}}$
	(s)	(s)						(%)	(%)	(deg)	(deg)
BV	223.5	22.1	71	−0.020	0.022	0.018	0.011	2.7	${}_{-1.4}^{+1.7}$	69	${}_{-18}^{+18}$
BV	283.3	39.7	70	−0.019	0.022	0.009	0.011	2.1	${}_{-1.3}^{+1.7}$	77	${}_{-25}^{+25}$
BV	433.4	112.4	70	−0.020	0.022	0.019	0.011	2.8	${}_{-1.4}^{+1.7}$	68	${}_{-17}^{+17}$
BV	671.5	127.7	50	−0.027	0.031	0.023	0.016	3.6	${}_{-2.0}^{+2.4}$	70	${}_{-19}^{+19}$
BV	1117.2	298.9	54	−0.022	0.029	0.027	0.014	3.5	${}_{-1.8}^{+2.1}$	64	${}_{-18}^{+18}$
BV	1734.1	298.9	38	−0.027	0.041	0.036	0.020	4.5	${}_{-2.5}^{+3.0}$	63	${}_{-20}^{+20}$
R	215.3	13.9	70	−0.025	0.022	0.029	0.011	3.8	${}_{-1.5}^{+1.7}$	65	${}_{-12}^{+12}$
R	245.8	18.6	71	−0.029	0.022	0.010	0.011	3.0	${}_{-1.4}^{+1.6}$	80	${}_{-16}^{+16}$
R	293.8	31.5	70	−0.028	0.022	0.023	0.011	3.6	${}_{-1.5}^{+1.6}$	70	${}_{-13}^{+13}$
R	386.5	63.2	70	−0.019	0.022	0.014	0.011	2.4	${}_{-1.4}^{+1.7}$	71	${}_{-21}^{+21}$
R	623.4	175.8	61	−0.024	0.026	0.007	0.013	2.5	${}_{-1.5}^{+1.9}$	82	${}_{-24}^{+23}$
R	1117.2	298.9	45	−0.029	0.035	0.008	0.017	3.0	${}_{-2.0}^{+2.6}$	83	${}_{-27}^{+27}$
R	1734.1	298.9	31	−0.006	0.051	0.020	0.026	2.1	${}_{-1.6}^{+4.0}$	53	${}_{-43}^{+110}$
I	215.2	13.9	70	−0.036	0.022	0.023	0.011	4.2	${}_{-1.5}^{+1.6}$	74	${}_{-11}^{+11}$
I	245.7	18.6	70	−0.018	0.022	0.003	0.011	1.8	${}_{-1.2}^{+1.7}$	86	${}_{-29}^{+29}$
I	292.6	30.3	70	−0.022	0.022	0.020	0.011	3.0	${}_{-1.4}^{+1.7}$	69	${}_{-16}^{+16}$
I	380.6	59.7	70	−0.012	0.022	0.012	0.011	1.7	${}_{-1.2}^{+1.7}$	67	${}_{-32}^{+34}$
I	618.7	180.5	63	−0.024	0.025	0.007	0.012	2.5	${}_{-1.5}^{+1.9}$	82	${}_{-22}^{+22}$
I	1117.2	298.9	45	−0.007	0.035	0.003	0.017	0.8	${}_{-0.5}^{+2.9}$	78	${}_{-69}^{+92}$
I	1734.1	298.9	33	0.019	0.048	−0.025	0.024	3.2	${}_{-2.3}^{+3.7}$	154	${}_{-148}^{+23}$
White	52.0	6.1	264	-0.076	0.005	-0.015	0.005	7.7	${}_{-1.1}^{+1.1}$	96a	${}_{-4}^{+4}$
White	78.4	5.0	147	⋯	⋯	⋯	⋯	$\gt 2.2$	${}_{-0.6}^{+0.6}$	⋯	⋯
White	108.6	8.8	135	-0.020	0.012	0.003	0.012	2.0	${}_{-1.5}^{+2.6}$	85a	${}_{-43}^{+44}$
White	149.6	12.3	103	0.012	0.014	0.002	0.014	1.2	${}_{-0.8}^{+3.1}$	4a	${}_{-2}^{+175}$
White	200.7	16.0	78	0.021	0.019	0.003	0.019	2.1	${}_{-1.5}^{+4.3}$	4a	${}_{-3}^{+174}$

Note. Here t${}_{\mathrm{mid}}$ corresponds to the mean observing time, ${t}_{\exp }$ to the length of the observation window, and S/N to the signal-to-noise ratio of the OT. The Stokes parameters q–u, the polarization degree P, and the polarization angle θ are corrected for instrumental effects. The P and θ uncertainties are quoted at a 2σ confidence level.

