LIMITS ON OPTICAL POLARIZATION DURING THE PROMPT PHASE OF GRB 140430A

On 2014 April 30, at ${t}_{0}=20:33:36\;\mathrm{UT},$ the Burst Alert Telescope (BAT; Barthelmy et al. 2005) on board the Swift satellite triggered on the long GRB 140430A and immediately slewed to the burst (Siegel et al. 2014). The BAT gamma-ray LC shows a multi-peaked structure with two intense peaks: the first one starts at approximately $-10\;{\rm{s}}$ and ends at $\sim 10\;{\rm{s}},$ and the second softer one starts at $\sim 140\;{\rm{s}}$ and ends at $\sim 200\;{\rm{s}}$ post trigger. There are at least two slightly fainter and softer peaks centered at $\sim 25\;{\rm{s}}$ and $\sim 575\;{\rm{s}}.$ The T₉₀ (15–350 keV) of $174\;\pm 4\;{\rm{s}},$ fluence (15–150 keV) of $1.1\pm 0.2\times {10}^{-6}\;\mathrm{erg}\;{\mathrm{cm}}^{-2}$, and time-averaged spectrum power-law index Γ of 2.0 ± 0.2 (Krimm et al. 2014) put this GRB toward the long-soft end of Swift GRBs (Sakamoto et al. 2011). Fitting the BAT time-averaged spectrum with a typical Band function assuming α = −1 and β = −2.3 gives ${E}_{\mathrm{peak}}^{\mathrm{obs}}\sim 20\;\mathrm{keV}$ and, moving to $1-{10}^{4}\;\mathrm{keV}$ in the host rest frame at a redshift of z = 1.6, gives an isotropic-equivalent energy of ${E}_{\gamma ,\mathrm{iso}}=(1.3\pm 0.4)\times {10}^{52}\;\mathrm{erg}.$

The Swift X-ray Telescope (XRT; Burrows et al. 2005) began follow-up observations at $50.8\;{\rm{s}},$ while gamma-ray emission was still ongoing. A bright and uncataloged fading X-ray source has been detected at R.A.(J2000) = 06^h51^m446, decl.(J2000) = +23°01'25'' with an enhanced 90% confidence uncertainty of 19 (Evans et al. 2014). The X-ray LC at early times is dominated by at least three bright flares, centered at 154, 171, and 222 s, as seen in Figure 1. The first two flares track the gamma-ray LC both temporally and in brightness (see Figures 1 and 3). The last flare is followed by a steep decay. From $\sim 500$ to $\sim 3900\;{\rm{s}}$ a data gap in X-ray is due to the Earth limb constraint. At later times, the X-ray LC shows a decay until $\sim {10}^{5}\;{\rm{s}}.$

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When transforming the X-ray LC obtained from the XRT LC repository (Evans et al. 2009) from flux to flux density units, we took into account strong spectral evolution at early times and by assuming a power-law spectrum with a given spectral index for each point (see Figure 5), we calculated the flux density at $10\;\mathrm{keV}$ by integrating the energy spectrum in the 0.3–10 keV interval. At later times, we instead assumed an average spectral index for every point (see Section 3.1).

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The Swift Ultraviolet/Optical Telescope (UVOT; Roming et al. 2005) began observing the GRB field at $183\;{\rm{s}}$ and found a candidate afterglow at the position consistent with the XRT, with estimated magnitude in the UVOT White filter of $18.17\pm 0.09\;\mathrm{mag}$ (Breeveld & Siegel 2014).

LT responded to the Swift GRB alert automatically and started observations with the RINGO3 instrument at 20:35:40 UT, i.e., 124 s after the BAT trigger (Melandri et al. 2014). Fast response to the trigger resulted in obtaining the optical observations contemporaneously with the ongoing gamma-ray and X-ray emission during high-energy flares at early times (Figure 3). Observations continued for the next hour, during which the majority of the observations were performed with RINGO3, with a $6\times 10\;{\rm{s}}$ sequence of IO:O observations with an SDSS r' filter inserted at $\sim 33\;\mathrm{minutes}$ to allow for real-time afterglow identification during the observations.

RINGO3 is a novel three-band fast-readout optical imaging polarimeter, which uses a polaroid that rotates once per second. By analyzing relative intensities at eight different orientations of the polaroid, the polarization for each source in the image can be measured, while summing the data from all rotation angles allows derivation of the total flux of each source. Short $125\;\mathrm{ms}$ exposures and zero read-out noise allows optimization of frame co-adding in the data post-processing stages. In addition, a light entering the instrument and passing the rotating polaroid is split into three beams using a pair of dichroic mirrors, and simultaneously imaged using 3 separate EMCCD cameras. The wavelength bands¹⁵ are determined by dichroics: V ranges from ∼350 to 640 nm, R ranges from ∼650 to 760 nm, and I ranges from ∼770 to 1000 nm. The transmittance and response in the UV and IR parts of these bands is further affected by the camera quantum efficiency. On average, the wavelength bands are approximately equivalent to the VRI Johnson-Cousins photometric system. The wavelength range covered is largest for the V-equivalent band, thereby providing the highest signal-to-noise ratio (S/N) of the three cameras.

Data from RINGO3 were automatically stacked to produce frames with 10 and $60\;{\rm{s}}$ exposures. Frames were cleaned using the Singular Spectrum Analysis decomposition procedures (Golyandina et al. 2015), to remove vignetting and fringing. All together, the LT data set originally consisted of 65 frames in each of the three color bands. To enhance S/N at later times when the afterglow brightness was below $\sim 18\;\mathrm{mag},$ frames with $60\;{\rm{s}}$ exposure were co-added from $\sim {10}^{3}\;{\rm{s}}$ onward.

Because no standard stars' fields were available for the night of the GRB observations, photometric calibration was performed relative to the magnitudes of five non-saturated USNO-B1.0 stars in the field, using standard aperture photometry procedures. USNO I cataloged magnitudes were used to calibrate the I-equivalent RINGO3 band, R2 magnitudes to calibrate the R-equivalent RINGO3 band, and approximated $V\sim 0.444\times B1+0.556\times R2$ magnitudes to calibrate the V-equivalent RINGO3 band.¹⁶  While USNO-B1.0 magnitudes provide relatively poor absolute photometric accuracy ($\pm 0.3\;\mathrm{mag}$), the photometric stability throughout the observations was very good as shown by the variability in zero points being $\lt 0.1\;\mathrm{mag}$ in each RINGO3 band.

The afterglow of GRB 140430A was observed by the following facilities.

