Discovery and Follow-up Observations of the Young Type Ia Supernova 2016coj

Figure 3 shows our unfiltered light curve of SN 2016coj. In order to determine the first-light time t₀ (note that the SN may exhibit a "dark phase"), one can assume that the SN luminosity scales as the surface area of the expanding fireball, and therefore increases quadratically with time ($L\propto {t}^{2}$, commonly known as the t² model; Arnett 1982; Riess et al. 1999). The t² model fits well for several SNe Ia with early-time observations (e.g., SN 2011fe, Nugent et al. 2011 SN 2012ht, Yamanaka et al. 2014). Some studies also adopt a tⁿ model (n varies from ∼1.5 to ∼3.0; e.g., Conley et al. 2006; Ganeshalingam et al. 2011; Firth et al. 2015). Interestingly, Zheng et al. (2013, 2014) use a broken-power-law model to estimate the first-light time of SN 2013dy and SN 2014J. However, since our early-time photometric coverage of SN 2016coj is not as good as that of SN 2013dy and SN 2014J, we simply apply the t² model to fit the KAIT unfiltered data for the first few days (red solid circles in Figure 3); thereafter, the light curve starts deviating from the t² model. We also exclude Arbour's unfiltered detection (blue cross), considering the different response curve compared to the KAIT unfiltered data: Arbour's unfiltered band is closer to V (see Botticella et al. 2009), while KAIT's is closer to R (see Li et al. 2003).

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We find that the best t² model fit gives the first-light time to be MJD = 57531.33 ± 0.50, around May 23.33. Here the uncertainty (not including the "dark phase") is estimated by calculating the reduced ${\chi }^{2}$ ratio with the minimum reduced ${\chi }^{2}$ at a 90% confidence level, when t₀ changes around the best-fitted value while all the other parameters are fixed with the best-fitted value. Note that the uncertainty does not include any systematic error caused by the t² model fitting. For example, if we include (or exclude) one data point before and after the data set we used, the best-fit first-light time deviates −0.4 to 1.0 days from the above first-light time. Therefore, there could be a systematic error of up to 1.0 day from this method, which we did not include in the following analysis. Our results show that the first detection (from an image by R. Arbour) was merely 0.6 ± 0.5 days after first light, or 0.9 days from KAIT's first detection on May 24. This makes SN 2016coj one of the earliest detected SNe Ia—slightly later than SN 2013dy (∼2.4 hr after first light; Zheng et al. 2013) and SN 2011fe (∼11.0 hr after first light; Nugent et al. 2011), but similar to SN 2009ig (∼17 hr after first light; Foley et al. 2012).

Applying a low-order polynomial fit, we find that SN 2016coj reached a peak magnitude of 12.91 ± 0.03 at MJD = 57547.31 in KAIT unfiltered data. Although we do not present B-band data because no B-band template image is currently available, the fit allows us to determine the B-band peak time: MJD = 57547.35, similar to the result with unfiltered data. This means SN 2016coj was discovered only 4.9 days after the fitted first light, or 11.1 days before maximum light.

The distance modulus of the host galaxy NGC 4125 is quite uncertain (with a range of 30.04–32.80 mag) owing to different measurements (e.g., de Vaucouleurs & Olson 1984; Tully 1988; Willick et al. 1997; Blakeslee et al. 2001; Tonry et al. 2001; Humphrey 2009; Tully et al. 2013). However, some of them are outdated, or adopted an inappropriate H₀ value. The one with the smallest uncertainty (and also the latest estimate) is 31.90 ± 0.14 mag (Tully et al. 2013), which was based on ${H}_{0}=74.4$ km s⁻¹ Mpc⁻¹, quite close to the current widely accepted value of ${H}_{0}\approx 70$. We therefore adopt this distance for the following ananlysis. With $E{(B-V)}_{\mathrm{MW}}=0.02$ mag (Schlafly & Finkbeiner 2011) and very small (even negligible) host-galaxy extinction (see Sections 3.2 and 3.5), this implies that SN 2016coj has ${M}_{R}=-19.0\pm 0.2$ mag at peak brightness. Our preliminary measurement of B-band data, assuming the host background contamination is small, shows that the B-band peak is ∼13.1 ± 0.1 mag and ${\rm{\Delta }}{m}_{15}(B)=1.25\pm 0.12$ mag. This gives ${M}_{B}\approx -18.9\pm 0.2$ mag, but we expect ${M}_{B}\approx -19.1$ mag from the Phillips (1993) relation with the above value of ${\rm{\Delta }}{m}_{15}(B);$ thus, SN 2016coj is a normal-brightness SN Ia. Its ${\rm{\Delta }}{m}_{15}(B)=1.25\pm 0.12$ mag is also typical of normal SNe Ia (see also Section 3.3 for the spectral classification).