^aHere θ is not calibrated with polarimetric standard stars.

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The MASTER–SAAO VWF and MASTER–IAC VWF cameras started observations at ${T}_{0}+30.7$ and 38.6 s, respectively; by ∼T₀ + 50 s, the OT signal-to-noise ratio falls under 5, and the photometry is discarded. We standardize the VWF white band with the r band using five stars of 8–10 mag from the Pan-STARRS DR1 catalog (Chambers et al. 2016).

MASTER–SAAO II and MASTER–IAC II observed the OT since 45.9 and 48 s postburst, respectively. Given this instrumental setup, we align and average the field frames from the two orthogonal polaroid positions and derive a single photometric measurement per site. Additionally, we apply the RINGO3 photometric criterion, and we only accept OT detections with signal-to-noise ratios over 20 (see Section 2.1.1). We standardize the MASTER II white band to the r band using five stars of 13–15 mag from the Pan-STARRS DR1 catalog. During MASTER II observations, these stars present an ∼0.04 mag deviation from the mean. Both MASTER VWF and MASTER II photometry are corrected for mean Galactic extinction A_r = 0.034 ± 0.001 mag (Schlegel et al. 1998) and presented in Table 1 and Figure 1.

There have been several lower-bound polarization measurements with only one MASTER II site (Gorbovskoy et al. 2016; Troja et al. 2017). For GRB 190114C, MASTER–SAAO II and MASTER–IAC II responded to the BAT trigger almost simultaneously—since ∼47 s postburst and with an initial temporal lag of ∼2.2 s—allowing us to completely sample the Stokes plane and measure the polarization degree and angle.

To derive the polarization, we first subtract the relative photometric zero-point between the MASTER–SAAO and MASTER–IAC observations using field stars. Due to the temporal lag between the two telescopes sites and the fading nature of the source, we also correct for the relative intensity by interpolating over the two time windows. Following the RINGO3 calibration, we use the Clarke & Neumayer (2002) method to derive the Stokes q–u parameters, the polarization degree/angle, and the confidence levels (see Section 2.1.3). We use RINGO3 polarization measurements of the CD-27 1309 star (P = 0.1%–0.3%) to subtract MASTER II instrumental polarization (P  ∼ 7%); by doing this, the polarization contribution from the interstellar medium is also removed. During MASTER II observations, the CD-27 1309 star shows deviations of ∼0.3% from the mean.

Although the burst is bright at that time, the signal-to-noise ratio and polarization degree rapidly drop within the first ∼100 s; we discard observations after ∼T₀ + 200 s. Additionally, we derive a lower bound of the polarization degree at ∼T₀ + 73 s—because the 0°/90° MASTER–IAC II frames were not taken—using ${P}_{\mathrm{low}}=({I}_{2}-{I}_{1})/({I}_{1}+{I}_{2})$, where I₁ and I₂ are the source intensity at each orthogonal polaroid position (see Gorbovskoy et al. 2016 and Troja et al. 2017 for the procedure). In Table 2, we present the Stokes parameters and polarization degree and angle for the MASTER II observations. We note that the angle is not calibrated with polarimetric standard stars, which implies that we cannot determine its evolution from MASTER II to RINGO3 observations.

Taking advantage of the simultaneity of RINGO3 three-band imaging, we attempt to infer the evolution of the optical spectral index. To guarantee a spectral precision of ∼0.05–0.06 mag per measurement, we take the lowest signal-to-noise ratio light curve (BV band) and we dynamically coadd frames so the OT reaches a signal-to-noise ratio threshold of ≥40. Following that, we coadd R/I frames using the BV-band binning, and for every three-band spectral energy distribution (SED), we fit a power law.

In Figure 6, we present the evolution of the optical spectral index ${\beta }_{\mathrm{opt}}^{\,\star };$ this index is not corrected for host galaxy extinction (see Section 3.3.3), which makes this measurement an upper limit of the intrinsic β_opt. Spectral indexes exhibit a decreasing behavior from ${\beta }_{\mathrm{opt}}^{\star }\sim 1.5$ to 1 masked by the uncertainties. Due to the number of measurements available, we perform a Wald–Wolfowitz runs test (Wald & Wolfowitz 1940) of all the points against the median value to check for a trend. If there is no real decrease of the spectral index, the data should fluctuate randomly around the median. In this case, a run is a consecutive series of ${\beta }_{\mathrm{opt}}^{\,\star }$ terms over or under the median. The temporal evolution of the spectral indexes displays significantly smaller number of runs than expected with a p-value$\,=\,2\times {10}^{-15}$, which rejects the hypothesis of randomness and indicates that a temporal trend from soft to harder spectral indexes is likely. This result is in agreement with the chromatic nature of the break observed in the RINGO3 light curves.

