SN 2013ej: A TYPE IIL SUPERNOVA WITH WEAK SIGNS OF INTERACTION

Broadband photometric observations in UBVRI filters have been carried out from 2.0 m IIA Himalayan Chandra Telescope (HCT) at Hanle and ARIES 1.0 m Sampurnanand Telescope (ST) and 1.3 m Devasthal Fast Optical Telescope (DFOT) at Nainital. Additionally, SN 2013ej has been also observed with Swift Ultraviolet/Optical Telescope (UVOT) in all six bands.

Photometric data reductions follow the same procedure as described in Bose et al. (2013). Images are cleaned and processed using standard procedures of IRAF software. DAOPHOT routines have been used to perform point-spread function photometry and extract differential light curves. To standardize the SN field, three Landolt standard fields (PG 0231, PG 2231, and SA 92) were observed on 2013 October 27 with 1.0 m ST under good photometric night and seeing (typical FWHM ∼21 in V band) condition. For atmospheric extinction measurement, PG 2231 and PG 0231 were observed at different air masses. The SN field has been also observed in between standard observations. The standardization coefficients derived are represented in the following transformation equations:

$$\begin{eqnarray*}\begin{array}{ccc}u & = & U+(7.800\pm 0.005)-(0.067\pm 0.009)\cdot (U-B)\\ b & = & B+(5.269\pm 0.007)-(0.060\pm 0.009)\cdot (B-V)\\ v & = & V+(4.677\pm 0.004)-(0.056\pm 0.005)\cdot (B-V)\\ r & = & R+(4.405\pm 0.005)-(0.038\pm 0.010)\cdot (V-R)\\ i & = & I+(4.821\pm 0.006)-(0.048\pm 0.006)\cdot (V-I)\end{array}\end{eqnarray*}$$

where u, b, v, r, and i are instrumental magnitudes corrected for time, aperture, and airmass, and U, B, V, R, and I are standard magnitudes. The standard deviations of the difference between the calibrated and the standard magnitudes of the observed Landolt stars are found to be ∼0.03 mag in U, ∼0.02 mag in BR, and ∼0.01 mag in VI. The transformation coefficients were then used to generate eight local standard stars in the field of SN 2013ej, which are verified to be non-variable and have brightness similar to the SN. These stars are identified in Figure 1, and the calibrated UBVRI magnitudes are listed in Table 2. These selected eight local standards were further used to standardize the instrumental light curve of the SN. One of these stars (star B) is common to that used in the study by Richmond (2014), and its BVRI magnitudes are found to lie within 0.03 mag of our calibrated magnitudes. Our calibrated magnitudes for SN 2013ej are also found to be consistent within errors with that presented in earlier studies of the event (Valenti et al. 2014; Richmond 2014). The standard photometric magnitudes of SN 2013ej are listed in Table 3.

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Table 2.  Eight Local Standards in the Field of SN 2013ej with Corresponding Coordinates ($\alpha ,\delta$) and Calibrated Magnitudes in UBVRI. Errors Quoted Here Include Both Photometric and Calibration Errors

Star	${\alpha }_{\rm{J}2000}$	${\delta }_{\rm{J}2000}$	U	B	V	R	I
ID	(h m s)	(° ' '')	(mag)	(mag)	(mag)	(mag)	(mag)
A	1:36:57.9	+15:51:19.4	16.773 ± 0.0325	16.867 ± 0.0259	16.297 ± 0.0193	15.939 ± 0.0163	15.567 ± 0.0207
B	1:36:23.0	+15:47:45.3	15.102 ± 0.0289	15.109 ± 0.0302	14.580 ± 0.0234	14.253 ± 0.0183	13.888 ± 0.0260
C	1:36:50.4	+15:40:01.9	16.588 ± 0.0318	16.525 ± 0.0277	15.798 ± 0.0200	15.372 ± 0.0157	14.925 ± 0.0187
D	1:36:52.7	+15:40:39.4	14.811 ± 0.0318	14.561 ± 0.0265	13.817 ± 0.0184	13.384 ± 0.0167	12.976 ± 0.0196
E	1:37:03.4	+15:41:39.2	17.140 ± 0.0386	17.064 ± 0.0251	16.407 ± 0.0200	16.008 ± 0.0160	15.601 ± 0.0206
F	1:37:09.0	+15:41:20.4	18.804 ± 0.1537	17.800 ± 0.0282	16.769 ± 0.0249	16.146 ± 0.0167	15.583 ± 0.0205
G	1:36:57.6	+15:46:22.7	13.934 ± 0.0272	13.756 ± 0.0219	12.991 ± 0.0160	12.555 ± 0.0161	12.155 ± 0.0240
H	1:37:09.0	+15:48:00.6	16.974 ± 0.0434	16.172 ± 0.0249	15.175 ± 0.0157	14.598 ± 0.0170	14.062 ± 0.0194

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This SN was also observed with UVOT (Roming et al. 2005) in six bands (viz., uvw2, uvm2, uvw1, uvu, uvb, uvv) on the Swift spacecraft (Gehrels et al. 2004). The UV photometry was obtained from the Swift Optical/Ultraviolet Supernova Archive¹¹ (SOUSA; Brown et al. 2014). The reduction is based on that of Brown et al. (2009), including subtraction of the host galaxy count rates, and uses the revised UV zero points and time-dependent sensitivity from Breeveld et al. (2011). The UVOT photometry is listed in Table 3. The first month of UVOT photometry was previously presented by Valenti et al. (2014).

