Puzzling High-Velocity Calcium Absorption Features Of Type Ia Supernovae

Type Ia supernovae (SNe Ia) have been precise distance indicators because of their relatively homogeneous brightness (e.g. Phillips, 1993; Phillips et al., 1999; Riess et al., 1998, 2019; Perlmutter et al., 1999; Freedman et al., 2019; Jha et al., 2019). They are believed to be caused by explosive thermonuclear burning triggered either in the core of a nearly-Chandrasekhar-mass white dwarf (WD) (e.g. Nomoto, 1982; Khokhlov, 1991; Hillebrandt & Niemeyer, 2000; Maeda et al., 2010, 2018; Flörs et al., 2020) or on the surface of a sub-Chandrasekhar-mass WD (e.g. Kushnir et al., 2013; Pakmor et al., 2013; Blondin et al., 2018; Shen et al., 2018; Flörs et al., 2020). There are two popular scenarios proposed for their progenitor systems: (1) single degenerate scenario (SD) consists of a CO white dwarf (WD) and a non-degenerate companion star such as a main-sequence or red-giant star (e.g. Whelan & Iben, 1973; Nomoto, 1982). An example is PTF 11kx which shows a low velocity ($<1,000$ km/s) Ca II H&K along with narrow He I $\lambda$5876 in its spectra (e.g. Dilday et al., 2012). The low velocity Ca substances were likely ejected from a symbiotic nova progenitor, while He lines indicate a non-degenerate companion star. (2) double degenerate scenario (DD) consists of two WDs (e.g. Iben & Tutukov, 1984; Webbink, 1984). The DD scenario may explain, for example, the lack a companion star with luminosity greater than a few percent of the sun associated with the famous nearby SN 2011fe (e.g. Li et al., 2011).

Detailed information about SN Ia, for example the element distributions, the kinematics or the temperature are mostly obtained through spectroscopic analysis of absorption features. Important features include at least: Si II $\lambda$6355 whose velocity is often chosen to represent the velocity of the ejecta; C II $\lambda$6580 which serves as an indicator of unburnt carbon (e.g. Thomas et al., 2011; Folatelli et al., 2012); Si II $\lambda$5972 as an indicator of the photospheric temperature and peak luminosity as well (Nugent et al., 1995; Blondin et al., 2012; Zhao et al., 2015); variable sodium lines, H and He lines as indicators of thick CSM (e.g. Patat et al., 2007; Blondin et al., 2009; Dilday et al., 2012). According to the velocity gradient of Si II $\lambda$6355, SNe Ia can be grouped into subgroups of ‘Faint’, ‘high-velocity gradient’ (HVG), and ‘low-velocity gradient’ (LVG) SNe Ia (Benetti et al., 2005). Based on the line strengths of Si II $\lambda$6355 and $\lambda$5972, SNe Ia are grouped into ‘core-normal’ (CN), ‘broad-line’ (BL), ‘cool’, and ‘shallow silicon’ (SS) SNe Ia (Branch et al., 2009). According to the velocity of Si II $\lambda$6355 ($V_{Si6355}$), SNe Ia are mostly grouped into ‘Normal-Velocity’ (NV) SNe Ia which have $V_{Si6355}\lessapprox 12,000$ km/s and ‘High-Velocity’ (HV) SNe Ia which have $V_{Si6355}>12,000$ km/s (Wang et al., 2009, 2013).

The formation of the absorption features on ejecta of SN Ia mostly occur by coherent scattering (e.g. Bongard et al., 2008), with a photon energy lower than ionization energy but high enough to excite the electron temperately to the higher level ($E_{higher}$). The ‘vibrating’ electron soon fell back to the lower level ($E_{lower}$), and emitted a photon with the same energy in random direction. Generally speaking, the line strength of the feature increases with the oscillation strength and the ion abundance, and decrease with the lower level ($E_{lower}$)¹¹1ref: https://supernova.lbl.gov/$\sim$dnkasen/tutorial/ and excitation energy $E_{exc}=E_{higher}-E_{lower}$ (e.g. Zhao et al., 2021). The features are mainly produced by absorption in photosphere (PHO), but they are also contributed by a high-velocity feature (HVF) component, which is attributed to absorption in distant regions. The velocity of a HVF is typically between 17,000 and 25,000 km/s. The most studied one is the HVF of Ca II NIR. Its correlations with observables such as the decline rate, the B-V color and the host galaxies have been investigated with different samples (e.g., Childress et al., 2014; Maguire et al., 2014; Silverman et al., 2015), in an attempt to improve the calibration of the peak luminosity. It has been suggested that HVFs may be related with enhancements of element abundance, matter density, or ionization in outermost layers of the ejecta (e.g. Gerardy et al., 2004; Mazzali et al., 2005; Tanaka et al., 2008).