For the X-ray spectral analysis, we use the available BAT-XRT observations that correspond to the time intervals of Figure 6. With this choice, the first spectrum is before the slope change of the optical light curve at ∼400–500 s postburst (see Section 3.1). Due to the synchrotron nature of the afterglow, the models used for this analysis comprise either a single power law or connected power laws.

We extract the time-resolved 0.3–10 keV XRT spectra using the web interface provided by Leicester University²¹ based on heasoft (v6.22.1; Blackburn 1995). Energy channels are grouped with the grppha tool so that we have at least 20 counts bin^–1 to ensure the Gaussian limit and adopt χ² statistics. The first four time intervals were observed in WT mode and the final one in PC mode. For modeling WT observations, we only consider energies ≥0.8 keV due to an instrumental effect that was reported in Beardmore (2019). Simultaneous time-resolved, 15–150 keV spectra with BAT are extracted for the first three time intervals using the standard BAT pipeline (e.g., see Rizzuto et al. 2007) and are finally grouped in energy to ensure a >2σ significance.

The combined BAT-XRT spectra are modeled under xspec (v. 12.9.1; Arnaud et al. 1999) using χ² statistics with a simple absorbed power law (powerlaw*phabs*zphabs) that accounts for the rest-frame host galaxy total hydrogen absorption, ${N}_{{\rm{H}},\mathrm{HG}}$, and the Galactic²² ${N}_{{\rm{H}},\mathrm{MW}}=7.54\times {10}^{19}\,{\mathrm{cm}}^{-2}$ (Willingale et al. 2013). By satisfactorily fitting each spectrum with a power law, we find that the 0.3–10 keV and 15–150 keV spectra belong to the same spectral regime and that there is no significant spectral evolution during the first ∼200–6000 s postburst. In Figure 7, we fit all five spectra with a single spectral index. The fit procedure results in a spectral index β_x = 0.94 ± 0.02, rest-frame hydrogen absorption ${N}_{{\rm{H}},\mathrm{HG}}\,=(9.3\pm 0.2)\times {10}^{22}\,$ cm⁻², ${\chi }^{2}/\mathrm{dof}\,=\,422/466$, and p-value = 0.89. Due to the high column density absorption among the soft X-rays, the slope is mainly constrained by the hard X-rays.

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We obtain the combined BAT-XRT-RINGO3 SEDs by coadding those RINGO3 frames that correspond to a given X-ray epoch and then deriving the absolute flux-calibrated photometry (see Section 2.1.2).

Broadband SEDs are also modeled under xspec using χ² statistics with a simple absorbed power law (powerlaw*zdust*zdust*phabs*zphabs) that accounts for total hydrogen absorption (see Section 3.3.2), Galactic extinction (E${}_{B\mbox{--}V,{\rm{MW}}}\,=0.0124\pm 0.0005;$ Schlegel et al. 1998), and a rest-frame Small Magellanic Cloud (SMC) dust extinction profile for the host galaxy (Pei 1992).

The optical and X-ray fluxes do not connect with a simple absorbed power law. Consequently, we test for a break between the two spectral regimes (using the bknpower model). For all five SEDs, we link all parameters relating to absorption, extinction, and spectral indexes, and we leave the break frequency as a free parameter for each SED. From the broken power-law fit (see Figure 8), we obtain a spectral index β_opt = 0.43 ± 0.02 for the optical and β_x = 0.93 ± 0.02 for the X-ray with ${\chi }^{2}/\mathrm{dof}\,=439/481$ and p-value = 0.82. The break evolves as ${E}_{\mathrm{break},\{\mathrm{1,2},\mathrm{3,4,5}\}}=1.4\pm 0.3\,$, $1.6\pm 0.2\,$, 1.6 ± 0.3, 0.65 ± 0.14, 0.54 ± 0.12 keV. We derive high-extinction ${{\rm{A}}}_{{\rm{v}},\mathrm{HG}}\,=1.49\,\pm 0.12\,$ mag or, equivalently, ${E}_{{B}-{V},\mathrm{HG}}=0.51\pm 0.04$ and absorption ${N}_{{\rm{H}},\mathrm{HG}}=(9.0\pm 0.3)\times {10}^{22}\,$ cm⁻² at the host galaxy rest frame. We achieve compatible results within 1σ for spectral indexes, energy breaks, and total hydrogen absorption using Large Magellanic Cloud/Milky Way dust extinction profiles, which gives ${{\rm{A}}}_{{\rm{v}},\mathrm{HG}}=1.64\pm 0.13\,$and $1.72\pm 0.12\,$ mag, respectively.

