Can Helium-detonation Model Explain the Observed Diversity of Type Ia Supernovae?

We display extinction corrected ($B-V$)₀ color curves of our sample in Figure 1. For those SNe with known extinction, the values given in the literature are used. Otherwise, we fit the multi-band light curves with SNooPy2 (Burns et al., 2011) to get the host galaxy extinction in addition to the Galactic extinction (Schlafly & Finkbeiner, 2011). Intrinsic colors from Burns et al. (2014) are used to infer the host extinction $E(B-V)_{host}$ as well as $R_{Vhost}$. SN 2019ein is the only object with both new and published photometry, our new results are consistent with the previous works (Kawabata et al., 2020; Pellegrino et al., 2020).

At four days after the first light, the ($B-V$)₀ color ranges from $\sim-$0.2 mag to 0.4 mag. This color dispersion gradually decreases to 0.3 mag several days later. Among our sample, SN 2017erp shows the reddest color in the early phase, i.e., ($B-V$)₀ $\sim$ 0.5 mag at $t\sim$ 2.8 days, and it quickly evolves to $\sim$ 0.05 mag at $t\sim$ 8 days, indistinguishable from other objects. SN 2017cfd shows the bluest color, i.e., $\sim-$0.2 mag at $t\sim$ 2.5 days, and the color mildly evolved after that. The distribution of ($B-V$)₀ seems to be continuous for our sample. Stritzinger et al. (2018) claim that the early-time colors of SNe Ia tend to show evidence for two populations, i.e., red and blue. We overplot their sample together with our new sample in Figure 1(a). Among the new sample, SN 2018yu and SN 2019ein seem to be located between the red and blue groups, suggesting that the red and blue distinction is not sharp. It should be noted that the uncertainties are relatively large and fall within either the red or blue group for most of the data points in this sample. More early-time observations are needed to distinguish whether it is a continuous or bimodal distribution.

To examine the color evolution for different sub-types of SNe Ia, we marked HV and NV group with different colors as shown in Figure 1(b). One can see that the HV objects initially have red colors and then evolve bluewards with ($B-V$)${}_{0}~{}\sim-$0.1 mag at $t\sim$ 5 days. The distribution for the NV group is much wider in the early phase, ranging from $-$0.2 mag to +0.4 mag. The 91T/99aa-like objects are hot and luminous, with some common features such as weak Si II features around the maximum and early excess flux (Jiang et al., 2018). In the ($B-V$)₀ color evolution diagram, these slow decliners tend to dominate the blue side at the early time.

To investigate the unburnt carbon in the ejecta, we examine the dominant C II absorption feature in optical spectra (i.e., C II $\lambda$6580) of the spectra. This feature appears as a notch or a plateau on the red edge of Si II $\lambda$6355 absorption feature. We display the C II $\lambda$6580 region in the early spectra of all objects in Figure 2. Objects with (without) C II $\lambda$6580 feature belong to NV (HV) group except for one HV object, SN 2019ein, which has a C II $\lambda$6580 feature that quickly disappears within three days of the first light. This trend is consistent with Parrent et al. (2011). The mean $\Delta m_{15}$($B$) of objects with carbon features (carbon-positive objects) and objects without carbon features (carbon-negative objects) are 1.08 $\pm$ 0.03 mag and 1.06 $\pm$ 0.03 mag, respectively, suggesting there is no trend between light curve widths and C II features as reported by Maguire et al. (2014) and Thomas et al. (2011).

The carbon-negative objects have ($B-V$)${}_{0}>$ 0.1 mag at the very early phase and evolve rapidly blueward, consistent with one-dimensional He-detonation models with thin helium shell (see Figure 6 of Polin et al. (2019)), which have little unburnt carbon left after the explosion (but see Section 4). Two NV objects, SN 2011fe and iPTF13ebh, also have possible C I lines detection in their NIR spectra (Hsiao et al., 2013, 2015). However, Heringer et al. (2019) questioned the identifications of these features because their simulations do not show significant neutral carbon.