The $0.6\;{\rm{m}}$ TELMA robotic telescope at the BOOTES-2 astronomical station at IHSM/UM-CSIC La Mayora, Spain (Castro-Tirado et al. 2012) started observing the afterglow with the COLORES imaging spectrograph at $30\;{\rm{s}}$ after the BAT trigger with ${r}^{\prime }$- and ${i}^{\prime }$-band filters. The detected peak magnitude was ${r}^{\prime }\;\sim$ 16.1 mag. Due to poor observing conditions, the observations resulted in poor image quality. Nevertheless, we could extract the ${r}^{\prime }$-band magnitude for two early epochs, which are represented in Figure 2. The first epoch is marginally contemporaneous with the second gamma-ray peak in BAT LC. Due to the significantly poorer temporal sampling of BOOTES data compared to the later optical data, we did not include the BOOTES points in the subsequent detailed LC analysis.

IAC-80 $0.82\;{\rm{m}}$ telescope (Observatorio del Teide) observed the afterglow between 25.0 and $40.9\;\mathrm{minutes},$ providing a $3\times 300\;{\rm{s}}$ sequence of observations in BVR-band filters (Gorosabel et al. 2014).

OSN $1.5\;{\rm{m}}$ telescope (Observatorio de Sierra Nevada) observed the afterglow between 6.7 and $78\;\mathrm{minutes},$ providing 280 frames all together in I band, while gradually extending the exposure time from 5 to $60\;{\rm{s}}.$ To enhance signal-to-noise at early times, we coadded the frames to similar binning as the LT frames, while at late times we used $240\;{\rm{s}}$ binning.

STELLA-I $1.2\;{\rm{m}}$ robotic telescope (Observatorio del Teide) observed the afterglow between 2.9 and $32.5\;\mathrm{minutes}$ in the r' band filter, providing 52 frames with $20\;{\rm{s}}$ exposure times. To enhance the signal-to-noise, we coadded the frames to $60\;{\rm{s}}$ binning at early times and to $120\;{\rm{s}}$ binning at late times.

The 10.4 m Gran Telescopio Canarias (GTC) telescope observed the afterglow at ∼3.5 × 10³ s, obtaining an optical spectra with the OSIRIS imaging spectrograph (Cepa et al. 2000). Data was reduced and calibrated the usual way using IRAF and custom tools coded up in python. We clearly detect several absorption lines, from which a redshift $z=1.600\pm 0.001$ is derived, consistent with Krühler et al. (2014).

Frames from IAC, OSN, and STELLA telescopes have been calibrated against the same USNO-B1.0 stars and in the same manner as the LT frames. The resulting LCs are plotted in Figure 3. Comparison between data points from the RINGO3 instrument (using dichroics) and data points from other telescopes (using standard filters) confirms that RINGO3 bands are well approximated by the VRI-equivalent photometric system. All calibrated magnitudes were later corrected for the Galactic extinction of ${E}_{B-V}=0.12\;\mathrm{mag}$ in the direction of the burst (Schlafly & Finkbeiner 2011), and converted to flux densities using Fukugita et al. (1996). The complete photometry is available in Table 4.

The X-ray LC shows strong variability and rapid flaring activity at early time. Flaring of the soft gamma-ray emission is also seen at this time, up to $\sim 200\;{\rm{s}}$ post burst, simultaneous with the X-ray flares and showing similar temporal structure in the LC (Figures 1 and 3). At the end of the steep X-ray decay phase at $\sim 500\;{\rm{s}},$ the X-ray data gap occurs due to Earth occultation and lasts until $4000\;{\rm{s}}.$ During this time, the X-ray LC indicates the likely presence of the canonical X-ray afterglow plateau phase (Nousek et al. 2006). From $4000\;{\rm{s}}$ to $\sim 1.3\times {10}^{5}\;{\rm{s}}$, the decay is best described by a broken power law with a poorly constraint break time ${t}_{{\rm{b}}}\sim 9700\;{\rm{s}},$ and with decay indices ${\alpha }_{1}=0.51\pm 0.32$ pre-break and ${\alpha }_{2}=0.85\pm 0.06$ post-break (${\chi }_{\mathrm{red}}^{2}=0.99$). The X-ray upper limit obtained at $4.6\times {10}^{5}\;{\rm{s}}$ is not consistent with a simple extrapolation of the late time decay, indicating the possible occurrence of a jet break after ${10}^{5}\;{\rm{s}}.$

The time-averaged spectrum formed from the early time data (Windowed Timing—WT mode, see Figure 1) can be well fitted with the absorbed power-law. Fixing the Galactic absorption column to ${N}_{\mathrm{HI}}^{\mathrm{Gal}.}=2.13\times {10}^{21}\;{\mathrm{cm}}^{-2}$ (Willingale et al. 2013), the resulting intrinsic absorption at z = 1.6 is ${N}_{\mathrm{HI}}^{\mathrm{Host}}=(3.4\pm 1.4)\times {10}^{21}\;{\mathrm{cm}}^{-2},$ and the power-law photon index of the spectrum is ${\rm{\Gamma }}=\beta +1=2.10\pm 0.04$ (Evans et al. 2009). All values are consistent with the late time data (Photon Counting—PC mode, see Figure 1).

To discuss the early time X-ray emission properties, we modeled the early X-ray LC with a combination of an underlying power-law decay and three superimposed bumps described by the Norris profile (Norris et al. 2005):

$$\begin{eqnarray}{F}_{{\rm{X}}}(t) & = & {F}_{0}{\left(\displaystyle \frac{t}{{t}_{0}}\right)}^{-{\alpha }_{\mathrm{decay}}}\\ & & +\displaystyle \sum _{i=1}^{3}{F}_{i}\mathrm{exp}\left(2\sqrt{\displaystyle \frac{{\tau }_{1,i}}{{\tau }_{2,i}}}\right)\;\mathrm{exp}\left(-\displaystyle \frac{{\tau }_{1,i}}{\tilde{t}}-\displaystyle \frac{\tilde{t}}{{\tau }_{2,i}}\right),\end{eqnarray} \tag{ 1 }$$

where F₀ is the power-law normalization factor and ${\alpha }_{\mathrm{dec}}$ is the overall power-law decay index, F_i  is a normalization constant of superimposed bumps, τ_1,i and τ_2,i are factors determining the shape of each bump, and $\tilde{t}$ is the time measured from the start of each bump as determined from LC. From parameters of Norris profiles for each bump, it is possible to obtain peak times as ${t}_{\mathrm{peak},i}=\sqrt{{\tau }_{1,i}{\tau }_{2,i}}$ and peak durations as ${\rm{\Delta }}{t}_{i}={\tau }_{2,i}\;\sqrt{1+4\sqrt{{\tau }_{1,i}/{\tau }_{2,i}}}$ (Norris et al. 2005). The results of fitting this model (Equation (1)) to early X-ray LC are presented in Table 1. We note that the second X-ray bump is poorly fitted with the Norris profile because the height of the peak is significantly above the fitted function (see Figure 1), but the obtained peak time and width are nevertheless reasonable.