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Under the fireball model framework, the evolution of the spectral and temporal properties of the afterglow satisfies closure relations (Sari et al. 1998; Zhang & Mészáros 2004; Zhang et al. 2006; Racusin et al. 2009; Gao et al. 2013). These depend on the electron spectral index p, density profile of the surrounding medium (interstellar medium (ISM) or wind), cooling regime (slow or fast), and jet geometry. In the reverse shock scenario, the total light-curve flux can be explained by a two-component model that combines the contribution of the reverse and forward shock emission (Kobayashi 2000; Kobayashi & Zhang 2003a; Zhang et al. 2003).

When the fireball starts to decelerate at t_peak,r, the reverse shock emission produces a bright optical peak; for GRB 190114C, this happened prior to the MASTER/RINGO3 observations. For an ISM profile, slow cooling regime and with the optical band in between the typical synchrotron and cooling frequency, ${\nu }_{{\rm{m}},{\rm{r}}}\lt {\nu }_{\mathrm{opt}}\lt {\nu }_{{\rm{c}},{\rm{r}}}$, the emission should decay²³ with ${\alpha }_{{\rm{r}}}=(3p+1)/4\sim 2$ for a typical p ∼ 2.3. Later on, the forward shock peaks when the typical synchrotron frequency ${\nu }_{{\rm{m}},{\rm{f}}}$ crosses the optical band. In the ${\nu }_{{\rm{m}},{\rm{f}}}\lt {\nu }_{\mathrm{opt}}\lt {\nu }_{{\rm{c}},{\rm{f}}}$ spectral regime, the forward shock emission will follow an expected decay with ${\alpha }_{{\rm{f}}}=3(p-1)/4\sim 1$, which flattens the light curve. Consequently, the reverse–forward shock model consists of a power law with a temporal decay ${\alpha }_{{\rm{r}}}$ for the reverse shock component plus a forward shock contribution that has an expected rise of 0.5 and decay of ${\alpha }_{{\rm{f}}}$. The GRB 190114C light curves suggest that the forward shock peak time ${t}_{\mathrm{peak},{\rm{f}}}$ happens before or during MASTER/RINGO3 observations and it is masked by the bright reverse shock emission.

In the left panel of Figure 9, we attempt the simplest model by considering that the forward shock peaks before the MASTER observations (${t}_{\mathrm{peak},{\rm{r}}},{t}_{\mathrm{peak},{\rm{f}}}\ll 30\,$s). We leave the reverse and forward shock electron indexes as free parameters. The light curve is best modeled with two power-law components that decay as ${\alpha }_{\mathrm{opt},{\rm{r}}}=2.35\pm 0.05$ and ${\alpha }_{\mathrm{opt},{\rm{f}}}\,=0.905\pm 0.009$ (see Table 3). However, the MASTER residuals present a trend, and the model underestimates by ∼0.8 mag the late-time observations in the r band reported in the GCN circulars. A decay of ∼0.7–0.8 was reported by Kumar et al. (2019b) and Singh et al. (2019) hours to days postburst, which is inconsistent with the ${\alpha }_{\mathrm{opt},{\rm{f}}}$ derived. In addition, UVOT white-band emission was also decaying as α = 1.62 ± 0.04 since ∼70 s postburst with a change to α = 0.84 ± 0.02 at ∼400 s (Ajello et al. 2020).

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In the right panel of Figure 9, we consider a model in which the forward shock peaks during MASTER/RINGO3 observations. In this model, the two emission components decay as ${\alpha }_{\mathrm{opt},{\rm{r}}}=1.711\pm 0.012$ and ${\alpha }_{\mathrm{opt},{\rm{f}}}=0.707\pm 0.010$, and the forward shock peaks at ${t}_{\mathrm{peak},{\rm{f}},\{{BV},{r},{R},{I}\}}=805\pm 19$, $831\pm 47$, $931\pm 18$, $1083\pm 20\,$ s (see Table 3). Both reverse and forward shock decay indexes are compatible with an electron index $p\sim 1.95$. Allowing different peak times for each band is preferred over a fixed peak time model, consistent with a chromatic emergence of the forward shock that moves redward through the bands. The typical synchrotron break frequency is expected to evolve through RINGO3 bands like ${\nu }_{{\rm{m}},{\rm{f}}}\propto {t}^{-{\alpha }_{{\rm{m}}}}$ with ${\alpha }_{{\rm{m}}}=1.5;$ we find α_m ∼ 1.4.

