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# Simultaneous Radio and Optical Polarimetry of GRB 191221B Afterglow

Yuji Urata, Kenji Toma, Stefano Covino, Klaas Wiersema, Kuiyun Huang, Jiro Shimoda, Asuka Kuwata, Sota Nagao, Keiichi Asada, Hiroshi Nagai, et al.

► To cite this version:

Yuji Urata, Kenji Toma, Stefano Covino, Klaas Wiersema, Kuiyun Huang, et al. Simultaneous Radio and Optical Polarimetry of GRB 191221B Afterglow. Nature Astronomy, 2023, 7 (1), pp.80-87.
10.1038/s41550-022-01832-7. hal-03903585

HAL Id: hal-03903585

https://hal.science/hal-03903585v1

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# Simultaneous radio and optical polarimetry of GRB 191221B afterglow

Received: 28 August 2021

Accepted: 14 October 2022

Published online: 8 December 2022

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Yuji Urata Ⓘ¹,²✉, Kenji Toma Ⓘ³,⁴, Stefano Covino Ⓘ⁵, Klaas Wiersema⁶,⁷,⁸, Kuiyun Huang⁹,¹⁰, Jiro Shimoda¹¹, Asuka Kuwata⁴, Sota Nagao⁴, Keiichi Asada¹², Hiroshi Nagai¹³,¹⁴, Satoko Takahashi¹⁴,¹⁵,¹⁶, Chao-En Chung¹, Glen Petitpas¹⁷, Kazutaka Yamaoka¹⁸, Luca Izzo Ⓘ¹⁹, Johan Fynbo Ⓘ²⁰, Antonio de Ugarte Postigo Ⓘ²¹, Maryam Arabsalmani Ⓘ²²,²³ & Makoto Tashiro Ⓘ²⁴,²⁵

Gamma-ray bursts (GRBs) are the most luminous transients in the universe and are utilized as probes of early stars, gravitational wave counterparts and collisionless shock physics. In spite of studies on polarimetry of GRBs in individual wavelengths that characterized intriguing properties of prompt emission and afterglow, no coordinated multi-wavelength measurements have yet been performed. Here we report the first coordinated simultaneous polarimetry in the optical and radio bands for the afterglow associated with the typical long GRB 191221B. Our observations successfully caught the radio emission, which is not affected by synchrotron self-absorption, and show that the emission is depolarized in the radio band compared with the optical one. Our simultaneous polarization angle measurement and temporal polarization monitoring indicate the existence of cool electrons that increase the estimate of jet kinetic energy by a factor of more than 4 for this GRB afterglow. Further coordinated multi-wavelength polarimetric campaigns would improve our understanding of the total jet energies and magnetic field configurations in the emission regions of various types of GRBs, which are required to comprehend the mass scales of their progenitor systems and the physics of collisionless shocks.

Gamma-ray burst (GRB) 191221B was detected on 21 December 2019, 20:39:13 UT, and its X-ray afterglow was rapidly identified by the Neil Gehrels Swift Observatory¹. The optical afterglow was discovered by the MASTER auto-detection system². Optical polarization with a possible time evolution in the early afterglow phase was also detected by the Southern African Large Telescope (SALT) and Very Large Telescope (VLT) (Extended Data Table 1)³. The redshift was measured as z = 1.148 based on metal absorption lines in the optical afterglow observed by VLT/X-shooter⁴. The isotropic equivalent energy of $E_{y,iso} = (3.6 \pm 0.4) \times 10^{53}$ erg and the rest-frame peak energy of the time-integrated spectrum $E_{\text{peak}}^{\text{src}} = 810 \pm 65$ keV were derived by the Konus-Wind observation (with the standard cosmological parameters,

the Hubble constant $H_0 = 67.3 \text{ km s}^{-1} \text{ Mpc}^{-1}$, the matter density parameter $\Omega_M = 0.315$ and the dark energy density parameter $\Omega_A = 0.685)⁵. The duration of the prompt emission in the 15–350 keV band is 48.0 ± 16.0 s (ref. ⁶). These prompt emission properties obey the empirical $E_{\text{peak}}^{\text{src}} - E_{y,iso}$ correlation (Extended Data Fig. 1) and indicate that GRB 191221B is one of the typical long GRBs.

The first semi-simultaneous polarimetry for the afterglow between millimetre and optical bands was conducted at 2.5 days after the burst by using Atacama Large Millimetre/submillimetre Array (ALMA) and VLT (Fig. 1). The VLT observation measured a linear polarization degree (PD) of 1.3 ± 0.2% (here we employed the systematic errors of 0.1% reported by ref. ⁷ and the range with $3\sigma$ confidence level is 0.9–1.8%)
<figure><img src="image_4.png" /><figcaption>**Fig. 1** | Spectral flux distribution and polarization spectrum of GRB 191221B afterglow at 2.5 days. **a,** Spectral flux distribution (red points). The black dotted line is the forward shock model fit to the observed data. **b,** PDs at 97.5 GHz (3σ upper limit) and optical R band (red points), and polarization spectrum of the simple one-zone model (grey dashed line), the plasma-scale magnetic field model (purple dash-dotted line) and the cool electron model (green solid line). **c,** PAs at 97.5 GHz (1σ range) and optical R band (red points). The observed difference of PAs with ~90% confidence level (that is, 16.6 ± 9.6°) supports the cool electron model. The plasma-scale magnetic field model predicts a constant PA over the frequencies (for example, purple dash-dotted line). All error bars represent 1σ uncertainties.</figcaption></figure>

with a polarization angle (PA) of 61.6 ± 6.3° at the R band. Hereafter, we note 1σ errors for our measurements without special notification. The low dust extinction and Serkowski law⁵ show an intrinsic origin of the polarization (Methods, Extended Data Figs. 2–4 and Extended Data Table 2). The PD is consistent with other optical afterglows (an average of 1.6% across 84 polarimetric measurements)⁹. The ALMA observation put the upper limit on PD of 0.6% with a 3σ confidence level at 97.5 GHz. The detection in Stokes U maps and non-detection in Stokes Q maps (Extended Data Fig. 5) constrained the range of PA to be 37.7–52.3° with a 1σ confidence level. Therefore, this simultaneous polarimetry between optical and radio bands indicates depolarization in the radio band. The significantly low upper limit is also consistent with the first detection of linear polarization in the GRB radio afterglow (that is, 0.2% for the low-luminosity GRB 171205A)¹⁰.

