Type II Supernova Spectral Diversity. I. Observations, Sample Characterization, and Spectral Line Evolution^*

A total of four SNe II (SN 1986L, SN 1988A, SN 1990E, and SN 1990K) were extensively observed at CTIO by the Cerro Tololo SN program (PIs: Phillips and Suntzeff, 1986–2003). These SNe have been analyzed in previous works (e.g Schmidt et al. 1993; Turatto et al. 1993; Cappellaro et al. 1995; Hamuy 2001).

The Calán/Tololo survey was a program of both discovery and follow-up of SNe. A total of 50 SNe were obtained between 1989 and 1993. The analysis of SNe Ia was published by Hamuy et al. (1996). Spectral and photometric details of six SNe II were presented by Hamuy (2001). In this analysis, we include these SNe II and an additional object, SN 1993K.

The Supernova Optical and Infrared Survey carried out a program to obtain optical and IR photometry and spectroscopy of nearby SNe ($z\lt 0.08$). In the course of 1999–2000, 20 SNe were observed, 6 of which are SNe II. Details of these SNe were published by Hamuy (2001, 2003), Hamuy et al. (2001), and Hamuy & Pinto (2002).

Between 2002 and 2003 the Carnegie Type II Supernova Survey observed 34 SNe II. While optical spectroscopy and photometry of these SNe II have been previously used to derive distances (Olivares 2008; Jones et al. 2009), the spectral observations have not been officially released until now.

The Carnegie Supernova Project I (CSP-I) was a five-year follow-up program to obtain high quality optical and near-infrared light curves and optical spectroscopy. The data obtained by the CSP-I between 2004 and 2009 consist of ∼250 SNe of all types, of which 75 correspond to SNe II. The first SN Ia photometry data were published in Contreras et al. (2010), while their analysis was done by Folatelli et al. (2010). A second data release was provided by Stritzinger et al. (2011). A spectroscopy analysis of SNe Ia was published by Folatelli et al. (2013). Recently, Stritzinger et al. (2017) and Taddia et al. (2017) published the photometry data release of stripped-envelope supernovae. The CSP-I spectral data for SNe II are published here for the first time, while the complete optical and near-IR photometry will be published by C. Contreras et al. (2017, in preparation).

The data presented here were obtained with a large variety of instruments and telescopes, as shown in Table 6. The majority of the spectra were taken in long-slit spectroscopic mode with the slit placed along the parallactic angle. However, when the SN was located close to the host, it was necessary to pick a different and more convenient angle to avoid contamination from the host. The majority of our spectra cover the range of ∼3800 to ∼9500 Å. The observations were performed with the Cassegrain spectrographs at 1.5 m and 4.0 m telescopes at Cerro Tololo, with the Wide Field CCD Camera (WFCCD) at the 2.5 m du Pont Telescope, the Low Dispersion Survey Spectrograph (LDSS2; Allington-Smith et al. 1994) on the Magellan Clay 6.5 m telescope and the Inamori Magellan Areal Camera and Spectrograph (IMACS; Dressler et al. 2011) on the Magellan Baade 6.5 m telescope at Las Campanas Observatory. At La Silla, the observations were carried out with the ESO Multi-Mode Instrument (EMMI; Dekker et al. 1986) in medium resolution spectroscopy mode (at the NTT) and the ESO Faint Object Spectrograph and Camera (EFOSC; Buzzoni et al. 1984) at the NTT and 3.6 m telescopes. We also have three spectra for SN 2006ee obtained with the Boller & Chivens CCD spectrograph at the Hiltner 2.4 m Telescope of the MDM Observatory. Table 6 displays a complete journal of the 888 spectral observations, listing for each spectrum the UT and Julian dates, phases, wavelength range, FWHM resolution, exposure time, airmass, and the telescope and instrument used.

The distribution of the number of spectra per object for our sample is shown in Figure 2. Seven SNe (SN 1993A, SN 2005dt, SN 2005dx, SN 2005es, SN 2005gz, SN 2005me, and SN 2008H) only have one spectrum, while 90% of the sample have between 2 and 12 spectra. SN 1986L is the object with the most spectra (31), followed by SN 2008bk with 26. On average, we have 7 spectra per SN and a median of 6. There are 87 SNe II for which we have five or more spectra, 32 that have 10 or more, and 6 objects with over 15 spectra (SN 1986L, SN 1993K, SN 2007oc, SN 2008ag, SN 2008bk, and SN 2008if). In the current work, 4% of our obtained spectra are not used for analysis. 3% correspond to spectra with low S/N that does not allow for useful extraction of our defined parameters, while 1% are related with peculiarities in the spectra (see Section 5 for more details). Despite this, these spectra are still included in the data release and are noted in Table 6.