Even though both models are compatible with the spectral evolution of the optical index ${\beta }_{\mathrm{opt}}^{\,\star }$ (see Figure 10), the model with the forward shock peak during MASTER/RINGO3 observations is preferred by early- and late-time observations over an early-time forward shock peak (see Table 3 and Figure 9). Photoionization of dust could also cause similar color evolution—with a red-to-blue shift—during the very early stages of the GRB and mainly during the prompt phase (e.g., Perna et al. 2003; Morgan et al. 2014; Li et al. 2018). However, the GRB 190114C blue-to-red color change favors the interpretation of the passage of an additional spectral component through the optical band: the transition from reverse shock–dominated outflow to forward shock emission (e.g., see GRB 061126, Perley et al. 2008; GRB 080319, Racusin et al. 2008; and GRB 130427A, Vestrand et al. 2014). From Table 4, GRB 061126 is also identified among the 70 GRBs of Li et al.'s (2018) classification of color trends as a reverse-to-forward shock transition. Additionally, the reverse–forward shock scenario is supported by radio data (Laskar et al. 2019b).

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After the main γ-ray prompt bulk emission ≳30 s postburst, BAT light curve presents a tail of extended emission that we model with a simple power law until ∼240 s. This model yields α_γ = 0.936 ± 0.015 and ${\chi }^{2}/\mathrm{dof}\,=\,2524/1112$ (see Figure 11). We notice that a broken power-law model does not increase the significance of the fit.

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The GRB 190114C X-ray light curve has no shallow phase (see Yamazaki et al. 2019 for other GeV/TeV events) and decays as α_x = 1.345 ± 0.004 through all Swift XRT observations (see Figure 11; ${\chi }^{2}/\mathrm{dof}\,=\,1608/1052$), which is similar to the expected α_x ∼ 1.2 decay for the normal spherical stage (Nousek et al. 2006; Zhang et al. 2006). However, Figure 11 late-time residuals show signs of a possible break, as the XRT light-curve model tends to overestimate the flux; the last two observation bins lay 2.6σ and 3.8σ away from the chosen model. To account for a possible change of the slope steepness during the late-time afterglow, we fit a broken power-law model that yields ${\alpha }_{{\rm{x}}1}=1.321\pm 0.005$, ${\alpha }_{{\rm{x}}2}=1.49\pm 0.02$, and a break time at (1.8 ± 0.3) × 10⁴ s, with ${\chi }^{2}/\mathrm{dof}\,=\,1530/1051$. This means a change of Δα_x = 0.17 ± 0.04 in the temporal decay rate that does not have any spectral break associated; we exclude the passage of a break frequency. For GRB 090102 X-ray afterglow (see Table 4), Gendre et al. (2010) found a similar temporal break from α₁ = 1.29 ± 0.03 to α₂ = 1.48 ± 0.10 at a comparable time ${1.9}_{-0.8}^{+1.5}\times {10}^{4}\,{\rm{s}}$ and without any spectral change. Consequently, we explore the possibility of a jet break. From Sari et al.'s (1999) formulation, the jet opening angle is

$$\begin{eqnarray}&&{\theta }_{{\rm{j}}}\approx 0.0297{\left(\displaystyle \frac{{t}_{{\rm{j}}}}{1{\rm{h}}{\rm{r}}}\right)}^{3/8}{\left(\displaystyle \frac{{E}_{{\rm{i}}{\rm{s}}{\rm{o}}}}{2.4\times {10}^{53}{\rm{e}}{\rm{r}}{\rm{g}}}\right)}^{-1/8}{\left(\displaystyle \frac{1+z}{1.4245}\right)}^{-3/8}\end{eqnarray} \tag{ 1 }$$

for an ISM-like environment and assuming typical values of circumburst density n = 1 cm⁻³ and radiative efficiency η = 0.2. Taking into account that the jet opening angle distribution of long GRBs peaks around 5.9° (Goldstein et al. 2016), ${E}_{\mathrm{iso}}=(2.4\pm 0.5)\times {10}^{53}\,$ erg (Frederiks et al. 2019), and $z=0.4245\pm 0.0005$ (Castro-Tirado et al. 2019), the jet break should be visible at ${t}_{{\rm{j}}}\sim {10}^{5}\,$ s. A jet break at $(1.8\pm 0.3)\times {10}^{4}\,$ s—implying ${\theta }_{{\rm{j}}}\sim 3.1^\circ$—is possible, and, given the scarcity of GCN observations around the break time, we cannot rule it out.

