ASYMMETRIES IN SN 2014J NEAR MAXIMUM LIGHT REVEALED THROUGH SPECTROPOLARIMETRY

SN 2014J was discovered by Fossey et al. (2014) on 2014 January 21.805 (UT) in the nearby starburst galaxy M82. The distance to the galaxy as determined by Dalcanton et al. (2009) is $D=3.5\pm 0.3$ Mpc, making SN 2014J the closest SN Ia in several decades. Early Palomar Transient Factory spectra showed that SN 2014J followed a similar evolution to SNe such as SN 2011fe, but with slightly higher ejecta velocities (Goobar et al. 2014). The authors noted, however, that strong attenuation at bluer wavelengths indicated that the SN was suffering from a significant amount of extinction along the line of sight. The maximum light Si ii λ6355 velocity, measured from the middle of the absorption line, was ${v}_{\mathrm{Si}{\rm{II}},0}=-{\rm{12,000}}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (Marion et al. 2015), placing SN 2014J slightly inside the Wang et al. (2009) high-velocity (HV) classification (the HV group is defined as having ${v}_{\mathrm{Si}{\rm{II}},0}\lt -{\rm{11,800}}\,\mathrm{km}\,{{\rm{s}}}^{-1}$), which is a proxy for the velocity gradient when spectroscopic sampling is sparse. However, using their spectra from [−0.4, +9.1] days, Marion et al. (2015) found a velocity gradient $\dot{v}=42\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{day}}^{-1}$, placing SN 2014J in the low velocity gradient (LVG) group of Benetti et al. (2005). Foley et al. (2014) measured a peak brightness ${B}_{\max }=11.85\pm 0.02$ mag on $\mathrm{JD}=\mathrm{2,456,690.5}\pm 0.2$ and a decline rate parameter ${\rm{\Delta }}{m}_{15}{(B)}_{\mathrm{obs}}=0.95\pm 0.01\,\mathrm{mag}$ (both values uncorrected for reddening).

The intrinsic colors of SNe Ia are believed to be nearly homogeneous with a slight dependence on light-curve shape (Phillips et al. 1999). Based on this assumption, the extinction law of an SN is generally determined by comparing the observed colors or spectra to unreddened standards. The low R_V value exhibited by highly extincted SNe Ia would imply that the interstellar dust along the line of sight has a small average grain size if the extinction is dominated by ISM dust (Whittet 1992). However, Wang (2005) showed that these low values can possibly be explained by dust in a circumstellar environment scattering and reddening the SN light. Simulations by Goobar (2008) later showed that scattering and reddening could give rise to a power-law wavelength-dependent extinction law of the form ${A}_{\lambda }\sim {\lambda }^{p}$. They found a good fit to the heavily extinguished SN 2006X if LMC-like grains, described by a power $p=-2.5$, are confined within a circumstellar shell of ${R}_{\mathrm{CSM}}={10}^{16}\,\mathrm{cm}$ (Goobar 2008). By comparison, their simulations show that Galactic dust follows a shallower extinction law with $p=-1.5$.

Due to its proximity, SN 2014J was well studied in UV–optical–NIR wavelengths, and the wavelength dependence of the extinction law has been analyzed by a number of groups. Goobar et al. (2014) and Amanullah et al. (2014), using similar optical and NIR photometry, determined that a simple (one-parameter) reddening law characterized by ${R}_{V}\sim 1.4$ due to ${A}_{V}\sim 1.7\mbox{--}1.9\,\mathrm{mag}$ of extinction could adequately match their data. This was achieved by artificially reddening SN 2011fe, which was not thought to be affected by much extinction, with a Milky-Way-like extinction law, while allowing $E(B-V)$ and R_V to vary. Equally consistent with the Amanullah et al. (2014) data set was a power-law model with an index $p=-2.1$. The photometric and spectroscopic measurements of Foley et al. (2014) were also inconsistent with a reddening law characterized by R_V = 3.1. Additionally, they found that a multiple-component extinction model gave an overall better fit to their spectroscopic data of SN 2014J than with either a simple reddening or circumstellar model alone. Their best-fit model included interstellar dust with properties (${R}_{V}=2.59\pm 0.02$) similar to some lines of sight in the Milky Way (Cardelli et al. 1989) and a circumstellar component that scattered light similar to the LMC. However, Johansson et al. (2014) did not find an IR excess in 3.6 μm and 4.5 μm Spitzer data, which placed limits on ${M}_{\mathrm{dust}}\lt {10}^{-5}\,{M}_{\odot }$ within 10¹⁷ cm of the explosion and thus argued against the circumstellar medium (CSM) scattering models. Optical and UV photometry obtained with Swift also conclude that SN 2014J's extinction is due to interstellar dust since the light curves are well matched by a reddened SN 2011fe template without the need for invoking CSM scattering (Brown et al. 2015). Similar results were found with an extended data set between 0.2 and 2 μm (Amanullah et al. 2015).