Table 1.  Early X-Ray LC Best-fit (Power-law + 3 Norris Peaks) Parameters

Peak	Interval	Peak Time	Duration	Δ t/t	Δ F/F
	$({\rm{s}})$	${t}_{\mathrm{peak}}\;({\rm{s}})$	${\rm{\Delta }}t\;({\rm{s}})$
1	144–160	154.6 ± 1.7	18.7 ± 4.9	0.12	1.77
2	160–200	173.2 ± 0.8	22.0 ± 1.1	0.13	6.47${}^{*}$
3	200–496	218.5 ± 0.7	37.3 ± 1.0	0.17	11.42

Note. Peak times, durations, and flux ratios of three X-ray flares obtained from the early-time fit (see Section 3.1). The underlying power-law component has a decay index of ${\alpha }_{\mathrm{decay}}=4.3\pm 0.1.$ The ${\chi }_{\mathrm{red}}^{2}$ of the fit is ${\chi }_{\mathrm{red}}^{2}=1.19$ with 146 dof. ${}^{*}$ Because the fit underestimates the flux of the second peak (see the text), Δ F/F for the second peak could be larger by a factor of ∼2.

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Short variability timescales (Δt/t) and large amplitude variability (ΔF/F) of early time X-ray flares, as presented in Table 1, are commonly observed in early X-ray LCs for both long and short duration GRBs (Chincarini et al. 2010; Margutti et al. 2010, 2011; Bernardini et al. 2011).

Figure 3 shows the calibrated optical LC of GRB 140430A, which is complex and could not be described by a simple power-law behavior. Overall, the LC is qualitatively described by at least two long-lasting emission episodes joined by a plateau phase at $\sim 2000\;{\rm{s}}.$ The excellent temporal sampling at early time, however, reveals additional components.

We fitted optical LCs with phenomenological models as typically used in the literature for optical afterglows. Possible theoretical models will be discussed in Section 4. We used a combination of two Beuermann profiles (B), i.e., smoothly connected broken power-laws (Beuermann et al. 1999; Guidorzi et al. 2015a), for broad components, and (following Krühler et al. 2009) two Gaussian profiles (G) corresponding to early time flares:

$$\begin{eqnarray}F(t) & = & \displaystyle \sum _{i=1}^{2}{B}_{i}\times \displaystyle \frac{1+{\alpha }_{{\rm{R}},{\rm{i}}}/{\alpha }_{{\rm{D}},{\rm{i}}}}{{(t/{t}_{{\rm{P}},{\rm{i}}})}^{-{\alpha }_{{\rm{R}},{\rm{i}}}}+({\alpha }_{{\rm{R}},{\rm{i}}}/{\alpha }_{{\rm{D}},{\rm{i}}}){(t/{t}_{{\rm{P}},{\rm{i}}})}^{{\alpha }_{{\rm{D}},{\rm{i}}}}}\\ & & +\displaystyle \sum _{j=1}^{2}{G}_{j}\times \mathrm{exp}\left(\displaystyle \frac{-{(t-{t}_{{\rm{P}},{\rm{j}}})}^{2}}{2{\sigma }_{j}^{2}}\right),\end{eqnarray} \tag{ 2 }$$

where B_i and G_j are normalization constants, t_P are peak times, ${\alpha }_{{\rm{R}}}$ are rise indices, and ${\alpha }_{{\rm{D}}}$ are decay indices. Parameters σ_j from Gaussian profiles can be connected with the overall duration of the bump as ${\rm{\Delta }}t\approx 2\times \mathrm{FWHM}\approx 2\times 2\sqrt{2\mathrm{ln}2}\sigma .$ Note that we fixed the smoothing parameter from a more general Beuermann equation to s = 1, due to not very well constrained peak shapes of broad Beuermann components (using s = 0.5 and s = 2 does not change results). We also note that the Gaussian description of the temporal profile is not physically motivated, but provides reasonable values of peak time and width.

We fitted all three wavelength bands simultaneously with different normalization factors for each color. For Beuermann profiles, we assumed common ${t}_{{\rm{P}},{\rm{i}}},$ ${\alpha }_{{\rm{R}},{\rm{i}}},$ and ${\alpha }_{{\rm{D}},{\rm{i}}},$ while, for Gaussian profiles, we assumed different ${t}_{{\rm{P}},\ {\rm{j}}}$ and σ_j for each color. We used the Levenberg–Marquardt algorithm, assuming that photometric uncertainties are normally distributed. The fitting method provides the best-fit values and 1σ uncertainties of free parameters (Table 2). The resulting ${\chi }^{2}=168$ with degrees of freedom (dof) = 125 has low P-value of $P=0.006,$ indicating that the model does not describe our complex data set well. Nevertheless, when testing different models by adding or removing Beuermann and/or Gaussian components, the fit did not improve and the residuals increased.

Table 2.  Optical LC Best-fit (2 Beuermann + 2 Gaussian) Parameters

Beuermann Peaks (Underlying Components):
Peak	Peak Time (s)	${\alpha }_{\mathrm{rise}}$	${\alpha }_{\mathrm{decay}}$	${F}_{{\rm{p}}}\;(\mathrm{mJy})$
1, V	∼260	3.37 ± 1.65	0.97 ± 0.12	0.420
1, R				0.507
1, I				0.569
2, V	∼2900	2.73 ± 0.44	0.79 ± 0.03	0.095
2, R				0.115
2, I				0.129
Gaussian Peaks (Early Time Flares):
Peak	Peak Time (s)	Duration (s)	Δ t/t	Δ F/F
1, V	168.4 ± 2.7	95.9 ± 21.1	0.57 ± 0.13	1.72
	${\alpha }_{\mathrm{rise}}=6.2$	${\alpha }_{\mathrm{decay}}=3.8$
1, R	166.5 ± 4.5	133.4 ± 25.8	0.80 ± 0.16	1.76
	${\alpha }_{\mathrm{rise}}=5.0$	${\alpha }_{\mathrm{decay}}=2.7$
1, I	170.6 ± 6.7	175.9 ± 31.1	1.03 ± 0.19	1.68
	${\alpha }_{\mathrm{rise}}=4.2$	${\alpha }_{\mathrm{decay}}=2.2$
2, V	239.7 ± 3.8	46.4 ± 23.2	0.19 ± 0.10	0.37
	${\alpha }_{\mathrm{rise}}=4.4$	${\alpha }_{\mathrm{decay}}=4.5$
2, R	257.8 ± 5.5	47.0 ± 26.9	0.18 ± 0.10	0.37
	${\alpha }_{\mathrm{rise}}=4.2$	${\alpha }_{\mathrm{decay}}=5.0$
2, I	259.3 ± 7.5	20.9 ± 17.5	0.08 ± 0.07	0.43
	${\alpha }_{\mathrm{rise}}=8.7$	${\alpha }_{\mathrm{decay}}=11.0$

