ALMA Detection of a Linearly Polarized Reverse Shock in GRB 190114C

The interaction of gamma-ray burst (GRB) jets with their ambient medium generates two shocks: (i) a relativistic forward shock (FS) in the ambient medium that powers the long-lasting X-ray to radio afterglow radiation, and (ii) a short-lived reverse shock (RS) propagating into, and decelerating, the jet (Sari et al. 1998; Zhang & Kobayashi 2005). Whereas observations and modeling of the FS emission reveal the burst energetics, outflow geometry, and the density structure of the pre-explosion environment, the self-similar hydrodynamic evolution of the FS is insensitive to the composition of the jet itself.

Instead, the composition (baryon content), initial Lorentz factor, and magnetization of GRB jets can be probed through the short-lived RS emission (Granot & Königl 2003; Granot & Taylor 2005; Zhang & Kobayashi 2005). The expected signature of RS synchrotron radiation is a bright optical flash as the shock crosses the ejecta (typically lasting a few tens of seconds) followed by a radio flare (typically lasting a few days), a phenomenon predicted to be prevalent, if not ubiquitous, in GRBs (Akerlof et al. 1999; Sari & Piran 1999). Isolating the RS requires careful decomposition of the observed multi-frequency (radio-to-X-ray) spectral energy distribution (SED) at different epochs into FS and RS contributions (Laskar et al. 2013; Perley et al. 2014; van der Horst et al. 2014; Laskar et al. 2016; Alexander et al. 2017; Laskar et al. 2018a, 2018b).

RS emission is expected to be polarized, particularly if the jet contains large-scale ordered magnetic fields advected from the central engine (Granot & Königl 2003; Granot & Taylor 2005), and thus RS polarization observations provide a powerful measure of ejecta magnetization (Mundell et al. 2013). The degree of RS polarization is sensitive to the magnetic field anisotropy in the jet, with levels of up to ≈60% expected in the presence of ordered magnetic fields or ≲10% in the case of tangled fields (Granot 2003; Granot & Königl 2003; Lyutikov et al. 2003). The polarization angle is predicted to remain stable in jets with large-scale magnetic fields (Lazzati et al. 2004), or vary randomly with time if the field is produced locally by plasma or magnetohydrodynamic (MHD) instabilities (Gruzinov & Waxman 1999). Thus measurements of polarization degree and position angle, and of the evolution of these quantities with time, should provide diagnostics for the magnetic field structure in GRB jets.

Polarized RS emission in the radio or millimeter band has not been detected to date due to sensitivity and response time limitations, with the best limits of ≲7% (linear) and ≲9% (circular) for likely RS emission in GRB 991216 at 8.46 GHz, 1.5 days after the burst (Granot & Taylor 2005), and <3.9% (linear) and <2.7% (circular) at 1.5 days after the burst for the strong RS observed in GRB 130427A (van der Horst et al. 2014). However, RS emission, although visible for up to ∼ a week in the cm-band, is often self-absorbed at these frequencies (Laskar et al. 2013, 2016, 2018a, 2018b); as self-absorption suppresses intrinsic polarization (Toma et al. 2008), this could potentially explain the cm-band upper limits. In contrast, RS emission is expected to be optically thin in the mm-band; however, the limited sensitivity and response time of mm-band facilities has precluded such a measurement to date.

Here, we present Atacama Large Millimeter/submillimeter Array (ALMA) Band 3 (97.5 GHz) full Stokes observations of GRB 190114C, beginning at 2.2 hr after the burst and lasting for 3 hr, together with the Karl G. Jansky Very Large Array (VLA) observations spanning 4.7–6.3 hr after the burst. Our data reveal the first polarization detection⁹ at radio or millimeter frequencies. By combining the radio, millimeter, optical, and X-ray observations, we demonstrate that the mm-band flux is dominated by an RS, which allows us to constrain the magnetic field geometry in the outflow powering this burst. We assume Ω_m = 0.31, Ω_λ = 0.69, and H₀ = 68 km s⁻¹ Mpc⁻¹. All times are relative to the Swift trigger time and in the observer frame, unless otherwise indicated.