Spectroscopic observations have been carried out at 10 phases during 12–125 days. Out of these, nine epochs of low-resolution spectra are obtained from Himalaya Faint Object Spectrograph and Camera (HFOSC) mounted on the 2.0 m HCT. Spectroscopy on the HCT/HFOSC was done using a slit width of 1.92 arcsec, and grisms with resolution λ/Δλ = 1330 for Gr7 and 2190 for Gr8, and bandwidth coverage of 0.38–0.64 μm and 0.58–0.84 μm, respectively. One high-resolution spectrum is obtained from the ARC Echelle Spectrograph (ARCES) mounted on the 3.5 m ARC telescope located at Apache Point Observatory (APO). ARCES is a high-resolution cross-dispersion echelle spectrograph; the spectrum is recorded in 107 echelle orders covering a wavelength range of λ ∼ 0.32–1.00 $\mu \rm{m}$, at a resolution of R ∼ 31,500 (Wang et al. 2003). A summary of spectroscopic observations is given in Table 4.

Spectroscopic data reduction was done under the IRAF environment. Standard reduction procedures are followed for bias subtraction and flat fielding. Cosmic-ray rejections are done using a Laplacian kernel detection algorithm for spectra, L.A.Cosmic (van Dokkum 2001). One-dimensional low-resolution spectra were extracted using the apall task. Wavelength calibration was done using the identify task applied on FeNe and FeAr (for HCT) arc spectra taken during observation. Wavelength calibration was cross-checked against the [O i] λ5577 sky line in the sky spectrum, and it was found to lie within 0.3–4.5 Å of the actual value. Spectra were flux-calibrated using standard, sensfunc, and calibrate tasks in IRAF. For flux calibration, spectrophotometric standards were used that were observed on the same nights as the SN spectra were recorded. All spectra were tied to the absolute flux scale using the observed flux from UBVRI photometry of the SN. To perform the tying, the individual spectrum is multiplied by a wavelength-dependent polynomial, which is convolved with UBVRI filters and then the polynomial is tuned to match the convolved flux with observations. The one-dimensional calibrated spectra were corrected for heliocentric velocity of the host galaxy (658 $\;\mathrm{km}\;{\rm{s}}^{-1}$; Table 1) using the dopcor task.

The optical light curves of SN 2013ej in UBVRI and six UVOT bands are shown in Figure 3. UBVRI photometric observations were done at 38 phases during 12–209 days (from plateau to nebular phase). The duration of the plateau phase is sparsely covered, while denser follow-up initiated after 68 days. The plateau phase lasted ∼85 days, with an average decline rate of 6.60, 3.57, 1.74, 1.07, and 0.74 mag (100 days)⁻¹ in UBVRI bands, respectively. Since 95 days, the light curve declines very fast until 115 days, after which it settles to a relatively slow declining nebular phase. During this phase, the decline rates for UBVRI bands are 0.98, 1.22, 1.53, 1.42, and 1.55 mag (100 days)⁻¹, respectively.

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SN 2013ej has been also observed by Swift UVOT at 35 phases during 7 to 139 days. The UVOT UV band light curves decline steeply during the first 30 days at a rate of 0.182, 0.213, and 0.262 mag day⁻¹ in uvw1, uvw2, and uvm2 bands, respectively, thereafter settling into a slow declining phase until it reaches the end of the plateau.

SN 2013ej experiences a steeper plateau decline than that observed for SN 1999em (Leonard et al. 2002c), SN 1999gi (Leonard et al. 2002b), SN 2012aw (Bose et al. 2013), and SN 2013ab (Bose et al. 2015). For example, the SN 2012aw plateau declines at a rate of 5.60, 1.74, and 0.55 mag (100 days)⁻¹ in UBV bands; similarly for SN 2013ab, decline rates in UBVRI are 7.60, 2.72, 0.92, 0.59, and 0.30 mag (100 days)⁻¹ and 0.169, 0.236, 0.257 mag day⁻¹ in UVOT uvw1, uvw2, and uvm2 bands (during the first 30 days).

The absolute V-band (M_V) light curve of SN 2013ej is plotted in Figure 4 and is compared with other well-studied SNe II (after correcting for extinction and distance). In Table 5 we list the plateau slope of all compared Type II events. The comparison shows that the decline rate of SN 2013ej during this phase is highest (1.74 mag (100 days)⁻¹) among most other SNe, except three SNe IIL SN 1980 K, SN 2000dc, and SN 2013by, where SN 1980 is among the very first observed prototypical Type IIL event. The early plateau ($\lt 40$ days) light curve of SN 2013ej is identical to that of SN 2009bw. However, unlike most other SNe IIP, e.g., SN 2009bw and SN 2013ab, which become flatter during the late plateau, SN 2013ej continues to decline almost at a steady rate until the end of the plateau (∼85 days). The mid-plateau ${M}_{V}=-14.7$ mag for SN 2013ej, which places it in the class of normal luminous Type II events. SN 2013ej is comparable with fast-declining and short-plateau SNe in the sample of Anderson et al. (2014b). Following the plateau phase, V-band light drops very fast to reach the slow-declining nebular phase (1.53 mag (100 days)⁻¹), which is powered by the radioactive decay of ⁵⁶Co to ⁵⁶Fe. The fall of M_V during the plateau-nebular transition is ∼2.4 mag, which is on the higher side of the compared events. The closest comparison is SN 2009bw and SN 2012 A, which exhibit a drop of ∼2.4 and ∼2.5 mag, respectively. This also indicates a low amount of ⁵⁶Ni mass synthesized during the explosion, which we shall further discuss in the next section.