We obtained optical spectra of SN 2016coj nearly daily for a month (Figure 4), sometimes obtaining multiple spectra in a given night.

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We first examine the Na i D absorption feature in several of our high-S/N spectra. The Na i D absorption feature is often converted into reddening, but with large scatter over the empirical relationship according to Poznanski et al. (2011); they estimated a systematic scatter of 0.3 mag (1σ) in $E(B-V)$ with the relation of the Na i D absorption equivalent width. The absorption is not clearly detected at the Na i D wavelength for both the Milky Way component and the host-galaxy component. However, there appears to be a weak absorption feature consistent with the Milky Way Na i D wavelength. If real, this could be associated with the Milky Way extinction, which has $E{(B-V)}_{\mathrm{MW}}=0.02$ mag according to Schlafly & Finkbeiner (2011). Since we do not detect similar absorption at the host-galaxy wavelength of Na i D, we can put an upper limit of $E(B-V)\lesssim 0.02$ mag on host-galaxy extinction. However, if the weak absorption feature is caused by noise instead of Milky Way gas, we can determine an upper limit on $E(B-V)$ through comparison with our spectra of SN 2013dy (Zheng et al. 2013), where we clearly detect the Na i D absorption with the same instrument setting. For SN 2013dy, the equivalent width (W_λ) is ∼0.5 Å from both the Milky Way and host galaxy, giving $E(B-V)=0.15$ mag. Our similar-quality data on SN 2016coj should allow a detection of 1/3 (or less) of Na i D absorption if it exists, yielding an upper limit of $E(B-V)\lesssim 0.05$ mag of host-galaxy extinction. Lastly, we also estimate a $3\sigma$ upper limit on the W_λ of an undetected feature in a spectrum using the equation presented by Leonard (2007): ${W}_{\lambda }(3\sigma )=3{\rm{\Delta }}\lambda {\rm{\Delta }}I\sqrt{{W}_{\mathrm{line}}/{\rm{\Delta }}\lambda }\sqrt{1/B},$ where Δλ is the spectral resolution element (in Å), ${\rm{\Delta }}I$ is the 1σ root-mean-square fluctuation of the flux around a normalized continuum level, ${W}_{\mathrm{line}}$ is the full-width at half-maximum intensity (FWHM) of the expected line feature, and B is the number of bins per resolution element. For our high-S/N Kast spectra, we measure Δλ ≈ 4.0 Å), Δ ≈ 0.015, ${W}_{\mathrm{line}}\approx 12.0\,\mathring{\rm{A}}$, and B = 1, which gives ${W}_{\lambda }(3\sigma )\approx 0.3\,\mathring{\rm{A}}$, and $E(B-V)\lesssim 0.09$ mag of host-galaxy extinction.

All of the above suggests that the host-galaxy extinction of SN 2016coj is likely to be very small, consistent with the nondetection of Na i D absorption in our high-resolution spectra (see Section 3.5). However, note that since the Na i D versus extinction relation has large scatter, even a nondetection of Na i D does not fully exclude the possibility that there may be some dust along the SN line of sight.