As the C II $\lambda$6580 features are usually weak and sometimes appear as a plateau, it is not easy to measure the pseudo-equivalent widths (pEWs). Therefore we use a semi-quantitative score ($s_{c}$ to describe their intensity. The scoring criteria and examples are as follows:

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  0: no C II $\lambda$6580 feature, such as the first spectrum of SN 2002bo;

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  1: the feature appears as a plateau, such as the first spectrum of SN 2013gy;

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  2: the feature appears as a notch, such as the first spectrum of SN 2011fe;

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  3: the feature is strong enough to affect the profile of Si II $\lambda$6355 feature, such as the first spectrum of SN 2012cg.

We use the highly parameterized code SYNAPPS (Thomas, Nugent & Meza, 2011) to identify the carbon absorption features. The difference between 0 and 1 is obtained by comparing the spectra with carbon-free SYNAPPS fit, i.e., if the spectrum has no absorption feature but deviated from the fit, we score 1, otherwise we score 0. Other spectra are scored by eye inspection. Four representative SYNAPPS fits for $s_{c}=0-3$ are overplotted in Figure 2. We plot the scores of all early spectra in Figure 3. This analysis confirms the trend mentioned above, namely that HV objects have quickly disappearing C II $\lambda$6580 feature or no such feature at all while NV objects generally have such a feature and last for a longer time. All three 91T/99aa-like objects also have strong C II feature at early phase. We will discuss the implications of these results for the explosion mechanisms in Section 4.

We use multiple Gaussian profiles to fit the photospheric-velocity features (PVFs) and HVFs of Ca II NIR triplet (CaIR3). The velocity and pEW of each absorption feature can be measured from the fit. Previous studies indicate that the HVFs of CaIR3 are common in the spectra of SNe Ia (Zhao et al., 2015). We plot the CaIR3 region in the early spectra of our sample in Figure 4. In Figure 5, we investigate the velocity evolution of this spectral feature, and found that all HV objects tend to have very high velocity, i.e., $>$ 30,000 km s^-1, at $t\sim$ +3 days. In comparison, the CaIR3 HVFs of all NV objects tend to have velocities below 30,000 km s^-1, except two luminous 99aa-like objects, iPTF16abc and SN 2017cbv. Among the NV objects, SN 2017erp has the highest velocities with an early-time velocity of $\sim$ 29,000 km s^-1. The velocities of SN 2009ig and SN 2012fr are always above the NV groups while the velocity of SN 2019ein declines rapidly and becomes lower than the NV groups. The median velocity of the CaIR3 HVFs of HV group is $\sim$ 6,000 km s^-1 higher than that of NV group at the early phase, and the difference gradually decreases to $\sim$ 2,000 km s^-1 at $\sim$ +14 days after explosion.

In order to constrain the physical origin of SNe Ia by combining early- and late-time observations and host galaxy properties, we study $v_{\rm Si,max}$, the velocity shift of late-time [Fe II] $\lambda$7155 features, $v_{\rm[Fe~{}II]}$, and the host galaxy mass of the sample (see Figure 6). The spectral features from inner Fe-group regions dominate the late-time spectra, including [Fe II] $\lambda$7155, which is the strongest optical feature formed from the deflagration ashes. The SNe Ia with higher $v_{\rm Si,max}$ have more redshifted $v_{\rm[Fe~{}II]}$, implying asymmetric explosions for some SNe Ia (Maeda et al., 2010; Maguire et al., 2018). We add several SNe Ia with these parameters from the literature (Pan et al., 2015; Maguire et al., 2018; Rose et al., 2019; Pan, 2020). We measure $v_{\rm[Fe~{}II]}$ of SNe 2017cbv and 2013gy using the Gaussian fit (see Section 3.3) and the host galaxy mass of SNe 2002dj, 2007le, 2010ev, 2013cs, 2013gy and 2019ein, using the same method adopted in Pan (2020). Pan et al. (2015) and Pan (2020) found that HV objects only occur in galaxies with $M_{stellar}>3\times 10^{9}~{}(\sim 10^{9.5}$) $M_{\odot}$. Therefore we choose the boundary between massive and low-mass galaxies as log($M_{stellar}/M_{\odot}$) = 9.5. We notice that all HV objects have redshifted $v_{\rm[Fe~{}II]}$ while NV objects have both redshifted and blueshifted $v_{\rm[Fe~{}II]}$. Moreover, all objects with redshifted $v_{\rm[Fe~{}II]}$ tend to reside in massive galaxies while objects with blueshifted $v_{\rm[Fe~{}II]}$ are located in both massive and low-mass galaxies. The $v_{\rm[Fe~{}II]}$ seems to have a double-peak distribution (see the top panel of Figure 6) with one at $\sim-$1000 km s^-1 and the other at $\sim$+1500 km s^-1, respectively, which may indicate two populations. Nevertheless, the Si II velocity distribution measured around the maximum light does not reproduce the double Gaussian profile as reported by Wang et al. (2013), which means that our sample size is still too small. According to the mass-metallicity relation (Tremonti et al., 2004; Kewley & Ellison, 2008), massive galaxies have on average higher metallicity than low-mass galaxies, suggesting that objects with redshifted $v_{\rm[Fe~{}II]}$ (including all HV objects) have metal-rich progenitor environments. We will discuss the implications of these phenomena in Section 4.