For pure forward shock emission in fireball model conditions, one would expect that if the optical and X-ray share the same spectral regime, the emission will decay at the same rate. Taking into account that ${\alpha }_{\mathrm{opt},{\rm{f}}}=0.707\pm 0.010$, ${\alpha }_{0.3\mbox{--}10\mathrm{keV}}\,=1.345\pm 0.004$, and ${\alpha }_{15\mbox{--}350\mathrm{keV}}=0.936\pm 0.015$, we find a difference of ${\rm{\Delta }}{\alpha }_{{\rm{f}}}={\alpha }_{{\rm{x}}}-{\alpha }_{\mathrm{opt},{\rm{f}}}=0.638\,\pm 0.011$ between the 0.3–10 keV/optical decay rates and ${\rm{\Delta }}{\alpha }_{{\rm{f}}}=0.23\pm 0.02$ for the 15–350 keV/optical emission, which implies that there is at least one break frequency between the X-ray and the optical. This interpretation is also supported by the need for a spectral break between these two bands that changes the slope by Δβ = 0.50 ± 0.03 (see Section 3.3.3).

For an ISM medium profile, slow cooling regime, and with the cooling frequency between the optical and X-ray bands, an electron index of p ∼ 1.95 (see Section 4.1.1) implies spectral indexes of ${\beta }_{\mathrm{opt},\mathrm{CR}}\sim 0.48$ and ${\beta }_{{\rm{x}},\mathrm{CR}}\sim 0.98$, which are in agreement with ${\beta }_{\mathrm{opt}}=0.43\pm 0.02$ and ${\beta }_{{\rm{x}}}=0.93\pm 0.02$ derived from the broadband SED modeling (see Section 3.3.3). The evolution of ${E}_{\mathrm{break}}$ for the last three SEDs is also consistent with the passage of the cooling frequency ${\nu }_{{\rm{c}}}\propto {t}^{-{\alpha }_{{\rm{c}}}}$ with ${\alpha }_{{\rm{c}}}\sim 0.5$.

A difference of ${\rm{\Delta }}{\alpha }_{{\rm{f}}}=\pm 0.25$ is expected if the cooling frequency lies between the X-ray/optical bands. Taking into account that ${\alpha }_{\mathrm{opt},{\rm{f}}}=0.707\pm 0.010$, ${\alpha }_{15\mbox{--}350\mathrm{keV}}=0.936\,\pm 0.015$, and ${\alpha }_{80\mathrm{keV}-8\mathrm{MeV}}=0.99\pm 0.05$ (Minaev & Pozanenko 2019), we find that the 15–350 keV/optical emission ${\rm{\Delta }}{\alpha }_{{\rm{f}}}=0.23\pm 0.02$ and the 80 keV–8 MeV/optical emission Δα_f = 0.28 ± 0.05 are consistent with ${\rm{\Delta }}{\alpha }_{{\rm{f}}}=\pm 0.25$. However, this relation does not hold for the 0.3–10 keV/optical emission with ${\rm{\Delta }}{\alpha }_{{\rm{f}}}=0.638\pm 0.011$. Furthermore, the steepness of the X-ray light curve ${\alpha }_{{\rm{x}},{\rm{f}}}=1.345\pm 0.004$ implies a softer ${\beta }_{{\rm{x}},\mathrm{CR}}\sim 1.23$, ${p}_{{\rm{x}}}\sim 2.46$, which does not agree with either the observed spectral indexes or the preferred model for the optical emission. Out of the 68 GRBs of Zaninoni et al.'s (2013) sample, only 19% of GRBs follow Δα_f = 0, ±0.25 for all XRT X-ray/optical light-curve segments. The GRB 190114C belongs to the 41% of the GRB population for which no light-curve segments Δα_f satisfy the fireball model conditions for forward shock emission. Additionally, out of the six GRBs of Japelj et al.'s (2014) sample with reverse–forward shock signatures, only GRB 090424 fulfills Δα_f = 0, ±0.25.