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Spectral reduction was achieved in the same manner for all data, using IRAF and employing standard routines, including bias subtraction, flat-fielding correction, one-dimensional (1D) spectral extraction and sky subtraction, wavelength correction, and flux calibration. Telluric corrections have only been applied to data obtained after 2004 October.

In Appendix A (spectral series), we show plots with the spectral series for all SNe of our sample.

To constrain the explosion epoch for our sample, we compare the first spectrum of each SN II with a library of spectral templates provided by SNID and then, we choose the best match. For each SN, we examined multiple matches, putting emphasis on the fit of the blue part of the spectrum between 4000 and 6000 Å. This region contains many spectral lines that display a somewhat consistent evolution with time, unlike the dominant H_α profile at redder wavelengths. Explosion epoch errors from this spectral matching are obtained by taking the standard deviation of several good matches of the observed spectrum of our selected object with those from the SNID library. H_α is the dominant feature in SN II spectra; however, its evolution and morphology varies greatly between SNe in a manner that does not aid in the spectral matching technique. We therefore ignore this wavelength region.

The red part of the spectrum can be ignored during spectral matching in a variety of ways: (1) using the SNID options; or (2) checking only the match in the blue part. For the former, SNID gives to the user the alternative to modify some parameters. In our case, we can constrain the wavelength range using wmin and wmax. Hence, the structure used is "snid wmin = 3500 wmax = 6000 spec.dat". For the latter, we just need to ignore visually the red part of the spectra and explore the matches obtained by SNID until we find a good fit in the blue part.²⁵

From the SNID library, we use those template SNe that have well constrained explosion epochs, meaning SNe II with explosion epoch errors of less than five days (see Table 2). Specifically, we used SN 1999em (Leonard et al. 2002b), SN 1999gi (Leonard et al. 2002a), SN 2004et (Li et al. 2005), SN 2005cs (Pastorello et al. 2006), and SN 2006bp (Dessart et al. 2008). In the database of SNID, there are a total of 166 spectra. However, these templates do not provide a good coverage of the overall diversity of SNe II within our sample/the literature. Most of the SNe in the library are relatively "normal," with only one subluminous event (SN 2005cs). This means that any non-normal event within our sample will probably have poor constraints on its explosion epoch using these templates. For this reason, we decided to use some of our own well-observed SNe II to complement the SNID database.

We created a new set of spectral templates using our own SNe II nondetection limits. SNe II are included as new SNID templates if they have errors on explosion epochs (through nondetection constraints) of less than five days. Given this criterion, we included 22 SNe, which show significant spectral and photometric diversity. In this manner, the new SNID templates were constructed using ∼150 spectra and prepared using the logwave program included in the SNID packages. Adding our own template SNe to the SNID database, we can now use a total of 27 template SNe II to estimate the explosion epoch. Table 2 shows the explosion epoch and the maximum dates in V-band for the reference SNe, as well as the explosion epoch for our new templates. We note an important difference between our templates and previous ones in SNID: for the newer templates, epochs are labeled with respect to the explosion epoch, while for the older templates epochs are labeled with respect to maximum light (meaning that one then has to add the "rise time" to obtain the actual explosion date, see Table 2).

With the inclusion of these 22 SNe to SNID, we estimated the explosion epoch for our full sample. An example of the best match is shown in Figure 3. We can see that the first spectrum of SN 2003iq (October 16th) is best matched with SN 2006bp, SN 2004et, SN 1999em, and SN 2004fc 12, 13, 7, and 9 days from explosion, respectively. Taking the average, we conclude that the spectrum was obtained at 10 ± 7 days since the explosion. Table 1 shows the explosion epoch for each SN as well as the method employed to derive it, while Table 7 shows all the details of spectral matching and nondetection techniques. Appendix B (SNID matches) shows the plots with the best matches for each SN in our sample.