In this section, we further examine the differences and connections between NV and HV objects and provide implications for the explosion mechanism. Stritzinger et al. (2018) studied a sample of 13 SNe Ia, suggesting that they can be divided into red and blue groups according to the early $B-V$ color, and the red group has a rapid evolution from red to blue. Jiang et al. (2018) reached a similar conclusion with 23 young SNe Ia. Han et al. (2020) also found that these two groups may exist by adding a sample of six more supernovae, although we note that the distinction between these two sub-classes is less significant when these events are added (see Fig. 5 of Han et al. (2020)). Our sample largely overlaps with the samples used in the above works, and the results inferred from the common sample are consistent. Bulla et al. (2020) studied the $g-r$ (similar to $B-V$) curves of 65 SNe Ia from ZTF, discovered within five days from the first light, and they found that the early colors were uniformly distributed and did not show any evidence for two separate groups. Our research adds a few new objects to this sample with early observations and also shows that the $B-V$ colors do not have a distinct bimodal distribution, either. One or more mechanisms, including companion interaction, ⁵⁶Ni distribution and CSM interaction can affect the early-time light and color curves. However, quality of current color curves is not high enough to distinguish different processes, and it is difficult to constrain the explosion mechanism from them.

The absence or presence of very weak carbon signal among spectra of HV group requires an explosion mechanism with high carbon-burning efficiency. The He-detonation scenario leaves almost no carbon after the explosion (Polin et al., 2019; Townsley et al., 2019). However, small amount of carbon could leave weak orientation-dependent absorption features in the spectra, which are hardly observable at the north side²²2We regard the helium detonation point (n₁ direction in Figure 7) as north pole throughout the paper. (n₁ - n₃ in Figure 7) but could be strongest at the south pole (n₅ in Figure 7). Therefore, a portion of NV objects with carbon absorption features could be observed from the south side of He-detonation while HV objects could be observed from the north side. This is consistent with the viewing-angle effect of Si II velocity (around maximum) in the He-detonation model, where ejecta move at higher velocities in the northern hemisphere and lower velocities in the southern hemisphere (Bulla et al., 2016b; Townsley et al., 2019). In Figure 7, we show the spectral region around the Si II $\lambda$6355 line predicted for the He-detonation “model 3m” presented by Kromer et al. (2010). This model is a modified version of “model 3” from Fink et al. (2010) where the helium shell is polluted by 34$\%$ of ¹²C to reduce the production of iron-group elements in the shell and thus provide a better match to the observed spectra of SN Ia (see Kromer et al. 2010 for more details). Simulations have been carried out using the radiative transfer code ARTIS (Kromer & Sim, 2009).