Note. The fit was performed simultaneously in V, R, and I bands, with peak times, ${\alpha }_{\mathrm{rise}},$ ${\alpha }_{\mathrm{decay}}$ of the Beuermann profiles taken as common parameters among all three bands. Parameters for Gaussian profiles (peak time and width) were taken differently for each band. F_p is the flux density at the time of the peak for each of the two Beuermann profiles, and although the peak flux density is different for each band, we assumed a common flux density ratio between the first and the second Beuermann peak for all bands (the ratio obtained from the fit is 0.23 ± 0.03). Δt/t is calculated as duration divided by peak time. Δ F/F is calculated as the ratio between difference of flux density at the time of the Gaussian peak and flux density of the underlying Beuermann peak, divided by flux density of the underlying Beuermann peak. Based on Figure 4, estimates of the maximum power-law rise (${\alpha }_{\mathrm{rise}}$) and decay (${\alpha }_{\mathrm{decay}}$) indices for Gaussian peaks are also given for each optical band.

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To obtain additional information from the fitted model, especially the power-law rise and decay indices, both data and best-fit models are represented in differential plots in log–log scale (Figure 4). Although data show large scatter and relatively large uncertainties, which results in large scatter in the differential plot, the best-fit model shows that during the first optical flare the initial rising part power-law index is between ${\alpha }_{\mathrm{rise}}\sim 4$ and ${\alpha }_{\mathrm{rise}}\sim 6$ (depending on wavelength), followed by a decay with a power-law index between ${\alpha }_{\mathrm{decay}}\sim 2$ and ${\alpha }_{\mathrm{decay}}\sim 4.$ During the second optical flare, both rising and decaying indices are around ∼5 (the I-band fit is not very constraining for the second flare). The LC then shows more smooth behavior with a decaying power-law index ${\alpha }_{\mathrm{decay}}\sim 1$ from $\sim 300\;{\rm{s}}$ to $\sim {10}^{3}\;{\rm{s}}.$ We note that at that time, the afterglow has dimmed for more than $1.5\;\mathrm{mag}$ and photometric uncertainties, especially for RINGO3 frames due to low sensitivity, become larger, but OSN I-band and STELLA r'-band points, which are available at that time, are of much better quality and thus more constraining. The differential plot between ∼1000 and $\sim 3000\;{\rm{s}}$ thus shows a smooth transition from decay to a plateau phase, and then back to decay phase with a slightly shallower decay index ${\alpha }_{\mathrm{decay}}\sim 0.8.$

At early times, due to simultaneous sampling of the LC in three visible wavelength bands and in the X-ray band, we could study the temporal evolution of SED. The spectral index of the X-ray emission (${\beta }_{{\rm{X}}}$), obtained from the Swift Burst Analyser (Evans et al. 2010), can be compared to the power-law slope of the optical SED (${\beta }_{\mathrm{OPT}}$), obtained from fitting a power law to optical data points, or to the broadband optical to X-ray extrapolated spectral index (${\beta }_{{\rm{R}}-{\rm{X}}}$), obtained from fitting a power-law to optical R-band and contemporaneous X-ray ($10\;\mathrm{keV}$) flux densities. We neglected the contribution of host galaxy extinction in optical bands, due to its low upper limit (see the end of this section and Figure 6). SED evolution is presented in Figure 5.

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We see from Figure 5 (bottom panel) that at early times the X-ray spectral index is highly variable and that it tracks the X-ray LC throughout the flares. The hard-to-soft spectral evolution is observed. At the end of the last prominent X-ray flare at $\sim 240\;{\rm{s}}$ the X-ray emission becomes extremely soft (${\beta }_{{\rm{X}}}\sim 2.5$) during the steep decay phase, but then it hardens at later times, when flaring is no longer present, and stays around the value of ${\beta }_{{\rm{X}}}=1.10\pm 0.04,$ as obtained from the late time XRT spectral fit (Evans et al. 2009) and consistent with our late time SED fit (Figure 6).

The temporal evolution of optical to X-ray extrapolated index (${\beta }_{{\rm{R}}-{\rm{X}}}$) and optical spectral index (${\beta }_{\mathrm{OPT}}$) helps us understand if emission powering early time X-ray flares also manifests itself in the optical domain. The first thing that we notice is that at early times the variability of the spectral index in broadband optical to X-ray SED is not as prominent as in the X-ray alone. The emission tends to be harder at the beginning, changing to softer at later times (after $\sim 400\;{\rm{s}}$), when it is consistent with ${\beta }_{{\rm{X}}}.$

The temporal behavior of the optical spectral index (${\beta }_{\mathrm{OPT}}$) suggests some degree of variability at early times but it is difficult to quantify this given the uncertainties. The statistical significance of variations in ${\beta }_{\mathrm{OPT}}$ is low, as the constant fit to ${\beta }_{\mathrm{OPT}}$ over the time interval 140–450 s gives an acceptable fit of average spectral index ${\beta }_{\mathrm{OPT}}=0.97\pm 0.08,$ with reduced ${\chi }^{2}$ of 1.4 and P-value of 0.12. After $300\;{\rm{s}}$ the spectral index implied by the best fitting model converges to ${\beta }_{\mathrm{OPT}}\;=0.65\pm 0.06,$ while the variations implied by the RINGO3 data at later times become less constraining due to large uncertainties.