An independent measure of host galaxy extinction is possible through high-resolution absorption spectra, which reveal weak interstellar features. Atomic and molecular lines, as well as diffuse interstellar bands (DIBs), are found in the spectrum of SN 2014J at velocities that arise within the gas of M82 (Welty et al. 2014). The equivalent width (EW) of the DIB 5780 Å, in particular, has been shown to be a proxy for host galaxy ISM reddening (Phillips et al. 2013, and references within). The strength of this DIB along the line of sight to SN 2014J gives an estimate of ${A}_{V}\sim 1.95\,\mathrm{mag}$ for the visual extinction (Welty et al. 2014). Therefore, nearly all of the extinction measured by SN 2014J photometry can be accounted for with interstellar dust.

Temporal variations detected in some high-resolution spectra of SNe Ia have been proposed as evidence of CSM near the SN explosion (Patat et al. 2007). The width and intensity of the Na i doublet lines of SN 2006X were found to vary with time between −2 and +61 days after maximum light. The authors proposed that the evolution in the line profiles was caused by the ionization of the CSM by UV radiation of the SN, which slowly recombines with time. The gas near the SN that undergoes ionization could be due to successive nova eruptions or from the stellar wind of a red giant companion star. Variability of the Na i lines does not seem to be a common property of SNe Ia because only 3 of 17 SNe Ia with multi-epoch high-resolution spectra have shown changes in the EW of their Na i lines (Patat et al. 2007; Simon et al. 2009; Dilday et al. 2012; Sternberg et al. 2014). Variability was also detected in SN 1999cl using low-resolution spectra (Blondin et al. 2009). The ability to detect these variations, however, depends on the window of observations and the geometry of the CSM. Foley et al. (2014), who had the most complete sample of high-resolution spectra in the weeks around maximum light, did not see any changes in the Na i lines of SN 2014J between −10 and +18 days after the peak brightness. Maeda et al. (2016) confirmed these results with a data set that extends to 255 days after maximum and find that all of the Na D absorptions arise in interstellar dust ∼40 pc in the foreground.

The detection of a light echo near the explosion sites of some SNe Ia is also considered to be evidence of CSM. Whether CSM light echoes have been detected is the subject of current debate. SN 1998bu was shown to have two echoes at distances $\lt 10$ pc and at 120 pc from the SN; the former has been argued to be created by circumstellar dust (Garnavich et al. 2001). A more extended echo was present in SN 2006X, leading to estimates of a cloud of dust located at $27\mbox{--}170$ pc (Wang et al. 2008b). This was hinted to at least have a partial local origin, although see Crotts & Yourdon (2008) for an alternate analysis. Light echoes in SN 2014J were first discovered by Crotts (2015), with further analysis of the light echo expansion presented by Yang et al. (2015). The authors find a luminous inner arc created by a foreground dust sheet at 222 pc and a faint outer ring consistent with foreground dust at 367 pc. Multiple inner echoes are also seen at smaller radii, indicating a complex ISM within M82.