The synchrotron self-absorption (SSA) effect, which suppresses polarization below the SSA frequency ($v_a$), is not a reliable explanation for the observed depolarization. ALMA observations at 97.5 GHz, 145 GHz and 203 GHz (Fig. 2, Table 1 and Extended Data Table 3) show that the light curve at the 97.5 GHz band exhibited a broken power-law evolution with power-law indices of $\alpha = 0.26 \pm 0.02$ (before the break) and $\alpha = -1.62 \pm 0.13$ (after the break), and a break time at $3.77 \pm 0.35$ days, where and hereafter we describe the temporal and spectral properties of the flux density as $F_v \propto t^{\alpha}v^\beta$ ($t$ and $v$ are time since the burst in days and frequency). The multi-frequency measurements (Fig. 3) showed that the spectral slope changed from positive power-law index of $\beta \approx 0.602 \pm 0.007$ at 1.5 days and $\beta \approx 0.32 \pm 0.15$ at 2.5 days to

<figure><img src="image_5.png" /><figcaption>**Fig. 2** | Radio afterglow light curve of GRB 191221B A with the simultaneous optical (R band) polarimetric observation. The red dashed line indicates the best fitted smoothly connected broken power-law functions of the 97.5 GHz light curve. The radio light curves and the optical R band photometric measurement are described by the standard forward shock synchrotron radiation model. Differences in the early optical afterglow (green small circles) and its wiggles may be caused by the magnitude-to-flux conversion of optical observations made by the very broad-band clear filter. The forward shock model describes the passing of synchrotron spectral peak over the ALMA observing band around 4 days, which is consistent with observed spectrum change between 2.5 and 9.5 days (Fig. 3). All error bars represent 1σ uncertainties.</figcaption></figure>

a negative one ($\beta \approx -0.7$) at 9.5 and 18.4 days. These spectral slopes are in disagreement with the SSA effect which leads to $\beta = 2$ (refs. ¹¹,¹²).

These afterglow properties are instead reproduced by the standard model¹¹,¹² of optically thin synchrotron emission from an expanding shock in a uniform density medium with an isotropic energy that increases with time by long activity of the central engine $E_{iso} = 9.4 \times 10^{52} t^{0.25}$ erg, an ambient medium density $n = 5.9 \text{ cm}^{-3}$, a fraction of shocked energy transferred to non-thermal electrons $\epsilon_e = 6.5 \times 10^{-2}$, that to magnetic field $\epsilon_B = 1.2 \times 10^{-2}$, the energy spectral slope of non-thermal electrons $p = 2.4$, the jet opening half-angle $\theta_J = 2.6^\circ$ and the viewing angle $\theta_V = 1.9^\circ$ (Methods). The model lines in the top panel of Figs. 1 and 2 are the results of our numerical calculations of synchrotron flux by taking account of the equal observed times of photons¹³,¹⁴. The model also explains the X-ray and optical afterglows (Extended Data Fig. 6). The peak frequency at ~200 GHz in the top panel of Fig. 1 is the synchrotron frequency of minimum-energy electrons $v_m$, and the temporal and spectral changes around $t \approx 4$ days are found to be consistent with the crossing of $v_m$ at the observed frequencies. The energy scale is comparable to the observed gamma-ray energy $E_{\gamma,iso}$, and the micro-physical parameters are also consistent with other cases¹⁵. The deviation of the observed radio flux from the model light curve at 1.5 days (Fig. 2) and its slightly hard spectrum (Fig. 3) would imply an additional emission component, but it is negligible at $t \ge 2.5$ days (see Methods for more discussion).

If the magnetic field is ordered in the emitting shocked region, the PD of synchrotron emission is ≈70% at $v > v_m$ while it is 50% at $v < v_m$, and the polarization direction is perpendicular to both the magnetic field direction and the line of sight in the comoving frame, where the electron momentum distribution is assumed to be isotropic¹⁶. Usually, however, the magnetic field in the shocked region is tangled through its amplification process from the field of the ambient medium by some type of instability¹⁷,¹⁸ and, therefore, the net polarization of observed synchrotron emission is reduced, depending on the magnetic field configuration in the visible region. One may consider a simple one-zone
<table><caption>Table 1 | Radio polarization observing log. Measurements with no special notation are summarized with 1σ errors</caption><thead><tr><th>Time (days)</th><th>Frequency (GHz)</th><th>PD (%)</th><th>PA (°)</th><th>I flux (mJy)</th><th>Q flux (mJy)</th><th>U flux (mJy)</th></tr></thead><tbody><tr><td>0.476</td><td>97.5</td><td>&lt;0.84 (3σ)</td><td>–</td><td>3.587±0.008</td><td>–</td><td>–</td></tr><tr><td>1.458</td><td>97.5</td><td>&lt;0.60 (3σ)</td><td>–</td><td>4.912±0.005</td><td>–</td><td>–</td></tr><tr><td>2.525</td><td>97.5</td><td>&lt;0.64 (3σ)</td><td>37.7–52.3</td><td>3.949±0.007</td><td>0.006 (r.m.s.)</td><td>-0.023±0.006</td></tr><tr><td>5.482</td><td>97.5</td><td>&lt;1.3 (3σ)</td><td>–</td><td>2.371±0.090</td><td>0.007 (r.m.s.)</td><td>0.007 (r.m.s.)</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>Fig. 3 | Spectral flux distributions of the GRB 191221B afterglow at 1.5, 2.5, 9.5 and 18.4 days after GRB. The photometry with high signal-to-noise characterized the spectral slope $\beta$ as 0.602 ± 0.007 at 1.5 days, 0.32 ± 0.15 at 2.5 days and -0.7 at 9.5 and 18.4 days, respectively. The changing of spectral indices from positive to negative indicated the passing of the spectral peak frequency through the radio band. All error bars represent 1σ uncertainties.</figcaption></figure>

model in which the PDs at various frequencies, that is, $v > v_m$ and $v < v_m$, are reduced by the same factor$^{19–21}$ (the grey dashed line in Fig. 1b), but this model is ruled out by the observed PD data in the radio and optical bands.