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To check the validity of spectral matching, we compare the explosion epoch estimated with this technique and those with nondetections. These two estimations are displayed in Table 7. From the second to the seventh column, the spectral matching details are shown (spectrum date, best match found, days from maximum—from the SNID templates—days from explosion, average, and explosion date), while from eighth to tenth, those obtained from the nondetection (nondetection date, discovery date, and explosion date). The differences between both methods are presented in the last column. Such an analysis was previously performed by Anderson et al. (2014b), where good agreement was found. With the use of our new templates, we are able to improve the agreement between different explosion epoch constraining methods, thus justifying their inclusion. Figure 4 shows a comparison between both methods, where the mean absolute error between them diminishes from 4.2 (Anderson et al. 2014b) to 3.9 days. Also the mean offset decreases from 1.5 days in Anderson et al. (2014b) to 0.5 days in this work. Cases where explosion epochs have changed between Anderson et al. (2014b) and the current work are noted in Table 1. Nevertheless, although this method works well as a substitute for nondetections, exact constraints for any particular object are affected by any peculiarities inherent to the observed (or indeed template) SN. For example, differences in the color (and therefore temperature) evolution of events can mimic differences in time evolution, while progenitor metallicity differences can delay/hasten the onset of line formation. Further improvements of this technique can only be obtained by the inclusion of additional, well-observed SNe II in the future.

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${{\rm{H}}}_{\alpha }$ $\lambda 6563$ is the dominant spectral feature in SNe II. It is usually used to distinguish different SN types using the initial spectral observation. This line is present from explosion until nebular phases, showing, in the majority of cases, a P-Cygni profile. Although the P-Cygni profile has an absorption and emission component, SNe display a huge diversity in the absorption feature.

Gutiérrez et al. (2014) showed that SNe with little absorption of ${{\rm{H}}}_{\alpha }$ (smaller absorption to emission (a/e) values) appear to have higher velocities, faster declining light curves, and tend to be more luminous. Here we show that H_α displays a large range of velocities in the photospheric phase, from 9500 to 1500 km s⁻¹ at 50 days (see the first two panels in Figure 11, which correspond to the ${{\rm{H}}}_{\alpha }$ velocity derived from the FWHM of the emission component and from the minimum flux of the absorption, respectively).

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The diversity of ${{\rm{H}}}_{\alpha }$ in the photospheric phase is also observed through the blueshift of the emission peak at early times (Dessart & Hillier 2008; Anderson et al. 2014a) and the boxy profile (Inserra et al. 2011, 2012). The former is associated with differing density distributions of the ejecta, while the latter with an interaction of the ejecta with a dense CSM. In the nebular phase this shift in ${{\rm{H}}}_{\alpha }$ emission peak has been interpreted as evidence of dust production in the SN ejecta. Despite the fact that this is an important issue in SNe II, only a few studies (e.g., Sahu et al. 2006; Kotak et al. 2009; Fabbri et al. 2011) have focussed on these features.

In Figure 12, we show an example of the evolution of the ${{\rm{H}}}_{\alpha }$ P-Cygni profile in SN 1992ba. We can see in early phases a normal profile, which evolves to a complicated profile around 65 days. Cachito on the blue side of ${{\rm{H}}}_{\alpha }$ is present from 65 to 183 days.

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H_β $\lambda 4861$, ${{H}}_{\gamma }$ $\lambda 4341$, and ${{\rm{H}}}_{\delta }$ $\lambda 4102$ like ${{\rm{H}}}_{\alpha }$ are present from the first epochs. In earlier phases, these lines show a P-Cygni profile; however, from ∼15 days the spectra only display the absorption component, giving space to Fe-group lines. The range of velocities of ${{\rm{H}}}_{\beta }$, ${{\rm{H}}}_{\gamma }$, and ${{\rm{H}}}_{\delta }$ at 50 days post-explosion vary from 8000 to 1000 km s⁻¹ (see Figure 11).

Although ${{\rm{H}}}_{\delta }$ is a common line in SNe II, we do not include a detailed analysis of this line because in many cases the spectra are noisy in the blue part of the spectrum. Besides, like other lines in the blue, this line is blended with Fe-group lines later than 30 days.

Around 30 days from explosion ${{\rm{H}}}_{\gamma }$ starts to blend with other lines, such as Ti ii and Fe ii. Meanwhile, in a few SNe, the ${{\rm{H}}}_{\beta }$ absorption feature is surrounded by the Fe line forest. Our later analysis shows that SNe displaying this behavior are generally dimmer and lower velocity events (see Section 8 for more details).

