11institutetext: School of Physics, Trinity College Dublin, College Green,
Dublin 2, Ireland
11email<EMAIL_ADDRESS>22institutetext: Oskar Klein Centre, Department of
Astronomy, Stockholm University, SE-10691 Stockholm, Sweden 33institutetext:
Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489
Berlin, Germany 44institutetext: Institute of Space Sciences (ICE, CSIC),
Campus UAB, Carrer de Can Magrans, s/n, E-08193, Barcelona, Spain
55institutetext: Institut d’Estudis Espacials de Catalunya (IEEC), E-08034
Barcelona, Spain 66institutetext: Univ Lyon, Univ Claude Bernard Lyon 1, CNRS,
IP2I Lyon/IN2P3, UMR 5822, F-69622, Villeurbanne, France 77institutetext:
Department of Physics, Lancaster University, Lancs LA1 4YB, UK
88institutetext: Oskar Klein Centre, Department of Physics, Stockholm
University, SE-10691 Stockholm, Sweden 99institutetext: Université Clermont
Auvergne, CNRS/IN2P3, LPCA, F-63000 Clermont-Ferrand, France
1010institutetext: National Research Council of Canada, Herzberg Astronomy &
Astrophysics Research Centre, 5071 West Saanich Road, Victoria, BC V9E 2E7,
Canada 1111institutetext: Institute of Astronomy and Kavli Institute for
Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
1212institutetext: Department of Physics and Astronomy, Northwestern
University, 2145 Sheridan Rd, Evanston, IL 60208, USA 1313institutetext:
Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA),
Northwestern University, 1800 Sherman Ave, Evanston, IL 60201, USA
1414institutetext: Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS
50B-4206, Berkeley, CA 94720, USA 1515institutetext: Department of Astronomy,
University of California, Berkeley, 501 Campbell Hall, Berkeley, CA 94720, USA
1616institutetext: Nordic Optical Telescope, Rambla José Ana Fernández Pérez
7, ES-38711 Breña Baja, Spain 1717institutetext: Caltech Optical
Observatories, California Institute of Technology, Pasadena, CA, 91125, USA
1818institutetext: Cahill Center for Astrophysics, California Institute of
Technology, MC 249-17, 1200 E California Boulevard, Pasadena, CA, 91125, USA
1919institutetext: Division of Physics, Mathematics and Astronomy, California
Institute of Technology, Pasadena, CA, 91125, USA 2020institutetext: IPAC,
California Institute of Technology, 1200 E. California Boulevard, Pasadena,
CA, 91125, USA

# ZTF SN Ia DR2: The spectral diversity of Type Ia supernovae in a volume-
limited sample

U. Burgaz 11 0000-0003-0126-3999 K. Maguire 11 0000-0002-9770-3508 G.
Dimitriadis 11 0000-0001-9494-179X L. Harvey 11 0000-0003-3393-9383 R. Senzel
11  0009-0002-0243-8199 J. Sollerman 22 0000-0003-1546-6615 J. Nordin 33
0000-0001-8342-6274 L. Galbany 4455 0000-0002-1296-6887 M. Rigault 66
0000-0002-8121-2560 M. Smith 77 0000-0002-3321-1432 A. Goobar 88
0000-0002-4163-4996 J. Johansson 88 0000-0001-5975-290X P. Rosnet 99 M.
Amenouche 1010 0009-0006-7454-3579 M. Deckers 11 0000-0001-8857-9843 S. Dhawan
1111 0000-0002-2376-6979 M. Ginolin 66 0009-0004-5311-9301 Y.-L. Kim 77
0000-0002-1031-0796 A. A. Miller 12121313 0000-0001-9515-478X T. E. Muller-
Bravo 4455 0000-0003-3939-7167 P. E. Nugent 14141515 000-0002-3389-0586 J. H.
Terwel 111616 0000-0001-9834-3439 R. Dekany 1717 0000-0002-5884-7867 A. Drake
1818 M. J. Graham 1919 0000-0002-3168-0139 S. L. Groom 1414
0000-0001-5668-3507 M. M. Kasliwal 1919 0000-0002-5619-4938 S. R. Kulkarni
1919 K. Nolan 1919 0009-0002-4724-7118 G. Nir 1414 0000-0002-7501-5579 R. L.
Riddle 1717 0000-0002-0387-370X B. Rusholme 2020 0000-0001-7648-4142 Y. Sharma
1919 0000-0003-4531-1745

More than 3000 spectroscopically confirmed Type Ia supernovae (SNe Ia) are
presented in the Zwicky Transient Facility SN Ia Data Release 2 (ZTF DR2). In
this paper, we detail the spectral properties of 482 SNe Ia near maximum
light, up to a redshift limit of z $\leq$ 0.06. We measure the velocities and
pseudo-equivalent widths (pEW) of key spectral features (Si ii $\lambda 5972$
and Si ii $\lambda 6355$) and investigate the relation between the properties
of the spectral features and the photometric properties from the SALT2 light-
curve parameters as a function of spectroscopic sub-class. We discuss the non-
negligible impact of host galaxy contamination on SN Ia spectral
classifications, as well as investigate the accuracy of spectral template
matching of the ZTF DR2 sample. We define a new subclass of underluminous SNe
Ia (‘04gs-like’) that lie spectroscopically between normal SNe Ia and
transitional 86G-like SNe Ia (stronger Si ii $\lambda 5972$ than normal SNe Ia
but significantly weaker Ti ii features than ‘86G-like’ SNe). We model these
‘04gs-like’ SN Ia spectra using the radiative-transfer spectral synthesis code
tardis and show that cooler temperatures alone are unable to explain their
spectra; some changes in elemental abundances are also required. However, the
broad continuity in spectral properties seen from bright (‘91T-like’) to faint
normal SN Ia, including the transitional and 91bg-like SNe Ia, suggests that
variations within a single explosion model may be able to explain their
behaviour.

###### Key Words.:

ZTF ; supernovae: general ; Type Ia Supernovae

##  1 Introduction

Type Ia supernovae (SNe Ia) are commonly accepted to be the thermonuclear
explosion of a carbon–oxygen (C/O) white dwarf (WD) in a binary system (Hoyle
& Fowler, 1960; Maoz et al., 2014). SNe Ia are proven to be reliable distance
estimators and are used as “standardisable candles” to measure extragalactic
distances, where observations of distant SNe Ia led to the discovery of the
accelerating expansion of the Universe (Perlmutter et al., 1997, 1999; Riess
et al., 1998, 2016). However, the exact nature and the explosion mechanism of
their progenitors still remain in question (e.g., Khokhlov, 1991; Maeda &
Terada, 2016). Even though several progenitor scenarios are proposed for SNe
Ia, the most commonly considered progenitor scenarios are the single
degenerate scenario (SD, Whelan & Iben, 1973; Nomoto et al., 1997), which
consists of a C/O WD and a non-degenerate companion such as a main-sequence
star or an evolved star (Helium star or a red giant), and the double
degenerate model (DD, Iben & Tutukov, 1984; Webbink, 1984), which consists of
two WDs that result in the explosion of one or both of the WDs.

The spectra of SNe Ia around maximum light are relatively homogeneous, with
absorption lines of intermediate-mass elements dominating, such as Si ii
$\lambda 6355$, Si ii $\lambda 5972$, Si ii $\lambda 4130$, Ca ii H&K, Ca ii
near-infrared triplet, S ii $\lambda 5454$ and S ii $\lambda 5640$ (Zhao et
al., 2021). While Si ii $\lambda 6355$ absorption is the most prominent
feature in SNe Ia spectra near maximum light, in peculiar cases such as SN
1991T (Filippenko et al., 1992b; Phillips et al., 1992) and SN 1999aa
(Filippenko et al., 1999) this feature appears extremely weak. These SNe Ia
(91T-like, 99aa-like) exhibit slow decline rates in their light curves and
have higher peak absolute magnitudes on average. Strong Ti ii absorption
around 4300 Å is also present in some subluminous classes of SNe Ia (e.g., SN
1991bg-like; Filippenko et al., 1992a). The estimated brightness of 91bg-like
SNe Ia is roughly two magnitudes lower than that of a normal SN Ia.
‘Transitional’ events also exist that have spectral features and luminosities
between normal and faint SNe Ia, such as SN 1986G (Phillips et al., 1987) that
displayed weaker Ti ii absorption than seen in 91bg-like SNe Ia around maximum
light. The variation in spectral features in maximum light SN Ia spectra is
most likely due to varying temperatures in the ejecta (Nugent et al., 1995;
Hachinger et al., 2008) but the connection between luminosity, temperature,
and decline rate is still uncertain.