2.1. Gamma-Ray, X-Ray, and Optical

2.2. Radio: VLA

2.3. ALMA Polarization Observations

We obtained ALMA observations of GRB 190114C beginning 2.2 hr after the burst through program 2018.1.01405.T (PI: T. Laskar) in full linear polarization mode in Band 3, with two 4 GHz-wide basebands centered at 91.5 and 103.5 GHz, respectively. Weather conditions were excellent during the observation. The calibration sources were selected by ALMA, employing J0423-012 as flux density, bandpass, and polarization leakage calibrator, and J0348-274 as complex gain calibrator. The gain calibrator-source cycle time was ≈12 minutes, with 10.5 minutes on source, 30 s on the gain calibrator, and the remaining time used for slewing between the two. The scheduling block was repeated three times in succession in order to achieve sufficient parallactic angle coverage to simultaneously derive the instrumental polarization and the Stokes parameters of the leakage calibrator, with parallactic angle coverage on the leakage calibrator spanning ≈90°.

2.3.1. ALMA Data Analysis

We processed the ALMA data using CASA (McMullin et al. 2007), employing standard techniques (Nagai et al. 2016). In summary, following bandpass calibration, we computed the complex gain solutions on the polarization calibrator. We used these solutions to estimate the intrinsic Stokes parameters of the polarization calibrator, followed by the cross-hand delays, the XY-phase offset, and the calibrator's intrinsic polarization. We resolved the phase ambiguities in the Stokes parameters of the calibrator using the estimates derived from the gain calibration, and revised the gain solutions on the polarization calibrator. The ratio of the parallel hand (XX/YY) gains is uniform and within ≈2% of unity for all antennas after polarization calibration, while the rms gain ratio is uniform across antennas at the ≈1.2% level. The leakage (D-terms) were found to be at the ≈1% level for individual antennas, as expected for the ALMA 12 m array (Nagai et al. 2016).

We used flux density values of (4.15 ± 0.08) mJy at 91.5 GHz and (3.89 ± 0.06) mJy at 103.5 GHz for J0423-012 from the ALMA calibrator catalog, to which we fit a power-law model to fix the flux density scale for each channel. We subsequently calibrated the remainder of the data set using standard interferometric techniques (flux density and gain), and generated Stokes IQUV images of the calibrators and the target, as well as an image of the total linear polarization, .

The mm-band afterglow is clearly detected in Stokes I, with a signal-to-noise of ≈580, allowing us to divide the source data set into individual scans. We fit for the flux density of the source in the image plane using imfit. The derived flux density values are listed in Table 1. The mm afterglow fades by ≈40% between 2.2 and 5.2 hr after the burst (Figure 1; top panel).

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2.3.2. Measurement of Polarization and Validation Against Potential Instrumental Effects

The P image of GRB 190114C reveals a point source with flux density 61 ± 14 μJy (undebiased) at a position consistent with the position in the Stokes I image (Figure 2). The rms noise level in the Stokes QUV images is ≈10 μJy. We split the uv data into the three individual runs of the scheduling block, and re-imaged the target. The detection in the first P image is 6.6σ (statistical), and the polarized intensity declines by ≈50% over the course of the observation (Figure 1; bottom panel). The limit on Stokes V is 30 μJy, corresponding to a formal 3σ limit on circular polarization of Π_V < 0.3% (statistical only) relative to the mean Stokes I; however, the 1σ systematic circular polarization calibration uncertainty is ≈0.6%.

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We plot the values of Stokes Q and U, measured by fixing the position and beam parameters using the Stokes I image, in Figure 3. A rotation in the plane of polarization is apparent from the Stokes QU images. As images of P are biased for faint sources, we do not measure P from images of polarized intensity, but rather from the measured QU values directly using a Monte Carlo method. We generate 10⁵ random realizations from the individual Q and U measurements and calculate , the polarization angle, , and the fractional linear polarization, Π = P/I. For the latter, we incorporate the uncertainty in the measurement of Stokes I. We plot the derived distributions of P, χ, and Π in Figures 3 and 4, and list the median and standard deviations of the distributions in Table 2.