He i $\lambda 5876$ is present in very early phases when the temperature of the ejecta is high enough to excite the ground state of helium. As the temperature decreases, the He i line starts to disappear due to low excitation of He i ions (around 15 days; Dessart & Hillier 2010; Roy et al. 2011). At ∼30 days, the Na i D $\lambda 5893$ absorption feature arises in the spectrum at a similar position where He i was located. This new line evolves with time to a strong P-Cygni profile, displaying velocities between 8000 and 1500 km s⁻¹ at 50 days from explosion (Figure 11).

In many SNe II (or indeed SNe of all types), at these wavelengths one often observes narrow absorption features arising from slow-moving line-of-sight material from the interstellar medium, ISM (or possibly from circumstellar material, CSM). Such material can constrain the amount of foreground reddening suffered by SNe; however, we do not discuss this here.

When the SN ejecta has cooled sufficiently, Fe ii features start to dominate SNe II spectra between 4000 and 6500 Å. The first line that appears is Fe ii $\lambda 5169$ on top of the emission component of ${{\rm{H}}}_{\beta }$. With time Fe ii $\lambda 5018$ and $\lambda 4924$ emerge between ${{\rm{H}}}_{\beta }$ and Fe ii $\lambda 5169$. Fe ii $\lambda 5169$ becomes a Fe ii blend later than ∼30–40 days. At ∼50 days, the 4000–5500 Å region is completely filled with these lines and the continuum is diminished due to Fe ii line-blanketing. The ${{\rm{H}}}_{\gamma }$ and ${{\rm{H}}}_{\delta }$ absorption features are blended with Fe-group lines, such as Fe ii, Ti ii, Sc ii, and Sr ii. Between ∼5400 and 6500 Å other metal lines appear in the spectra. Lines such as Sc ii/Fe ii $\lambda 5531$, Sc ii M, Ba ii $\lambda 6142$, and Sc ii $\lambda 6247$ get stronger with time.

As we can see in Figure 11, the Fe-group lines show a range of velocities between 7000 and 500 km s⁻¹ at 50 days. The peak of the distribution of the Fe ii group lines velocities is around 4000 km s⁻¹. In the case of Ba ii, the peak is lower (around 3000 km s⁻¹).

Although Fe ii lines always appear at late phases, few SNe show the iron line forest at 30 days. This feature appears earlier in low velocity/luminosity SNe (see Section 8).

The Ca ii NIR triplet is a strong feature in the spectra of SNe II. This line appears at ∼20–30 days as an absorption feature, but with time it starts to show an emission component. The Ca ii NIR triplet results in a blend of λ8498 and λ8542 in the bluer part and a distinct component, λ8662 on the red part. In SNe II with higher velocities these lines are blended producing a broad absorption and emission profile; however, in low velocity SNe, we see two absorption components and one emission in the red part. The velocities of the Ca ii NIR triplet range between 9000 and 1000 km s⁻¹ at 50 days. In the nebular phase, the Ca ii NIR triplet is also present; however, at this epoch, it only exhibits the emission component.

Although in the majority of our spectra we cannot see Ca ii H and K $\lambda 3945$, due to the poor signal-to-noise in this region, this line is present in the photospheric phase of SNe II.

While the Ca ii NIR triplet is a prominent feature in SNe II, we do not include its analysis in the subsequent discussion, given that the overlap of lines makes a consistent comparison of velocities and pseudo-equivalent widths (pEWs) difficult.

The O i $\lambda \lambda 7772$, 7775 doublet (hereafter O i $\lambda 7774$) and O i $\lambda 9263$ are the oxygen lines in the optical spectra of SNe II. These lines are mainly driven by recombination and they appear when the temperature decreases sufficiently. The O i $\lambda 7774$ line is relatively strong and emerges around 20 days from explosion; however, in the majority of cases it is contaminated by the telluric A-band absorption (∼7600–7630 Å), which hinders detailed analysis. O i $\lambda 9263$ is weaker and appears one month later than O i $\lambda 7774$. These lines are present until the nebular phase and their expansion velocity at 50 days post-explosion goes from ∼7000 to 500 km s⁻¹, as can be seen in Figure 11.

The extra absorption component on the blue side of the ${{\rm{H}}}_{\alpha }$ P-Cygni profile, called here "Cachito," is seen in early phases in some SNe (e.g., SN 2005cs, Pastorello et al. 2006; SN 1999em, Baron et al. 2000) as well as in the plateau phase (e.g., SN 1999em, Leonard et al. 2002b SN 2007od, Inserra et al. 2011). However, its shape and strength is completely different in the two phases. Baron et al. (2000) assigned the term "complicated P-Cygni profile" to explain the presence of this component on the blue side of the Balmer series. They concluded that these features are due to velocity structures in the expanding ejecta of the SNe II. A few years later, Pooley et al. (2002) and Chugai et al. (2007) argued that this extra component might originate from ejecta—circumstellar (CS) interactions, while Pastorello et al. (2006) earmarked this feature as Si ii $\lambda 6355$.