Several classification schemes have been proposed to investigate the
spectroscopic diversity seen in SNe Ia, in particular the velocity evolution
with time of the Si ii $\lambda 6355$ feature, as well as the relative
strength of the Si ii $\lambda 6355$ and Si ii $\lambda 5972$ features. Based
on the velocity evolution of Si ii $\lambda 6355$, Benetti et al. (2005)
divided SNe Ia into three groups: ‘high-velocity gradient (HVG)’, ‘low-
velocity gradient (LVG)’, and a ‘faint’ group that consisted of subluminous
91bg-like events. Another classification scheme based on the pseudo equivalent
width (pEW) of the Si ii absorption features of 5972 and 6355 Å was introduced
by Branch et al. (2006, 2009). There are four subgroups in this scheme: ‘core
normal’, ‘cool’, ‘broad line’, and ‘shallow silicon’. Wang et al. (2009b)
proposed a classification scheme purely based on the velocity of the Si ii
$\lambda 6355$ absorption feature near maximum light, where SNe Ia with
expansion velocities, $v_{\mathrm{Si}}$, of $v_{0}\gtrsim$ 12,000 km s-1 are
defined as ‘High Velocity (HV) SNe Ia’ and those with
$v_{\mathrm{Si}}\lesssim$ 12,000 km s-1 are defined as ‘Normal Velocity (NV)
SNe Ia’. The observed diversity in velocity is suggested to be independent of
light curve evolution and may be attributed, at least in part, to a viewing
angle effect in explaining the diversity of HV/NV SNe Ia (Maeda et al., 2010).
It has been suggested that HV SN Ia exhibit differences in their light curve
evolution (Wang et al., 2008, 2009b; Burgaz et al., 2021), shorter explosion
to maximum light rise time (Ganeshalingam et al., 2011), have redder intrinsic
B-V colour (Pignata et al., 2008), may have different extinction laws (Wang et
al., 2009b; Foley & Kasen, 2011) and may be more concentrated towards the
centres of their host galaxies (Wang et al., 2013).

In this paper, we present the analysis of the spectroscopic features of the
second Zwicky Transient Facility (ZTF) Data Release (DR2) SNe Ia, obtained as
part of the Zwicky Transient Facility survey from 2018 - 2020 (Bellm et al.,
2019; Graham et al., 2019; Masci et al., 2019; Dekany et al., 2020), as well
as the link to their photometric properties. The ZTF is an optical time-domain
survey that has been in operation since 2018. It spectroscopically confirmed
nearly 4000 low-redshift SNe Ia between 2018 and 2020, without biases in terms
of host-galaxy properties (i.e. massive galaxies were not specifically
targeted). In Section 2, we present the sample selection, spectroscopic
classifications and the data reduction. Section 3 discusses the measurements
of spectral features (velocities and equivalent widths) and the accuracy of
spectral template matching SN Ia sub-classes. In Section 4, we examine the
spectroscopic sub-classes and how photometric properties and spectral features
are related. Conclusions and possible future works are presented in Section 5.

##  2 Sample selection and spectral measurements

In this section, we discuss the overall properties of the ZTF SNe Ia in the
DR2 and the methods used to analyse their spectra. In Section 2.2, we describe
the ZTF SN Ia sample, including redshift determination, light-curve
parameters, optical spectroscopy, and the methodology for their initial
spectral classifications. In Section 2.2, we detail the cuts made on the
sample to obtain our desired maximum light spectral sample. Finally, in
Section 2.3, we present the method used to measure properties, such as
velocities and equivalent widths, from the spectra.

###  2.1 ZTF SN Ia Data Release 2

The ZTF DR2 SN Ia sample contains 3628 spectroscopically confirmed SNe Ia
discovered from 2018 to 2020 (see  Rigault et al. subm. and  Smith et al. in
prep. for further details) that had optical ZTF light curves obtained for
them. Thanks to the Bright Transient Survey (BTS) program, most of them were
obtained near or before peak brightness. 61% of the ZTF SN Ia DR2 sample has
host spectroscopic redshifts, among which 71% coming from DESI through the
MOST Host program (Soumagnac et al., 2024). 9% comes from identifiable host
galaxy lines in the SN spectra and the remaining 30% are derived from template
matching using snid (Blondin & Tonry, 2007)

Smith et al. (in prep.) compared the known redshift values from host
catalogues and snid redshifts for SNe Ia in the sample and found good overall
agreement with a redshift dispersion of $3\times 10^{-3}$, corresponding to a
velocity dispersion of $\sim 500$ km s-1.

The majority of optical spectra from ZTF come from the low-resolution integral
field spectrograph, SED machine (SEDm, Blagorodnova et al., 2018; Rigault et
al., 2019; Kim et al., 2022) on the 60-inch telescope at the Mount Palomar
observatory. These spectra are supplemented by spectra from several other
telescopes with higher resolution, as discussed in  Smith et al. (in prep.).
All the spectra are corrected to the rest-frame using an estimate of its host
galaxy redshift and corrected for Milky Way extinction (Schlafly & Finkbeiner,
2011) using a total-to-selective extinction ratio, RV of 3.1.

As part of the ZTF DR2 analysis, a spectral typing effort was made to identify
the sub-classifications of the DR2 sample into the classes of ‘normal SN Ia’
(Wang et al., 2009a; Nugent et al., 2011), ‘91bg-like’ (Filippenko et al.,
1992a), ‘91T-like’(Filippenko et al., 1992b), ‘Ia-peculiar’ or if the sub-
classification was unclear, ‘SN Ia-unclear’. The classification were
accomplished in two steps. Firstly, users were invited to a specially designed
web tool called the ‘typingapp’111https://typingapp.in2p3.fr/dashboard that
allowed them to see best SNID fits of each individual spectra with several
sub-types and the phase-redshift distributions. These snid fits (Blondin &
Tonry, 2007) using priors based on the light-curve phase estimates from the
SALT2 (Guy et al., 2007) light curve fit and a redshift prior based on host
galaxy spectral features, where this was available. Its sole purpose is to
classify all SNe with spectral information only (hence, no host information
was shown to users). Users could see the light curve but this was only for
confirming spectral phases relative to the light curve phase. Then, each user
selected and reported sub-types for the SNe on the typingapp. The spectra of
each SN Ia, along with their best fitting snid matches, were visually
inspected by multiple members of the ZTF SN Ia working group to determine the
most likely sub-classification for each event. Secondly, a more thorough
subclassification, targeted at the events with $z\leq 0.06$ (the redshift
range studied in this work), was performed (see Section 3.1). A detailed
methodology for these classifications is also presented in  Dimitriadis et al.
(in prep.).

###  2.2 Sample Selection

Table 1: Summary of the cuts applied to obtain our final spectral sample.

| Criteria | No. of SNe
---|---|---
Full ZTF SN Ia DR2 |  | 3628
with good LC coverage |  | 2959
with basic LC quality cut* |  | 2790
with redshift cut |  $z$ $\leq$ 0.06 | 1093
with phase cut |  $-$5 d $\leq$ $t_{0}$ $\leq$ 5 d | 546
with non-peculiar SNe Ia |  | 526
with spectra quality cut | SNR $\geq$ 5 | 482

*Cuts of $-4<x_{1}<4$, $\sigma_{x_{1}}<0.6$, $c<0.8$, $\sigma_{c}<0.35$, $\sigma_{t_{0}}<1$ d (see Section 2.2).

Figure 1: Left: Redshift distribution of the full ZTF SN Ia sample (grey
dashed line, 2959 SNe Ia) with good light curve coverage, the sample with a
redshift limit at z $\leq$ 0.06 (blue dashed line, 1093 SNe Ia), and SNe Ia
passing our other cuts that have a spectrum at $-$5 to 5 d with respect to
maximum light (red solid line, 482 SNe Ia). Middle: The rest-frame phase
distribution of all good light curve coverage ZTF SNe Ia spectra at $-$5 to 5
d (grey) and with the redshift cut of z $\leq$ 0.06. Right: SALT2 $x_{1}$
distribution of the ZTF SN Ia sample.

In this study, we focus on an analysis of maximum light spectra of SNe Ia and
therefore, apply a number of cuts on the photometry and spectra to achieve a
relatively clean and unbiased sample with well constrained spectral phases.
Table 1 shows all the criteria used to define the final sample along with the
number of remaining SNe Ia after each cut.