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Swift UVOT absolute magnitude light curves of SN 2013ej are shown in Figure 5 and compared with other well-observed SNe II. The sample is selected in such a way that SNe have at least a month of observations. Most SNe are not followed for more than a month by Swift, mainly because of the large distances or high extinction values. However, both these factors work in favor of SN 2013ej, making it possible to have about 4 months of observations. Moreover, with the location of the SN being in the outskirts of a spiral arm of NGC 0628, the background flux contamination is also negligible. The comparison shows that the SN 2013ej UV light curves are identical to SN 2012aw. SN 2013ej also shows a similar UV-plateau trend as observed in SN 2012aw (Bayless et al. 2013), which is expected but rarely detected for SNe IIP/L.

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Broadband color provides important information to study the temporal evolution of the SN envelope. In Figure 6, we plot the intrinsic colors $U-B,B-V,V-R$, and $V-I$ for SN 2013ej and compare its evolution with Type II-pec SN 1987 A and SNe IIP SN 1999em, SN 2004et, SN 2012aw, and SN 2013ab. All the colors show a generic signature of fast cooling ejecta until the end of the plateau (∼110 days). With the start of the nebular phase it continues to cool at a much slower rate in $V-I$ and $V-R$ colors, whereas $U-V$ and $B-V$ show a bluer trend. This is because, as the SN enters the nebular phase, the ejecta become depleted of free electrons, thereby making the envelope optically thin and so unable to thermalize the photons from radioactive decay of ⁵⁶Co to ⁵⁶Fe.

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We compute the pseudo-bolometric luminosities following the method described in Bose et al. (2013), which include SED integration over the semi-deconvolved photometric fluxes after correcting for extinction and distance. SN bolometric luminosities during early phases ($\leqslant 30$ days) are dominated by UV fluxes, while after mid-plateau (∼50 days) UV contribution becomes insignificant as compared to the optical counterpart (e.g., as seen in SN 2012aw and SN 2013ab; Bose et al. 2013, 2015). Similarly, during late phases $\gt 100$ days, near-infrared becomes dominant over optical fluxes. However, during most of the light-curve evolution, optical fluxes still provide significant contribution. We compute pseudo-bolometric luminosities in the wavelength range of U to I band (3335–8750 Å). We also computed a UV–optical pseudo-bolometric light curve with wavelength starting from the uvw2 band (wavelength range of 1606–8750 Å). The UV contribution enhances the luminosity significantly during early phases, whereas it is almost negligible after mid-plateau.

In Figure 7, we plot a pseudo-bolometric light curve for SN 2013ej and compare it with other SN light curves computed using the same technique. We also include UV–optical bolometric light curves for SN 2012aw and SN 2013ab, along with SN 2013ej for comparison. Although the UV–optical light curve is initially brighter than the optical light curve, they completely coincide by the end of the plateau phase (85 days). It is evident from the comparison that SN 2013ej experienced a steep decline during the plateau phase, but with a much shorter duration. This is consistent with the anticorrelation observed between plateau slope and duration for SNe II (Blinnikov & Bartunov 1993; Anderson et al. 2014b). The UV–optical bolometric light decreases by 0.83 dex during the plateau phase (from 12 to 85 days), followed by an even faster drop by 0.76 dex in a short duration of 21 days (from 90 to 111 days). Thereafter, the SN settles in a slow-declining nebular phase. The tail luminosities are significantly lower than other normal-luminosity IIP events, e.g., SN 2013ej luminosities are lower by ∼0.5 dex (at 200 days) than that of SNe II SN 1987 A, SN 1999em, SN 2004et, and SN 2012aw, but higher than subluminous events like SN 2005cs. Another noticeable dissimilarity of the tail light curve is its high decline rate. The SN 2013ej tail luminosity declines at a rate of 0.55 dex (100 days)⁻¹, which is much higher than that expected from radioactive decay of ⁵⁶Co to ⁵⁶Fe. This is possibly because of inefficient gamma-ray trapping in the ejecta and thus incomplete thermalization of the photons. We shall further explore this in Section 7 in context of modeling the light curve.

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During the explosive nucleosynthesis of silicon and oxygen, at the time of shock breakout in CCSNe, radioactive ⁵⁶Ni is produced. The nebular phase light curve is mainly powered by the radioactive decay of ⁵⁶Ni to ⁵⁶Co and ⁵⁶Co to ⁵⁶Fe with half-life times of 6.1 and 77.1 days, respectively, emitting γ-rays and positrons. Thus, the tail luminosity will be proportional to the amount of radioactive ⁵⁶Ni synthesized at the time of explosion. We determine the mass of ⁵⁶Ni using the following two methods.