Spectra produced by our He-detonation model are shown in Figure 7 for five different viewing angles from north to south and at three different epochs: 5, 10 and 15 days after the explosion. Similarly to the observations, the C II $\lambda$6580 feature in the model spectra appears as a notch or a plateau on the red edge of Si II $\lambda$6355 absorption feature. This carbon feature is absent for observers at the north pole and becomes stronger when moving towards the southern hemisphere, consistent with the idea that HV objects with little or no carbon could be He-detonation explosions viewed from the ignition side, while a portion of NV objects are viewed from the opposite side. Figure 7 also shows how the presence of C II $\lambda$6580 quickly weakens with time and disappears 15 days after the explosion (corresponding to $\sim$2 to 5 days before peak going from south to north) even for an observer in the southern hemisphere. We plot the He-detonation spectra at 5 days from two directions, n₁ and n₃, in SN 2002bo and SN 2011fe sub-figure of Figure 2. Despite the line profiles of Si II $\lambda$6355 do not entirely match the observations, the non-detection of C II feature in the spectrum of SN 2002bo is reproduced while SN 2011fe does have such a feature in the early spectra. The DDT model is another candidate mechanism which leaves unburned carbon near the surface due to the deflagration process (Seitenzahl et al., 2013). Therefore it cannot explain the absence of carbon in the outer ejecta of HV objects.

The HVFs have three proposed origins: density enhancement (DE), abundance enhancement (AE) and ionization effect (IE) (Mazzali et al., 2005; Tanaka et al., 2008). The extremely high velocities of CaIR3 is ubiquitous among the early spectra of HV objects, implying that they may originate from the same mechanism. Synthesized Ca from He-detonation at the north side can reach a velocity of more than 30,000 km s^-1 while the Ca at the south side has much lower velocity (Figure 7). Townsley et al. (2019) also argue that the double-layer structure in the He-detonation model may produce AE in the outer ejecta and thus explain both HVFs and PVFs of Si and Ca. Interaction between SN ejecta and CSM can produce DE or IE effect (Mulligan & Wheeler, 2018; Mulligan et al., 2019), though it is difficult to consistently demonstrate the difference in HVFs of HV and NV SNe Ia. The DDT simulations that is most consistent with the observations of normal SNe Ia have multiple ignition sparks (N40 and N100 in Sim et al. (2013), which has 40 and 100 sparks, respectively), therefore they are close to spherical symmetry. In principle, the DDT model can result in high-velocity ejecta (e.g., Khokhlov (1991)). Although some 3D simulations (e.g., the N1 and N3 models from Seitenzahl et al. (2013)) can reproduce the high-velocity intermediate mass elements (IME) at the outermost layer of the supernova ejecta, the ⁵⁶Ni yields seems to be higher than that observed for normal SNe Ia. Current DDT models seem to have difficulties in producing the HVF of some SNe Ia, especially those extremely HVFs seen in SN 2019ein (Pellegrino et al., 2020).

HV and NV groups were initially classified according to the $v_{\rm Si,max}$ (i.e., Wang et al. (2009b)). The observed $v_{\rm Si,max}$ distribution of SNe Ia tends to exhibit a double Gaussian distribution, while these two components have an overlapping regions (see Figure 1 of Wang et al. (2013) and Figure 3 of Zhang et al. (2020)). The HV profile is much broader, reaching a velocity as low as $<$ 10,000 km s^-1, while the high-velocity tail of the NV profile extends a little into the HV region. If asymmetric He-detonation is the explosion mechanism responsible for the HV SNe Ia, a portion of NV objects may have the same explosion mechanism but with different viewing angles, which can explain the higher-velocity and broader Gaussian distribution. Objects like SN 2017erp with several characteristics of HV group such as red early-time color, quickly disappeared C II feature and relatively high velocity of CaIR3 HVFs, may have the same origin as the HV group, and their low $v_{\rm Si,max}$ might result from the geometrical effect.