The ZTF gri-band light curves of the SNe Ia in the sample were fit with
version 4222https://sncosmo.readthedocs.io/en/stable/ of the SALT2 light-curve
fitter (Guy et al., 2007), which gives the light-curve stretch, x1, colour
$c$, and the time of maximum light, t0 (Rigault et al. subm.). To select a
suitable sample for this work with reliable phases and light curve properties
to have enough photometry data, we follow the light curve coverage constraints
of  Smith et al. (in prep.) of requiring each SN to have at least two
detections in two filters both pre- and post-maximum light (relative to t0)
and a total of at least seven detections across all filters. In order to have
a well constrained sample, we further applied the following criteria: x1 of
$-$4 to 4 with an uncertainty $<0.6$; $c$ ¡ 0.8 with an uncertainty $<0.35$.

Based on survey simulations, the ZTF DR2 sample is expected to be complete for
normal SNe Ia up to a redshift (z) of $z$ $\leq$ 0.06  (Amenouche et al. in
prep.). After the photometry cuts, we select SNe Ia with $z\leq$ 0.06 and that
have at least one spectrum between $-$5 to 5 days with respect to the time of
maximum light ($t_{0}$) with an uncertainty of $<1$d, where the velocity
evolution within this range has been shown to be small (e.g. Maguire et al.,
2014).

We have included the bright 91T-like, bright transitional 99aa-like, normal,
transitional (Hsiao et al., 2015; Gall et al., 2018) and 91bg-like objects in
our sample. We disregarded all the peculiar subtypes. These subtypes include;
‘03fg-like’ SNe Ia (Howell et al., 2006), which are overluminous and show slow
evolving light-curve features, ‘02cx-like’ SNe Ia (Li et al., 2003) that are
underluminous and spectroscopically weird, ‘02es-like’ SNe Ia (Ganeshalingam
et al., 2012) that look similar to underluminous SNe Ia with a slow light-
curve evolution, ‘SN Ia-csm’ (Benetti et al., 2006) that show strong
interaction with circumstellar medium around them (Dilday et al., 2012). These
peculiar objects and their properties are explained and studied in detail in
Dimitriadis et al. (in prep.)

The initial spectral typing ( Dimitriadis et al. in prep.) for our sample of
482 SNe Ia resulted in preliminary identification of 377 normal SNe Ia, 35
91bg-like, 18 91T-like, and 52 SNe Ia (those without sub-classification, which
will be referred to as ‘Ia-unclear’ throughout the text). However, there is a
subjective aspect to some of these classifications, e.g., where no further
sub-classifications are taken into account while typing and making a final
decision. One of our main aims was to assess the accuracy of this spectral
template matching process and assign sub-classes using objective measurements
of features present in the spectra, and this is discussed further in Section
3.1.

In order to measure the velocities and pseudo-equivalent widths (pEW) from the
Si ii $\lambda 6355$ feature, we only selected the spectra with high signal-
to-noise ratio (SNR) higher than 5. The SNR is estimated from the Si ii
$\lambda 6355$ absorption feature, where the estimate is the ratio of the
depth of the feature to the standard deviation in the selected continuum
region. After all the cuts were applied, the final sample consists of 657
spectra of 482 unique SNe Ia between -5 to 5 days (Table 1). The redshift,
phase and light curve width parameter $x_{1}$ distributions are presented in
Fig. 1, split into the good light curve coverage ZTF DR2 SN Ia sample (grey),
the sample after the redshift cut of $z\leq$ 0.06 has been applied (blue), and
the maximum light ($-$5 to 5 days) sample (red).

###  2.3 Velocity and width measurements

Figure 2: The velocity (left), pEW (middle) and FWHM (right) of Si ii $\lambda
5972$ (blue diamonds) and Si ii $\lambda 6355$ (black circles) from the ZTF
DR2 SN Ia sample as a function of rest-frame phases with respect to SALT2
maximum light. The black and blue dashed lines in the right panel represent
the linear regression fits to the FWHM of Si ii $\lambda 6355$ and Si ii
$\lambda 5972$, respectively.

In order to study the spectroscopic properties of our SN Ia sample, we have
performed several measurements on different spectral features. There are
several methods to fit SN Ia spectral features seen in the optical spectra.
Blondin et al. (2006) used a method based on smoothing the spectra and
choosing the minimum value to obtain the line velocities. Childress et al.
(2013) used a different method by applying multiple Gaussian fittings since
there are triplets such as Ca ii NIR that overlap. In this work, we adapt the
method of Childress et al. (2013) to obtain the line expansion velocities and
pseudo-equivalent widths of Si ii $\lambda 5972$ and Si ii $\lambda 6355$.

We start our study of the spectral absorption features by first defining a
continuum for each feature. This is done visually for each spectrum by
selecting regions on either side of the feature to which a line is fitted to
define the continuum. The spectrum is then divided by the continuum to
normalize each absorption profile. We apply a double Gaussian fit for the
absorption features of Si ii $\lambda 6355$ line, which is a doublet of Si ii
$\lambda$6347 and $\lambda$6371 features. We force both doublet components to
have the same widths, velocities, and strengths since these lines tend to
saturate in the assumed optically thick regime (Childress et al., 2013).
Another double Gaussian fit is applied to the absorption features of Si ii
$\lambda 5972$ doublet (Si ii $\lambda$5958 and $\lambda$5979), where we again
fix the individual line components to have same widths, velocities and
strengths.

We estimate the uncertainties on the fit parameters by varying the positions
of the visually picked continuum regions on other side of the feature and
repeating the Gaussian fitting. These uncertainties are combined with the
uncertainties on the individual fits to give a total uncertainty for the fit
parameters. We do not want to exclude the SNe Ia with template-matched
redshifts because this may bias our sample by preferentially removing fainter
host galaxies that are are less likely to have a host galaxy spectrum. For 105
SNe Ia in our sample, the redshift comes from snid template matching, and in
order to account for the redshift uncertainty discussed in Section 2.1, we add
500 km s-1 in quadrature to the Si ii velocity uncertainties.

The pseudo-equivalent width (pEW) of each feature is calculated based on the
Gaussian fit parameters. For some SNe Ia in the sample, the Si ii $\lambda
5972$ feature is quite weak and for these events, we calculated the 3$\sigma$
upper limit of the Si ii $\lambda 5972$ feature by forcing a fit at the
expected Si ii $\lambda 5972$ location to find the residuals of the fit and
calculate the root mean square of the residuals. We infer the full width at
half maximum (FWHM) of the Si ii $\lambda 5972$ feature based on the relation
between the FWHM of Si ii $\lambda 6355$ and of Si ii $\lambda 5972$ for SNe
Ia where both exist. For that, we first calculated the mean FWHM of Si ii
$\lambda 5972$ (159$\pm$25 Å) and Si ii $\lambda 6355$ (100$\pm$28 Å), where
both exist, to estimate a scaling factor of $\sim$ 1.6 (see the right panel of
Fig. 2 for the two fits, each showing similar linear relations that yields a
scaling factor of $\sim$ 1.6). After correcting for the relation, we use the
estimated FWHM of Si ii $\lambda 5972$ to calculate the 3$\sigma$ upper limits
of its pEW.

The velocity, pEW and FWHM of the Si ii $\lambda 5972$ and Si ii $\lambda
6355$ features are shown as a function of phase in Fig. 2. The results of the
fits for each feature and spectrum are given in Table 4. The distributions of
velocity, pEW and FWHM are seen to be relatively flat in the phase range
studied here of $-$5 to +5 d with respect to maximum light. No further
correction for evolution within this phase range is applied.

##  3 Analysis

One of the aims of our study is to assess the accuracy of the sub-
classification of the DR2 SN Ia sample that used the method explained above
(Section 2.1). We also investigate the possible spectral transition from the
‘normal’ to ‘91T-like’ SNe Ia in Section 3.1.1 and ‘normal’ to ‘91bg-like’ SNe
Ia in Section 3.1.2. The impact of host galaxy contamination on SN Ia
classifications and the Si ii feature is discussed in Section 3.2 and Section
3.3, respectively.