One of the most actively discussed magnetic field amplification processes is the Weibel instability, which occurs at relativistic collisionless shocks and generates strong magnetic fields with random directions on a plasma skin depth scale$^{17,19,22,23}$. In this case, the field component parallel to the shock plane may be dominant. This anisotropy results in a sizable PD at each position of the shock, although the field is tangled on the tiny scale$^{24,25}$. We numerically calculated the net linear polarization in various frequencies based on the synchrotron emission model explained above (see Methods for more details). As shown in the middle panel of Fig. 1, the PD at $v \lesssim v_m$ is much lower than that at $v > v_m$ since the surface brightness distribution is significantly non-uniform at the frequencies $v > v_m$ (refs. $^{13,14}$). This property can be consistent with the data. However, this model has a clear prediction that the PAs at $v > v_m$ and $v \lesssim v_m$ are the same or 90° different$^{14}$. The difference in the observed PAs at the radio and optical bands (the bottom panel of Fig. 1) does not support this model. The temporal evolution of PD is also incompatible with this model (Extended Data Fig. 6).

Another possible process of magnetic field amplification is magnetohydrodynamic instabilities at the shock. These include Richtmyer–Meshkov instability, which occurs in the case of ambient medium with inhomogeneous density$^{18,26}$. In this case, the magnetic field directions in the shocked region can be random mainly on hydrodynamic scales comparable to the typical width of the bright region in the shock downstream, and the internal Faraday depolarization can be significant in the radio band if the number of non-thermal electrons is a fraction $f(\le 1)$

of the total shocked electrons$^{21}$. The fraction $1-f$ of the total shocked electrons remain so cool that they cause the Faraday depolarization on the emission from the non-thermal electrons. The true isotropic energy is $E_{iso}/f$ and the true fraction of non-thermal electron energy is $\epsilon_{iso}f$ in this case$^{27}$. We calculate the PD in the one-zone model similar to the procedure in Sokoloff et al.$^{28}$, and plot the model in the middle panel of Fig. 1 (see more details in Methods). To explain the observed PDs, the Faraday rotation in the shocked region should be significant at $v < 100$ GHz. This leads to an upper limit $f \lesssim 0.3$. The difference in the surface brightness distributions in the optical and radio bands or the contribution from the ordered magnetic field$^{28}$ explain the observed difference in PAs.

Our observations performed simultaneous polarimetry between the millimetre and optical bands for the typical long GRB 191221B. The multi-frequency observations of the afterglow were also described by the standard model. The measured radio PD was significantly lower than the optical one. Two plausible models that provide new insights into GRB sciences were considered for the origin of the polarization. The measured PAs and the PD temporal evolution indicated that the Faraday depolarization was caused by cool electrons in the hydrodynamic-scale magnetic field. Our observation consolidates a new methodology for revealing the total jet energies and collisionless shock physics of various types of GRBs. If $f$ is very small for low-luminosity GRBs and/or short GRBs, their true total jet energies are much larger than the current estimates, which may increase their neutrino production rates$^{29,30}$ and the lower bound of total explosion energies or mass scales of progenitor systems.

## Methods

### ALMA and Atacama Compact Array observations

A total of 11 epochs of radio observations were conducted using the ALMA and Atacama Compact Array (Table 1 and Extended Data Table 3). Four epochs (0.5, 1.5, 2.5 and 9.5 days) of observations were performed with the polarization mode at 97.5 GHz (that is, band 3). Multi-frequency observations were managed with the photometry mode at 145 GHz among 5 of the 11 epochs. At 1.5 and 2.5 days, two additional photometry observations at 203 GHz were also conducted. Semi-simultaneous optical polarimetry was also performed 2.5 days after the GRBs using the VLT.

Regarding the ALMA calibrations, the bandpass and flux were calibrated using observations of J1037-2934, and observations of J1036-3744 was used for the phase calibration. The polarization calibration was performed by observing J1058+0133. The raw data were reduced at the East Asian ALMA Regional Center using CASA (v.5.6.1)$^{31}$. We further performed interactive CLEAN deconvolution imaging with self-calibration. The Stokes $I$, $Q$ and $U$ maps were CLEANed with an appropriate number of CLEAN iterations after the final round of self-calibration. The off-source root mean square (r.m.s.) levels in $I$, $Q$ and $U$ are consistent with the expectations for thermal noise alone. The quantities that can be derived from the polarization maps are the polarized intensity ($\sqrt{Q^2 + U^2}$), PD (100$\sqrt{Q^2 + U^2}/f$%) and polarization position angle (1/2 arctan($U/Q$)). By applying the polarization calibration to the phase calibrator J1036-3744 and creating Stokes maps for 6, 9 and 18 epochs during the 3 h observing period, we confirm that the stability of linear PD is <0.02%, which is consistent with the systematic linear
polarization calibration uncertainty of 0.033% for compact sources. The Atacama Compact Array data were flagged, calibrated and imaged with standard procedures with CASA (v.5.6.1). The bandpass and flux were calibrated using observations of J1058+0133 and J1107-4449. Observations of J1018-3123 were used for the phase calibration.

## VLT spectroscopic observations

The VLT also obtained X-shooter spectra for the afterglow of GRB 191221B at -10 and -34 h after the GRB onset. X-shooter spectra cover a very large wavelength range, from the ultraviolet (UV) atmospheric cutoff to more than 2 µm. This range is covered by the three arms of the instrument: the UVB, visible (Vis) and near-infrared (NIR) arms. Observations consisted of two sets of 600 s exposures in the three arms using the AB nod-on-slit offset mode. Data in the UVB and Vis arms have been reduced using the stare mode standard data reduction, namely by extracting the science spectra as if they were obtained without any offset. The NIR arm was extracted using the standard X-shooter Nodding mode pipeline. Each single spectrum has been corrected for slit losses, due to the finite aperture of the X-shooter slit, and the residual sky emission subtracted. The final stacked spectrum has been finally corrected for telluric features, whose response correction for the Vis and NIR arms has been estimated from the spectrum of the standard telluric star³²⁻³⁴.