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Table 2.  ALMA Band 3 (97.5 GHz) Polarization Measurements of GRB 190114C

Time	Q	σQ	U	σU	P	σP	χ	σχ	Π	σΠ
(days)	(μJy)	(μJy)	(μJy)	(μJy)	(μJy)	(μJy)	(deg)	(deg)	(%)	(%)
0.114	89.5	14.6	32.0	15.3	96.3	14.6	9.8	4.6	0.87	0.13
0.154	55.9	14.5	−33.4	14.8	66.7	14.4	−15.4	6.6	0.76	0.16
0.202	1.84	14.5	−41.1	14.6	43.7	14.0	−43.7	11.7	0.60	0.19

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On applying the polarization calibration to the gain calibrator J0348-274, we find that drift in the linear polarized intensity of the calibrator is ≲0.15%, while its measured polarization angle is stable at the ≲1% level over the course of the 3 hr observation (Figure 4; bottom panel). Both values are within the specifications of ALMA Cycle 6 polarization observations.

One possible manifestation of any errors arising from leakage calibration is a scattering of flux density in the Stokes QU images away from the phase center. We check this by imaging the gain calibrator, which appears as a point source; observed secondary peaks in both Stokes Q and U images are ≲0.5% of the peak flux, consistent with noise. We also imaged the upper and lower basebands separately for both the flux density calibrator, phase calibrator, and GRB 190114C. The polarization properties of both calibrators and of GRB 190114C are consistent between the two basebands and thus stable across ALMA Band 3.

As linear polarization observations are a non-standard mode for ALMA, the data were also calibrated and imaged by a data analyst (Erica Keller) at ALMA before delivery. We compared the results of our reduction with those from ALMA, and also by imaging the calibrated measurement set provided by the Observatory. All three sets of images yield results consistent within measurement uncertainty. These tests indicate that the detection of linearly polarization in GRB 190114C is unlikely to arise from a calibration artifact.

As the focus of this Letter is on the ALMA polarization observations, we defer a discussion of the full multi-wavelength modeling to a future work (T. Laskar et al. 2019, in preparation). To provide context for the polarization detection, here we consider the basic properties of the afterglow at ≲0.3 days, during the time of the ALMA observations. We interpret this under the standard synchrotron framework (Sari et al. 1998; Granot & Sari 2002), for a given isotropic equivalent kinetic energy, and circumburst density parameter n₀ (for a constant-density environment) and (for a wind-like environment with density, ). We assume that the radiation is produced by nonthermal electrons accelerated to a power-law distribution with energy index p, with a fraction of the post-shock internal energy given to relativistic electrons and a fraction to magnetic fields. In this model, the observed SED is characterized by power laws connected at spectral breaks: the synchrotron self-absorption frequency (), the characteristic synchrotron frequency (), and the cooling frequency (), and is completely specified by the location of these break frequencies and the overall flux density normalization ().