For SN 1987 A, one of the most well-studied and well-observed events, the mass of ⁵⁶Ni produced in the explosion has been estimated quite accurately, to be 0.075 ± 0.005 ${M}_{\odot }$ (Arnett 1996). By comparing the tail luminosities of SN 2013ej and SN 1987 A at similar phases, it is possible to estimate the ⁵⁶Ni mass for SN 2013ej. In principle, true bolometric luminosities (including UV, optical, and IR) are to be used for this purpose, which are available for SN 1987 A, whereas for SN 2013ej we have only UV and optical observations. Thus, in order to have uniformity in comparison, we used only the UBVRI bolometric luminosities for both SNe and computed using the same method and wavelength range. We estimate the tail UBVRI luminosity at 175 days, by making a linear fit over 155–195 days, to be $2.90\pm 0.43\times {10}^{40}$ erg s⁻¹. Likewise, SN 1987 A luminosity is estimated to be $9.60\pm 0.06\times {10}^{40}$ erg s⁻¹ at similar phase. Thus, the ratio of SN 2013ej to SN 1987 A luminosity is 0.302 ± 0.044, which corresponds to a ⁵⁶Ni mass of 0.023 ± 0.003 ${M}_{\odot }$ for SN 2013ej.

Assuming that the γ-photons emitted from radioactive decay of ⁵⁶Co thermalize the ejecta, ⁵⁶Ni mass can be independently estimated from the tail luminosity as described by Hamuy (2003):

$$\begin{eqnarray*}&&{M}_{\mathrm{Ni}}=7.866\times {10}^{-44}\times {L}_{t}\mathrm{exp}\left[{\displaystyle \frac{({t}_{t}-{t}_{0})/(1+z)-6.1}{111.26}}\right]{M}_{\odot }\end{eqnarray*}$$

where ${t}_{0}$ is the explosion time, 6.1 days is the half-life time of ⁵⁶Ni, and 111.26 days is the e-folding time of the ⁵⁶Co decay. We compute tail luminosity L_t at 6 epochs within 153–185 days from the V-band data corrected for distance, extinction, and bolometric correction factor of 0.26 ± 0.06 mag during the nebular phase (Hamuy 2003). The weighted mean value of ${L}_{t}$ is found to be $5.45\pm 0.35\times {10}^{40}\;$ $\;\mathrm{erg}\;{\rm{s}}^{-1}$ corresponding to a mean phase of 170 days. This tail luminosity corresponds to a value of ${M}_{\mathrm{Ni}}=0.019\pm 0.002$ ${M}_{\odot }$.

We take the weighted mean of the estimated values from the above two methods and adopt a ⁵⁶Ni mass of 0.020 ± 0.002 ${M}_{\odot }$ for SN 2013ej.

Hamuy (2003) found a strong correlation between the ⁵⁶Ni mass and the mid-plateau (at 50 days) V-band absolute magnitude for SNe II, and this correlation was further confirmed by Spiro et al. (2014) specifically for low-luminosity events. Figure 8 shows the correlation of mid-plateau M_V versus ⁵⁶Ni mass for 34 events, including SN 2013ej. The SN lies within the scatter relation, but toward the lower mass range of ⁵⁶Ni than where most of the events cluster around (top right).

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The spectroscopic evolution of SN 2013ej is presented in Figure 9. Preliminary identifications of spectral features have been done as per previously studied SNe IIP (e.g., Leonard et al. 2002a; Bose et al. 2013). The spectrum at 12 days shows broad Hα, Hβ, and He i features on top of a hot blue continuum. The 35-day spectrum shows a relatively flat continuum with well-developed features of Hα, Hβ, and Fe ii along with blends of other heavier species like Ti ii and Ba ii. The He i line is no longer detectable; instead, Na i D features start to appear at a similar location. The spectra from 35 to 80 days represent the cooler photospheric phase, where the photosphere starts to penetrate deeper layers rich in heavier elements like Fe ii and Sc ii. During these phases, we see the emergence and development of various other heavy atomic lines and their blends such as Ti ii, Ba ii, Na i D, and Ca ii. Figure 10 shows the comparison of three plateau-phase spectra, viz., 12, 35, and 68 days, with other well-studied SNe IIP at similar epochs. The comparison shows that the spectrum of SN 2013ej is broadly identical to others in terms of observable line features and their evolution. A notable feature during the early spectrum (12 days) is the dip on the bluer wing of Hα profiles near 6170 Å, which can be attributed to the Si ii feature. Leonard et al. (2013) also identified this feature at ∼9-day spectra of SN 2013ej; however, due to the unlikeliness of such a strong Si ii feature at such early epochs, the possiblity of a non-standard red supergiant envelope or CSM interaction was suggested. However, such dips are detectable in 35- and 42-day spectra, which we identify as the Si ii feature in synow modeling.

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The spectra at 96 and 97 days represent the plateau-nebular transition phase. Thereafter, spectra at 109 and 125 days represent the nebular phase, where the ejecta has become optically thin. These spectra show the emergence of some emission features from forbidden lines of [O i] λ λ 6300, 6364 and [Ca ii] λ λ 7291, 7324, as well as previously evolved permitted lines of H i and the Na i λ5893 doublet (see Figure 11).

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Gutiérrez et al. (2014) found correlations between Hα absorption-to-emission strengths and light-curve parameters, i.e., plateau slope and duration of optically thick phase. Following their selection criteria for choosing the phase of SN spectra, i.e., 10 days after start of recombination, we selected the 42-day spectrum as the closet available phase to the criteria. The Hα absorption-to-emission ratio of EWs for SN 2013ej is found to be 0.23 ± 0.02, the optically thick phase is ∼85 days, and the B-band late-plateau (40–85 days) slope is ∼0.27 mag (100 days)⁻¹. The correlation for optically thick phase duration is found to follow that presented by Gutiérrez et al. (2014). For the plateau slope, the correlation also holds true, but here SN 2013ej lies in the borderline position of the scattered relation. However, it may be noted that Hα profiles are possibly contaminated by high-velocity (HV) features, as we describe in the following sections, which may result in deviation from correlation.