A full study of these spectra is well beyond our interest and, in this work, our goal is just to model the afterglow-only spectrum (the one obtained ~10 h after the burst) to derive an estimate of the optical extinction along the line of sight. This would allow us to compute a plausible maximum level of host-galaxy dust-induced (that is, non-intrinsic to the GRB afterglow) polarization. Properly connecting the three X-shooter arms requires a careful cross-calibration again beyond our interests, and therefore we limited our analysis to the UVB arm covering the rest-frame wavelength range from approximately 1,650 to 2,550 Å (from 3,450 to 5,500 Å in the observer frame). The resolution of the X-shooter spectra is 0.2 Å per bin. We first rebinned the spectra to 20 Å per bin by the algorithm described in Carnall³⁵ and then manually removed all the main emission or absorption lines. The resulting spectrum shows small-scale variations, which are probably an artefact of the reduction process related to the different orders of the Echelle spectrograph. This does not affect our fits, although we had to add, in quadrature, a systematic error of 7.5 × 10⁻¹⁸ erg s⁻¹ cm⁻² Å⁻¹ to the uncertainties computed by the reduction pipeline. We fit the afterglow spectrum in this wavelength range by a simple power law affected by rest-frame extinction following the Small or Large Magellanic Cloud or the Milky Way extinction curves³⁶,³⁷. The rest-frame extinction turns out to be very low, and therefore the three extinction recipes yield essentially the same results (see also ref. ³⁸): $\beta = -0.97^{+0.14}_{-0.07}$, $E_{\beta-V} < 0.038$ (95% upper limit). The best-fit for the Small Magellanic Cloud recipe is shown in Extended Data Fig. 2.

The VLT also obtained spectro-polarimetric observations with the Focal Reducer and low dispersion Spectrograph (FORS2) instrument at about 10 h after the GRB onset. These data have already been reported in Buckley et al.³. The data show (their Fig. 4) a fairly constant polarization level and position angle. In Buckley et al.³, spectro-polarimetry obtained with the SALT/Robert Stobie Spectrograph telescope ~3 h after the burst is also reported. The more modest signal-to-noise ratio S/N prevents us from carrying out further analyses on these data regarding the possible evidence for a Serkowski-law behaviour. We have downloaded the VLT spectrum and carried out a fit with a Serkowski law⁸ and the predictions for afterglow polarization in the optical band (that is, constant polarization). As expected, both scenarios can provide an acceptable fit to the data, although for the Serkowski law the wavelength corresponding to the polarization maximum is pushed into the far UV (~200 nm) to give a roughly constant polarization in the wavelength range covered by the FORS2 spectro-polarimetry. This is a rather unusual result but not totally unprecedented³⁹.

However, the Serkowski-law fit is not statistically favoured compared with the afterglow only, since it requires a larger number of free parameters. Therefore, when also considering the low extinction along the line of sight derived by the analysis of the X-shooter spectra, an intrinsic origin (that is, due to the afterglow) of the observed polarization compared with the dust-induced hypothesis appears to be more in agreement with the data.

## VLT polarimetric observations

Polarimetric observations were acquired using the FORS2 mounted on the VLT. A Wollaston prism was inserted in the light path to split the image of each object in the field into two orthogonal polarization components. A mask was used to avoid overlap of the two images; we used the FORS2 R band filter. For each position angle $\phi/2$ of the half-wave-plate rotator, we obtained two simultaneous images of cross-polarization at angles $\phi$ and $\phi + 90^\circ$. We obtained observations at position angles 0, 22.5, 45 and 67.5° of the half-wave plate. This technique allowed us to remove any differences between the two optical paths (ordinary and extraordinary ray), including the effects of seeing and airmass changes. With the same setup we also observed polarized and unpolarized standard stars so we could convert position angles from the telescope to the celestial reference frame, and to correct for the small instrumental polarization introduced by the telescope. Reduction, that is, bias, flat-field correction, bad pixel masking and so on, were carried out following standard recipes. Aperture photometry was obtained for the target and several nearby sources in the field. We also confirmed that the GRB polarization measurement is unaffected by Galactic dust-induced polarization (Extended Data Fig. 3.) We used custom software tools based on the Python Astropy library (http://www.astropy.org). More details on polarimetric data analysis are reported in Covino et al.⁴⁰ and Wiersema et al.⁴¹.

Extended Data Figure 6 shows the temporal evolution of polarization combined with the optical polarimetric results reported by Buckley et al.³. There are three epochs of optical observation including our measurements. Buckley et al.³ made two epochs of polarimetry during the wiggles of the optical afterglow and reported the marginal decrease of PD (by ~0.3%) over a timescale of ~7 h. We derived the PDs and PAs in the wavelength range of the R band based on the data reported by Buckley et al.³ (Extended Table 1). Based on the two-sample *t*-test, the PA between the radio and optical bands is different at an ~90% confidence level. The temporal evolution of PDs is also inconsistent with the plasma-scale magnetic field model. These properties do not support the plasma-scale magnetic field model.

## X-ray spectrum of GRB afterglows with optical polarimetry

We checked the hydrogen column density of the line of sight ($N_H$), which is one of the indicators of dust extinction of afterglows at their host galaxies. There are eight known z GRB afterglows, including GRB 191221B, available with optical polarimetry and Swift X-ray observations. For six events (GRB 080928, GRB 091018, GRB 091208B, GRB 110205A, GRB 121024A and GRB 131030A), the optical observations reported the detection of intrinsic polarization⁹,⁴¹⁻⁴⁵. For GRB 190114C, Jordana-Mitjans et al.⁴⁶ reported the detection of polarization induced by the dust in the host galaxy. The X-ray data obtained by the Swift/X-ray telescope were collected from the UK Swift Science Data Centre⁴⁷,⁴⁸. We rebinned the spectra so that each spectral bin contained more than five counts. Using the software XSPEC 12, we performed spectral fitting with a single power law modified with intrinsic and Galactic absorptions, the latter of which were fixed at values calculated from Willingale et al.⁴⁹. The XSPEC 12 model components TBabs and zTBabs that incorporate three absorption elements (that is, gas, molecules and grains)⁵⁰ were used to describe the spectral absorptions. The derived best-fitting values are summarized in Extended Data Table 2. Using the results presented in Schady et al.⁵¹, the measured $N_H$ are converted to the extinction at optical V-band $A_V$. Five events, including GRB 191221B,
exhibited an intrinsic absorption column density of order $10^{21}$. The intrinsic absorption column density of GRB 191221B is the smallest one ($N_H = 1.6^{+0.9}_{-0.8} \times 10^{21} \text{cm}^{-2}$). This result is consistent with the low dust extinction derived by the analysis of the VLT/X-shooter spectra. In contrast, the GRB 190114C X-ray spectrum is highly obscured by the intrinsic absorption column density of $N_H = 8.5 \times 10^{22} \text{cm}^{-2}$ (Extended Data Fig. 4). These results naturally explain the dust-induced optical polarization of GRB 190114C and support the intrinsic polarization observed in other events. Hence, these results also indicate the intrinsic origin of the optical polarization measured on the GRB 191221B optical afterglow.