Observations suggest that the HVFs are closely correlated with their corresponding PHO components (Zhao et al., 2015, 2016). This means that the substances of HVFs might be originally located in inner or near surface layers of the progenitor, and then moved to the outermost layers with their high velocities. A critical clue is an anti-correlation between the HVFs of Si II $\lambda$6355 and O I $\lambda$7773 for NV SNe Ia, which may be associated with burning of oxygen to silicon on the surface of the progenitor. These observations place new constraints on explosion models (e.g. Kato et al., 2018). Following our previous works (Zhao et al., 2016), we carried out an investigation of the HVF of Ca II H&K. Compared with Ca II NIR triplet whose main contributing lines (i.e. Ca II $\lambda$s 8542 and 8662) are quite separated in wavelength, Ca II H&K ’s two contributing lines at 3934 and 3968 Å  are much closer in wavelength. This significantly reduces the blending between the HVF of redder contributing line and the PHO of bluer contributing line, and hence improve the accuracy of the measurement. Note that Ca II H&K may be affected by Si II $\lambda$3850, but in most case very insignificantly (similar conclusions were made in Childress et al., 2014; Maguire et al., 2014; Silverman et al., 2015). For example, in the spectra we show latter, no clear sign of Si II $\lambda$3858 is seen. This is consistent with theoretical expectation. Compared with Si II $\lambda$4130 which itself is very weak (mean pseudo-equivalent width (pEW) at -10 days $\approx$ 13 Å for NV SNe Ia, no HVF), Si II $\lambda$3850 has a much smaller oscillation strength (0.5 vs. 5.1), and thus should be even weaker and has no HVF. But if necessary, this line can be removed by using a multiple Gaussian fitting.

This paper is organized as follows. In Section 2 we briefly describe the sample and measurement procedure. In Section 3 we focuses on the behaviors of the HVFs of Ca lines. Summary and discussion about the origin of HVFs of Ca are given in Section 4.

Measurement results for lines Si II $\lambda$6355, O I $\lambda$7773 and Ca II NIR have been reported in our previous works (Zhao et al., 2015, 2016)²²2Correction for Ca II NIR of SN 2013gs at -7.5 days: $V_{PHO}$= 13,200 km/s, $pEW_{PHO}$ = 21 Å, $V_{HVF}$= 19,742 km/s, $pEW_{PHO}$ = 9 Å.. Measurement results for line Ca II H&K are listed in Table LABEL:Tab1. The spectra are mainly from the database of the Harvard-Smithsonian Center for Astrophysics (CfA) Supernova Program (Matheson et al., 2008; Blondin et al., 2012). This allows us to restrict the diversity that is introduced by using data from different sources, as the observation conditions and spectral reductions could be very different for different observers. Others are mostly from the Berkeley Supernova Program (Silverman et al., 2012a, b; Stahl et al., 2020) and the Carnegie Supernova Project (CSP, Folatelli et al., 2013).

As usual, absorption features on the spectra (divided by the pseudo-continuum) are fitted with a multiple Gaussian function. For example, Ca II H&K is fitted with a double Gaussian function, which follows as $f(\lambda)=c_{1}exp(\frac{-(\lambda_{1}-\lambda_{0})^{2}}{2\sigma_{1}^{2}})+c_{2}exp(\frac{-(\lambda_{2}-\lambda_{0})^{2}}{2\sigma_{2}^{2}})$, where ‘$c$’ represents the amplitude, ‘$\sigma$’ represents the dispersion, $\lambda$ represents the wavelength, and $\lambda_{0}$ represents the rest-frame wavelength. Line velocity is calculated by $V=(\lambda^{2}-\lambda_{0}^{2})/(\lambda^{2}+\lambda_{0}^{2})\times 3\times 10^{5}$(km/s), while the pseudo-equivalent width $pEW=\int_{\lambda_{1}}^{\lambda_{2}}\frac{F_{C}(\lambda)-F(\lambda)}{F_{C}(\lambda)}d\lambda$, where $F$ represents the flux density and $F_{c}$ represents the continuum flux density.

Rest-frame wavelength of Ca II NIR is as usual set to be 8567 Å. But, it could be underestimated. A simple estimation weighted by oscillator strength would suggest a rest-wavelength of about 8584 Å. For Ca II H&K, the rest-wavelength is set to be 3945 Å. Measurement uncertainties are mainly due to continuum fitting (continuum is often more irregular at early phases than near maximum light), line blending (including the blending between PHO and HVF components), flux error (relatively higher at early phases than near maximum light, and relatively higher in violet and near-infrared bands than central optical band) and atmospheric absorption.

In this section, we report our measurement results of the HVFs of lines Ca II NIR and Ca II H&K. Of most interest are some that are different with the HVFs of Si II $\lambda$6355 and O I $\lambda$7773.

Our measurement results show that the HVFs of Ca II behave quite differently with HVFs of Si II and O I. They are much stronger and more persistent, and correlate very differently with their corresponding PHO components. Below we summarize our major findings, and discuss on their possible reasons.