An alternative to reconcile the optical with the soft X-ray emission is to assume that they belong to two spatially or physically different processes. Supporting the scenario of complex jet structure or additional emission components, we have chromatic breaks that cannot be explained by either a break frequency crossing the band or an external density change (Oates et al. 2011). For example, a two-component jet would produce two forward shocks that would be responsible for, respectively, the optical and the X-ray emission at late times (GRB 050802, Oates et al. 2007; GRB 080319, Racusin et al. 2008).

Polarization measurements intrinsic to the afterglow are complicated by the fact that GRB 190114C is a highly extincted burst. Because of the preferred alignment of dust grains, dust in the line of sight can induce nonnegligible degrees of polarization that vectorially add to the intrinsic afterglow polarization; late-time polarimetric studies of GRB afterglows show few percents of polarization (e.g., Covino et al. 1999, 2004; Greiner et al. 2004; Wiersema et al. 2012). For the GRB 190114C line of sight, the polarization of the CD-27 1309 star, ${P}_{\{{BV},R,I\}}=0.3 \% \,\pm 0.1 \% ,0.1 \% \pm 0.1 \% ,0.3 \% \pm 0.1 \%$, gives an estimation of the polarization induced by Galactic dust. For the host galaxy, we estimate the dust-induced polarization degree with the Serkowski empirical relation (Serkowski et al. 1975; Whittet et al. 1992)

$$\begin{eqnarray}&&P={P}_{\max }\exp \left[-K{\mathrm{ln}}^{2}\left(\displaystyle \frac{{\lambda }_{\max }}{\lambda }\right)\right],\end{eqnarray} \tag{ 4 }$$

where ${\lambda }_{\max }(\mu {\rm{m}})={{R}}_{{V}}/5.5$, $K=0.01\pm 0.05+(1.66\pm 0.09){\lambda }_{\max }$, and ${P}_{\max }\lesssim 9\,$E${}_{{B}-{V}}$. We introduce the redshifted host effect ${\lambda }_{\max }\longrightarrow (1+z){\lambda }_{\max ,\mathrm{HG}}$ (Klose et al. 2004; Wiersema et al. 2012), and we assume a Milky Way extinction profile with ${E}_{{B}-{V},\mathrm{MW}}=0.0124\pm 0.0005$ (Schlegel et al. 1998) and an SMC profile for the host galaxy with ${E}_{{B}-{V},\mathrm{HG}}\,=0.51\pm 0.04$. Taking into account the shape of the RINGO3 bandpasses, we find that the maximum polarization degree induced by the host galaxy dust is ${P}_{\{{BV},R,I\}}\lesssim 3.9 \% ,4.5 \% ,4.5 \%$, compatible with the constant 2%–4% polarization degree of the GRB detected since 109 s postburst.

Depending on the relative position of the polarization vectors (the alignment of dust grains to the intrinsic polarization vector of the ejecta), dust could either polarize or depolarize the outflow. If dust was depolarizing the intrinsic polarization, this would mean a gradual rotation of the angle as the percentage of polarized reverse shock photons decreases. The constant angle and polarization degree favor the interpretation that the ∼2%–4% ordered component is compatible with dust-induced levels (see Figure 5); i.e., the intrinsic polarization at that time is very low or negligible.

Although the early afterglow modeling implies that the ejecta from the central engine is highly magnetized for this event, the polarization degree of the reverse shock emission is very low, and the 2%–4% polarization signal is likely to be induced by dust. This is in contrast to the high polarization signals observed in other GRB reverse shock emission (GRB 090102, Steele et al. 2009; GRB 101112A, Steele et al. 2017; GRB 110205A, Steele et al. 2017, GRB 120308A, Mundell et al. 2013).

One possibility is that the low degree of polarization arises from other emission mechanisms in addition to synchrotron emission. Since the optical depth of the ejecta is expected to be well below unity at the onset of afterglow, most synchrotron photons from the reverse shock are not affected by IC scattering processes (the cooling of electrons is also not affected if the Compton y-parameter is small). The polarization degree of the synchrotron emission does not change even if the IC scattering is taken into account. However, the polarization degree is expected to be reduced for the photons upscattered by random electrons (i.e., SSC photons; Lin et al. 2017). We now consider whether this can explain the observed low polarization degree of the reverse shock emission.