3.1. Optical and X-Rays: Circumburst Density Profile

3.2. Radio and Millimeter: RS

The radio SED at 0.2 days comprising the VLA cm-band and ALMA mm-band data (Figure 5) can be fit with a broken power-law model, transitioning from β = 2 (fixed) to β = 0.3 ± 0.2 at ν_break = 24 ± 4 GHz. In addition, the mean Stokes I intra-band spectral index between the two ALMA basebands at 91.5 and 103.5 GHz is ≈−0.4, implying that the mm-band emission is optically thin at this time. The optical to mm-band spectral index of β_mm-opt = −0.24 ± 0.01 between the GROND K-band observation and the ALMA detection at 0.16 days is inconsistent with a single power-law extrapolation from the optical.¹² This shallow slope cannot be caused by the location of between the radio and optical bands¹³ because all light curves at should be flat in the wind model (or rising in the interstellar medium (ISM) model), while the ALMA light curve is declining over this period. Thus, the radio and mm-band emission arises from a separate component than that responsible for the X-ray and optical emission. We note that a similar radio-to-X-ray spectral index of β_radio,opt ≈ −0.25 in the case of GRB 130427A indicated the presence of an RS in that system (Laskar et al. 2013). The early optical r'-band light curve declines as α_opt = −1.4 ± 0.1 between the MASTER observation at ≈6 × 10⁻⁴ days¹⁴ and the NOT observation at ≈2 × 10⁻² days, flattening to between the NOT observation and the GROND observation at 0.16 days (Figure 5). The steep optical light curve at ≲2 × 10⁻² days can also not be explained as FS emission.

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We find that propagating the excess emission component dominating the radio and mm-band data at ≈0.2 days earlier, using the RS light curve evolution from Zou et al. (2005) and the SED shape from Laskar et al. (2013), can explain the optical observations at days, provided and for this component (Figure 5). This matches a Newtonian RS with¹⁵ , which is higher than expected for the wind environment but not unprecedented (Laskar et al. 2013, 2016, 2018a; Perley et al. 2014). The parameters for the FS that match the X-ray and optical light curves at ≲0.3 days are p ≈ 2.36, , , , erg, and A_V ≈ 2.2 mag. For these parameters, the FS is fast cooling until ≈0.2 days, with the spectral ordering for the FS at 10⁻² days. However, we note that we do not locate and thus the model parameters are subject to some degeneracies (possibly explaining the high value of ). We defer a more complete analysis of the FS and the joint RS–FS dynamics to future work.

We now derive constraints on the magnetic field structure in the jet using our polarization measurement. The low level of measured linear polarization in the mm-band,¹⁶ Π ∼ 0.6–0.9%, rules out an ordered transverse magnetic field (B_ord) in the ejecta with an angular coherence length θ_B ≳ 1/Γ, where Γ is the Lorentz factor of the emitting region, as such a field would produce a polarization of several tens of percent (Granot 2003; Granot & Königl 2003; Lyutikov et al. 2003). We now consider scenarios where the received radiation is a superposition of distinct emission components in regions comprising a transverse ordered field (B_ord) on the one hand, and a random (B_rand) magnetic field (Granot & Königl 2003) on the other. Such a scenario might correspond to co-located field components such as a shocked ISM with an ordered upstream field compressed at the FS and a random shock-generated B_rand, or to the superposition of emission from two distinct regions, e.g., a dominant B_ord in the shocked ejecta and a dominant B_rand in the shocked ISM. In such scenarios, Π and χ depend on the ratio of the intensities of synchrotron radiation due to the two magnetic field components, , and thus can vary with time (Granot & Königl 2003). However, the significant change in χ we measure would require comparable polarized intensities from the two components, with a ratio varying on the dynamical time. This is not easy to realize at , and where the 97.5 GHz light curve is dominated by RS emission, and thus such scenarios are disfavored.

Next, we consider a model where the observed polarization is the sum of emission from intrinsically polarized but mutually incoherent patches, each with a magnetic field ordered over a typical angular scale, θ_B (Granot & Königl 2003; Nakar & Oren 2004; Granot & Taylor 2005). In this model the visible region, θ ∼ 1/Γ_ej, around the line of sight gradually increases as the jet decelerates. The number of patches contributing to the observed emission is given by . In general, the ejecta lags behind the FS and Γ_ej ≲ Γ_sh; however, a Newtonian RS does not significantly decelerate the ejecta (Kobayashi 2000). For g ≈ 3 and k = 2, we have (Granot & Taylor 2005). Taking from Fermi/GBM¹⁷ , at the time of our mm-band polarization measurement. At this time, the Lorentz factor of the fluid shocked by the FS, (Granot & Sari 2002), so that Γ_ej ≈ 15.