## Afterglow modelling

The observed radio spectra and the light curves in the radio, optical and X-ray bands are explained by the standard forward shock model$^{11,12}$. The temporal change of the spectral slope in the range of 97.5–203 GHz (Fig. 3) and the breaks of the 97.5 and 145 GHz light curves (Fig. 2) at $t \approx 4$ days indicate the crossing of the synchrotron frequency of minimum-energy electrons $v_m$ at the observed frequencies. From the observed spectral slope $\beta \approx -0.7$ at $v > v_m$, the electron energy spectral index is estimated to be $p = -2\beta + 1 \approx 2.4$. Then the theoretical temporal decay indices at $v < v_m$ and at $v > v_m$ are $1/2$ and $3(1-p)/4 \approx -1.1$, respectively, in the case in which the collimated forward shock expands in a uniform density medium and its edge is not visible owing to the strong relativistic beaming. These are not consistent with the observed indices of approximately 0.26 ($t \lesssim 4$ days) and $-1.6$ ($t \gtrsim 4$ days). After the edge becomes visible (without sideways expansion of the shock), the geometrical flux reduction $\theta_j^2/(1/\Gamma)^2 \propto t^{-3/4}$ results in decay indices of $-1/4$ (at $v < v_m$) and $-1.8$ (at $v > v_m$), where $\theta_j$ and $\Gamma$ are the opening half-angle and Lorentz factor of the shock. The wind type ambient medium gives decay indices of $-3/4$ (at $v < v_m$) and $-2.3$ (at $v > v_m$). We find that the observed indices can be fit by the model in which the ambient density is uniform and the energy continues to be injected into the shock by long activity of the central engine$^{52,53}$. We note that our assumption of no sideways expansion of the shock is based on the results of high-resolution hydrodynamic simulations, which show that the collimated shock after the time of $1/\Gamma \approx \theta_j$ expands sideways logarithmically, not exponentially$^{54,55}$.

We performed numerical calculations of flux from the shock with a fixed $\theta_j$, which evolves following the Blandford–McKee self-similar solution, by taking account of the equal arrival time surface of the photons$^{13,14}$. Then we tried to fit the model flux to the observed data by adjusting the model parameters, namely the isotropic energy $E_{\text{iso}}$, the ambient medium density $n$, the fraction of shock energy carried by the electrons $\epsilon_e$, that carried by amplified magnetic field $\epsilon_B$ and the viewing angle $\theta_v$, as well as $\theta_j$ and $p$. This model can fit the data in the radio, optical and X-ray bands (Figs. 1 and 2, and Extended Data Fig. 6). The model parameters are constrained to be $E_{\text{iso}} = 9.4 \times 10^{52} t^{0.25}$ erg, $n = 5.9 \text{ cm}^{-3}$, $\epsilon_e = 6.5 \times 10^{-2}$, $\epsilon_B = 1.2 \times 10^{-2}$, $\theta_v = 1.9^\circ$, $\theta_j = 2.6^\circ$ and $p = 2.4$. These values of $n$, $\epsilon_e$ and $\epsilon_B$ are typical of GRB afterglows$^{15}$.

It is well known that X-ray flares with fast variability sometimes dominate the forward shock emission. If the flares have broad emission spectra, they might also affect the radio light curves. The slight deviations of radio data from the forward shock model light curves at $t = 0.5$ and $1.5$ days might be related to the X-ray flares observed at similar times. Since they have fast variability they may not contribute to the spectrum at $t = 2.5$ days. Figure 1 simply indicates that the standard forward shock synchrotron spectrum with the radio data at $t = 2.5$ days (that is, the peak flux $-5$ mJy, $v_m \approx 200$ GHz and the spectral index (at $v > v_m$) $\beta \approx -0.7$) can explain the optical data, and does not require any additional emission component.

The possibility that the short-lived reverse shock explains the radio emission at $t \gtrsim 1.5$ days is excluded since the minimum synchrotron frequency of the reverse shock$^{56}$ $v_m^r \approx 200$ GHz with the peak flux $-5$ mJy requires $\epsilon_e \approx 1$. We also examined possible long-lasting reverse shock

emission in the long-active central engine model, such as in our model shown above. Suppose the reverse shock emission is dominant in the radio band while the forward shock is dominant in the optical band; the difference in polarization in the two bands could be caused by possible differences in magnetic field structures in the two shocked regions. However, this scenario is also disfavoured owing to a high value of $\epsilon_e$. According to Sari and Mésáros$^{57}$, the minimum synchrotron frequencies of the forward and reverse shocks for our model parameters at $t = 1.5$ days are $v_m \approx 9.8 \times 10^{11}$ Hz and $v_m^r \approx 2.9 \times 10^{10}$ Hz, respectively, where the equal arrival time surface of the photons is not taken into account. To increase $v_m^r$ to a frequency at $v_m$, without changing the forward shock X-ray flux which is proportional to $\epsilon_e^{p-1} E_{\text{iso}}^{(p+2)/4}$, requires $\epsilon_e \approx 0.53$. This value is unusually high, compared to $\epsilon_e \lesssim 0.3$ estimated by systematic studies using well-sampled multi-frequency observations$^{15,58,59}$.

## Polarization in the plasma-scale magnetic field model

The synchrotron polarization depends on the magnetic field configuration at each position in the shocked fluid. Here we focus on the turbulent magnetic field with coherence length on a plasma skin depth scale, which is many orders of magnitude smaller than the shock width. Such a magnetic field is created by the Weibel instability at relativistic collisionless shocks$^{17,19,22,23}$, and in this case the field may be anisotropic, that is, $\xi^2 \equiv 2\langle B_{\parallel}^2 \rangle/(\langle B_{\perp}^2 \rangle) \neq 1$, where $\langle B_{\parallel}^2 \rangle$ and $\langle B_{\perp}^2 \rangle$ are the averages of the powers of the magnetic field components parallel and perpendicular to the shock normal, respectively. On the basis of this model, we can calculate the local Stokes Q and U parameters corresponding to the surface brightness of the shock by averaging the emissivity with respect to the field directions at each position, and we find that the synchrotron emission at each position is polarized owing to the anisotropy of the turbulent magnetic field$^{24,25,60}$. The polarization directions are symmetric around the line of sight, so that the net PD is non-zero only when the visible region of angular size $-1/\Gamma$ includes the jet edge and becomes asymmetric$^{24,25,60}$.