Optical and NIR broadband polarization of SN 2014J showed a degree of polarization that decreased quickly from shorter to longer wavelengths, with a peak in polarization at a much shorter wavelength than typically measured by Galactic stars (Kawabata et al. 2014). The authors proposed that the majority of the polarization was due to interstellar dust in M82 since the polarization angle was nearly constant across the spectrum. The wavelength dependence of the broadband measurements was better fit with an inverse power law than a Serkowski curve, which underestimated the IR polarization by 0.2%–0.3%. They concluded that this unusual behavior suggests that the polarizing dust grains of M82 have mean radii $\lt 0.1\,\mu {\rm{m}}$. These results were echoed by Patat et al. (2015) using spectropolarimetry of SN 2014J at day +1.

Here we present multiple epochs of optical spectropolarimetry of SN 2014J from maximum light to 111 days past-maximum with the paper organized as follows. In Section 2 we present the details of our observations and data reduction process. In Section 3, we discuss our estimate of the ISP and its implications for the dust of M82. We discuss the ISP-subtracted intrinsic polarization of SN 2014J in Section 4. In Section 5 we explore how the polarization of SN 2014J compares to other SNe before summarizing our conclusions in Section 6.

To determine the intrinsic polarization of the SN's ejected layers, we must first derive the contribution from aligned dust grains within the ISM, known as ISP. We present the polarization of Epoch 4, 51 days after maximum light, in Figure 1. The average continuum polarization declines monotonically from $\sim 7 \%$ at 4000 Å to ∼2% at 7500 Å. Earlier spectra that are closer to maximum light show a very similar level of continuum polarization, but have a strong modulation near 6150 Å, as seen in Figure 2, which is associated with line polarization intrinsic to the SN. Later spectra at +77, +104, and +106 days have a lower signal-to-noise ratio than Epoch 4, so we do not use them to determine the level of ISP.

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Both the Milky Way and the SN's host galaxy may contribute an ISP component to the observed continuum polarization. There are no Galactic stars within a 2° box centered on the SN with polarization measurements to the best of our knowledge (Heiles 2000). However, the highest degree of polarization measured for a star at a similar Galactic latitude to M82 is 0.76%, with 0.24% being the average among 17 stars with comparable latitudes. Therefore, we conclude that the Milky Way's contribution to the ISP is small in comparison to the polarization along the line of sight to SN 2014J. Hoffman et al. (2005) note that due to the vector nature of polarization, even if the Milky Way ISP is small compared with that of the SN, its contribution may cause a position angle rotation if the vector alignment is unfavorable. Using the ratio of the highest degree of polarization for a Galactic star noted above to the average polarization observed near 4500 Å in Epoch 4, we find that the intrinsic polarization angle of SN 2014J could differ by as much as $3\buildrel{\circ}\over{.} 9$ from what we observe (Hoffman et al. 2005, Equation (1)).

Our approach to estimating the host galaxy's ISP contribution is to wait until the ejecta has become optically thin to electron scattering during the SN's nebular phase. At this point any residual polarization is expected to be contributed by intervening dust. Because the spectrum shows a sharply decreasing degree of polarization with wavelength, a single value of q and u cannot properly describe the ISP. Instead, the wavelength dependence of the polarization spectrum, if due completely to the linear dichroism of interstellar dust, can be captured by fitting the data with the empirical Serkowski relation

$$\begin{eqnarray}&&{P}_{\mathrm{ISP}}(\lambda )={P}_{\max }\,\exp \left(-K\,\,{\mathrm{ln}}^{2}\,\,\displaystyle \frac{{\lambda }_{\max }}{\lambda }\right),\end{eqnarray} \tag{ 1 }$$

where ${\lambda }_{\max }$ is the wavelength at which the polarization reaches a maximum, P_max, while K controls the width of the curve (Serkowski et al. 1975). The relationship was determined from the optical polarization of Galactic stars, and typical values are ${\lambda }_{\max }=0.55\,\mu {\rm{m}}$ and a curve width dependent on ${\lambda }_{\max }$ such that $K=0.01\pm 0.05+(1.66\pm 0.9)\,{\lambda }_{\max }$, where ${\lambda }_{\max }$ is given in $\mu {\rm{m}}$ (Whittet et al. 1992). Because the peak in the degree of polarization of SN 2014J appears to be $\lt 0.4\,\mu {\rm{m}}$, as evident in Figure 1, the derived parameters will likely be peculiar. Our least-squares fitting routine yields $K=0.40\pm 0.03,$ ⁷ ${\lambda }_{\max }=0.0456\pm 0.1052\,\mu {\rm{m}}$, and ${P}_{\max }=45.04 \% \pm 30.56 \%$. Our values agree well with the results of Patat et al. (2015) even though we use a polarization spectrum obtained 50 days later. However, our results are not as easily compared to the broadband measurements, as Kawabata et al. (2014) held K fixed to fit their polarization, which was averaged over five epochs between −11 and +33 days.