###  3.1 Spectral (re-)classification of the sample

Table 2: Sub-type reclassification in ZTF DR2. The initial column is the original sub-classification from the DR2 typing effort. The numbers below do not represent the final numbers of each sub-type but only indicate changes in sub-typing from the initial assessment to our investigation. The number of events in final sample after removal of host contaminated events is given in Table 3. Sub-type | Initial | 91T-like | 99aa-like | normal | 04gs-like | 86G-like | 91bg-like | Ia-unclear
---|---|---|---|---|---|---|---|---
91T-like | 18 | - | 9 | 2 | - | - | - | 1
normal | 377 | - | 18 | - | 18 | 3 | - | 55
91bg-like | 35 | - | - | - | - | 8 | - | 3
Ia-unclear | 52 | 1 | 12 | 10 | - | - | - | -

To determine the accuracy of spectral-template matching, we have inspected in
detail the sub-classifications from the ZTF DR2 initial analysis of all 482
SNe Ia in our maximum light sample. As discussed previously, we do not study
the ‘Ia peculiar’ sub-type in this analysis. In order to check the accuracy of
the initial DR2 sub-typing, we visually inspected each SN Ia and compared to
known examples of each sub-class that we wanted to investigate. We created a
comparison sample from the peak spectra of SN 1991T for ‘91T-like’ SNe, SN
1999aa for bright transitional/‘99a-like’ SNe, SN 2011fe for normal SNe Ia, SN
2004gs for faint transitional/‘04gs-like’ SNe, SN 1986G for ‘86G-like’ SNe and
SN 1991bg for ‘91bg-like’ SNe. All spectra in our sample were visually
inspected and over-plotted against different subtypes to identify the closest
match for each, taking into account all key features. In Table 2, we show the
initial classifications of the DR2, as well as our changes to those initial
categories.

We are particularly interested in constraining the diversity of the events at
the two transition boundaries $-$ from normal to overluminous (e.g.,
‘91T-like’) and from normal to subluminous (e.g., ‘91bg-like’). Therefore, we
are investigating subtle differences in their spectral properties. In Section
3.1.1, we discuss the sub-classification criteria for SNe Ia around the normal
to overluminous boundary (‘99aa-like, 91T-like’). In Section 3.1.2, we discuss
the SN Ia sub-classification at the normal to underluminous boundary (‘04gs-
like’, ‘86G-like’, ‘91bg-like’).

There are 52 SNe Ia that were initially classified (prior to our analysis) as
‘Ia-unclear’, meaning that a sub-classification had not been made. In this
work, we have reclassified 23 of these cases into sub-classifications:
‘91T-like’, ‘99aa-like’, and ‘normal’. None of the ‘Ia-unclear’ were
reclassified into the underluminous sub-classes. The initial DR2
classification exercise identified 377 normal SNe Ia. However, we updated
these classifications to find a total 295 events with a ‘normal’ SN Ia
classification. (see Table 2 for the reclassification statistics and the
second column of Table 3) for the updated numbers in each class (before any
host contamination cuts).

We have also identified 59 SNe Ia that the initial DR2 typing did have a sub-
classification for but we have overturned to be ‘Ia-unclear’. This gives a
final total of 88 events with an ‘Ia-unclear’ classification based on our re-
classifications. The main causes of the lack of a sub-classification were
either host contamination, where one or more critical features were not
covered, or due to low S/N in the spectra. We discuss the impact of host
galaxy contamination in further detail in Section 3.2. We note that in this
analysis, we are only concerned with their spectral classifications and do not
consider any of their light curve properties such as $x_{1}$, $c$ or any
galaxy properties in determining our classification and base our
classifications purely on spectroscopic observations around peak.

####  3.1.1 The normal to 91T-like spectral transition

Figure 3: Examples of ‘91T-like’ (black) and ‘99aa-like’ (grey) maximum light
spectra are shown compared to the labelled spectra of SN 1991T, SN 1999aa and
SN 2011fe at similar phases. Key features for identifying these SNe Ia are
marked. Each spectrum has been corrected for MW extinction (Schlafly &
Finkbeiner, 2011).

In the normal to overluminous ‘91T-like’ region, updated classifications were
done by comparing the spectra in our sample at similar phases with the
overluminous prototype SN 1991T, the normal SN 2011fe and a transitional event
between these two classes, SN 1999aa (Fig. 3). ‘91T-like’ SN Ia spectra around
maximum light have weak Si ii features (6355 and 5972 Å) compared to normal SN
Ia spectra. S ii and Ca ii H$\&$K features are considerably weaker than in a
normal SN Ia, where Phillips et al. (2022) showed the lack of Ca ii H$\&$K
feature itself is an identifier for true ‘91T-like’ events. Objects with
spectral properties between ‘91T-like’ and ‘normal’ SNe Ia are classified
based on the transitional object SN 1999aa. While the Si ii $\lambda 6355$
feature of ‘99aa-like’ SNe Ia near maximum light are stronger than ‘91T-like’
SNe Ia, they are still on the lower side of ‘normal’ SNe Ia. The
classification of these transitional ‘99a-like’ objects follow the closeness
of pEW of Si ii $\lambda 6355$ to those in SN 1999aa. While some of these
classifications are subjective, our classifications align closely with the
method used to identify ‘91T-like’ events from Phillips et al. (2022) since
near maximum light the pEW separation of Si ii $\lambda 6355$ itself is well
established between these three sub-classes.

We visually inspected the 18 initially classified ‘91T-like’ objects and
reclassified 9 of them as bright transitional ‘99aa-like’ SNe Ia based on the
closer similarity of their Si ii $\lambda 6355$ feature strength to that of SN
1999aa than to SN 1991T or SN 2011fe. We confirm that in total seven of our
sample are true ‘91T-like’ SN Ia based on best-matching spectral comparisons
to ‘91T-like’ events. 39 SN are reclassified as ‘99aa-like’, where 9 events
where initially classified as ‘91T-like’, 19 events as ‘normal’ and 12 events
as ‘Ia-unclear’ (see Table 2).

####  3.1.2 The normal to 91bg-like spectral transition

Similarly to the overluminous spectral transition, we have also visually
inspected the sample to identify the diversity of subluminous events, spanning
from ‘normal’ to ‘91bg-like’ SNe Ia. ‘91bg-like’ events are generally
recognised spectroscopically by the strong Ti ii lines near 4300 Å around peak
brightness. A ‘W’ shaped S ii feature is less clearly visible than in a
‘normal’ SN Ia. Si ii $\lambda 5972$ and Si ii $\lambda 6355$ features and the
O i $\lambda$7773 feature are especially prominent. Based on their
spectroscopic similarities to those of SN 1991bg, 24 SNe in our sample are
identified as ‘91bg-like’.

SNe Ia identified as ‘86G-like’ are transitional events between ‘normal’ and
‘91bg-like’ SN Ia (Phillips et al., 1987). The spectra of SN 1986G had
stronger Si ii $\lambda 5972$ and Si ii $\lambda 6355$ features than normal
SNe Ia and some absorption due to Ti ii in the 4300 Å wavelength region but
this was not as strong as seen in ‘91bg-like’ events (Ashall et al., 2016),
which likely indicates an intermediate state between a ‘normal’ and ‘91bg-
like’ SNe Ia. By following the spectroscopic characteristic differences
mentioned above, we identified 11 SNe Ia in our sample as ‘86G-like’ events, 3
of them were originally classified as ‘normal’ and 8 as ‘91bg-like’,
demonstrating the difficulty in sub-classifying these events without careful
comparison of relevant features. The strength of the Ti ii feature is the main
feature used to separate the ‘91bg-like’ events and ‘86G-like’ events.
Examples of their maximum light spectra compared to other sub-classes are
shown in Fig. 4.

In our sample, we have also identified SNe Ia that do not meet the
spectroscopic criteria to be classified as ‘91bg-like’ or ‘86G-like’ but that
are spectroscopically most similar to a faint normal SN Ia, SN 2004gs (Park &
Li, 2004; Morrell et al., 2004; Blondin et al., 2012). SN 2004gs was first
discovered by Park & Li (2004) and classified as a SN Ia by Morrell et al.
(2004). SN 2004gs is $\sim$ 10 kpc away from its S0 type host galaxy,
PGC024286. SN 2004gs has been observed as a part of Center for Astrophysics
Supernova Program (CfA) and its spectral and light curve parameters are
published by Blondin et al. (2012), where it was classified as a ‘normal’ SN
Ia. However, SN 2004gs appears to be an intermediate state between a ‘normal’
SN Ia and a transitional ‘86G-like’ SN Ia. It shows significantly stronger Si
ii $\lambda 5972$, O i $\lambda$7773 and Ca ii NIR features and with weaker Ti
ii feature near 4300 Å than seen in a ‘normal’ SN Ia spectrum (see Fig. 5).
The Ti ii feature in the peak spectra is not as strong as a transitional
(86G-like) SN Ia but still present, while the Mg ii 4481 feature is more
prominent in SN 2004gs. We identify 18 SNe in our sample as similar to ‘04gs-
like’ (some of which are shown in Fig. 5) based on the existence of stronger
abundances of Si ii $\lambda 5972$, Si ii $\lambda 6355$, O i $\lambda$7773,
Ca ii NIR than ‘normal’ SNe with considerably weaker abundance of Ti ii near
4300 Å than ‘86G-like’ SNe. They were all initially classified in the DR2
typing effort as normal SNe Ia.