(1) For lines Si II $\lambda$6355 and O I $\lambda$7773, the pEWs of HVF and PHO components are positively correlated, i.e. $pEW_{HVF}\approx pEW_{PHO}/3$ (a relatively weak correlation for line Si II $\lambda$6355 is presented in Section 3.2, while a relatively strong correlation for line O I $\lambda$7773 is presented in Zhao et al. (2016)). This correlation may be caused by radiation conditions that changed in the same direction in PHO and HVF layers, such as the temperature and luminosity. For example, 1991T-like objects are believed to have a relatively higher temperature in both photosphere and HVF layer, while dimmer objects may have a colder photosphere and HVF layer.

(2) For lines Ca II NIR and Ca II H&K, however, the pEWs of HVF and PHO components are anti correlated, i.e. $pEW_{HVF}\approx-2\times pEW_{PHO}+c$, where $c$ is a constant (the correlation is relatively weak at early phases, and relatively strong near maximum light). Below are three possible reasons:

(I) The first possible reason is line competition. The ‘pEW’ reflects the absorption efficiency $N_{absorbed}/N_{total}$ (‘N’ represents the number of photons), which depends on ion abundance. When the ion was insufficient, there will be competition among all features of the same ion. However, since the HVF and PHO layers were two separate, independent layers with large distance (due to the huge velocity difference), the competition was unlikely the main reason.

(II) The second possible reason is the effect of $E_{lower}$. Both Ca II H&K and Ca II NIR have a rather low $E_{lower}$, but explaining with it may be difficult: (a) Firstly, the effect depends on multiple factors, most of which change in the same direction in HVF and PHO layers, for example the temperature. (b) Secondly, as mentioned before, the two layers were basically independent. (c) Thirdly, the slop $\Delta(pEW_{HVF}^{Ca})/\Delta(pEW_{PHO}^{Ca}$) is almost the same ($\approx$ -2) for Ca II NIR and Ca II H$\&$K which have different $E_{lower}$, and, is almost the same at -10 and +4 days when the ionization conditions changed.

(III) The third possible reason: similar to the anti-correlation between HVFs of Si and O (Zhao et al., 2016), this anti-correlation may also reflect the law of mass conservation: Suppose most calcium was synthesized in inner layers, part of the substances might successfully escape to the outermost layer and form the HVF, while others were blocked in the photosphere or even deeper layers. The more calcium escaped, the less would be left in inner layers. For Si and O, the blocking might be much weaker as the elements were synthesized/located near the surface, explaining the fact that there is no anti-correlation between pEWs of HVF and PHO components for the Si and O features.

There are other clues supporting this explanation: (a) As shown in Zhao et al. (2016), the photospheric velocities of Ca II NIR, O I $\lambda$7773 and Si II $\lambda$6355 are quite similar ($t\approx$-10 days), suggesting possibly serious collisions and mixing near the surface. (b) HVFs of Ca have much larger velocity than other HVFs ($\Delta V\approx$ 4,300 km/s), this contrasts with the fact that HVFs of O and Si have similar velocities. (c) A constant-like slop $\Delta(pEW_{HVF}^{Ca})/\Delta(pEW_{PHO}^{Ca}$) for both Ca II NIR and Ca II H&K.

(3) For lines Ca II NIR and Ca II H&K, there is a strong positive correlation between $\Delta V_{HP}$ and $R_{HP}$. A possible explanation is that some variable indirectly connects $\Delta V_{HP}$ and $R_{HP}$ and forms the positive correlation. But such intermediate variable has not been found (e.g., for Ca II H&K in Fig.4, Pearson’s coefficient p($\Delta m_{15}$,$\Delta V_{HP}$)= -0.17 while p($\Delta m_{15}$,$R_{HP}$)=+0.21). Also, it might be difficult to explain why the intermediate variable only correlates strongly with Ca II features.

Another possible explanation is that the correlation reflects the truth that a greater $\Delta V_{HP}$ corresponds to a greater kinetic energy of the HVF substances, and thus a greater chance to escape the blocking. For Si and O, however, the correlation is very weak or non-related, which can be explained as the ‘blocking effect’ was insignificant for Si and O that were originally located near the surface.

In conclusion, our measurements reveal two important correlations for Ca II NIR and Ca II H&K: an anti-correlation between pEWs of the PHO and HVF components, and a positive correlation between $\Delta V_{HP}$ and $R_{HP}$. In comparison, for O I $\lambda$7773 and Si II $\lambda$6355, $pEW_{HVF}\approx pEW_{PHO}/3$, while correlation between $\Delta V_{HP}$ and $R_{HP}$ is too weak to identify. The results are more consistent with the scenario that most calcium was synthesized in inner layers and then partially escaped to the outermost layer. However, further investigation and theoretical analysis are needed to determine the true reasons of these results.

We thank Keiichi Maeda, Xiaofeng Wang and the anonymous referee for their insightful suggestions which help improve the paper a lot. This research has made use of the CfA Supernova Archive, which is funded in part by the National Science Foundation through grant AST 0907903, the Berkeley/Lick Supernova Archives, which is funded in part by the US National Science Foundation, and the CSP Supernova Archive, which is supported by the World Premier International Research Center Initiative. Here we express our deep gratitude.

The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.