If the typical frequency of the forward shock emission is in the optical band ${\nu }_{{\rm{m}},{\rm{f}}}\sim 5\times {10}^{14}\,$ Hz at t ∼ 900 s, as our afterglow modeling suggests (right panel of Figure 9), it should be about ${\nu }_{{\rm{m}},{\rm{f}}}\sim 8\times {10}^{16}\,$ Hz at the onset of afterglow (${t}_{{\rm{d}}}\sim 30\,$s). Since the typical frequency of the reverse shock emission is lower by a factor of ∼Γ² (this factor weakly depends on the magnetization parameter R_B, but the inclusion of a correction factor does not change our conclusion; see Harrison & Kobayashi 2013 for more details), it is about ${\nu }_{{\rm{m}},{\rm{r}}}\sim {10}^{12}\,$ Hz at that time for ${\rm{\Gamma }}\sim {{\rm{\Gamma }}}_{{\rm{c}}}=260$. Assuming a random Lorentz factor of electrons in the reverse shock region ${\gamma }_{{\rm{m}},{\rm{r}}}\sim 20({\epsilon }_{{\rm{e}}}/3\times {10}^{-2})$, the typical frequency of the first SSC emission is in the optical band ${\nu }_{{\rm{m}},{\rm{r}}}^{\mathrm{IC}}\sim {\gamma }_{{\rm{m}},{\rm{r}}}^{2}{\nu }_{{\rm{m}},{\rm{r}}}\sim 5\times {10}^{14}\,$ Hz.

The optical depth of the ejecta at the onset of afterglow is given by $\tau ={\sigma }_{{\rm{T}}}{N}_{{\rm{e}}}/4\pi {R}_{{\rm{d}}}^{2}\sim ({\sigma }_{{\rm{T}}}/3){\rm{\Gamma }}{{nR}}_{{\rm{d}}}\sim 7\times {10}^{-6}n$, where ${\sigma }_{{\rm{T}}}$ is the Thomson cross section, N_e is the number of electrons in the ejecta, ${R}_{{\rm{d}}}\sim 2\,c{{\rm{\Gamma }}}^{2}{t}_{{\rm{d}}}\sim {10}^{17}\,$ cm is the deceleration radius, and we have used the fact that the mass of the ejecta is larger by a factor of Γ than that of the ambient material swept by the shell at the deceleration time. The spectral peak power of the first SSC emission is roughly given by ${F}_{\max }^{\mathrm{IC}}\sim \tau {F}_{\max ,{\rm{r}}}$, where ${F}_{\max ,{\rm{r}}}$ is the spectral peak power of the reverse shock synchrotron emission (e.g., Kobayashi et al. 2007). The ratio of the contributions from the first SSC and the synchrotron emission to the optical band is about $\tau {F}_{\max ,{\rm{r}}}/({F}_{\max ,{\rm{r}}}{({\nu }_{\mathrm{opt}}/{\nu }_{{\rm{m}},{\rm{r}}})}^{-(p-1)/2})$ ∼ $\tau {({\nu }_{\mathrm{opt}}/{\nu }_{{\rm{m}},{\rm{r}}})}^{1/2}$ ∼ $7\,\times {10}^{-6}n$ at the onset of the afterglow. Since the synchrotron emission dominates the optical band, the IC process does not explain the low polarization degree.

Consequently, we suggest that GRB 190114C large-scale ordered magnetic fields could have been largely distorted on timescales previous to reverse shock emission (see also GRB 160625B; Troja et al. 2017). We speculate that the detection of bright prompt and afterglow emission from teraelectronvolt to radio wavelengths in GRB 190114C, coupled with the low degree of observed optical polarization, may be explained by the catastrophic/efficient dissipation of magnetic energy from and consequent destruction of the order in the primordial magnetic fields of the outflow, e.g., via turbulence and reconnection at prompt emission timescales (ICMART; Zhang & Yan 2011; Deng et al. 2015, 2016; Bromberg & Tchekhovskoy 2016). For GRB 190114C, reconnection could be a mechanism for the production of the high-energy Fermi-LAT photons that exceed the maximum synchrotron energy (another possibility is SSC; Ajello et al. 2020). If the 7.7% ± 1.1% detection at 52 ± 6 s postburst is interpreted as due to a residual contribution from polarized prompt photons (as in GRB 160625B; Troja et al. 2017), this would further support the existence of ordered magnetic fields close to prompt emission timescales and their consequent destruction for reverse shock emission.

The sample of high-quality early-time polarimetric observations of GRB afterglows remains small ($\lt 10$), and for prompt emission, it is smaller still (2). Future high-quality early-time polarimetric observations at optical and other wavelengths are vital to determine the intrinsic properties of GRB magnetic fields and their role in GRB radiation emission mechanisms.