Figure 4: A sub-sample of ‘86G-like’ SN Ia spectra (shown in black) around maximum light are compared to those of SN 2004gs, SN 1986G, SN 1991bg and SN 2011fe at similar phases. Key features at identifying these SN Ia are shown. Each spectrum has been corrected for MW extinction.  Figure 5: A sub-sample of ‘04gs-like’ (shown in black) ZTF DR2 SNe Ia around maximum light plotted with the spectra of SN 2004gs, SN 1986G, SN 1991bg and SN 2011fe at similar phases for comparison. Key features at identifying these SN Ia are shown in the figure. Each spectrum in the figure are corrected for MW extinction.  Table 3: Classifications of ZTF DR2 volume limited SN Ia sample with different dDLR cuts. The number of remaining SNe in each sub-type is shown. dDLR cut | no cut |  $>$0.1 |  $>$0.2 |  $>$0.3
---|---|---|---|---
Ia-unclear | 88 | 66 | 42 | 27
91T-like | 7 | 7 | 7 | 4
99aa-like | 39 | 37 | 34 | 27
normal | 295 | 280 | 257 | 236
04gs-like | 18 | 17 | 17 | 14
86G-like | 11 | 11 | 11 | 10
91bg-like | 24 | 24 | 24 | 22
Total | 482 | 442 | 392 | 340

###  3.2 The impact of host galaxy contamination on SN Ia classification

Figure 6: Left: Local surface brightness compared with the dDLR of volume
limited ZTF DR2 sample. The fit shown with a black solid line on the plot is
used to estimate a dDLR value (vertical dashed line) based on the chosen
surface brightness magnitude of 20.1 mag (vertical dashed line). Middle: We
show the Si ii $\lambda 6355$ pEW against the velocity for three different
subtypes of SNe Ia: 91T-like (represented by squares), 99aa-like (represented
by diamonds), and normal (represented by circles). The data points for each SN
subtype are shown with increasing levels of host galaxy light contamination
(25, 50, 75, and 100 per cent) from top to bottom. Different colours represent
different galaxy types used to simulate the contamination effects. This allows
for the comparison of how various galaxy types influence the measured Si ii
$\lambda 6355$ pEW for each SN subtype and how the pEW is affected by
increasing galaxy contamination. Right: Local surface brightness plotted
against the pEW of Si ii $\lambda 6355$ feature. The gray dashed line
represents the equivalent value of dDLR where we applied our cut of dDLR =
0.2, based on the corresponding surface brightness magnitude of 20.1 mag,
showed with the gray dotted line. The red and blue dashed line represents the
regression line fitted to the all data and data with the dDLR cut,
respectively. The red and blue shaded regions represent the confidence
interval around corresponding regression lines. A strong correlation between
the pEW of Si ii $\lambda 6355$ and local surface brightness and its effect on
sub-typing is shown.

There are 88 SN Ia in our sample without a sub-classification, even after
visual inspection. Some of these spectra are visibly contaminated by host
galaxy light. Since 91T-like events have weak Si ii $\lambda 6355$ and Si ii
$\lambda 5972$, that could mean that it is preferentially classified as ‘Ia-
unclear’ if the S/N ratio is slightly lower or it is more contaminated by host
galaxy light where it cannot be easily distinguished from a ‘normal’ SN Ia. We
have investigated a number of methods of quantifying the impact of host galaxy
contamination on the SN Ia classifications and line measurements (pEW,
velocity).

Host galaxy properties of the ZTF DR2 sample is presented in  Smith et al. (in
prep.), where the software package
Host_Phot333https://github.com/temuller/hostphot/tree/main was applied to Pan-
STARRS DR2 (PS1; Chambers et al., 2016) images to obtain the Kron fluxes and
the Directional Light Radius (DLR; Sullivan et al., 2006; Smith et al., 2012;
Gupta et al., 2016). The DLR is the elliptical radius of a galaxy in the
direction of the SN. The measure of the offset of a SN from the centre of its
host galaxy that is scaled by the elliptical radius of the galaxy in the
direction of the SN is called the dDLR. It is a measure of the SN to host
galaxy centre separation corrected for the differing sizes of galaxies. The
dDLR distribution of the ZTF DR2 sample ranges from zero to seven but peaks at
a value of $\sim$0.2, with most SNe Ia having dDLR values of less than three.

The local surface brightness of the galaxy at the position of the SN can also
be estimated as a measure of the likely host contamination in our spectral
measurements. These values were estimated for SNe Ia in the ZTF DR2 using a
galaxy image decomposition involving four morphological models, bulge, disk,
bulge+disk and bulge+bar+disk  (Senzel et al. subm.). The model fits were
performed in surface brightness space (mag/arcsec2) and the local surface
brightness values used in this paper are sampled from the models at the
location of the SN. The galaxy models undergo several quality control steps
during the fitting procedure, ensuring that only well-fit and physically
accurate models make it into the final sample. From the original 3628 SNe Ia
in ZTF DR2, the final sample consists of 724 modelled galaxies. After the
applied selection criteria (see Sec. 2.2), 115 out of 482 SN Ia have surface
brightness values ($\sim$24 per cent).

The local surface brightness is likely a better measure than the dDLR of the
contamination of the SN spectra but unfortunately is only available for 24 per
cent of the SNe Ia in our final sample. We have compared our dDLR and local
surface brightness values in the g band for the SNe Ia that have both
measurements (see Fig. 6, left). We identify a clear trend between both
quantities, where the larger the dDLR (larger corrected offset from the host
centre), the fainter the underlying local surface brightness. A power law
model for dDLR and local surface brightness relation was found to fit the
quantities well.

We have colour coded in the SNe Ia in Fig. 6 and find that the ‘Ia-unclear’
sub-class is much more highly represented at small dDLR/bright local surface
brightness compared to normal events or other sub-classes. This suggests that
the inability to sub-classify is likely driven significantly by the
contamination from host galaxy light. However, since some sub-classes may have
host galaxy dependencies, e.g., a general preference for 91T-like events to
occur in star-forming host galaxies (Phillips et al., 2022), we want to bias
our sample as little as possible. Therefore, we would like to apply a balanced
cut on the dDLR/surface brightness values that removes a large percentage of
the ‘Ia-unclear’ that occur in the inner brighter regions of their host
galaxies but does not remove too many SNe Ia from our sub-classes with smaller
numbers of events.

To do this, we test the impact of removing events with dDLR less than 0.1,
0.2, and 0.3 compared to no cut on the sample on the different sub-types
(Table 3). By placing a cut to remove events that have dDLR$<$0.1, we would
remove $\sim$25 per cent of the ‘Ia-unclear’ sample, only $\sim$5 per cent of
the ‘normal’ SN Ia sample, two ‘99aa-like’ event and one ‘04gs-like’ event,
which is equivalent to 2 per cent of the other sub-types. Increasing this cut
to dDLR$<$0.2 would remove $\sim$52 per cent of the ‘Ia-unclear’
classification, $\sim$12 per cent of the ‘normal’ SN Ia sample, and $\sim$6
per cent from the rarer sub-classes. Increasing the cut to remove objects with
dDLR$<$0.3 removes $\sim$70 per cent of the ‘Ia-unclear’, $\sim$20 per cent of
the ‘normal’ SN Ia, and $\sim$20 per cent from the rarer sub-classes. At all
cut levels, a much more significant percentage of events without a sub-
classification (‘Ia-unclear’) is removed compared to the other sub-classes.
For our final sample, the choice of dDLR is somewhat arbitrary but we choose
to exclude all the events with dDLR$<$0.2 based on the minimal impact it has
on the rarer sub-types while removing nearly half of the ‘Ia-unclear’. Some of
the remaining ‘Ia-unclear’ in the sample are likely contaminated by host
galaxy features but may also not have the wavelength coverage for
identification of features necessary for sub-classification or low SNR at the
wavelengths of key features. This dDLR cut of 0.2 is equivalent to a local
surface brightness of 20.1 mag based on our power law model fit to the
relation (left panel of Fig. 6). It is this final sample of 392 SNe Ia (Table
3) that is considered in the subsequent analysis.