Maeda et al. (2010) and Maguire et al. (2018) found that SNe Ia with higher $v_{\rm Si,max}$ tend to exhibit redshifted [Fe II] features in the nebular phase, implying an asymmetric explosion mechanism for some SNe Ia. Pan et al. (2015) and Pan (2020) found that HV objects tend to occur in massive host galaxies, while NV objects are located in both low-mass and massive host galaxies. Our finding that all HV objects have redshifted $v_{\rm[Fe~{}II]}$ while the NV counterparts have both redshifted and blueshifted $v_{\rm[Fe~{}II]}$ can fit into the sub-M_ch He-detonation models, where one would observe a HV object with redshifted Fe-group features when viewing from He-detonation side (n₁ direction of Figure 7), and a NV object in the opposite side (south side) with blueshifted (or less redshifted) $v_{\rm[Fe~{}II]}$. The orientation-dependent Si-velocity trend is also in agreement with the synthetic spectra (see Figure 4 of Townsley et al., 2019). We also find that objects with redshifted $v_{\rm[Fe~{}II]}$, including all HV objects, are located in massive host galaxies (log($M_{stellar}/M_{\odot}$) $>$ 9.5), which implies that they have metal-rich progenitor environments. Metallicity plays an important role in the evolution of SNe Ia. Flörs et al. (2020) found that the sub-M_ch explosion simulations of $\sim$Z_⊙ progenitors can explain the Ni/Fe abundance measurements for the majority of normal SNe Ia while only a small fraction (11%) of their sample are in agreement with M_Ch DDT explosion models. The sub-M_ch models include both He-detonation and violent merger scenarios. However, polarisation measurements disfavor the strongly asymmetric violent merger scenario while support He-detonation and DDT models which are more symmetric (Bulla et al., 2016a, b). Therefore, we regard these results as supports of He-detonation scenario. Metal-rich environments and progenitors are more likely to produce CSM around the progenitor systems, consistent with the observations that SNe Ia of HV group are more likely to have abundant CSM than the NV group. (Foley et al., 2012a; Wang et al., 2012, 2019).

Polin et al. (2019) claim that the explosions of WDs with different masses, rather than the different viewing angles, may cause the range of $v_{\rm Si,max}$. Pan et al. (2015) and Pan (2020) confirmed that the HV group tends to have metal-rich progenitors. At a given mass, stars with higher metallicities generally produce less massive WDs, thus the HV group may originate from the sub-M_Ch progenitors. However, the one-dimensional models studied by Polin et al. (2019) cannot explain the asymmetries revealed from the nebular observations. The CaIR3 features of these models are also too weak to account for the observations.

To form a CO WD with a thin He shell as required by He-detonation model, we need the CO WD to accrete and accumulate helium from the companion star, either a He-star or a He-rich WD (Wang et al., 2017; Wang, 2018). One of the main differences between these two scenarios is the delay times – the time interval from the formation time of the primordial binaries to the supernova explosion. The CO WD + He-star channel has shorter delay times, therefore it should originate from younger populations (Wang et al., 2009a; Liu et al., 2017). Wang et al. (2013) found that the HV objects, similar to Ibc supernovae, are located in the inner and brighter regions of host galaxies than the NV objects, which suggests a origin of younger progenitor populations. Pan (2020) found that the host galaxies of the HV group does not tend to be younger than the NV group by analyzing the global specific star formation of the host galaxies. However, the global properties may not reflect the local properties which was utilised by Wang et al. (2013). SN 2012Z, the first SN Ia with detection of the progenitor system in prediscovery images, is believed to have a He-star as the companion star (McCully et al., 2014). V445 Pup, the only He nova discovered so far, is a WD with a $\sim$$M\rm_{Ch}$ mass and can accumulate accreted He from its He-star companion after the outburst (Kato et al., 2008; Woudt et al., 2009). It should be noted that a WD with a $\sim$$M\rm_{Ch}$ mass may not produce normal SN Ia through He-detonation explosion because the central density is too large and produce too much ⁵⁶Ni (Fink et al., 2010). A system similar to V445 Pup but with a less massive CO WD can be a better candidate for He-detonation explosion. Furthermore, the ejecta of the He nova outbursts may form circumstellar dust, which are more common around HV objects (Wang et al., 2019). Combining the younger progenitor environments, prediscovery progenitor system detection, possible progenitor candidate and CSM around progenitor system, we tend to favor CO WD + He-star system for the progenitor system of He-detonation scenario, although the possibility of CO WD + He-rich WD channel cannot be fully excluded.