SN 2013ej spectra have been modeled with synow ¹³ (Fisher et al. 1997, 1999; Branch et al. 2002) for line identification and its velocity estimation. synow is a highly parametrized spectrum synthesis code that employs the Sobolev approximation to simplify radiation transfer equations assuming a spherically symmetric SN expanding homologously. The strength of the synow code is its capability to reproduce P Cygni profiles simultaneously in synthetic spectra for a given set of atomic species and ionization states.

The applicability of synow is well tested in various core-collapse SN studies (e.g., Inserra et al. 2012; Bose et al. 2013; Milisavljevic et al. 2013; Bose & Kumar 2014; Takáts et al. 2014; Marion et al. 2014) for velocity estimation and analysis of spectral lines.

To model the spectra, we tried various optical depth profiles (viz., Gaussian, exponential, and power law) with no significant difference among them; however, we find the exponential profile ($\tau \propto \mathrm{exp}[-v/{v}_{e}]$) marginally better suited to match the absorption trough of observed spectra, where v_e, the e-folding velocity, is a fitted parameter. While modeling spectra, H i lines are always dealt with as a detached scenario. This implies that the velocity of the hydrogen layer is significantly higher and is thus detached from the photospheric layer, close to which most heavier atomic lines form, as assumed in the synow code. As a consequence of this, the Hα lines in synthetic spectra, which are highly detached, have flat-topped emissions with blueshifted absorption counterparts.

SN 2013ej spectra are dereddened and the approximate blackbody temperature is supplied in the model to match the spectral continuum. For the early spectrum (12 days), the local thermodynamic equilibrium (LTE) assumption holds, and thus synow could fit the continuum well, whereas at later epochs it fails to fit properly. The set of atomic species incorporated to generate the synthetic model spectrum are H i, He i, Fe ii, Ti ii, Sc ii, Ca ii, Ba ii, Na i, and Si ii. The photospheric velocity ${v}_{\mathrm{ph}}$ is optimized to simultaneously fit the Fe ii (λ λ 4924, 5018, 5169) P Cygni profiles, and H i lines are treated as detached. The optical depths and optical depth profile parameters, which is the e-folding velocity, are varied for individual species to fit respective line profiles. In Figure 12 we show the model fit of the 71-day spectrum. Most of the observable spectral features are reproduced well and are identified in the figure.

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Similarly, all spectra during 12–97 days are modeled with synow. The model fits for Fe ii (λ λ 4924, 5018, 5169), Hβ, and Hα spectral sections are shown in Figure 13. The atomic species that are important to model these features are H i, Fe ii, Ba ii, Ti ii, Sc ii, and Na i. In addition to these, Si ii is also used to model the dips in the blue wing of Hα P Cygni during 12–42 days. While modeling the Hα and Hβ profiles, synow was unable to properly fit the broad and extended P Cygni absorption troughs with a single regular component. In order to fit these extended troughs, we invoke the HV component of H i. Although no separate dip is seen, possibly due to low spectral resolution and overlapping of broad P Cygni profiles, the HV component can well reproduce the observed features in the synthetic model spectrum. The implication and interpretation of these HV components are further discussed in Section 5.4. The synow-derived velocities for Fe ii, Hα, and Hβ lines and corresponding HV components are listed in Table 6. The nebular spectra during 109–125 days have not been modeled, primarily due to limitations of the LTE assumption of synow, and also because nebular-phase spectra are dominated by emission lines rather than P Cygni profiles.

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Table 6.  Line Velocities of Hα, Hβ, Fe ii (λ λ 4924, 5018, 5169), and He i λ5876 as Estimated by Modeling the Observed Spectra of SN 2013ej with synow. Fe ii or He i Lines Velocities are Taken to Represent Photospheric Velocity (${v}_{\mathrm{phm}}$)

UT Date	Phasea	v(He i)	v(Fe ii)	v(H${}_{\alpha }$)	v(H${}_{\alpha }$) HVb	v(H${}_{\beta }$)	v(H${}_{\beta }$) HVb
(yyyy mm dd)	(day)	(103$\;\mathrm{km}\;{\rm{s}}^{-1}$)	(103$\;\mathrm{km}\;{\rm{s}}^{-1}$)	(103$\;\mathrm{km}\;{\rm{s}}^{-1}$)	(103$\;\mathrm{km}\;{\rm{s}}^{-1}$)	(103$\;\mathrm{km}\;{\rm{s}}^{-1}$)	(103$\;\mathrm{km}\;{\rm{s}}^{-1}$)
2013 Aug 04.86	12.1	8.8	⋯	9.6	⋯	9.7	⋯
2013 Aug 27.76	35.0	⋯	6.7	7.9	⋯	6.6	⋯
2013 Sep 03.90	42.1	⋯	5.8	7.2	8.5	5.4	6.4
2013 Sep 29.78	68.0	⋯	3.6	5.8	7.4	4.0	5.8
2013 Oct 02.89	71.1	⋯	3.3	5.4	7.3	3.8	5.8
2013 Oct 11.28	79.5	⋯	3.3	5.2	6.3	3.6	4.8
2013 Oct 27.87	96.1	⋯	2.7	4.9	6.3	3.5	4.8
2013 Oct 28.79	97.0	⋯	2.7	4.8	6.3	⋯	⋯

Notes.