It has been proposed that the wavelength dependence of the polarization is related to the extinction law through the relation ${R}_{V}\simeq 5.5{\lambda }_{\max }$ (Serkowski et al. 1975). The low ${\lambda }_{\max }$ value derived from polarization implies a low R_V consistent with photometric and spectroscopic estimates (Foley et al. 2014). However, near-ultraviolet (NUV) and optical photometry of M82 shows evidence of a 2175 Å bump in the galaxy's NUV color–color plots, suggesting that this particular galaxy may be more comparable to the Milky Way than other starburst galaxies, which often do not show the bump in their extinction laws (Hutton et al. 2014). In a further analysis of this photometry, which was taken in the years before the explosion of SN 2014J, the dust at a projected distance of 1 kpc from the nucleus, the same distance as the SN (Foley et al. 2014), has an ${R}_{V}\sim 3\mbox{--}4$ (Hutton et al. 2015). This is obviously in contrast to the low values of R_V measured after the explosion (Amanullah et al. 2014; Foley et al. 2014; Goobar et al. 2014). However, we note that Figure 5 in Hutton et al. (2015) displays a large range in selective extinction values near this distance.

Light that encounters dust located at interstellar distances from the SN acquires polarization through linear dichroism. The polarization angle in this case aligns with the magnetic field direction of the galaxy in which the grains are aligned. The polarization signal of scattering dust in the circumstellar environment, however, will be due to photons scattered into the line of sight. The perpendicular electric field vectors for dust distributed symmetrically about the line of sight would cancel completely, similar to an unresolved symmetric SN envelope (Höflich 1991). Therefore, to measure a net linear polarization, there must be some asymmetry in the dust's overall geometry, which will be reflected in the associated polarization angle.

To demonstrate how circumstellar dust may be present in their polarization spectrum, Patat et al. (2015) applied a multicomponent fit to their +1-day spectropolarimetric data of SN 2014J composed of a Serkowski curve for interstellar dust and a Rayleigh scattering component that dominates at short wavelengths. They find a respectable fit using K = 1.15 (held fixed), ${\lambda }_{\max }=0.35\,\mu {\rm{m}}$, and $P{(\lambda )={P}_{s}(0.4\mu {\rm{m}}/\lambda )}^{4}$ with ${P}_{s}=0.8{P}_{\max }$. From their Figure 6, we estimate ${P}_{\max }\sim 3.8 \%$, which gives ${P}_{s}=3.0 \%$ for the scattering component. Additionally, scattering contributes $\sim 40 \%$ of the total polarization at $0.4\,\mu {\rm{m}}$.

Because Patat et al. (2015) use a spectrum near maximum light, their fit may include a small level of intrinsic continuum polarization attributed to electron scattering in the SN ejecta. Later observations are less likely to have an intrinsic SN component, so we present a similar fit to our +51-day epoch in Figure 1. We find that our data are well described with ${\chi }^{2}=1.45$ using K = 1.15, ${\lambda }_{\max }=0.35\,\mu {\rm{m}}$, ${P}_{\max }=3.5 \%$, and ${P}_{s}=3.3 \%$, with scattering dominating at wavelengths less than $0.395\,\mu {\rm{m}}$. The scattering also contributes about 56% of the total polarization in our fit. We chose to hold K and ${\lambda }_{\max }$ fixed to decrease the number of free parameters by using the original K value presented by Serkowski et al. (1975) and ${\lambda }_{\max }$ chosen to represent one of the bluest peaks observed in the Milky Way (See Appendix). It is important to note that our fit in Figure 1 is just for illustrative purposes as a number of decompositions could potentially describe the observed polarization. For comparison, the multicomponent fit of Patat et al. (2015) gives a ${\chi }^{2}=2.42$ to our Epoch 4 data and is even worse, ${\chi }^{2}=7.01$, when compared to our maximum light epoch.