In general, Cachito appears around 5–7 days between 6100 and 6300 Å, and disappears at ∼35 days after explosion. Later than 40 days, the Cachito feature emerges closer to ${{\rm{H}}}_{\alpha }$ (between 6250 and 6450 Å) and it can be seen until 100–120 days. Figure 13 shows this component in SN 2007X. In early phases, this feature is marked with letter A and later with letter B. If attributed to ${{\rm{H}}}_{\alpha }$ the derived velocities are 18,000 and 10,000 km s⁻¹, respectively. A detailed analysis of this feature is presented in Section 8.4.

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As mentioned above, ${{\rm{H}}}_{\alpha }$, ${{\rm{H}}}_{\beta }$, the Ca ii NIR triplet, Na iD, O i, and Fe ii are also present in the nebular phase (later than 200 days since explosion); however, in the case of the Ca ii NIR triplet, its appearance changes, passing from absorption and emission components to only emission components when the nebular phase starts. The rest of the lines have the same behavior but at much later epochs. The emergence of forbidden emission lines signifies that the spectrum is now forming in regions of low density. At this phase, the ejecta has become transparent, allowing us to peer into the inner layers of the rapidly expanding ejecta. Lines such as [Ca ii] $\lambda \lambda 7291,$ 7323, [O i] $\lambda \lambda 6300,$ 6364, and ${{\rm{H}}}_{\alpha }$ are the strongest features visible in the spectra.

The [O i] doublet observed at nebular times is one of the most important diagnostic lines of the helium-core mass (Fransson & Chevalier 1987; Jerkstrand et al. 2012). Usually the doublet is blended; however, in SNe with low velocities these lines can be resolved (see, e.g., SN 2008bk). On the other hand, [Fe ii] $\lambda 7155$ is easily detectable, but in most cases it is blended with [Ca ii] $\lambda \lambda 7291,$ 7323, and He i $\lambda 7065$, which may hinder their analysis. In Figure 14, we can see the diversity found in the nebular spectra in our sample.

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The expansion velocities of the ejecta are commonly measured from the minimum flux of the absorption component of the P-Cygni line profile. Using the Doppler relativistic equation and the rest wavelength of each line, we can derive the velocity. To obtain the position of the minimum line flux (in wavelength), a Gaussian fitting was employed, which was performed with IRAF, using the splot package. As the absorption component presents a wide diversity (e.g., asymmetries, flat shape, extra absorption components), we repeat the process many times (changing the pseudo-continuum), and the mean of the measurements was taken as the minimum flux wavelength. As our measurement error, we take the standard deviation on the measurements. This error is added in quadrature to errors arising from the spectral resolution of our observations (measured in Å and converted to kilometers per second) and from peculiar velocities of host galaxies with respect to the Hubble flow (200 km s⁻¹). This means that, in addition to the standard deviation error, which realizes the width of the line and S/N, we take into account the spectral resolution, which, in our case, is the most dominant parameter to determine the error.

The particular case of the ${{\rm{H}}}_{\alpha }$ velocity was explored in Gutiérrez et al. (2014). Due to the difficulty of measuring the minimum flux in a few SNe with little or extremely weak absorption components, we derive the expansion velocity of ${{\rm{H}}}_{\alpha }$ using both the minimum flux of the absorption component and the full width at half maximum (FWHM) of the emission line.

In the case of O i λ 7774, where the telluric lines can affect our measurement of its absorption minimum, we only use SNe with a clear separation between the two features. This means that the number of SNe with O i measurements is significantly smaller (only 47 SNe) compared to the other measured features.

To calculate the time derivative of the expansion velocity in SNe II, we select the ${{\rm{H}}}_{\beta }$ absorption line. It is present from the early spectra, it is easy to identify and it is relatively isolated. To quantitatively analyze our sample, we introduce the Δv(H_β) as the mean velocity decline rate in a fixed phase range [t₀,t₁]: ${\rm{\Delta }}{\text{}}v({{\rm{H}}}_{\beta })=\tfrac{{\rm{\Delta }}{v}_{\mathrm{abs}}}{{\rm{\Delta }}t}=\tfrac{{v}_{\mathrm{abs}}({t}_{1})-{v}_{\mathrm{abs}}({t}_{0})}{{t}_{1}-{t}_{0}}$.