The spectra show absorption features from ions typically seen in SNe Ia including Ca ii, Si ii, Fe ii, Mg ii, S ii, and O i. We do not find a clear C ii feature (e.g., Zheng et al. 2013), which is found in over one-fourth of all SNe Ia (e.g., Parrent et al. 2011; Thomas et al. 2011; Folatelli et al. 2012; Silverman & Filippenko 2012). Strong absorption features of Si ii, including Si ii λ4000, Si ii λ5972, and Si ii λ6355, are clearly seen in all spectra. The Si ii λ5972 feature in SN 2016coj is quite strong relative to those in SN 2012cg and SN 2013dy, though it is relatively small if compared with a large SN Ia sample (see Silverman et al. 2012c).

We measure the individual line velocities from the minimum of the absorption features (see Silverman et al. 2012c for details) and show them in Figure 5. The velocities of all Si ii features decrease from ∼13,000–15,000 $\mathrm{km}\,{{\rm{s}}}^{-1}$ at discovery to ∼11,000–13,000 $\mathrm{km}\,{{\rm{s}}}^{-1}$ around maximum light, and they continue to decrease thereafter.

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In addition to the usual photospheric-velocity feature (PVF) of Ca ii H&K, SN 2016coj exhibits a high-velocity feature (HVF; e.g., Mazzali et al. 2005; Maguire et al. 2012, 2014; Folatelli et al. 2013; Childress et al. 2014; Silverman et al. 2015) in nearly all of the early-time spectra. This HVF appears to be detached from the rest of the photosphere, with a velocity of ∼25,000 $\mathrm{km}\,{{\rm{s}}}^{-1}$ at discovery and slowing down to ∼20,000 $\mathrm{km}\,{{\rm{s}}}^{-1}$ at ∼8 days after the fitted first-light time. The HVF feature of Ca ii H&K stays for a long time, being distinct until roughly age +11 days; thereafter, it is a high-velocity shoulder of the Ca ii H&K absorption.

A Ca ii near-infrared (NIR) triplet HVF is also found in the first few spectra that covered the wavelength range before maximum light, and the velocity of ≳22,000 $\mathrm{km}\,{{\rm{s}}}^{-1}$ is in good agreement with that of the Ca ii H&K HVF at early times, though it is slightly smaller in the first-epoch spectrum. Such HVFs are seen in a few other well-observed SNe Ia, including SN 2005cf (Wang et al. 2009) and SN 2012fr (e.g., Childress et al. 2013; Maund et al. 2013; Zhang et al. 2014). However, in SN 2016coj, the Ca ii NIR triplet HVF becomes weaker around peak brightness, and it completely disappears ∼8 days later and thereafter. This is different from the Ca ii H&K HVF, which is seen for a much longer time. It is not obvious why the HVF of the Ca ii NIR triplet goes away after peak brightness while the HVF of Ca ii H&K persists. One possibility is that the apparent HVF of Ca ii H&K after peak could actually be Si ii λ3858 (e.g., Foley 2013). In fact, it is possible that the early-time apparent HVF of Ca ii H&K could be a mixture of Si ii λ3858 (including both the HVF and PVF) plus the true HVF of Ca ii H&K. If so, the velocity of the Ca ii H&K HVF could be smaller than that shown in Figure 5, and thus more consistent with the velocity of the Ca ii NIR triplet HVF, but this case is too complicated to verify.

One note about the O i triplet feature is that we adopted only one component in our fit. However, our early-time spectra before peak brightness reveal that the O i triplet has a double absorption profile. Following the Zhao et al. (2016) method to fit the O i triplet with both HVF and PVH (Zhao et al. also adopted a second, faster HVF, but that is not clear in SN 2016coj), we find an HVF O i triplet velocity of ∼16,000 $\mathrm{km}\,{{\rm{s}}}^{-1}$ and a PVF O i triplet velocity of ∼12,000 $\mathrm{km}\,{{\rm{s}}}^{-1}$. The HVF velocity is smaller than that of both Ca ii H&K and the Ca ii NIR triplet. If the HVF really exists in the O i triplet, it suggests that the oxygen in the outer layers is not completely burned (see Zhao et al. 2016).