^aWith reference to the time of explosion JD 2,456,497.30. ^bHigh-velocity component used to fit the broad Hα and Hβ profile.

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Investigation of the spectral evolution sheds light on various important aspects of the SN, like interaction of ejecta with the circumstellar material, geometrical distribution of the expanding shell of ejecta, and formation of dust during late times. SN spectra are dominated by P Cygni profiles, which are direct indicators of expansion velocities, and they evolve with the velocity of the photosphere. As ejecta expand and opacity decreases, allowing photons to escape from deeper layers rich in heavier elements, we are able to see the emergence and growth of various spectral lines.

To illustrate the evolution of the Hα line, in Figure 14 a partial region of spectra is plotted in the velocity domain corresponding to rest wavelengths of Hα. At 12 days a broad P Cygni profile (FWHM ∼ 9500 $\;\mathrm{km}\;{\rm{s}}^{-1}$) is visible, which becomes narrower with time as the expansion slows down. The blueshifted absorption troughs are direct estimators of the expansion velocity of the associated line-forming layer. The emission peaks are found to be blueshifted (by ∼3200 $\;\mathrm{km}\;{\rm{s}}^{-1}$ at 12 days), which progressively decreases with a decrease in expansion velocity, and almost settling to zero velocity when the SN starts to enter the nebular phase (97 days). Such blueshifted emission peaks, especially during early phases, are generic features observable in SN spectra, e.g., SN 1987 A (Hanuschik & Dachs 1987), SN 1998 A (Pastorello et al. 2005), SN 1999em (Elmhamdi et al. 2003), SN 2004et (Sahu et al. 2006), SN 2012aw (Bose et al. 2013), SN 2013ab (Bose et al. 2015). These features are tied to the density structure of the ejecta, which in turn controls the amount of occultation of the receding part of ejecta, resulting in biasing of the emission peak (Anderson et al. 2014a), which is not limited to Hα but applicable to all spectral lines. However, such a blueshift is clearly detected for Hα, whereas for most other lines emission profiles are weak and peaks are contaminated by adjacent P Cygni profiles. A detailed SN spectral synthesis code like cmfgen (Dessart & Hillier 2005b) is capable of reproducing such blueshifted emission peaks.

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As inferred from Figure 10, the spectral evolution of SN 2013ej is almost identical to other typical SNe IIP. However, the comparison of 35- and 68-day spectra indicates that Fe ii lines are somewhat underdeveloped as compared to other SNe at similar phases. As seen in the 68-day comparison, the Fe ii (λ λ 4924, 5018, 5169) absorption dips are significantly weaker in comparison to that seen in other SNe.

Another prominent and unusual feature is seen in nebular spectra at 109 and 125 days, on top of Hα emission, and the same is marked as feature A in Figure 14. This unusual dip results in an apparent blueshift of the emission peak, which is in fact larger than that seen in the last plateau spectra at 97 days. Such evolution is unexpected and against the general trend of emission peak evolution in SNe. The low resolution of these spectra prohibits us from investigating this feature in detail. This feature can be split into two emission components, one redshifted at 1200 $\;\mathrm{km}\;{\rm{s}}^{-1}$ and another blueshifted by 1300 $\;\mathrm{km}\;{\rm{s}}^{-1}$ (see the Appendix for further explanation) with respect to the Hα rest position. Such an asymmetric or double-peaked Hα nebular emission has been observed in a number of SNe, e.g., SN 1999em (Leonard et al. 2002a) and SN 2004dj (Chugai et al. 2005). Leonard et al. (2002a) identified such a dip or notch in the Hα emission profile only during the nebular phase of SN 1999em, which they suggested as a possible ejecta–CSM interaction or asymmetry in the line-emitting region. In SN 2004dj, the asymmetry in nebular Hα spectra identified by Chugai et al. (2005) has been explained by bipolar distribution of ⁵⁶Ni with a spherical hydrogen envelope (Chugai 2006).

Progenitor stars prior to explosion develop stratified layers of different elements, which are generally arranged in an elemental sequence, hydrogen being abundant in the outermost shell, whereas heavier metals like iron predominate at deeper layers. However, at the time of shock breakout significant mixing of layers may occur. Spectral lines originating from different layers of the ejecta attain different characteristic velocities. Thus, study of velocity evolution provides important clues to the explosion geometry and the characteristics of various layers. Evolution of the photospheric layer is of special interest as it is directly connected to the kinematics and other related properties. The photosphere represents the layer of the SN atmosphere where optical depth attains a value of ~2/3 (Dessart & Hillier 2005a). Due to complex mixing of layers and continuous recession of the recombination front, no single spectral line can represent the true photospheric layer. During the plateau phase, Fe ii or Sc ii lines are the best estimator of photospheric velocity (${v}_{\mathrm{ph}}$). In early phases, when Fe ii lines are not strongly detectable, the best proxy for ${v}_{\mathrm{ph}}$ is He i, or Hβ (Takáts & Vinkó 2012) in even earlier phases.