We built late time broadband SED at $\sim 3200\;{\rm{s}},$ when photometric data in four optical bands are available. We took X-ray data from the XRT spectra repository (Evans et al. 2009) in the time interval 3–30 ks, in which there is no spectral evolution. The mean time was computed as ${\sum }_{i}({t}_{i}{\rm{\Delta }}{t}_{i})/{\sum }_{i}{\rm{\Delta }}{t}_{i},$ where t_i is the mid-time of individual exposure and ${\rm{\Delta }}{t}_{i}$ is the exposure time. By knowing the temporal power-law slope, we normalized obtained flux densities to the epoch of optical observations. Using XSPECv12.8, we fitted the Milky Way, Large Magellanic Cloud, and Small Magellanic Cloud (SMC) average extinction curves (Pei 1992) to our data set, combined with a single or a broken power-law slope. The best fit was obtained using a broken power-law and SMC extinction profile, which is most common for GRB SEDs (e.g., Japelj et al. 2015 and references therein). By fixing the difference of power-law slopes to ${\rm{\Delta }}\beta =0.5$ and fixing ${N}_{{\rm{H}},{\rm{X}}}^{\mathrm{Gal}.}=2.13\times {10}^{21}\;{\mathrm{cm}}^{-2}$ (Willingale et al. 2013), we obtained the following best-fit parameters: ${\beta }_{1}={0.68}_{-0.14}^{+0.13},$ ${\beta }_{2}=1.18,$ ${\nu }_{\mathrm{break}}={160}_{-140}^{+800}\;\times {10}^{15}\;\mathrm{Hz},$ ${N}_{{\rm{H}},{\rm{X}}}\lt 8\times {10}^{21}\;\mathrm{cm}{\ }^{-2}$, and ${A}_{{\rm{V}}}\lt 0.14,$ with ${\chi }^{2}/{\rm{d}}.{\rm{o}}.{\rm{f}}=24.8/21.$ The resulting late time broadband SED is presented in Figure 6.

At the time of our measurements (2014 April 30th), the RINGO3 polarimeter was in the process of commissioning. The data were taken when the full sensitivity of the instrument was not reached, resulting in low S/N obtained from our measurement. Consequently, only the upper limits could be obtained for polarization degree P.

The polarimetry was done using standard RINGO procedures (D. M. Arnold et al. 2015, in preparation), similarly as for GRB 120308A (Mundell et al. 2013), by first correcting the obtained Stokes parameters for instrumental-induced polarization and then by correcting the obtained polarization degree for instrumental depolarization. Corrections are obtained from the analysis of a full set of polarimetric standard stars.

To correctly obtain the uncertainties ($\pm 1\sigma$) on the degree of polarization P, we performed a Monte Carlo simulation taking into account normal distributed photometric uncertainties in each of the eight polaroid orientations. By generating 100,000 simulated flux values, we calculated the corresponding normalized Stokes parameters "q" and "u" following Clarke & Neumayer (2002). By fitting a 2D normal distribution to "qu" plane, we obtained the mean "q" and "u" values and σ contours, which were then used to determine the upper limits on P. Figure 7 shows both the distribution of obtained P values from these simulations and the "qu" scatter plots, for the RINGO3 epoch from 124 to 244 s. The final values on polarization degree for GRB 140430A at various RIGNO3 epochs from 124 to 424 s are summarized in Table 3 .

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Table 3.  GRB 140430A Optical Polarization Results

Interval (s)	V-eq. Band	R-eq. Band	I-eq. Band
124–185	$\lt 19\%$	$\lt 19\%$	$\lt 14\%$
185–244	$\lt 20\%$	$\lt 16\%$	$\lt 16\%$
244–304	$\lt 22\%$	$\lt 12{\%}^{*}$	$\lt 22\%$
304–364	$\lt 23\%$		$\lt 17\%$
364–424	$\lt 17\%$	$\lt 20\%$	$\lt 10\%$
124–244${}^{*}$	$\lt 12\%$	$\lt 16\%$	$\lt 12\%$
	$3\sigma \lt 22\%$	$3\sigma \lt 30\%$	$3\sigma \lt 26\%$

Note. $1\sigma$ (unless stated otherwise) upper limits on early time optical polarization degree P from three RINGO3 cameras, in various time intervals. ${}^{*}$ indicates that data have been coadded in two time intervals, to obtain a better S/N.

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Table 4.  GRB 140430A: Photometry