The strong absorption of Si ii λ6355 is commonly used to estimate the photospheric velocity. As shown in Figure 5, the Si ii λ6355 velocity of SN 2016coj decreases rapidly from ∼15,500 $\mathrm{km}\,{{\rm{s}}}^{-1}$ at discovery to ∼12,600 $\mathrm{km}\,{{\rm{s}}}^{-1}$ around peak brightness, and then slowly decreases to ∼11,600 $\mathrm{km}\,{{\rm{s}}}^{-1}$ at +11.0 days after peak. A velocity of ∼12,600 $\mathrm{km}\,{{\rm{s}}}^{-1}$ at peak brightness is ∼1500 $\mathrm{km}\,{{\rm{s}}}^{-1}$ higher than average in SNe Ia (e.g., Wang et al. 2013 $\gt 2.5\sigma$ away from the mean of their SN Ia velocity distribution fitted with a Gaussian).

Since the optical emission of SNe Ia comes mainly from the photosphere, the photospheric velocity evolution could be directly related to the optical light curves of SNe Ia (see Zheng & Filippenko 2017); therefore, it is important to understand the photospheric velocity evolution of SNe Ia. Here, we compare the photospheric velocity measurement of SN 2016coj with the three well-observed SNe Ia 2009ig (Foley et al. 2012; Marion et al. 2013), 2012cg (Silverman et al. 2012b), and 2013dy (Zheng et al. 2013). Note that while both SN 2012cg and SN 2009ig have an HVF identified for Si ii λ6355, we consider only the photospheric component.

Figure 6 displays the photospheric velocity evolution over time for the four SNe Ia. Overall, the photospheric velocity evolution is similar to the evolution seen in most SNe Ia (e.g., Benetti et al. 2005; Foley et al. 2011; Silverman et al. 2012c): the velocity drops rapidly at early times (within the first week after explosion), and then slowly but steadily decreases thereafter. For each of these four SNe, we consequently try to fit the early-time velocities (typically within 10 days after first light) with a power-law function, $v={C}_{1}t{^{\prime} }^{\alpha }$, where $t^{\prime}$ is the time after first light (t₀); the results are shown in the top panel of Figure 6 for each SN. This is very similar to the method that of Silverman et al. (2015, Figure 12) adopted, but they used a natural exponential function to fit the velocities before +5 days after peak brightness and also obtained reasonable fitting results. In fact, Piro & Nakar (2013, Equation (13)) mathematically show that the photospheric velocity could decay as a power law at early times. For the later velocities (typically $\gt 10$ days after first light), we then fit them with a linear function, $v={at}^{\prime} +{C}_{2}$ (results shown in the middle-top panel); Silverman et al. (2012c, Figure 5) also use the same method to fit their data around peak brightness. As seen in Figure 6, both the power-law function and the linear function can fit the corresponding data well, but only in their respective regimes—early-time data for the power-law function and later-time data for the linear function.

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As with the early-time light curve (Zheng et al. 2013, 2014), we find that a broken-power-law function is useful for fitting the photospheric velocity evolution; a low-index power-law function approximates the linear function found at late times. Specifically,

$$\begin{eqnarray}&&v=A{\left(\displaystyle \frac{t^{\prime} }{{t}_{b}}\right)}^{{\alpha }_{1}}{\left[1+{\left(\displaystyle \frac{t^{\prime} }{{t}_{b}}\right)}^{s({\alpha }_{1}-{\alpha }_{2})}\right]}^{-1/s},\end{eqnarray} \tag{ 1 }$$

where v is the photospheric velocity, A is a scaling constant, $t^{\prime}$ is the time after first light (t₀), t_b is the break time, ${\alpha }_{1}$ and ${\alpha }_{2}$ are the two power-law indices before and after the break (respectively), and s is a smoothing parameter. We apply this broken-power-law function to the entire data set of photospheric velocities for all four SNe until about a month after the explosion. Our fitting results (we fixed s to be −10) are listed in Table 2 and shown in the middle-bottom panels in Figure 6.