This parameter was measured over the interval [+15, +30] d, [+15, +50] d, [+30, +50] d, [+30, +80] d, and [+50, +80] d.

To quantify the spectral properties of SNe II, another avenue for investigation is the measurement and characterization of spectral line pEWs. The prefix "pseudo" is used to indicate that the reference continuum level adopted does not represent the true underlying continuum level of the SN, given that in many regions the spectrum is formed from a superposition of many spectral lines. The pEW basically defines the strength of any given line (with respect to the pseudo-continuum) at any given time. The simplest and most often used method is to draw a straight line across the absorption feature to mimic the continuum flux. Figure 15 shows an example of this technique applied to SN 2003bn. We do not include analysis of spectral lines where it is difficult to define the continuum level, due to complicated line morphology, such as significant blending between lines. For example, later than 20–25 days, all absorption features bluer than ${{\rm{H}}}_{\beta }$ are produced by blends of Fe-group lines plus other strong lines, such as Ca ii H & K and ${{\rm{H}}}_{\gamma }$. On the other hand, the Ca ii NIR triplet $\lambda \lambda 8498$, 8662 shows a profile that depends on the SN velocity (higher velocity SNe show a single broad absorption, while low velocity SNe show two absorption characteristics). These attributes make a consistent analysis between SNe difficult, and therefore we do not include this line in our analysis.

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We measure the ratio of absorption to emission (a/e) in ${{\rm{H}}}_{\alpha }$ until 120 days. In the same way, the pEWs of the absorption lines are measured, we evaluate the pEWs for the emission in ${{\rm{H}}}_{\alpha }$, thus we have: $a/e=\tfrac{p\mathrm{EW}({H}_{\alpha (\mathrm{abs})})}{p\mathrm{EW}({H}_{\alpha (\mathrm{emis})})}$.

Figure 18 shows the velocity evolution of 11 spectral features as a function of time. The first two panels of the plot show the expansion velocity of the H_α feature: on the left, the velocity derived from the FWHM and on the right that derived from the minimum absorption flux. As we can see, the behavior is similar; however, the velocity obtained from the minimum absorption flux is offset between 10% and 20% to higher velocities. Figure 19 shows this shift at 50 days. Velocities obtained from the minimum absorption flux are higher around ∼1000 km s⁻¹. However, it is possible to see few SNe (with higher ${{\rm{H}}}_{\alpha }$ velocities) showing higher values from the FWHM. Using the Pearson correlation test, we find a weak correlation, with a value of $\rho =0.37$. SNe II with narrower emission components display a larger offset between the velocity from the FWHM and that from the minimum of the absorption. In contrast, those SNe II displaying the highest FWHM velocities present comparatively lower minimum absorption velocities. We note also the presence of two outliers (extreme cases, the lowest and highest value). Figure 11 shows the velocity distribution for the 11 features at 50 days post-explosion. We can see that ${{\rm{H}}}_{\alpha }$ shows higher velocities than the other lines, followed by ${{\rm{H}}}_{\beta }$. The lowest velocities are presented by the iron-group lines. In Figure 18, it is possible to see that the ${{\rm{H}}}_{\beta }$ expansion velocity shows the typical evolution for a homologous expansion and like ${{\rm{H}}}_{\alpha }$, it is possible to see it from early phases. The iron lines display lower velocities than the Balmer lines. So, the highest velocity in SNe II is found in ${{\rm{H}}}_{\alpha }$, which implies that it is formed in the outer layers of the SN ejecta. Meanwhile, based on the lower velocities, the iron-group lines form in the inner part, closer to the photosphere. The O i line does not show a strong evolution. As we can see, its velocity evolution is almost flat.

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The lowest velocities are found in SN 2008bm, SN 2009aj, and SN 2009au. However, these SNe are distinct from the rest of the population. Unlike subluminous SNe II (such as SN 2008bk and SN 1999br)—that also display low expansion velocities—these events are relatively bright. They also show early signs of CS interactions, e.g., narrow emission lines. By contrast, SN 2007ab, SN 2008if, and SN 2005Z have the largest velocities.