###  3.3 The impact of host galaxy contamination on Si ii feature measurements

We demonstrated the direct impact of host contribution on SN Ia spectral sub-
typing in Section 3.2 and removed those events that are most heavily
contaminated. However, it is likely that host contamination is still present
in SNe Ia in our sample and we wish to determine what impact this may have on
the measured spectral parameters (velocity, pEW). We tested this by
artificially injecting host galaxy contamination into test SN Ia spectra from
our sample. We did this by taking spectra that were visually uncontaminated by
host light of a normal, a ‘91T-like’, and a ‘99aa-like’ SN Ia and combining
with template galaxy spectra of two spirals (Sa, Sb) and an elliptical (E)
from Kinney et al. (1996). Each SN spectrum was combined with each galaxy
template at varying flux ratios of galaxy contamination of 0.25, 0.5, 0.75 and
1 and then the combined spectra were fit with our spectral line analysis code
to determine the parameters of the Si ii $\lambda 6355$ features.

In middle panel of Fig. 6, we show the pEW of the Si ii $\lambda 6355$ feature
against its velocity for the three SN Ia sub-classes with varying host
contamination of the three different galaxy templates. We observed a
considerable decrease in the measured pEW of each sub-class as the host galaxy
contamination was increased, ranging from a 17 per cent change to almost 50
per cent in the normal SN Ia for the most contaminated spectrum. The velocity
measurement changes were smaller with an increase of up to 450 km s-1 for the
normal SN Ia and decrease in the 99aa-like event of 500 km s-1. A decrease in
pEW measurements in SN Ia spectra was also determined by Nordin et al. (2011)
due to host galaxy contamination.

In the right panel of Fig. 6, we show the g-band local surface brightness
against Si ii $\lambda 6355$ pEW for SNe Ia in our sample before the dDLR cut
of 0.2. A linear regression fit to the data is shown with red dashed line on
the right panel of Fig. 6. The events with an ‘Ia-unclear’ classification
cluster below a pEW of $\sim$70 Å. Based on our dDLR cut that removes values
below 0.2, this is equivalent to a value of 20.1 mag for the local surface
brightness. We then remove all SNe Ia with brighter local values than 20.1
mag, where the blue dashed line on the right panel of Fig. 6 shows the linear
regression fits for before and after the removal of the objects. After
removing objects brighter than 20.1 mag, the significance level between the
surface brightness and the pEW of Si ii $\lambda 6355$ seemed to decrease by
approximately two sigma. This suggests that the events heavily contaminated by
host galaxy light are driving this correlation. However, our tests of spectral
contamination indicate that the rest of the sample may also be affected,
leading to smaller measured values of the Si ii $\lambda 6355$ pEW than those
that are intrinsically present.

##  4 Results and Discussion

In Section 4.1, we present the ‘Branch’ classification diagram (Branch et al.,
2006) of the ZTF SN Ia DR2 sample based on their pEW values. We also discuss
the relative rates of SNe Ia in each of the subclasses and their key
differences. In Section 4.2 we present the pEW and velocity distributions of
‘normal’ SNe Ia from the ‘Wang’ classification scheme (based on pEW and
velocity of the Si ii $\lambda 6355$ feature) and investigate the properties
of NV and HV SNe Ia. The spectral properties and tardis analysis of faint
‘normal’ SNe Ia are presented in Section 4.3. In Section 4.4, the connection
between the spectral properties of SNe Ia and their SALT2 light curve
properties are presented.

Figure 7: Left: The pEW of Si ii $\lambda 5972$ plotted against the pEW of Si
ii $\lambda 6355$ based on sub-types of SNe Ia taken from Branch et al. (2006)
for the 392 SNe Ia from the ZTF DR2 sample with dDLR greater than 0.2. Branch
sub-type zones are shown with the black dashed lines following the limits from
Folatelli et al. (2013), with ‘SS’ for shallow Silicon, ‘CN’ for core normal ,
‘BL’ for broad line and ‘CL’ for cool events. Filled circles with different
colours represent the SN Ia types. Upper limits shown on the plots are plotted
as downward arrows (see Section 2.3). Right: Zoom-in plot of the SS SN Ia
region along with the histogram on top of the number of events of the
‘91T-like’, ‘99aa-like’ and ‘normal’ SN Ia sub-types in this region, showing
the transition from ‘91T-like’ (dark blue) to ‘99aa-like’ (cyan) to ‘normal’
(green) with increasing pEW of Si ii $\lambda 6355$.

###  4.1 Branch Classification

In Fig. 7, we present the pEW of the Si ii $\lambda 5972$ feature against the
pEW of the Si ii $\lambda 6355$ feature for spectra in the phase range of -5
to +5 days with respect to the time of maximum light, $t_{0}$. SNe Ia with a
dDLR less than 0.2 have been removed. In cases where multiple spectra are
available for a given SN within the phase range, the one nearest to maximum
light is chosen.

It is well established that the pEWs of the Si ii $\lambda 5972$ and Si ii
$\lambda 6355$ features are strongly correlated in the identification of SN Ia
sub-types (Branch et al., 2006), where they can be separated into four
spectral sub-classes: ‘core normal’ (CN), ‘shallow silicon’ (SS), ‘broad line’
(BL), and ‘cool’ (CL), based on the strength ratio of these features. We
follow the same criteria as Folatelli et al. (2013) to assign the ‘Branch’
sub-classes. A clustering analysis of the Branch diagram parameters using a
Gaussian mixture model suggested that these four broad classes are well-
defined statistically (Burrow et al., 2020).

In our sample, we have 35 SS, 122 CN, 51 BL and 56 CL coming from direct
measurements of the features. Using our three-sigma limits on the pEW of Si ii
5972 Å feature, we can assign a additional objects to the subclasses of 69 SS,
39 CN, 19 BL, and one CL. Out of 392 SNe Ia, $\sim$26$\%$ have a SS sub-class,
$\sim$41$\%$ have a CN sub-class, $\sim$18$\%$ have a BL sub-class and
$\sim$15$\%$ have a CL sub-class. Blondin et al. (2012) analysed SN Ia spectra
obtained by the Centre for Astrophysics (CfA) Supernova Program and assigned
Branch classifications using spectra around maximum light. Out of 218 SNe Ia
in their sample $\sim$15$\%$ have a SS sub-class, $\sim$40$\%$ have a CN sub-
class, $\sim$28$\%$ have a BL sub-class and $\sim$17$\%$ have a CL sub-class.
In another work, Folatelli et al. (2013) presented the optical spectra of SNe
Ia with the spectra obtained by the Carnegie Supernova Project (CSP; Hamuy et
al. (2006)). Out of 78 SNe Ia at maximum light in their sample, $\sim$13$\%$
have a SS sub-class, $\sim$32$\%$ have a CN sub-class, $\sim$28$\%$ have a BL
sub-class and $\sim$27$\%$ have a CL sub-class. Assuming Poissonian
uncertainties, on the relative percentages, our relative rates are broadly
comparable to those of CfA and CSP. However, our SS rate is slightly higher,
which may be due to the CfA and CSP studies not including events with only
upper limits on their Si ii 5972 Å feature but their spectra are generally
higher S/N than the mean of our sample.

In Fig. 7, we also show the spectral types (‘91T-like’, ‘99aa-like’, ‘normal’,
‘04gs-like’, ‘86G-like’, ‘91bg-like’, and ‘Ia-unclear’) we have identified for
the 392 SNe Ia in Section 3.1. The ‘normal’ SNe Ia fall generally fall into
the CN and BL region, with some at the boundary of the Si ii $\lambda 6355$
pEW between SS and CN (discussed more in Section 4.1.1). The ‘91bg-like’,
‘86G-like’, and ‘04gs-like’ SNe Ia are predominantly found in the CL region of
Fig. 7, while the ‘91T-like’ and ‘99aa-like’ events are found in the SS
region. These clusters of spectroscopic sub-classes in the Branch diagram are
not unexpected since the Si ii features are some of the main features used to
sub-classify SN Ia spectra.