Table 2.  Photospheric Velocity Fitting Results

	α	a	${\alpha }_{1}$	${\alpha }_{2}$	Reduced ${\chi }^{2}$
SN	Power Law	Lineara	Broken Power Lawb
SN 2009ig	−0.16 ± 0.04	−32 ± 31	−0.20 ± 0.14	0.03 ± 0.23	0.04
SN 2012cg	−0.28 ± 0.05	−77 ± 32	−0.39 ± 0.18	−0.09 ± 0.08	0.04
SN 2013dy	−0.22 ± 0.03	−54 ± 32	−0.34 ± 0.16	−0.11 ± 0.06	0.14
SN 2016coj	−0.18 ± 0.01	−95 ± 3	−0.23 ± 0.01	−0.11 ± 0.01	1.72

Notes.

^aIn units of $\mathrm{km}\,{{\rm{s}}}^{-1}$ day⁻¹. ^bThe smoothing parameter s was fixed to −10 during fitting, and the very small reduced ${\chi }^{2}$ for some SNe is largely caused by overestimating the velocity uncertainty.

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The power-law indices from both the power-law fitting (α) and broken-power-law fitting (${\alpha }_{1}$) at early times are consistent with the value of −0.22 adopted by Piro & Nakar (2014) when fitting three SNe Ia (SNe 2009ig, 2011fe, and 2012cg), and are also the value adopted by Shappee et al. (2016) when fitting ASASSN-14lp. The index from the broken power law (${\alpha }_{1}$) is slightly steeper than that from the power law (α). At late times (around maximum light) with linear fitting, the rate of velocity decrease from the fitting is slightly larger than the average rate of −38 km s⁻¹ day⁻¹ found by Silverman et al. (2012c) for a large sample of SNe Ia.

Overall, the broken-power-law function can fit the photospheric velocity evolution well for all four SNe until a month after explosion (see the small residuals at the bottom panel of Figure 6 and the reduced ${\chi }^{2}$ given in Table 2). This function also has the potential to fit the photospheric velocity evolution of most other SNe Ia as well, given that most SNe Ia have very similar velocity evolution (e.g., Silverman & Filippenko 2012; Silverman et al. 2012c). High-cadence spectroscopy is required to verify this, especially at early times. However, it currently remains unclear whether there is a good physical explanation behind the fitting; Piro & Nakar (2013) show that the photospheric velocity could decay as a power law at early times, but our broken-power-law function fitting extends to a much later time.

We use the SuperNova IDentification code (SNID; Blondin & Tonry 2007) to spectroscopically classify SN 2016coj. For nearly all of the spectra presented here, we find that SN 2016coj is spectroscopically similar to many normal SNe Ia. Compared to SN 1992A (${M}_{B}=-18.79$ mag and ${\rm{\Delta }}{m}_{15}(B)=1.47$ mag; Della Valle et al. 1998) and SN 2002er (${M}_{B}=-19.35$ mag and ${\rm{\Delta }}{m}_{15}(B)=1.33$ mag; Pignata et al. 2004), for example, SN 2016coj has similar spectra, absolute magnitude, and ${\rm{\Delta }}{m}_{15}(B)$. Another spectroscopic comparison is the so-called Si ii ratio, ${\mathfrak{R}}$(Si ii) (the ratio of Si ii λ5972 to Si ii λ6355), defined by Nugent et al. (1995) using the depths of spectral features and later by Hachinger et al. (2006) using their pseudo-equivalent widths. Hachinger et al. (2006) found a good correlation between the ${\mathfrak{R}}$(Si ii) and ${\rm{\Delta }}{m}_{15}(B)$ (see their Figure 13). We measure SN 2016coj to have ${\mathfrak{R}}$(Si ii) = 0.11 ± 0.4, with ${\rm{\Delta }}{m}_{15}(B)\,=1.25$ mag, placing SN 2016coj in the normal SN Ia region in Figure 13 of Hachinger et al. (2006), very close to SN 2002er. Thus, we conclude that SN 2016coj is a spectroscopically normal SN Ia, consistent with the photometric analysis given in Section 3.1.