The velocity decline rate of SNe II, denoted as Δv(H_β), has not been previously analyzed. We estimate Δv(H_β) in five different epochs (outlined above) to understand their behavior. We find that SNe with a higher decline rate at early times continue to show such behavior at later times. The median velocity decline rate for our sample between 15 and 30 days is 105 km ${{\rm{s}}}^{-1}$ day⁻¹, while between 50 and 80 days is 29 km ${{\rm{s}}}^{-1}$ day⁻¹. These results show an evident decrease in the velocity decline rate at two different intervals, which is consitent with homologous expansion.

The temporal evolution of pEWs for each of the 11 spectral features is shown in Figure 20. In general, the pEWs increase quickly in the first one to two months then level off. The first two panels show the pEW evolution of ${{\rm{H}}}_{\alpha }$. On the left is displayed the absorption, while on the right the emission component. The absorption component monotonically increases from 0, increasing to ∼100 Å; however, in a few SNe its evolution is different: from 70 days, the pEW decreases significantly. This behavior is observed in low and intermediate velocity SNe (e.g., SN 2003bl, SN 2006ee, SN 2007W, SN 2008bk, SN 2008in, and SN 2009N). Generally, these SNe show a very narrow ${{\rm{H}}}_{\alpha }$ P-cygni profile, and at around 70 days from explosion Ba ii $\lambda 6497$ appears in the spectra as a dominant feature (see Roy et al. 2011; Lisakov et al. 2017 for more details). In Figure 21, we can see the ${{\rm{H}}}_{\alpha }$ P-Cygni profile with the presence of Ba ii $\lambda 6497$, and the HV feature of hydrogen line (see Section 8.4 for more details) on the blue side of Ba ii.

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Figure 20 also shows the ${{\rm{H}}}_{\alpha }$ emission component evolution. An increment in the pEW in the majority of SNe is appreciable. There are a couple cases (e.g., SN 2006Y), displaying a quasi-constant evolution. The range of pEW of ${{\rm{H}}}_{\alpha }$ emission goes up 400 Å. In the case of ${{\rm{H}}}_{\beta }$, we can see that from 60 days there are few SNe with low pEW values, which show a quasi-constant evolution. SNe with this behavior are those that show the Fe ii line forest. The remaining SNe show an increase. The pEWs of iron-group lines grow with time; however, there is a group of SNe with pEW = 0. This indicates that some specific SNe do not have the line yet. For Sc ii/Fe ii, the Sc ii multiplet, Ba ii, and Sc ii, this is more obvious. On the other hand, the O i shows a quasi-constant behavior and Na i D shows a steady increase. Comparing the values, we can see that the absorption of ${{\rm{H}}}_{\alpha }$, ${{\rm{H}}}_{\beta }$, and Na i D have the highest values (from 0 to ∼120), while Fe ii $\lambda 4924$, Fe ii $\lambda 5018$, Sc ii/Fe ii, the Sc ii multiplet, Ba ii, Sc ii, and O i have the lowest ones (from 0 to ∼50).

The a/e evolution is displayed in Figure 22. One can see an increase until ∼60 days and then, the quantity remains constant or slightly decreases.

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The nature of Cachito has recently been studied. Its presence on the blue side of ${{\rm{H}}}_{\alpha }$ has given rise to multiple interpretations, such as HV features of hydrogen (e.g., Baron et al. 2000; Leonard et al. 2002b; Chugai et al. 2007; Inserra et al. 2011) or Si ii $\lambda 6355$ (e.g., Pastorello et al. 2006; Tomasella et al. 2013; Valenti et al. 2014). From our sample, 70 SNe show Cachito in the photospheric phase, between 7 and 120 days post-explosion; however, its behavior, shape, and evolution is different depending on the phase. To investigate the nature of Cachito, we examine the following possibilities.

• 1.  
  If Cachito is produced by Si ii, its velocity should be similar to those presented by other metal lines.
• 2.  
  If Cachito is related to HV features of hydrogen, its velocity should be almost the same as those obtained from ${{\rm{H}}}_{\alpha }$ at early phases. In addition, if it is present, a counterpart should be visible on the blue side of ${{\rm{H}}}_{\beta }$.

Analyzing our sample, we can detect Cachito in 50 SNe at early phases (before 40 days). Because of the high temperatures at these epochs, the presence of Ba ii $\lambda 6497$ is discarded. Assuming that Cachito is produced by Si ii, we find that 60% of SNe present a good match with Fe ii $\lambda 5018$ and Fe ii $\lambda 5169$ velocities.³⁰ Conversely, the rest of the sample shows velocities comparable to those measured at very early phases for ${{\rm{H}}}_{\alpha }$. Curiously, the Cachito shape is different between the two SN groups. In the former, the line is deeper and broader, while, in the latter, the line is shallow. In Figure 23, we present the velocity comparison for the former group, where a good agreement is found between Cachito, assumed as Si ii $\lambda 6355$ (blue), and the iron lines, Fe ii $\lambda 5018$ (green) and Fe ii $\lambda 5169$ (red).