tmid (s)	Exp (s)	Telescope	Band	Magnitude	${F}_{\nu }^{\mathrm{OPT}}$ (mJy)
139.4	10	LT	I	16.63 ± 0.17	0.696 ± 0.106
149.6	10	LT	I	16.48 ± 0.13	0.795 ± 0.095
159.8	10	LT	I	16.25 ± 0.13	0.985 ± 0.118
169.4	10	LT	I	16.04 ± 0.1	1.188 ± 0.113
179.6	10	LT	I	16.18 ± 0.11	1.044 ± 0.11
189.8	10	LT	I	16.33 ± 0.13	0.911 ± 0.107
199.4	10	LT	I	16.28 ± 0.14	0.959 ± 0.119
209.6	10	LT	I	16.16 ± 0.12	1.064 ± 0.118
219.2	10	LT	I	16.9 ± 0.26	0.551 ± 0.131
229.4	10	LT	I	16.44 ± 0.16	0.828 ± 0.118
249.2	10	LT	I	16.69 ± 0.16	0.657 ± 0.097
259.4	10	LT	I	16.39 ± 0.13	0.867 ± 0.107
269	10	LT	I	16.77 ± 0.15	0.607 ± 0.08
279.2	10	LT	I	16.58 ± 0.15	0.724 ± 0.1
289.4	10	LT	I	16.9 ± 0.22	0.547 ± 0.107
299	10	LT	I	16.77 ± 0.16	0.61 ± 0.089
334.1	60	LT	I	16.71 ± 0.08	0.637 ± 0.049
394.5	61	LT	I	16.91 ± 0.1	0.534 ± 0.05
454.7	60	LT	I	17.09 ± 0.15	0.453 ± 0.062
514.1	60	LT	I	17.17 ± 0.11	0.421 ± 0.044
574.1	60	LT	I	17.4 ± 0.13	0.34 ± 0.04
634.1	60	LT	I	17.54 ± 0.16	0.3 ± 0.044
692.9	57	LT	I	17.44 ± 0.14	0.328 ± 0.043
758.1	61	LT	I	17.51 ± 0.16	0.308 ± 0.044
818.3	60	LT	I	17.71 ± 0.18	0.258 ± 0.043
878.3	60	LT	I	17.49 ± 0.16	0.313 ± 0.045
938.3	60	LT	I	17.48 ± 0.15	0.317 ± 0.042
998.1	61	LT	I	17.78 ± 0.26	0.244 ± 0.057
1118.3	60	LT	I	18.28 ± 0.33	0.157 ± 0.046
1178.3	60	LT	I	17.74 ± 0.15	0.251 ± 0.035
1238.3	60	LT	I	17.76 ± 0.2	0.246 ± 0.046
1296.5	57	LT	I	17.53 ± 0.15	0.303 ± 0.042
1632.5	537	LT	I	17.87 ± 0.2	0.223 ± 0.041
2650.1	356	LT	I	18.14 ± 0.22	0.175 ± 0.035
3196.6	537	LT	I	18.05 ± 0.22	0.189 ± 0.037
427.8	55	OSN	I	17.1 ± 0.06	0.447 ± 0.026
513.8	60	OSN	I	17.23 ± 0.06	0.395 ± 0.023
585.9	60	OSN	I	17.31 ± 0.05	0.366 ± 0.018
658	60	OSN	I	17.38 ± 0.06	0.346 ± 0.019
730.3	60	OSN	I	17.53 ± 0.06	0.3 ± 0.016
855.9	60	OSN	I	17.76 ± 0.07	0.243 ± 0.015
929.7	60	OSN	I	17.75 ± 0.06	0.246 ± 0.014
1037.9	120	OSN	I	17.85 ± 0.06	0.224 ± 0.012
1182.1	120	OSN	I	17.93 ± 0.06	0.208 ± 0.012
1326.4	120	OSN	I	17.98 ± 0.06	0.198 ± 0.011
1471.1	120	OSN	I	17.96 ± 0.06	0.202 ± 0.011
1615.4	120	OSN	I	17.98 ± 0.06	0.198 ± 0.011
1760.1	120	OSN	I	17.9 ± 0.06	0.214 ± 0.011
1904.9	120	OSN	I	17.89 ± 0.06	0.216 ± 0.011
2121.2	240	OSN	I	17.89 ± 0.06	0.215 ± 0.012
2416.9	240	OSN	I	17.92 ± 0.06	0.21 ± 0.011
2713.1	240	OSN	I	17.9 ± 0.06	0.213 ± 0.011
3002.8	240	OSN	I	18.04 ± 0.06	0.188 ± 0.01
3289.9	240	OSN	I	18.13 ± 0.06	0.173 ± 0.01
3555	230	OSN	I	18.2 ± 0.06	0.162 ± 0.009
3808.7	240	OSN	I	18.24 ± 0.06	0.156 ± 0.009
4064.6	240	OSN	I	18.2 ± 0.06	0.161 ± 0.009
4313.5	210	OSN	I	18.2 ± 0.06	0.163 ± 0.009
4553.9	240	OSN	I	18.31 ± 0.06	0.147 ± 0.008
37.8	16	BOOTES	r'	16.14 ± 0.15	1.711 ± 0.235
79.8	17	BOOTES	r'	16.48 ± 0.14	1.25 ± 0.16
139.4	10	LT	R	17.19 ± 0.18	0.545 ± 0.088
149.6	10	LT	R	16.73 ± 0.12	0.827 ± 0.093
159.8	10	LT	R	16.82 ± 0.15	0.762 ± 0.104
169.4	10	LT	R	16.46 ± 0.09	1.056 ± 0.09
179.6	10	LT	R	16.66 ± 0.12	0.881 ± 0.096
189.8	10	LT	R	16.87 ± 0.12	0.73 ± 0.082
199.4	10	LT	R	16.79 ± 0.12	0.786 ± 0.087
209.6	10	LT	R	16.93 ± 0.15	0.693 ± 0.094
219.2	10	LT	R	17.09 ± 0.19	0.597 ± 0.102
229.4	10	LT	R	17.33 ± 0.24	0.483 ± 0.105
249.2	10	LT	R	17.02 ± 0.15	0.635 ± 0.088
259.4	10	LT	R	17 ± 0.15	0.648 ± 0.089
269.6	10	LT	R	17.09 ± 0.14	0.596 ± 0.079
279.2	10	LT	R	17.21 ± 0.17	0.534 ± 0.083
289.4	10	LT	R	17.08 ± 0.16	0.603 ± 0.09
299	10	LT	R	17.18 ± 0.18	0.549 ± 0.092
334.1	60	LT	R	17.5 ± 0.11	0.408 ± 0.039
394.5	61	LT	R	17.47 ± 0.1	0.418 ± 0.038
454.7	60	LT	R	17.49 ± 0.11	0.413 ± 0.042
514.7	60	LT	R	17.68 ± 0.12	0.345 ± 0.037
574.1	60	LT	R	17.78 ± 0.12	0.315 ± 0.033
634.1	60	LT	R	17.78 ± 0.12	0.314 ± 0.035
692.9	57	LT	R	18.19 ± 0.16	0.217 ± 0.033
758.1	61	LT	R	18.01 ± 0.12	0.254 ± 0.029
818.3	60	LT	R	18.04 ± 0.14	0.248 ± 0.032
878.3	60	LT	R	18.61 ± 0.22	0.148 ± 0.029
938.3	60	LT	R	18.21 ± 0.16	0.214 ± 0.03
998.7	61	LT	R	18.29 ± 0.2	0.199 ± 0.036
1118.3	60	LT	R	18.33 ± 0.2	0.191 ± 0.034
1178.3	60	LT	R	18.51 ± 0.23	0.164 ± 0.034
1238.3	60	LT	R	18.4 ± 0.18	0.18 ± 0.029
1296.5	57	LT	R	18.22 ± 0.15	0.211 ± 0.029
1632.4	597	LT	R	18.34 ± 0.16	0.188 ± 0.027
2610	478	LT	R	18.32 ± 0.17	0.193 ± 0.029
3215.1	597	LT	R	18.53 ± 0.21	0.159 ± 0.03
306.2	60	STELLA	r'	17.33 ± 0.06	0.476 ± 0.025
410.5	60	STELLA	r'	17.55 ± 0.05	0.386 ± 0.019
514.9	60	STELLA	r'	17.78 ± 0.05	0.312 ± 0.016
619.3	60	STELLA	r'	17.83 ± 0.05	0.299 ± 0.015
723.7	60	STELLA	r'	18.05 ± 0.06	0.243 ± 0.014
828.1	60	STELLA	r'	18.17 ± 0.07	0.218 ± 0.013
932.3	60	STELLA	r'	18.28 ± 0.09	0.198 ± 0.016
1088.8	120	STELLA	r'	18.35 ± 0.08	0.185 ± 0.013
1297.5	120	STELLA	r'	18.28 ± 0.07	0.197 ± 0.012
1506.3	120	STELLA	r'	18.35 ± 0.08	0.185 ± 0.014
1714.9	120	STELLA	r'	18.29 ± 0.09	0.195 ± 0.016
2001	30	LT-IO:O${}^{*}$	R	18.4 ± 0.1	0.177 ± 0.016
5240	100	NOT${}^{*}$	R	18.78 ± 0.02	0.125 ± 0.002
24516	600	VATT${}^{*}$	R	20.07 ± 0.03	0.038 ± 0.001
110916	1500	VATT${}^{*}$	R	21.7 ± 0.1	0.008 ± 0.001
3004.3	10	GTC	r'	18.62 ± 0.01	0.173 ± 0.002
3160.9	10	GTC	r'	18.62 ± 0.01	0.179 ± 0.002
2305.2	300	IAC	R	18.38 ± 0.03	0.179 ± 0.004
129	11	LT	V	18.2 ± 0.25	0.277 ± 0.062
139.4	10	LT	V	18 ± 0.18	0.331 ± 0.055
149.6	10	LT	V	17.54 ± 0.11	0.499 ± 0.05
159.8	10	LT	V	17.12 ± 0.08	0.732 ± 0.05
169.4	10	LT	V	17.11 ± 0.07	0.739 ± 0.048
179.6	10	LT	V	17.21 ± 0.08	0.677 ± 0.052
189.8	10	LT	V	17.21 ± 0.08	0.673 ± 0.051
199.4	10	LT	V	17.53 ± 0.1	0.504 ± 0.045
209.6	10	LT	V	17.72 ± 0.12	0.423 ± 0.048
219.2	10	LT	V	17.67 ± 0.14	0.444 ± 0.059
229.4	10	LT	V	17.53 ± 0.12	0.501 ± 0.056
249.2	10	LT	V	17.49 ± 0.11	0.52 ± 0.052
259.4	10	LT	V	17.68 ± 0.12	0.44 ± 0.046
269	10	LT	V	17.77 ± 0.11	0.404 ± 0.042
279.2	10	LT	V	17.84 ± 0.14	0.381 ± 0.048
289.4	10	LT	V	17.77 ± 0.1	0.404 ± 0.038
299	10	LT	V	17.73 ± 0.11	0.42 ± 0.044
334.1	60	LT	V	17.82 ± 0.07	0.384 ± 0.023
394.1	60	LT	V	17.79 ± 0.05	0.393 ± 0.019
453.9	61	LT	V	18.14 ± 0.09	0.286 ± 0.023
514.7	60	LT	V	18.31 ± 0.09	0.246 ± 0.021
574.1	60	LT	V	18.29 ± 0.08	0.249 ± 0.018
634.1	60	LT	V	18.53 ± 0.1	0.2 ± 0.019
692.9	57	LT	V	18.55 ± 0.11	0.197 ± 0.019
758.1	61	LT	V	18.34 ± 0.08	0.239 ± 0.017
818.3	60	LT	V	18.86 ± 0.14	0.148 ± 0.019
878.3	60	LT	V	18.67 ± 0.11	0.176 ± 0.017
938.3	60	LT	V	18.62 ± 0.09	0.185 ± 0.015
998.7	61	LT	V	18.59 ± 0.1	0.19 ± 0.018
1118.3	60	LT	V	18.72 ± 0.12	0.169 ± 0.018
1178.3	60	LT	V	18.77 ± 0.12	0.161 ± 0.018
1238.3	60	LT	V	18.81 ± 0.1	0.155 ± 0.014
1296.5	57	LT	V	18.89 ± 0.12	0.144 ± 0.015
1632.4	597	LT	V	18.81 ± 0.1	0.155 ± 0.015
2596.7	537	LT	V	18.69 ± 0.08	0.172 ± 0.013
3195.4	537	LT	V	18.76 ± 0.09	0.161 ± 0.013
1826.4	300	IAC	V	18.81 ± 0.03	0.155 ± 0.004
1647.6	300	IAC	B	19.24 ± 0.03	0.135 ± 0.004