####  4.1.1 How rare are 91T-like events?

The SS Branch sub-class (those with both weak Si ii $\lambda 5972$ and Si ii
$\lambda 6355$ features) is made up of $\sim$33 per cent ‘99aa-like’, $\sim$32
per cent ‘normal’ SNe Ia, $\sim$28 per cent ‘Ia-unclear’, and $\sim$7 per cent
‘91T-like’. All ‘91T-like’ and ‘99aa-like’ SNe Ia in our sample are in the SS
region. While we see similar rates of ‘normal’ and ‘99aa-like’ SNe Ia in the
SS region (see right panels of Fig. 7), true ‘91T-like’ SNe Ia remain rare at
$\sim$7 per cent. All ‘91T-like’ SNe Ia have shallower Si ii $\lambda 6355$
features than the ‘99aa-like’ events. The ‘91T-like’ SNe Ia all have Si ii
$\lambda 6355$ pEW values below 31 Å, while the ‘99aa-like’ SNe Ia have values
in the range of 32 to 63 Å. Only four ‘99a-like’ SNe Ia have a pEW Si ii
$\lambda 6355$ value higher than 55 Å (55, 60, 62 and 63 Å). Normal SNe Ia
start to dominate the population with Si ii $\lambda 6355$ pEW above $\sim$55
Å. Conversely, only two ‘normal’ SNe Ia have pEW Si ii $\lambda 6355$ values
lower than $\sim$55 Å, at 51.5$\pm$${}^{\text{0.4}}_{\text{0.6}}$ and
54.5$\pm$${}^{\text{1.8}}_{\text{2.8}}$ Å.

Fig. 7 shows that most SNe Ia without a sub-classification (‘Ia-unclear’) are
on the lower end of the pEW Si ii $\lambda 6355$ distribution. Approximately
70 per cent of the 42 SNe Ia without a sub-classification are in the SS
region. We have shown in Section 3.2 that significant host contamination has
the impact of decreasing the measured pEW of the Si ii lines, while also
making sub-classification more difficult in general. Therefore, it is
unsurprising that the majority of events without a sub-classification are
among the events with the weakest Si ii pEW values. In the most extreme case
where the host galaxy contamination is comparable to the SN flux, the pEW of
the Si ii $\lambda 6355$ feature may be up to 35 Å weaker due to host
contamination than the intrinsic SN measurement. This could result in many of
the unclassified ‘Ia-unclear’ class moving into the core normal region on the
Branch diagram (see bottom right panel of Fig.7).

The rareness of the ‘91T-like’ events can not be explained by the host
contamination because significant host contamination decreases the pEW. Even
if we assume all ‘Ia-unclear’ that have similar Si ii $\lambda 6355$ pEW
values to those of the ‘91T-like’ SNe ($<$31 Å) are also ‘91T-like’, the rate
is still less than 5 per cent of all SNe Ia in our sample.

Phillips et al. (2022) identified a sample of ‘91T-like’ events based on their
Si ii $\lambda 6355$ pEW as a function of phase, the time of maximum in the i
band relative to the B band, and the presence of a clear secondary maximum in
the i band. Their Si ii $\lambda 6355$ pEW cutoff was $<40$ Å at B-band
maximum to $<50$ Å at +10 days relative to maximum light. Our maximum-light
($-$1 to +5 d) ‘91T-like’ SNe are defined by the visual inspection method
discussed in Section 3.1.1 and broadly in agreement with Phillips et al.
(2022). They identified that their ‘91T-like’ events are overluminous in their
Hubble residuals compared to other SS and CN SNe with similar light curve
decline rates.

Several ‘normal’ SS SNe Ia are spectroscopically quite similar to the SNe Ia
in lower limits of CN SNe Ia, showing a continuity in the pEW of Si ii
$\lambda 6355$ feature from SS to CN class. Hence, the defined separation at a
pEW of Si ii $\lambda 6355$ at 70 Å between SS and CN becomes less relevant
than the separation between ‘99aa-like’ and ‘normal’ SN Ia at $\sim$ 55 Å. A
recent study from Chakraborty et al. (2023) shows that ‘99aa-like’ SN Ia can
be separated into two groups, one showing similar LC properties to ‘91T-like’
SN Ia and other closer to brighter end of ‘normal’ SN Ia, suggesting the later
one bridging a continuity from normal to bright end of SN Ia. O’Brien et al.
(2023) did tardis based analysis on ‘91T-like’ SN Ia and ‘normal’ SN Ia.
Through the effect of abundances and ionisation states of intermediate-mass
elements in the spectra of these sub-types, it is concluded that continuity is
seen between the ‘normal’ and ‘91T-like’ SN Ia.

####  4.1.2 The diversity of ‘cool’ events

The CL SN Ia sub-class of Branch et al. (2006) consists of SNe Ia with deeper
Si ii $\lambda 5972$ absorption (Fig. 7), often associated with low-luminosity
events. The ‘91bg-like’ and ‘86G-like’ events are seen to dominate the CL
class, but there are faint normal SNe Ia (‘04gs-like’) that fall into this
region in Fig. 7 as well. We have visually inspected these events and find
that all 17 ‘04gs-like’ SNe Ia in the CL class have the strong Si ii $\lambda
5972$ of ‘91bg-like’ and ‘86G-like’ events but have significantly less Ti ii
$\lambda$4300\. These faint SN Ia also have stronger Ca ii NIR and O i in
their spectra than ‘normal’ SNe Ia, populating the region between ‘normal’ and
the ‘86G-like‘ events. While these faint SNe Ia do not show any preference in
Fig. 7, other than all being in CL class, they do exhibit a clear difference
in their light curve properties (see Section 4.4). Seven SNe Ia in the CL
region did not have key features in their spectra or were still host
contaminated, making us unable to sub-classify them.

####  4.1.3 A continuum from ‘core normal’ and to ‘broad-line’

In Fig. 7, the Branch classification of CN is dominated by SNe Ia that are
also spectroscopically classified as ‘normal’ SNe Ia ($\sim$95 per cent). This
suggests that the vast majority of ‘normal’ SNe Ia can be identified by solely
the pEW of their Si ii $\lambda 6355$ and Si ii $\lambda 5972$ features. There
is only one ‘91bg-like’ event and one ‘86G-like’ event falling in this CN
group. Both of these events displayed significant host contamination in their
spectra (although they have dDLR values above our cut-off of 0.2), diminishing
the Si ii $\lambda 5972$ feature, hence lowering the pEWs of these SNe Ia (see
Section 3.2) from likely CL to CN.

The BL SN Ia sub-class is exclusively SNe Ia that are visually
spectroscopically classified as ‘normal’ SNe Ia. This is likely because their
most common spectral match in the snid database is the BL SN Ia, SN 2002bo
(Benetti et al., 2004; Stehle et al., 2005). The most extreme BL in our sample
is SN 2018ccl, with a very high Si ii $\lambda 6355$ pEW of $\sim$197 Å. This
extreme case is similar to SN 1984A (Branch et al., 2006), which had a Si ii
$\lambda 6355$ pEW of $\sim$200 Å.

Previous studies have found that a significant fraction of SNe Ia possess
secondary, high-velocity absorption components, predominantly in the Si ii
$\lambda 6355$ and Ca ii NIR features (Hatano et al., 1999; Quimby et al.,
2006; Childress et al., 2013; Maguire et al., 2014) up to maximum light. The
findings of  Harvey et al. (subm.) suggest that up to 42$\pm$12 per cent of BL
SN Ia classifications are due to the presence of an additional high-velocity
component that broadens the line. Burrow et al. (2020) used Gaussian mixture
models to investigate the Branch diagram from their data and showed that when
the Si ii $\lambda 6355$ velocity is taken into account in the analysis, the
BL group is nearly distinct from the other Branch sub-classes, which further
supports the case of the BL class being highly affected by the HV components
since the combined velocity would be higher when two blended components are
present.

###  4.2 ‘Wang’ Classification and Velocity-pEW Relation

Figure 8: Pseudo equivalent widths of the Si ii $\lambda 6355$ feature plotted
against the velocity of the same line ($v_{\mathrm{Si}}$) near maximum light
($-$5 to $5$ days). Where several measurements exist for a given SN in the
phase range used, we selected the one closest to maximum light. Different
colours represent different sub-types used in this study. Green filled and
open circles represent the NV SNe Ia and HV SNe Ia within the ‘normal’ SNe Ia
in our sample, respectively.