We numerically calculated the linear PDs in various frequencies based on the light curve model explained above. The parameter value $\xi^2 = 0.56$ leads to an optical PD of $\approx 1.3\%$ at $t \approx 2.5$ days. In the optical band, the surface brightness has a peak at $\theta \approx 1/\Gamma$ from the line of sight, while in the radio band, the region around $\theta \approx 0$ with low local PD is also bright$^{13}$, so that the net radio PD is lower$^{14}$. As a result, the model polarization spectrum at 2.5 days (Fig. 1, middle panel) is consistent with the upper limit on the radio PD. In this model, however, the PA in the radio band is the same as that in the optical band. The difference in the observed PAs at the radio and optical bands does not support this model.

The temporal changes of optical PD and PA in this model are plotted in Extended Data Fig. 6. The PD changes as the angular size of the visible region $-1/\Gamma$ increases. It has a maximum value when $1/\Gamma \approx \theta_v + \theta_v^r$. The PA experiences a sudden $90^\circ$ change at $t \approx 0.06$ day, and it is constant before and after that time. The model with $\xi^2 = 0.56$ exhibits a PD as high as $\approx 5\%$ at $t \approx 0.4$ day, which is not consistent with the observed data. The less anisotropic turbulence leads to lower PD, as shown by the model with $\xi^2 = 0.81$ in Extended Data Fig. 6, but it also appears incompatible with the observed data.

## Faraday depolarization model

The low PD in the radio band could be ascribed to an internal Faraday depolarization effect by cool electrons. The standard forward shock model usually assumes that all shocked electrons gain energy from shocked protons and form a power-law energy distribution $d\text{r}/\text{dy} \propto \gamma^p$ for $\gamma \gtrsim \gamma_m \approx \epsilon_e(m_p/m_e)\Gamma$ (here $\gamma$, $m_p$, $m_e$ are the electron Lorentz factor, proton mass, and electron mass). Plasma particle simulations showed that all the electrons gain energy from shocked protons$^{61}$, but this has not yet been confirmed by observations. Indeed, the forward shock model in which only a fraction $f(<1)$ of the total electrons is energized
can also explain the observed afterglow light curves and spectra²⁷. In this case, a fraction 1-f of the total electrons remains as cool thermal electrons with the Lorentz factor $\bar{\gamma}_m = \eta\Gamma$, where $\eta$ is a factor of the order of unity if the cool electrons are just isotropized at the shock front, and the correct physical parameters are $E'_{iso} = E_{iso}/f$, $n' = n/f$, $\epsilon'_e = \epsilon_e/f$ and $\epsilon'_B = \epsilon_B/f$. The cool electrons cause Faraday depolarization of the synchrotron emission of the non-thermal electrons above the self-absorption frequency²¹.

We assume that the magnetic field in the shocked fluid is turbulent on a hydrodynamic scale, which is comparable to the typical width of the bright region in the shock downstream. Such a field can be created by magnetohydrodynamic instabilities at the shock, such as the Richtmyer–Meshkov instability¹⁸,²⁶. For simplicity, we consider that the globally ordered magnetic field is negligible and that the plasma in the visible region consists of N random cells, in each of which the magnetic field is ordered. At the optical band, for which the Faraday effect is not significant, the net PD is $P_0 \approx \frac{(p+1)}{(p+7/3)} \frac{1}{\sqrt{N}}$, so that $N \approx 5,000$ can explain the optical PD $\approx 1\%$. The Faraday rotation effect within the emission region results in the PD being²⁸ $P_0[(1 - e^{-5})/S]$, where $S = (\nu/\bar{\nu}_V)^{-4}$ and $\bar{\nu}_V$ is the frequency at which the Faraday depth is unity, $\bar{\nu}_V \approx 200 (1 + z)^{-15/16} \left(\frac{1-f}{10f}\right)^{1/2} \eta^{-1} \sqrt{\ln \bar{\gamma}_m} N^{-1/12} \left(\frac{E_{iso}}{10^{52} \text{ erg}}\right)^{3/16} \eta^{9/16} \left(\frac{\epsilon_B}{0.01}\right)^{1/4} \left(\frac{\tau}{1 \text{ day}}\right)^{-1/16}$ GHz (ref.²¹). The middle panel of Fig. 1 shows the Faraday depolarization model for the radio and optical data, which indicate $\bar{\nu}_V \gtrsim 100$ GHz. This leads to $f^{-1} - 1 \gtrsim 2.5\eta^2(\ln \bar{\gamma}_m)^{-1}$.

## Data availability

Processed data are presented in the tables and figures in the paper. The ALMA data are available from the ALMA Science Archive. The VLT data are available from the ESO Science Archive Facility.

## Code availability

We used standard data reduction tools in Python and CASA³¹. The theoretical calculation code of the flux and polarization used in this work is not publicly available. Results presented in this work are available from the corresponding author upon reasonable request.

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## Acknowledgements

This work is based on observations collected at the European Southern Observatory (ESO) under ESO programmes O104.D-0600(C) and O104.D-0600(A). This paper makes use of the following ALMA data: ADS/JAO.ALMA#2019.1.01016.T, 2019.1.01484.T. ALMA is a partnership of ESO (representing its member states), National Science Foundation (USA) and National Institutes of Natural Sciences (Japan), together with National Research Council Canada (Canada), Ministry of Science and Technology and Institute of Astronomy and Astrophysics, Academia Sinica (Taiwan), and Korea Astronomy and Space Science Institute (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, Associated Universities, Inc./National Radio Astronomy Observatory and National Astronomical Observatory of Japan. This work is supported by the Ministry of Science and Technology of Taiwan grant nos. MOST 105-2112-M-008-013-MY3 (Y.U.) and 106-2119-M-001-027 (K.A.). This work is also supported by Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research No. 18H01245 (K.T.) and No. 20J01086 (J.S.) and by the Graduate Programme on Physics for the Universe (GP-PU), Tohoku University (A.K.). K.W. acknowledges support through a UK Research and Innovation Future Leaders Fellowship awarded to B. Simmons (MR/T044136/1), and support through an Alan Turing Institute Post-Doctoral Enrichment Award. We thank the East Asian ALMA Regional Center, especially P.-Y. Hsieh for support in the ALMA observations.