Linear polarization is expressed as the quadratic sum of the Q and U Stokes vectors, $P=\sqrt{{Q}^{2}+{U}^{2}}$. The position angle on the sky is given by $\theta =(1/2)\,{\tan }^{-1}(U/Q)$, taking into account the quadrant in the Q–U plane where the inverse tangent angle is located. Since P is a positive-definite quantity, it is overestimated in situations where the S/N is low. It is thus typical to express the "debiased" (or bias-corrected) form of P as ${P}_{\mathrm{db}}=\sqrt{({Q}^{2}+{U}^{2})-({\sigma }_{Q}^{2}+{\sigma }_{U}^{2})}$, where ${\sigma }_{Q}$ and ${\sigma }_{U}$ are the uncertainties in the Q and U Stokes parameters. Note, however, that at low S/N, ${P}_{\mathrm{db}}$ is also not a fully reliable function because it has a peculiar probability distribution (Miller et al. 1988). Thus, for extracting statistically reliable values of polarization within a particular waveband, we have binned the calibrated Q and U Stokes spectra separately over the wavelength range of interest before calculating P and θ. All quoted and listed values in Table 3 were determined in this manner, while Figure 7 displays ${P}_{\mathrm{db}}$. For θ, if $({\sigma }_{Q}^{2}+{\sigma }_{U}^{2})\gt ({Q}^{2}+{U}^{2})$, then we set a 1σ upper limit on P of $\sqrt{{\sigma }_{Q}^{2}+{\sigma }_{U}^{2}}$. In cases where $P/{\sigma }_{P}\lt 1.5$, θ is essentially undetermined and is not graphically displayed.

Table 3.  Polarization of SN 2016coj

Epoch	${P}_{V}$ a(%)	${\theta }_{V}$(deg)	${P}_{\mathrm{cont}}$	${\theta }_{\mathrm{cont}}$(deg)
6.9	0.27(0.01)	54.3(0.8)	0.51(0.01)	55.4(0.9)
16.0	0.20(0.01)	52.6(0.8)	0.38(0.01)	53.4(0.8)
24.0	0.16(0.01)	39.2(1.6)	0.06(0.02)	09.0(4.3)
44.0	0.39(0.04)	41.0(1.3)	0.28(0.03)	30.0(2.2)

Note.

^aV-band and continuum integrated over wavelength ranges of 5050–5950 Å and 6700–7150 Å, respectively. Uncertainties are statistical.

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3.4.1. Interstellar and Instrumental Polarization

3.4.2. Intrinsic Polarization

Our spectropolarimetry results are shown in Figure 7 and the integrated broadband measurements are listed in Table 3. On day 6.9, the source exhibits weak polarization in the continuum at a level of ∼0.3%, integrated over the wavelength range of 6700–7150 Å. This is consistent with the weak levels of continuum polarization that are typically associated with SNe Ia (Wang & Wheeler 2008), though we note that some fraction of the polarization, perhaps half, could potentially be contributed by ISP. Strong polarization is exhibited across prominent line features, particularly Si ii λ6355 and the Ca ii NIR triplet, at levels of ∼0.9% and ∼0.6%, respectively. The Ca ii polarization feature appears to exhibit two peaks, perhaps associated with the high- and low-velocity components. The position angles across the polarized line features, particularly Si ii, are close to that of the continuum, which suggests an axisymmetric configuration for the SN.

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By day 16.0, the continuum polarization is consistent with having no change relative to day 6.9, while Si ii has increased in strength slightly to peak at this epoch. A Gaussian fit to the Si ii feature indicates a line polarization of 0.9 ± 0.1% with respect to the continuum level. For Ca ii polarization, the enhancement of the high-velocity component from day 6.9 has disappeared and the peak of the lower-velocity component has increased by ∼0.3%.