Additionally, we find an average angle of $\theta =39^\circ \pm 1.78$ between 5000 and 7000 Å in Epoch 4, which is in agreement with the earlier-epoch polarization measurements of Kawabata et al. (2014) and Patat et al. (2015). Greaves et al. (2000) determined that a 40° angle describes the magnetic field structure of M82, thus suggesting that if there is circumstellar dust polarizing light by scattering, the dust must be oriented nearly identical to the dust lanes of M82 (Patat et al. 2015). Hoang (2015) discussed a toy model that may be able to explain the lack of change in angle. If small grains that undergo Rayleigh scattering are trapped within an accretion disk aligned in the magnetic equatorial direction of the white dwarf and the magnetosphere of the star contains a size distribution of grains reminiscent of the Galaxy, the polarization vectors that emerge from the two grain populations will be parallel. However, Hoang (2015) mentions that these dust grains will likely be swept away within $1\mbox{--}2$ hr after the explosion, depending on the ejecta velocity, and therefore are not expected to be observable at the epochs of polarization we discuss here. We note that because the contribution of the small Milky Way ISP may rotate the observed polarization angle by as much as $3\buildrel{\circ}\over{.} 9$ from its intrinsic value (see Section 3.1), this makes it more likely that such an apparent alignment between the circumstellar dust of the SN and the ISP of M82 could occur by simple chance.

We have presented both the results of fitting a Serkowski function that assumes transmission through dust of a single distribution and the results of a two-component model that includes transmission through dust and a scattering component. However, because there are concerns with adopting either scenario, we also present a low-order polynomial fit to the rotated Stokes parameters (RSPs) of q_RSP and u_RSP of Epoch 4. We use the fits to determine the nonvarying ISP and in turn the SN's intrinsic polarization. We note that this prescription for determining the ISP from a late epoch makes use of the assumption that the continuum polarization is null as a result of the ejecta that is optically thin to electron scattering.

The rotated parameters are derived by revolving the $q\mbox{--}u$ plane through an angle θ such that all of the continuum polarization then lies along q_RSP, while u_RSP represents deviations from the dominant axis (Trammell et al. 1993; Leonard et al. 2001). Presenting the SN's intrinsic P as the rotated quantities allows us to avoid the high level of bias that accompanies the traditional determination of P through $P=\sqrt{{q}^{2}+{u}^{2}}$ and also avoid the problems caused by the asymmetric error distribution of P for low signal-to-noise data in the debiased formula $P=\pm \sqrt{| {Q}^{2}+{U}^{2}-\tfrac{1}{2}({\sigma }_{Q}^{2}+{\sigma }_{U}^{2})| }$ (Wardle & Kronberg 1974).

To calculate the RSP, we use the form ${q}_{\mathrm{RSP}}=q\,\cos \,2\theta +u\,\sin \,2\theta$ and ${u}_{\mathrm{RSP}}=-q\,\sin \,2\theta +u\,\cos \,2\theta$ and use the mean polarization angle derived between 5000 and 7500 Å in Epoch 4 as our θ since the angle is nearly constant over all epochs. We then subtract the following best-fit polynomials from the rotated observed Stokes vectors:

$$\begin{eqnarray}{q}_{\mathrm{ISP}} & = & 4.57-17.10(\lambda -0.5\,\mu {\rm{m}})+27.10{(\lambda -0.5\mu {\rm{m}})}^{2},\\ {u}_{\mathrm{ISP}} & = & -0.004-0.008(\lambda -0.5\,\mu {\rm{m}}),\end{eqnarray} \tag{ 2 }$$

and the remainder is considered to be intrinsic to the SN. The statistical uncertainties on the coefficients of the q_ISP polynomial are, respectively, 0.02, 0.28, and 1.12, while the uncertainties on the u_ISP fit are 0.013 and 0.090.