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Later than 40 days, we detect Cachito in 43 SNe. Proceeding with the velocity comparison, we can discard its identification as Si ii or Ba ii $\lambda 6497$ (the latter, visible in few SNe from 60 days, see Figure 21), which suggests that Cachito is associated to hydrogen. During the plateau, it is possible to see Cachito as a shallow absorption feature only in ${{\rm{H}}}_{\alpha }$ and/or as a narrow and deeper absorption on the blue side of both ${{\rm{H}}}_{\alpha }$ and ${{\rm{H}}}_{\beta }$ (see an example in Figure 24). According to Chugai et al. (2007), the interaction between the SN ejecta and the RSG wind should result in the emergence of these HV absorption features. They argue that the existence of a shallow absorption feature is the result of the enhanced excitation of the outer unshocked ejecta, which is visible on the blue side of ${{\rm{H}}}_{\alpha }$ (and He i λ10830). At early times, the ${{\rm{H}}}_{\beta }$ Cachito feature is not predicted by Chugai et al. (2007), who argue that the optical depth is too low at the line-forming region. They also discuss that in addition to the HV shallow absorption, an HV notch is formed in the cool dense shell (CDS) located behind the reverse shock. Given the relatively high ${{\rm{H}}}_{\alpha }$ optical depth of the CDS, a counterpart could be seen in ${{\rm{H}}}_{\beta }$ as well. We found that 63% of the SNe with Cachito during the plateau show a counterpart in ${{\rm{H}}}_{\beta }$ with the same velocity as that presented on ${{\rm{H}}}_{\alpha }$, which favors the interpretation as CS interaction. The HV notch of H i is found in 27 SNe; however, in the low velocity/luminosity SNe, it is only present in ${{\rm{H}}}_{\alpha }$. After 50 days, the blue part of the spectrum (<5000 Å) is dominated by metal lines, which may hinder its detection. Nonetheless, we argue that these can be HV H i because at least one low velocity/luminosity SN, SN 2006ee, shows a Cachito feature on the blue side of both H_α and H_β, at around 50 days with consistent velocities. A summary of the analysis is displayed in Figure 25, where the ${{\rm{H}}}_{\alpha }$ (red), HV ${{\rm{H}}}_{\alpha }$ (blue), H_β (cyan), and HV ${{\rm{H}}}_{\beta }$ (green) velocity evolution is presented for 20 SNe.

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In addition to the 70 SNe where Cachito can be identified either with Si ii or HV features of H i, we find six SNe II that display Cachito at certain epochs; however, its exact properties do not align with the above interpretations (because of differences in shape and/or velocity). These are SN 2003bl, SN 2005an, SN 2007U, SN 2008br, SN 2002gd, and SN 2004fb. In summary, 59% of the full SNe sample show Cachito at some epoch, while 41% never show this feature. Soon after shock break-out, all SNe II have extremely high temperature ejecta. Therefore, if we were able to obtain spectral sequences shortly after explosion, the Si ii feature would always be observed. However, observationally, this is not the case because there are many SNe II within our sample without Si ii detections. This is simply an observational bias, due to the lack of data at very early times. Nevertheless, for SNe II that stay hotter for longer, the probability of detecting Si ii becomes larger. We therefore speculate that SNe II that have detected Si ii at early times have larger radii, which leads to a slower cooling of the ejecta and hence facilitates Si ii detection. Interestingly, when we split the sample into those SNe II that do and do not display the Si ii line, those where the line is detected are found to have lower a/e values, with only a 4% chance that the two populations are drawn from the same underlying distribution. This is also consistent with the previous finding that those SNe II with evident He i detections at around 20 days post-explosion are also found to have lower a/e values, suggesting that the value of a/e is related to ejecta temperature evolution.

In the case of those SNe II displaying Cachito consistent with HV features, these are most likely produced by the interaction of the SN ejecta with the RSG wind, where the exact shape and persistence of Cachito is related to the wind density Chugai et al. (2007). In Figure 26, one can observe the significant diversity in the different detection of Cachito.

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