Note. Magnitudes are not corrected for the Galactic extinction, while flux densities are. ${}^{*}$ indicates data obtained from GCN Circulars.

Download table as:  ASCIITypeset images: 1 2 3

We discuss the behavior of the LCs at early time in more detail and show that the initial optical flares appear to be more consistent with a prompt rather than afterglow origin.

4.1.1. Prompt Origin

4.1.2. Afterglow Origin

An alternative scenario for the first optical flare is emission from an external shock, possibly reverse-shock emission. Examining the temporal behavior and following Japelj et al. (2014), we neglected the second optical flare, normalized the optical LCs to a common band using normalization parameters from Table 2, and modeled the resultant data set with a set of reverse- plus forward-shock LCs, assuming a thin- or thick-shell limit and interstellar medium (ISM) environment of constant density (Kobayashi 2000; Zhang et al. 2003; Japelj et al. 2014; Figure 8). The values emerging from the best model are ${t}_{\mathrm{peak},\mathrm{FS}}\approx 444\;{\rm{s}},$ ${t}_{\mathrm{peak},\mathrm{RS}}\approx 162\;{\rm{s}},$ ${R}_{{\rm{B}}}\equiv {\epsilon }_{{\rm{B}},{\rm{r}}}/{\epsilon }_{{\rm{B}},{\rm{f}}}\approx 2.5,$ $p\approx 2.3,$ ${\epsilon }_{{\rm{e}}}\approx 0.2,$ ${{\rm{\Gamma }}}_{0}\sim 40,$ however, the modeling cannot sufficiently explain the data set, as indicated by the resultant residuals that suggest the presence of an additional emission component during the first optical peak. Another contradiction comes from the fact that the initial steep rise $\alpha \sim 5$ can only be explained by the thin-shell case, but the fact that the duration of the burst (${T}_{90}\sim 174\;{\rm{s}}$) is larger than the peak time of the optical emission strongly suggests the thick-shell case (Zhang et al. 2003). Furthermore, the initial rise is too steep to be explained by the reverse-shock from the wind-type environment (Kobayashi & Zhang 2003).

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A complementary test of external shock emission is that of color evolution. In the context of reverse shock emission, no color evolution is expected because the reverse shock peak is typically attributed to the change in dynamics of the ejecta, rather than due to the passage of the spectral break, unless these two events coincide. However, the combination of two peaks as presented in Figure 8 indicates that the forward shock peak should be due to the typical synchrotron passage, and a change in spectral index from $\beta =-1/3$ to $\beta =(p-1)/2$ is expected (Sari et al. 1998). Using the three-band optical data for GRB 140430A, we searched for color evolution around the optical peak times. As can be seen in Figure 5, no such color evolution as predicted by the theory is observed during the apparent forward shock peak.