## Author contributions

Y.U., K.T., S.C. and K.W. initiated the study. Y.U. and K.T. mainly wrote the texts of this manuscript. Y.U., S.C., K.W., K.H. and S.T. managed the Target of opportunity (ToO) observations and main data analysis. G.P. provided valuable thoughts for establishing efficient ToO managements. K.T., J.S., A.K. and S.N. managed the theoretical interpretations. A.K. played the principal role in numerical modelling. K.A. and H.N. checked the ALMA results. C.-E.C., K.Y. and M.T. provided $N_H$ analysis for evaluating the intrinsic absorption using X-ray data. L.I., J.F., A.d.U.P. and M.A. provided VLT/X-shooter data. All of the authors contributed to the data analysis and discussed the results and the texts.

## Competing interests

The authors declare no competing interests.

## Additional information

*Extended data* is available for this paper at
https://doi.org/10.1038/s41550-022-01832-7.

**Correspondence and requests for materials** should be addressed to Yuji Urata.

**Peer review information** *Nature Astronomy* thanks Shuang-Nan Zhang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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© The Author(s), under exclusive licence to Springer Nature Limited 2022

<footnote n="1">¹Institute of Astronomy, National Central University, Chung-Li, Taiwan. ²MITOS Science Co., Ltd., New Taipei, Taiwan. ³Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai, Japan. ⁴Astronomical Institute, Graduate School of Science, Tohoku University, Sendai, Japan.</footnote>

<footnote n="5">⁵Istituto Nazionale di Astrofisica/Brera Astronomical Observatory, Merate (LC), Italy. ⁶Department of Physics, University of Warwick, Coventry, UK.</footnote>

<footnote n="7">⁷School of Physics and Astronomy, University of Leicester, Leicester, UK. ⁸Physics Department, Lancaster University, Lancaster, UK. ⁹Center for General Education, Chung Yuan Christian University, Taoyuan, Taiwan. ¹⁰Department of Optoelectric Physics, Chinese Culture University, Taipei, Taiwan.</footnote>

<footnote n="11">¹¹Department of Physics, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan. ¹²Academia Sinica Institute of Astronomy and Astrophysics, Taipei, Taiwan. ¹³National Astronomical Observatory of Japan, Mitaka, Japan. ¹⁴Department of Astronomical Science, School of Physical Sciences, The Graduate University for Advanced Studies, SOKENDAI, Mitaka, Japan. ¹⁵Joint ALMA Observatory, Vitacura, Chile. ¹⁶NAOJ Chile Observatory, Vitacura, Chile. ¹⁷Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA. ¹⁸Institute for Space-Earth Environmental Research (ISEE), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan. ¹⁹DARK, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark. ²¹The Cosmic Dawn Center Niels Bohr Institute Copenhagen University Jagtvej, Copenhagen N, Denmark. ²¹Artemis, Observatorie de la Côte D'Azur, Université Côte d'Azur, CNRS, Nice, France. ²²Excellence Cluster ORIGINS, Garching, Germany. ²³Ludwig-Maximilians-Universität, München, Germany. ²⁴Department of Physics, Saitama University, Shimo-Okubo, Japan. ²⁵Institute of Space and Astronautical Science, JAXA, Sengen, Tsukuba, Japan.</footnote>

<footnote>✉e-mail: yjurata@gmail.com</footnote>
<figure><img src="image_7.png" /><figcaption>**Extended Data Fig. 1** | $E_{\text{src,peak}}^{\text{src}} - E_{\text{iso}}^{\text{relation}}$. $E_{\text{src,peak}}^{\text{src}} - E_{\text{iso}}^{\text{relation}}$ (Amati et al. 2002, Yamaoka et al. 2017)$^{62,63}$. GRB 191221B, marked with the red box point, obeys the relation. All error bars represent $1 - \sigma$ uncertainties.</figcaption></figure>
<figure><img src="image_8.png" /></figure>

**Extended Data Fig. 2** | Fit by a simple power-law and SMC (Gordon et al. 2003) extinction curve for the ultraviolet arm of the VLT-X-shooter. Fit by a simple power-law and SMC (Gordon et al. 2003) extinction curve for the ultraviolet arm of the VLT-X-shooter. The black solid line is the best-fit and the dashed line shows

the unextinguished afterglow spectrum. Marginalizing the power-law index and normalization, it turns out that the amount of rest-frame extinction is below 0.038 mag (95% upper limit).
<figure><img src="image_9.png" /></figure>

**Extended Data Fig. 3** | Stokes raw Q and U measurements for field stars and the GRB afterglow. Stokes raw Q and U measurements for field stars and the GRB afterglow. Green and blue circles indicate field stars and the afterglow, respectively. The orange box shows the weighted average of the field stars.
<figure><img src="image_10.png" /><figcaption>**Extended Data Fig. 4** | X-ray spectrum for GRB191221B (a) and GRB190114C (b) afterglows. X-ray spectrum for GRB191221B (a) and GRB190114C (b) afterglows. a, GRB191221B X-ray afterglow spectrum described by a single power law modified with intrinsic and Galactic adsorptions, the latter of which is fixed at $N_H = 8.6 \times 10^{20} \text{ cm}^{-2}$. The derived best-fitting values of the intrinsic absorption column density and spectral index are $N_H = (1.6^{+0.9}_{-0.8}) \times 10^{21} \text{ cm}^{-2}$ and</figcaption></figure>

$\beta = -0.96 \pm 0.06$, respectively, with reduced $\chi^2$/dof = 0.88/246. b, GRB190114C X-ray afterglow spectrum. The highly obscured spectrum with the intrinsic absorption column density of $N_H = (8.5^{+0.3}_{-0.3}) \times 10^{22} \text{ cm}^{-2}$ is reasonable for the dust induced origin of polarization observed in the optical afterglow reported by Jordana-Mitjans et al. (2020)⁴⁶ error bars represent $1 - \sigma$ uncertainties.
<figure><img src="image_11.png" /></figure>

Extended Data Fig. 5 | Stokes I (a), Q (b), and U (c) maps of the GRB191221B afterglow taken on 2019 December 24 (2.5 days after the burst). Stokes I (a), Q (b), and U (c) maps of the GRB191221B afterglow taken on 2019 December 24

(2.5 days after the burst). The ALMA beam size is shown in the open circles. The map null detection on the Stokes-Q map constrained the range of PA of 37.7-52.3 deg with 1 − σ uncertainties.
<figure><img src="image_12.png" /></figure>

**Extended Data Fig. 6** | GRB 191221B afterglow light curves in X-ray, optical, and radio bands together with optical and radio polarization variabilities.