We binned the observed polarization as high as 47 Å to check for any variability in the continuum polarization among the various epochs and find none, as shown in Figure 2. We quantify the lack of variability in two ways. First, we fit a power law of the form $P{(\lambda )=c(\lambda /0.55\mu {\rm{m}})}^{-\beta }$ to the spectrum of each epoch prior to ISP subtraction and find that the fits are in good agreement with each other. Additionally, the best-fit $K-{\lambda }_{\max }$ we derive from fitting the Serkowski curve to each epoch lies within the 4σ confidence contour drawn relative to Epoch 4's best fit (see Figure 10). Although there is some scatter in the best-fit $K-{\lambda }_{\max }$ with time, the degrees of polarization defined by these curves at 5500 Å all agree within $\sim 0.01 \%$. If circumstellar dust is present at close enough distances to the SN, we expect the polarization to change as the dust is evaporated by radiation, which would in turn change the grain size distribution as small grains disappear. Calculations by Amanullah & Goobar (2011) find that sublimation will deplete dust that resides at $r\leqslant {10}^{16}\,\mathrm{cm}$, which is nearly equivalent to 4 lt-day. This is prior to all of our spectropolarimetric observations, so it is not surprising that we do not see variability in the degree of polarization among our epochs. Therefore, we assume that the ISP remains constant and does not change with time, allowing the same ISP correction to be applied to each epoch of observation.

Assuming that the continuum polarization is defined by a region of the spectrum that is free of strong lines, we measure the average continuum between 6600 and 7400 Å in Epochs 1–4 to have an intrinsic polarization of 0.09% ± 0.07%, 0.01% ± 0.17%, 0.14% ± 0.17%, and 0.03% ± 0.07%, respectively. Therefore, all epochs are consistent with zero polarization. This low value is in agreement with other normal SN Ia measurements, which typically show $\lt 0.3 \%$ polarized continua light (Wang & Wheeler 2008). The subluminous SNe Ia SN 1999by and SN 2005ke and the normal SN 2011fe have shown higher detections of 0.5%–0.7% (Howell et al. 2001; Patat et al. 2012; P. Milne et al. 2016, private communication). The small degree of continuum polarization indicates that globally the photosphere is nearly spherically symmetric and is consistent with less than 10% deviation from a perfect sphere (Höflich 1991).

Near maximum light, changes in the polarization degree are clearly detected at the Si ii λ6355 line. Figure 7 shows the first two epochs' degree of polarization in velocity space. In Epoch 1, the polarization in q_RSP rises to a peak near $-{\rm{14,000}}\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Furthermore, a broad depression in the u_RSP spectrum forms from $-{\rm{14,500}}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ to $-4000\,\mathrm{km}\,{{\rm{s}}}^{-1}$ across the Si ii line. Meanwhile, the continuum has an average u_RSP value of 0.08% ± 0.07% at this epoch. We use the u_RSP spectrum to quote a polarization measurement for Si ii at this epoch and find an average ${P}_{\mathrm{Si}{\rm{II}}}=0.54 \% \pm 0.05 \%$ between $-{\rm{13,500}}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and $-9500\,\mathrm{km}\,{{\rm{s}}}^{-1}$. We also note that the Si ii polarization peaks near the line's absorption minimum, which we measure to be at $-{\rm{11,000}}\,\mathrm{km}\,{{\rm{s}}}^{-1}$.

In the following epoch at +7 days, the peak in q_RSP has increased to $0.46 \%$ at $-{\rm{14,000}}\,\mathrm{km}\,{{\rm{s}}}^{-1}$, but this value decreases to 0.32% ± 0.13% if averaged over $-{\rm{15,000}}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ to $-{\rm{12,000}}\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Meanwhile, the feature in u_RSP has grown more complex with three dips present over the same wavelength range as Epoch 1. We measure a peak polarization level of 0.37% ± 0.05% between $-{\rm{10,000}}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and $-7000\,\mathrm{km}\,{{\rm{s}}}^{-1}$.