By day 24.0, the continuum and Si ii line polarization appears to have dropped substantially for wavelengths shortward of 7000 Å, with no significant change apparent at longer wavelengths; polarization in the continuum region is undetected at this epoch. If real, such a continuum polarization drop roughly one week after peak would be reminiscent of the evolution of SN 2001el (Wang et al. 2003). However, by day 44.0 the continuum polarization appears to have regained the strength exhibited on day 16.0 and earlier. Si ii has restrengthened as well, while declining in radial velocity along with the minimum of the weakening absorption profile. Based on this unexpected restrengthening, we exercise caution regarding the temporarily weakened polarization on day 24.0 because we are concerned that this could be the result of a systematic error. The drop in polarization appears to have only affected the Stokes q parameter (derived from exposures with polarimeter waveplate angles at 0° and 45°). Each of our three q sequences of the SN are consistent, and we see no such change in the q parameter of our standard-star observations from the same night. Thus, if the change on day 24.0 is the result of systematic error (e.g., some unknown temporary source of instrumental polarization above our typical limit of $\lt 0.05$%), then it must have occurred over an hourly timescale. Alternatively, a subsequent rise in continuum polarization on day 44.0 could result from the appearance of weak line features in the chosen continuum region (6700–7150 Å), but, in this case, we would not expect the simultaneous rise in the Si ii feature. As a final possibility, the temporary influence of a separate light-echo component, possibly associated with dust in the host ISM, could result in the observed fluctuation; this possibility has the advantage of accounting for the brief change in the continuum and line polarization simultaneously, and it would also explain why the reddest wavelengths are not significantly affected.

Overall, the spectropolarimetric character of SN 2016coj is consistent with the trends exhibited by "normal" SNe Ia. For example, Maund et al. (2010) reported a correlation between the polarization of the Si ii λ6355 feature, measured near or before peak luminosity, and the radial-velocity decline rate of the absorption minimum (also see Leonard et al. 2006), physically interpreted as evidence for a single geometric configuration for normal SNe Ia. At peak brightness on day 16.0, the line polarization of 0.9 ± 0.1% combined with our measured value of −95 km s⁻¹ day⁻¹ for the velocity evolution, shows that SN 2016coj falls where expected on the correlated distribution of SNe Ia reported by Maund et al. (2010), and within the range of high-velocity explosions.

We examine the APF high-resolution spectra for narrow absorption features, such as those that were identified in APF spectra of SN 2014J (Graham et al. 2015). We began spectral monitoring with the APF based on an early classification and the assumption of a host-galaxy distance smaller than that adopted here. The object's peak apparent brightness ended up being ∼3 mag fainter than that of SN 2014J, and fainter than the projected minimum we typically require for triggering the APF. For this reason, the S/N of our SN 2016coj APF spectra is quite low. Instead of ceasing our APF monitoring, we obtained multiple observations over several nights in order to stack our spectra, but ultimately we do not identify any absorption features of Na i D λλ5889.95, 5895.92, Ca ii H&K λλ3933.7, 3968.5, K i λλ7664.90, 7698.96, Hα λ6562.801, Hβ λ4861.363, or the diffuse interstellar bands (λ ≈ 5780, 5797, 6196, 6283, 6613 Å).

Since the Na i D feature is most useful for constraining the presence of circumstellar material and line-of-sight host-galaxy dust extinction, and owing to grating blaze is in a region of relatively higher S/N (∼10), we estimate an upper limit on its W_λ in the following way. The flux of the continuum-normalized stacked APF spectra in the region of Na i D, shown in black in Figure 8, has a standard deviation of σ ≈ 0.038. As an upper limit on the depth of an absorption feature that we could have detected, we use 3σ ≈ 0.11. Our instrumental configuration for the Levy spectrograph results in a spectral resolution of Δλ ≈ 0.03 Å, from which we estimate that the minimum FWHM of a detected feature is 3Δλ ≈ 0.1 Å. Assuming a Gaussian profile for this hypothetical absorption, we constrain the Na i D feature to have ${W}_{\lambda }\lesssim 0.56\,\mathring{\rm{A}}$. Based on Figure 9 of Phillips et al. (2013), this puts an upper limit on host-galaxy extinction of ${A}_{V}\lesssim 0.2$ mag (with $E(B-V)=0.07$ mag assuming R_V = 3.1). Although this is a rather large upper limit, it is consistent with the small host-galaxy extinction constrained from our low-resolution spectra (see Section 3.2) and also with the low extinction expected given the early type of the host, NGC 4125.

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