GRB 191221B afterglow light curves in X-ray, optical, and radio bands together with optical and radio polarization variabilities. a, Multi-frequency light curves. Dotted lines indicate the model light curves fitted to radio, optical, and X-ray data observed by ALMA and VLT. Differences in the early optical afterglow (green small circles) and its wiggles may be caused by the magnitude-to-flux conversion

of optical observations made by the very broad-band clear filter. b, PD temporal evolution in optical R band (purple stars and lines) and radio 97.5 GHz band (3 − σ upper limits with red symbols and lines). The solid and dashed lines indicate the plasma-scale turbulent magnetic field model with ξ² = 0.56 (solid) and ξ² = 0.81 (dashed). c, PA in the optical R band. The purple dashed-dot lines indicate the plasma-scale turbulent magnetic fields model with any ξ². All error bars represent 1 − σ uncertainties. The upper limits are at the 3 − σ level.
<table><caption>Extended Data Table 1 | Summary of Optical Polarization. Summary of Optical Polarization. Measurements with no special notation are summarized with 1-σ errors. *The values for 0.121 and 0.417 days were derived in the wavelength range of R band based on data reported by Buckley et al (2021)³</caption><thead><tr><td>Days</td><td>Band</td><td>PD [%]</td><td>PA [deg]</td></tr></thead><tbody><tr><td>0.121</td><td>R*</td><td>1.4 ± 0.1*</td><td>68 ± 5</td></tr><tr><td>0.417</td><td>R*</td><td>1.0 ± 0.1*</td><td>57 ± 5</td></tr><tr><td>2.525</td><td>R</td><td>1.3 ± 0.1</td><td>61.6 ± 6.3</td></tr></tbody></table>
<table><caption>Extended Data Table 2 | X-ray spectral properties for 8 known-z GRBs with optical polarimetry. X-ray spectral properties for 8 known-z GRBs with optical polarimetry</caption><thead><tr><th>Events</th><th>Redshift</th><th>Galactic N<sub>H</sub> (10<sup>20</sup> cm<sup>-2</sup>)</th><th>Intrinsic N<sub>H</sub> (10<sup>22</sup> cm<sup>-2</sup>)</th><th>Spectral index (β<sub>X</sub>)</th><th>Reduced χ<sup>2</sup> / dof</th><th>A<sub>V</sub> (mag)</th></tr></thead><tbody><tr><td>GRB080928</td><td>1.692</td><td>7.16</td><td>0.42<sup>+0.16</sup><sub>-0.15</sub></td><td>-1.07 ± 0.07</td><td>1.12/204</td><td>0.13</td></tr><tr><td>GRB091018</td><td>0.971</td><td>3.07</td><td>0.35<sup>+0.06</sup><sub>-0.05</sub></td><td>-1.02 ± 0.05</td><td>0.98/266</td><td>0.11</td></tr><tr><td>GRB091208B</td><td>1.063</td><td>5.75</td><td>1.68<sup>+0.29</sup><sub>-0.25</sub></td><td>-1.13 ± 0.09</td><td>1.09/188</td><td>0.51</td></tr><tr><td>GRB110205A</td><td>2.22</td><td>1.70</td><td>0.56<sup>+0.15</sup><sub>-0.14</sub></td><td>-0.93 ± 0.05</td><td>0.97/264</td><td>0.17</td></tr><tr><td>GRB121024A</td><td>2.298</td><td>7.87</td><td>1.37<sup>+0.38</sup><sub>-0.34</sub></td><td>-1.00 ± 0.08</td><td>0.71/175</td><td>0.42</td></tr><tr><td>GRB131030A</td><td>1.293</td><td>5.62</td><td>0.59<sup>+0.11</sup><sub>-0.10</sub></td><td>-1.07 ± 0.06</td><td>0.97/244</td><td>0.18</td></tr><tr><td>GRB190114C</td><td>0.425</td><td>0.75</td><td>8.5<sup>+0.3</sup><sub>-0.3</sub></td><td>-1.09 ± 0.06</td><td>1.05/517</td><td>2.6</td></tr><tr><td>GRB191221B</td><td>1.148</td><td>8.62</td><td>0.16<sup>+0.09</sup><sub>-0.08</sub></td><td>-0.96 ± 0.06</td><td>0.88/246</td><td>0.05</td></tr></tbody></table>
<table><caption>Extended Data Table 3 | Photometric Observing Log. Photometric Observing Log. Measurements are summarized with 1-σ errors and statistical errors only. *The optical flux at 2.385 days was derived using the acquisition images taken as part of the acquisition sequence of the VLT imaging polarimetry</caption><thead><tr><td>Days</td><td>Frequency [GHz]</td><td>Flux density [mJy]</td></tr></thead><tbody><tr><td>1.523</td><td>97.5</td><td>4.579 ± 0.038</td></tr><tr><td>4.455</td><td>97.5</td><td>3.093 ± 0.042</td></tr><tr><td>8.375</td><td>97.5</td><td>1.320 ± 0.030</td></tr><tr><td>9.482</td><td>97.5</td><td>1.213 ± 0.016</td></tr><tr><td>13.352</td><td>97.5</td><td>0.685 ± 0.035</td></tr><tr><td>17.422</td><td>97.5</td><td>0.477 ± 0.053</td></tr><tr><td>18.449</td><td>97.5</td><td>0.464 ± 0.017</td></tr><tr><td>33.425</td><td>97.5</td><td>0.206 ± 0.039</td></tr><tr><td>33.444</td><td>97.5</td><td>0.200 ± 0.019</td></tr><tr><td>1.471</td><td>145</td><td>5.823 ± 0.125</td></tr><tr><td>2.442</td><td>145</td><td>4.742 ± 0.099</td></tr><tr><td>8.444</td><td>145</td><td>1.046 ± 0.063</td></tr><tr><td>9.401</td><td>145</td><td>0.906 ± 0.022</td></tr><tr><td>18.431</td><td>145</td><td>0.352 ± 0.018</td></tr><tr><td>1.498</td><td>203</td><td>7.051 ± 0.589</td></tr><tr><td>2.505</td><td>203</td><td>4.434 ± 0.205</td></tr><tr><td>2.385</td><td>4.59×10<sup>5</sup></td><td>0.027 ± 0.003*</td></tr></tbody></table>