The maximum degree of polarization, Π₀ = (1–β)/(5/3–β), where β is the spectral index (Granot & Taylor 2005). Because the ALMA band is near the peak of the SED (Figure 5), we take , yielding Π₀ ∼ 0.6. The observed polarization is a random walk of N steps in the QU plane, with , which implies θ_B ∼ Π/(Γ_ejΠ₀) ≈ 10⁻³. The uncertainty on this estimate from the signal-to-noise of the measurement of Π is ≈15%; however, larger systematic uncertainties arise from the approximations used in the RS dynamics as well as the stochastic nature of the 2D random walk.

In this model, the polarization angle is expected to vary randomly over the dynamical timescale as new patches enter the visible region. The mm-band light curve spans a factor of ≈2.2 in time. During this period, Γ_sh declines from ≈34 to ≈28 from our afterglow model and Γ_ej declines from ≈16 to ≈11. Assuming θ_B remains constant, the number of emitting patches increases by a factor of ≈2 over this period, which may be sufficient to change the average χ as we observe. Whereas we expect fluctuations in Π over this period, our measurements do not have sufficient signal-to-noise to resolve such variations (Figure 3).

Finally, we note that the gradual change observed in χ rules out any globally axisymmetric magnetic field configuration, regardless of our viewing angle and of the jet's exact axisymmetric angular structure; for example: (i) a global toroidal magnetic field (Lazzati et al. 2004; Granot & Taylor 2005); and (ii) an axisymmetric jet viewed from an angle θ_obs > 0 from its symmetry axis together with a shock-produced random magnetic field B_rand that is symmetric around the local shock normal (tangled in three dimensions on angular scales ≪ 1/Γ, with some non-negligible degree of anisotropy, as a locally isotropic field would produce no net polarization), as in this case the direction of polarization is expected to remain constant well before the jet break time (Ghisellini & Lazzati 1999; Sari 1999; Granot & Königl 2003).

We present the first detection and measurement of the temporal evolution of linearly polarized emission in the radio/millimeter afterglow of a GRB, and validate that our measurement does not arise from a calibration artifact. Our detection constitutes the first measurement of a polarized RS signature at radio or millimeter frequencies. The degree of linear polarization decreases from Π = (0.87 ± 0.13)% to Π = (0.60 ± 0.19)% from 2.2 to 5.2 hr after the burst, and the polarization position angle rotates from χ = (10 ± 5)° to χ = (−44 ± 12)° over this period. The smooth variation in χ rules out axisymmetric models such as a global toroidal field in the GRB jet. If the emission arises from small patches of coherent magnetization, then the size of these regions is constrained to θ_B ≈ 10⁻³ radian. Future work on GRB 190114C that evaluates the degeneracies in the FS parameters and compares the derived properties of the forward and reverse shocks to infer the dynamics of the jet, may refine these parameters. ALMA polarimetric observations of a sample of GRBs will reveal whether sub-percent levels of polarization are ubiquitous, thus constraining global jet models.

We thank Mark Lacy and Robert Laing for helpful discussions, Erica Keller at ALMA for providing the calibrated measurement sets for a verification of the science results, and the anonymous referee for feedback. This Letter makes use of the following ALMA data: ADS/JAO.ALMA#2018.1.01405.T. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. VLA observations for this study were obtained via project 18A-088. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. K.D.A. acknowledges support provided by NASA through the NASA Hubble Fellowship grant #HST-HF2-51403.001 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. J.G. and R.G. are supported by the Israeli Science Foundation under grant No. 719/14. The Berger Time-Domain Group at Harvard is supported in part by NSF under grant AST-1714498 and by NASA under grant NNX15AE50G. R.B.D. acknowledges support from the National Science Foundation under grant 1816694. This work makes use of data supplied by the UK Swift Science Data Centre at the University of Leicester and of data obtained through the High Energy Astrophysics Science Archive Research Center On-line Service, provided by the NASA/Goddard Space Flight Center.