The importance of obtaining spectropolarimetric data to learn details about the ejecta distribution is showcased by Figure 7. The flux profile of the Si ii line shows only minor changes between the first and second epochs; however, the polarization profiles have evolved significantly. McCall (1984) predicted that the polarization profile should peak at an absorption line's minimum since the absorbing ejecta blocks the direct, unpolarized light from the photosphere along the line of sight. We see this in Epoch 1, where the peak in u_RSP occurs nearly in alignment with the absorption trough. With the evolution in the polarization profile in Epoch 2, we see that the asymmetry in the line has changed with the line depth in the ejecta as the fastest and the slowest material are now nearly just as polarized as the line center. The absorption trough's polarization has also decreased significantly between the two epochs from $0.63 \%$ to $0.26 \%$ at the same velocity slice, indicating that the more direct light from the photosphere is not being absorbed as readily as a week prior.

In the last two epochs analyzed at +23 and +51 days, the Si ii feature is no longer detected in the polarization spectra (see Figures 5 and 6). By +23 days, the Si ii λ6355 feature is still present in the flux spectrum, but Fe ii has begun encroaching on the wings and a combination of Fe ii, Co ii, and Cu ii is present between 6100 and 6800 Å at +51 days (Vallely et al. 2016). With the lack of Si ii in both the flux and polarization spectra, it is not surprising that the polarization angle no longer shows smooth changes across this region of the spectrum. In general, the angle has become more erratic because the error in polarization angle is very large when the degree of polarization is nearly zero.

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Overall, the spectropolarimetric evolution of SN 2014J is similar to previous SN Ia observations and theory (Wang & Wheeler 2008). Line polarization is typically visible near maximum light and often at levels less than 1%. Earlier measurements showed line polarization that peaked before maximum; however, SN 2014J joins a growing sample of SNe Ia that peak later (see Figure 9). In the weeks following maximum light, the photosphere recedes deeper into more uniform ejecta, or the regions of asymmetric material become optically thin, causing the line polarization to fade with time. This often occurs within 2 weeks after the light-curve peak, but one SN Ia has shown repolarization of the Ca ii NIR lines nearly 40 days after maximum (Patat et al. 2009). Zelaya et al. (2013) also report levels of 2%–4% for the Ca ii NIR triplet of SN 2007sr at +63 days. Earlier measurements are not available, so it is not clear whether this is a repolarization of the line.

Although the polarized spectra are useful for comparing the levels of polarization of different SNe Ia, investigating the data on the $q\mbox{--}u$ plane is often more enlightening. Figure 8 shows the q_RSP and u_RSP polarization for the range 5900–6400 Å, which includes the Si ii absorption line. Each data point corresponds to a q_RSP–u_RSP vector pair with the wavelength represented by the symbol's color. In the first epoch, the Si ii feature forms a loop as the u_RSP polarization steadily increases from the blue toward the middle of the line and then begins to decrease toward the red. The middle of the absorption trough shows the highest degree of polarization, extending just beyond the 0.5% level depicted as a dashed line. Moving to the second epoch, the complex nature of the u_RSP spectrum can be seen here as well, as three loops form past the $0.25 \%$ polarization circle. Finally, by the third and fourth epochs, when we are unable to definitely identify the Si ii polarization, the loop behavior has diminished as well.

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Loops in the q–u plane occur as the polarization angle rotates on the sky. If the distribution of Si ii were axisymmetric, the ${q}_{\mathrm{RSP}}\mbox{--}{u}_{\mathrm{RSP}}$ vector pairs would arrange themselves in a straight line on the plane. The presence of a loop, rather than a linear collection of points, suggests that the distribution of Si ii is not axisymmetric throughout the ejecta. Similar loop features have been found in a number of SNe Ia such as SN 2001el (Wang et al. 2003), SN 2004S (Chornock & Filippenko 2008), SN 2009dc (Tanaka et al. 2010), and SN 2011fe (P. Milne et al. 2016, private communication). Kasen et al. (2003) used parameterized models to explore possible origins of the HV Ca ii loop of SN 2001el. Either an ellipsoidal shell rotated with respect to the photosphere or large-scale clumpy matter could create the change in polarization angle. Both of these scenarios would partially block polarized light of the underlying continuum, leading to line polarization.