Line velocities can be estimated either by directly locating the P Cygni absorption troughs, as done using the splot task of IRAF, or by modeling the line profiles with velocity as one of the inputs, as we do in synow. In Figure 15, we plot the line velocities of Hα, Hβ, Fe ii (λ λ 4924, 5018, 5169), and Sc ii (λ λ 4670, 6247), using the absorption minima method. It is evident that Fe ii and Sc ii line velocities are very close to each other and are formed at deeper layers, whereas Hα and Hβ line velocities are consistently higher at all phases as they form at larger radii. The synow estimated photospheric velocities are also plotted for comparison, which are very close to the Fe ii and Sc ii velocities estimated from the absorption minima method. Here the synow-derived photospheric velocities are estimated by modeling the He i line for the 12-day spectrum and Fe ii lines for the rest of the spectra. Velocities for various lines estimated using synow are tabulated in Table 6.

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Figure 17 shows the comparison of photospheric velocity of SN 2013ej with other well-studied SNe II, SN 1987 A, SN 1999em, SN 1999gi, SN 2004et, SN 2005cs, SN 2012aw, and SN 2013ab. For the purpose of comparison the absorption trough velocities have been used, taking the mean of the Fe ii line triplet, or He i lines at early phases where Fe ii lines are not detectable. The velocity profile of SN 2013ej is very similar to other normal SNe IIP, SN 1999em, SN 1999gi, SN 2004et, SN 2012aw, and SN 2013ab; on the other hand, velocities of SN 2005cs and SN 1987 A are significantly lower. The velocity profile of SN 2013ej is almost identical with SN 2004et, SN 2012aw, and SN 2013ab, whereas it is consistently higher than SN 1999gi and SN 1999em by ∼800–900 $\;\mathrm{km}\;{\rm{s}}^{-1}$. For comparison of H i (Hα and Hβ) velocities, we have chosen all those events that are at least photometrically and spectroscopically similar to SN 2013ej. Comparison reveals that H velocities during later phases (60–100 days) are consistently higher than all comparable events. SN 2012aw and SN 2013ab have photospheric velocities identical to SN 2013ej, but their H velocities are significantly lower by large values, e.g., for SN 2013ej the Hα velocity at 80 days is higher by 1500 $\;\mathrm{km}\;{\rm{s}}^{-1}$ and Hβ is higher by 2400 $\;\mathrm{km}\;{\rm{s}}^{-1}$. Likewise, H velocities for SN 1999em and SN 1999gi are even lower at similar phases. Although SN 2004et H i velocities are somewhat on the higher end, they are still significantly less than those of SN 2013ej. It is also noted that, at 12 days, SN 2013ej H i velocities are consistent and similar to those of other normal SNe, but as it evolves, these velocities decline relatively slowly, ultimately turning into a higher velocity profile after ∼40 days.

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As discussed in Section 5.2, the broad and extended Hα or Hβ absorption profiles are not properly reproduced using a single H i velocity component in synow, and those profiles can only be fitted by incorporating HV components along with the regular one. Figure 16 shows the comparison of synow fits for the 68-day Hβ profile with various single-velocity components, as well as for combined two-velocity components. A single-velocity component at 5600 $\;\mathrm{km}\;{\rm{s}}^{-1}$ can match the blue wing well and partially the trough, whereas it does not match the red side at all. Similarly, a single-velocity component at 4000 $\;\mathrm{km}\;{\rm{s}}^{-1}$ can partially match the red slope of the trough, but it does not include the trough and the extended blue wing. By only matching the trough position, the model fits for a single velocity of 5300 $\;\mathrm{km}\;{\rm{s}}^{-1}$, which does not fit either the blue or the red wing. Even though the "detachment" of H i from the photosphere in the synow model makes the fit of the red wing worse by steepening it further, it is still conclusive that none of these single-velocity components can properly reproduce the absorption profile. It is only by including two velocity components together in the model that we could reproduce the entire Hβ profile. Such a scenario starts to appear from the 42-day spectrum, which only becomes stronger as the line evolves until 97 days. The Hα troughs are also reproduced in a similar fashion. However, it may be noted that such an extended H i feature may also be explained as a possible outcome of a different (complex and extended) density profile that synow cannot reproduce.

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The comparison of Hα and Hβ velocities with other normal SNe IIP (see Figure 17), estimated by directly locating the P Cygni absorption troughs, shows that SN 2013ej velocities are significantly higher and decline relatively slowly (especially during later phases; 60–100 days) as compared to those seen in typical SNe IIP, e.g., SN 1999em, SN 1999gi, SN 2012aw, and SN 2013ab. On the other hand, the photospheric velocity comparison with other SNe IIP does not show any such anomaly. We suggest that this is the effect of blending with H i HV components in Hα and Hβ, which we could separate out while modeling these broad features with synow having two velocity components. The regular Hα and Hβ velocities estimated from synow decline at a normal rate consistent to that seen in other SNe (see Figure 17), whereas the HV components remain at higher velocities of 1000–2000 $\;\mathrm{km}\;{\rm{s}}^{-1}$, declining at a relatively slower rate. It is also interesting to note that the velocity difference between the regular and HV component for Hα and Hβ is similar at the same epochs. Chugai et al. (2007) identified similar HV absorption features associated closely with Hα and Hβ troughs in SN 1999em and SN 2004dj, which remained constant with time. The presence of such HV features has also been detected in SN 2009bw (Inserra et al. 2012) and SN 2012aw (Bose et al. 2013), which is suggestive of interaction of SN ejecta with preexistent CSM. Similar to SN 2013ej, HV signatures have been detected all throughout the plateau-phase evolution of SN 2009bw, while in SN 2012aw such features were only detected at the late plateau phase (55–104 days). Although we found HV components in SN 2013ej by modeling the extended P Cygni troughs, we are unable to visually detect two individual velocity components, which is possibly because of our signal-to-noise-ratio-limited spectra and weaker strength of HV components. Chugai et al. (2007) argued that SN ejecta can interact with the cooler dense shell of CMS material, which might have originated from the pre-SN mass loss in the form of stellar winds. Their analysis showed that such an interaction can lead to the detection of HV absorption features on bluer wings of Balmer lines due to enhanced excitation of the outer layers of unshocked ejecta. We therefore suggest a weak or moderate ejecta–CSM interaction in SN 2013ej. X-ray emission from SN 2013ej has also been reported by Margutti et al. (2013), who measured a 0.3–10 keV count rate of 2.7 ± 0.5 cps, translating into a flux of $\sim 1.1\times {10}^{-13}$ erg s⁻¹cm⁻² (assuming a simple power-law spectral model with photon index Gamma = 2). Such X-ray emission may also indicate an ejecta–CSM interaction suffered by SN 2013ej.