Moreover, the origin of early optical peaks is not consistent with density fluctuations in the circumburst medium—changes in temporal slopes during the optical flares would require prohibitively high density fluctuations to explain them (Nakar & Granot 2007). In summary, we therefore favor an internal shock origin for the early optical flares, as described in Section 4.1.1.

After the initial flaring episode (after $300\;{\rm{s}}$), the optical emission shows decay with power-law index ${\alpha }_{\mathrm{decay}}\approx 1,$ which is consistent with the forward-shock afterglow origin. This is also supported by the late time broadband SED, which is best modeled using a broken power-law (see Section 3.3), with the difference of spectral indices ${\rm{\Delta }}\beta \approx 0.5,$ as expected for a cooling break (Sari et al. 1998). Due to a cooling frequency lying between optical and X-ray, one would expect that X-ray LC would decay steeper than optical, but this is not evident at late time, when X-ray and optical decay indices are comparable. The contradiction can be explained if the surrounding environment is not a constant ISM medium, but stratified medium with circumburst medium density given by $n=A\;{R}^{-k}$ (Chevalier & Li 2000). In this case, temporal decay indices for forward shock emission are given by ${\alpha }_{\mathrm{decay}}=-(3p(4-k)+5k-12)/(4(4-k))$ and ${\alpha }_{\mathrm{decay}}=-(3p-2)/4,$ before and after the cooling break, respectively. Similar temporal decay indices from different spectral regimes are thus possible in environments with $k\sim 4/3.$

At $\sim 2000\;{\rm{s}}$, the optical LC shows a transition from a power-law decline with ${\alpha }_{\mathrm{decay}}\sim 1$ to a plateau phase, followed by a power-law decline with ${\alpha }_{\mathrm{decay}}\sim 0.8$ (Table 2). Consistent power-law decline after the plateau phase is also obtained from the X-ray LC. This could be explained in the context of late time continued energy injection by a central engine (e.g., Rees & Mészáros 1998; Zhang & Mészáros 2002; Zhang et al. 2006). A shallower decay index after the plateau phase implies gradual and continuous energy injection. Following Sari & Mészáros (2000), we can estimate that the change in the optical decay slope of the forward shock corresponds to the change in the power-law exponent of the ejected mass distribution ($M(\gt \gamma )\propto {\gamma }^{-s}$) from $s\approx 1$ (instantaneous case) to $s\sim 2,$ which is typical for moderate continuous energy injection.

Density bumps or voids in the surrounding medium can produce bumps in the afterglow LCs (Uhm & Zhang 2014), but the decay index is expected to return to the same value as before the peak, which is not the case in this GRB (the difference is ∼0.2). Similarly, multi-component jets, together with a possibility that an outflow is seen slightly off-axis, can produce LCs with additional re-brightening (Kumar & Piran 2000), but if the circumburst environment stays of the same type, the LC behavior before and after the re-brightening should be similar.

GRB polarimetry offers a direct probe of the structure of magnetic fields within the emission region. Late-time optical measurements taken hours to days after the burst show low values of linear polarization of a few percent, consistent with synchrotron emission from a tangled magnetic field in the shocked ISM (e.g., Greiner et al. 2003; Lazzati et al. 2003; Wiersema et al. 2012, 2014). Circular polarization was recently detected at the $0.6\%$ level, which although small, is larger than expected theoretically (Wiersema et al. 2014). In contrast, measurements of the early afterglow, taken hundreds of seconds after the burst, when the properties of the original fireball are still encoded in the emitted light, can show high linear polarizations up to $30\%,$ particularly when a reverse shock can be identified in the LC—this is consistent with theoretical predictions for a large-scale ordered magnetic flow advected from the central engine (Steele et al. 2009; Uehara et al. 2012; Mundell et al. 2013).

High degrees of gamma-ray polarization ($P\;\sim$ 40%–60%) have been measured during the prompt emission for a number of GRBs, using dedicated instruments on INTEGRAL and IKAROS satellites (e.g., Götz et al. 2009, 2013, 2014; Yonetoku et al. 2012), despite the highly variable and peaked nature of prompt flares. The origin of the prompt emission is still unknown but these polarization levels suggest that magnetic fields play an important role. However, because gamma-ray polarization measurements are difficult to obtain, and often accompanied by large systematic uncertainties, the measurement of optical polarization at early times would provide additional constraints on the origin of the prompt emission.

GRB 140430A provides a unique opportunity, as its optical emission was detected during the ongoing prompt emission. The upper limits we derive on linear optical polarization in the very early afterglow (see Section 3.4) are relatively low at $P\;\lt$ 22%–30% ($1\sigma$) or $P\;\lt$ 22%–30% ($3\sigma$), during the first optical flare. The polarization limit of $P\lesssim 20\%$ ($1\sigma$) during the second optical flare is less constrained due to S/N limitations. If early time optical flares originate from within the internal shock region in the jet and if the jet is threaded with large-scale and ordered magnetic fields, we would expect the emission to be highly polarized (up to $60\%,$ depending on electron distribution). In contrast, the observed polarization could be reduced in a number of scenarios if (a) the magnetic field is tangled locally, (b) there exists a number of patches within a region of size $1/{\rm{\Gamma }}$ where the magnetic field is ordered locally but our viewing angle at the time of observation is already larger due to smaller Γ (e.g., Gruzinov & Waxman 1999; Granot & Königl 2003; Lyutikov et al. 2003), (c) there are multiple, unresolved but highly variable optical components that average temporally to a lower net value of polarization, or (d) emission from spatially distinct regions—such as internal shock and the external reverse shock regions (see discussion in Section 4.1)—each with high polarization but different position angles are observed simultaneously, resulting in an apparent lower total polarization degree.

In summary, the total degree of early time optical polarization for GRB 140430A measured during the high-energy X-ray and gamma-ray flares is lower than the commonly obtained levels of prompt gamma-ray polarization measurements of other GRBs and lower than that attributed to reverse-shock emission in GRB 120308A (Mundell et al. 2013). As described above, the intrinsic polarization of this GRB may be low or the vector averaging of different highly polarized components may explain the lower net observed polarization. Definitive interpretations of prompt gamma-ray emission will be possible when measurements of both prompt gamma-ray polarization and contemporaneous optical polarization are available for comparison in the same GRB.