Having characterized the event both photometrically and spectroscopically, we may now revisit the aspects that favor SN 2013ej as a Type IIL event. The SN was originally classified as Type IIP (Valenti et al. 2013) based on spectroscopic similarity to SN 1999gi. Due to the same underlying physical mechanisms that govern both Type IIP and IIL SNe, early spectra may not clearly distinguish these subclasses of SNe II. The distinguishing factor among IIP and IIL is nominal and mainly depends on light-curve characteristics. SN 2013ej shows a decline of 1.74 mag (100 days)⁻¹ (see Table 5) or ∼0.87 mag in 50 days, which definitely falls in the criteria of SNe IIL as proposed by Faran et al. (2014). In Figure 4, the spread of template light curves for Type IIP and IIL (Faran et al. 2014) is shown along with M_V light curves of the SN sample. It is evident that under this scheme of classification, SN 2013ej is not a Type IIP; rather, it is marginally within the range of Type IIL template light curves. This is also justified from the point of the basic idea behind these classifications, that Type IIP must show a "plateau" of almost constant brightness for some time (∼90 days), which is not the case with SN 2013ej. Due to the very fact that SN II light curves and physical properties exhibit a continuum distribution rather than a bi-modality (Anderson et al. 2014b), SN 2013ej shows intermediate characteristics in the SN II diversity.

One distinguishing spectroscopic property Faran et al. (2014) found for SNe IIL is the overall higher photospheric (Fe ii λ5196) velocity and flatter H i (Hβ and Hα) velocity profiles as compared to Type IIP counterparts. Although Fe ii velocities are on the higher end as compared to typical SN IIP velocities, we do not find it to be a remarkable enough deviation to distinguish SN 2013ej from the Type IIP sample. However, we do see an anomaly in Hα and Hβ absorption minima velocity profiles, as they start off with velocities consistent with those of Type IIP but decline relative slowly (see Section 5.4 for more details of this feature), ultimately surpassing faster-declining IIP velocity profiles after 50 days. This characteristic feature of H i velocities for SN 2013ej is typical for most SNe IIL, as found by Faran et al. (2014).

Faran et al. (2014) proposed a possible explanation for the flatter velocity profiles in SNe IIL, which is due to the lack of hydrogen in deeper and slow-expanding layers of ejecta, resulting in higher H i absorption velocities arising mostly from the outer layer. However, for SN 2013ej we suggest that the flattening of Hα and Hβ velocity profiles is due to the contamination of the HV component of H i (see Section 5.5). An indication of CSM interaction in SN 2013ej may also be inferred from X-ray detection by Margutti et al. (2013). Valenti et al. (2015) found SN 2013by, a Type IIL SN, to be moderately interacting with CSM. This led them to question the prevalence of the CSM interaction among SNe IIL in general. SNe IIL originate from progenitors similar to IIPs but have lost a significant fraction of hydrogen before explosion during pre-SN evolution. Hence, it may not be usual to detect HV H i signatures in Hα and Hβ absorption profiles as a consequence of ejecta–CSM interaction. A moderate or weak interaction may produce an HV component blending with Hα and Hβ profiles, which may result in a shift in absorption minima, rather than a prominent secondary HV dip. Such a scenario may perfectly explain the relatively higher and flatter H i velocity profiles of most SNe IIL as compared to IIP counterparts, found by Faran et al. (2014) based on direct velocity estimates of absorption minima.

Another example of CSM interaction in Type IIL is SN 2008fq, which does show a strong interaction signature like a Type IIn (Taddia et al. 2013), but also shows a steep decline like IIL during the first 60 days (Faran et al. 2014). PTF11iqb (Smith et al. 2015) is also an SN IIn, having prominent CSM interaction signatures, but with signatures of IIL like a steeper light curve. Initial spectra of this SN showed IIn characteristics; however, late plateau spectra revealed features similar to Type IIL. PTF11iqb originated from a progenitor identical to Type IIP/L, instead of a luminous blue variable as expected for a typical IIn. However, because of the rare detection of Type IIL events and the fast decline in magnitudes, we do not have sufficient information to investigate a CSM interaction in all such objects. Thus, the question still remains open whether all or most SNe IIL interact with CSM and whether the flatter H i absorption minima velocity profiles are a consequence of interaction.