The ‘Wang’ classification scheme introduced by Wang et al. (2009b) of normal
velocity (‘NV’, $v_{\mathrm{Si}}\lesssim$ 12,000 km s-1) and high velocity
(‘HV’, $v_{\mathrm{Si}}\gtrsim$ 12,000 km s-1) is solely based on the velocity
of the Si ii $\lambda 6355$ absorption feature around the peak of the SN light
curve (Fig. 8). This classification only applies to normal SNe Ia, and all
other sub-types, including the ‘Ia-unclear’, are excluded from the
classification scheme. 257 out of 392 SN Ia in our sub-sample are classified
as ‘normal’, and we assigned 191 SNe Ia as ‘NV SN Ia’ (74$\%$) and 66 SNe Ia
as ‘HV SNe Ia’ (26$\%$). The mean velocity and the mean pEW 6355 of the ‘NV
SNe Ia’ in our sample are $-$ 10,954$\pm$47 km s-1 and 86$\pm$1 Å,
respectively (Fig. 8). The mean velocity and the mean pEW 6355 of the ‘HV SNe
Ia’ in our sample are $-$ 13,072$\pm$130 km s-1 and 103$\pm$4 Å, respectively.
These are broadly consistent with the results of Blondin et al. (2012), where
the mean velocity and the mean pEW 6355 of the NV SNe Ia were estimated as
$\sim-$11,000 km s-1 and $\sim$95 Å. Small differences are not unexpected
given differences in the origins of host galaxy redshifts (snid compared to
spectroscopic), the impact of smoothing, as well as our wider spectral phase
range of $\pm$5 d from maximum light, compared to $\pm$3 d from maximum light
in Blondin et al. (2012). Since in our sample we have more early spectra (Fig.
1) and for ‘normal’ SNe Ia the earlier spectra tends to have smaller pEW
values (Folatelli et al., 2013) than the after maximum light ones, this could
explain the average pEW of Si ii $\lambda 6355$ in our sample being smaller by
a few angstroms compared to Blondin et al. (2012).

As can be seen in Fig. 8 ‘99aa-like’ objects have a similar velocity
distribution to ‘normal’ SNe Ia, with an average Si ii $\lambda 6355$ velocity
of 10,935$\pm$184 km s-1 but a lower average pEW of 46$\pm$1 Å. ‘91T-like’
objects in our sample on average slightly slower than the ‘normal’ and ‘99aa-
like’ objects with an average Si ii $\lambda 6355$ velocity of 10,676$\pm$247
km s-1 and have smaller pEWs of 26$\pm$2 Å. ‘91bg-like’ objects also show
similar velocities with an average Si ii $\lambda 6355$ velocity of
10,266$\pm$156 km s-1 and higher pEWs of 91$\pm$4 Å.

Figure 9: Top: Custom model spectra created for SN 2021rhu compared to a +0.3
d relative to g-band peak spectrum of SN 2004gs (black solid line). Each
colour represent a different temperature setting while keeping the rest of the
initial conditions as same. Spectra shown are normalised by their value at
4000 Å to better line up the Ti ii and Si ii features. It is seen that the
varying temperature impacts the strength of the Si ii $\lambda 5972$ features
but has no considerable impact on the Ti ii feature. Bottom: A set of spectral
configuration of N100 (red) model and the custom model created for SN 2021rhu
(dark blue model). The ratios of each model mixed is shown next to each model
spectrum (calculated in log space). The best match of SN 2004gs is with the
40:60 model, which implies that the abundances of the 04gs-like faint SNe Ia
are in between the transitional 86G-like and the normal SNe Ia. SN 2004gs is
less luminous than SN 2021rhu, slightly cooler and therefore, has a stronger
Si ii $\lambda 5972$ feature.

###  4.3 Are 04gs-like events a continuum from normal SNe Ia?

To determine if the intermediate spectral features of SN 2004gs between those
of normal and sub-luminous (‘86G-like’) SNe Ia can be achieved by temperature
or abundances changes, we use the 1D Monte Carlo radiative transfer code
tardis (Kerzendorf & Sim, 2014; Kerzendorf et al., 2020). The input parameters
for tardis consist of the luminosity, the time elapsed since the explosion,
the photospheric velocity, and profiles of abundance and density. tardis works
under the assumption that a distinct, well-defined photosphere emits a
blackbody continuum, bridging the transition between the optically thick and
thin regions of the ejected material.tardis is commonly used and has proven to
be successful at applying constraints to the broad range of SN ejecta coming
from different sub-types such as ‘91T-like’ SNe Ia (O’Brien et al., 2023),
normal SNe Ia (O’Brien et al., 2021; Ogawa et al., 2023), ‘02cx-like’ SNe Ia
(Magee et al., 2016; Srivastav et al., 2020), and ‘86G-like’ SNe Ia (Harvey et
al., 2023). By varying the input parameters, namely the luminosity and
abundance profile, we aim to have a self-consistent model that can produce the
primary key features (Ti ii , Si ii, O i, and Ca ii NIR) of a photospheric-
phase spectrum (+0.3 d relative to g-band peak) for SN 2004gs.

Firstly, we investigate the effect of changing the photospheric temperature,
choosing our abundance and density profiles to be the custom SN 2021rhu model
from Harvey et al. (2023). This model was chosen as it reproduces well the Ti
ii evolution in the 86G-like event, SN 2021rhu, which appears to be a stronger
variation of the peculiarity seen in SN 2004gs. With the photospheric velocity
at 10,500 km s-1 and the time since explosion at 16.8 d (input parameters for
the $-$1.4 d spectrum of SN 2021rhu), we vary the photospheric temperature
through the requested luminosity parameter to evaluate the effect upon the
morphology of the Ti ii feature at $\sim$4300 Å. We run these simulations at
six temperatures in the range of 9300 to 12700 K (Fig. 9, top panel). While
there is a large evolution with the changing temperature in the Si ii $\lambda
5972$ feature and therefore, the Si ii 5972 to Si ii 6355 Å ratio, there is
little evolution in the Ti ii feature, which fails to match the faint Ti ii
seen in SN 2004gs spectra, while having a strong Si ii $\lambda 5972$ feature.

We subsequently investigate various blended models between this custom model
for SN 2021rhu and the delayed detonation N100 model (Röpke et al., 2012;
Seitenzahl et al., 2013). The time since explosion is once again taken as 16.8
d, and the photospheric velocity as 10,500 km s-1, with the luminosity
parameter fixed as log10(L/L⊙) = 9.2 to align with the spectrum of 2004gs;
lower than the log10(L/L⊙) = 9.3 for SN 2021rhu. We start with the pure N100
model, mixing in more of the SN 2021rhu abundance profile with each step but
leaving the temperature fixed. In each step we mix in 20 per cent more of the
SN 2021rhu abundance profile in log space until it becomes the pure SN 2021rhu
model. The resulting abundance profile, X, can be expressed as,

$\log_{10}(X)=A\log_{10}{X_{\text{N100}}}+(1-A)\log_{10}{X_{\text{2021rhu}}}$
(1)

where A is the fraction of the N100 abundance profile, $X_{\text{N100}}$ is
the abundance profile of the N100 model, and $X_{\text{2021rhu}}$ is the
abundance profile of the SN 2021rhu model.

As the temperature remains fixed between these simulations (only varying the
abundances between the pure N100 and the SN 2021rhu-matched models) the Si ii
ratio stays relatively constant for each mixing step, matching the observed
spectrum closely. However, due to the changing abundances, there is
significant variation in the Ti ii feature, with the best match for the weaker
Ti ii line seen in SN 2004gs compared to SN 2021rhu coming from the 40:60
model (Fig. 9, bottom panel). This model consists of 40 per cent of the N100
model abundances and 60 per cent of the SN 2021rhu model bundances (scaled in
log space), and produces the strong Si ii $\lambda 5972$ feature and
relatively strong O i and Ca ii NIR features, along with the relatively weaker
Ti ii 4300 Å feature to match the SN 2004gs spectrum well. Our findings
suggest that variations in temperature alone are insufficient to produce the
spectral properties seen in faint normal SNe Ia compared to normal SNe Ia. A
combination of both temperature and abundance profile is key in the formation
of these events and suggests that there is a potential continuum from normal
to faint SNe Ia.

Nugent et al. (1995) suggested that temperature may be the dominant
explanation for the spectral sequence seen in SNe Ia around maximum light. The
spectra generated in Nugent et al. (1995) were synthesised with a model
derived from the W7 deflagration model (Nomoto et al., 1984). They augmented
the Ti abundance by a factor of 10 and were able to reproduce the range of
morphologies for the Ti ii feature from SN 1991bg through the transitional
objects to the normal population simply by altering the temperature, unlike
our findings here. The W7 Ti abundance is very compact, dropping off sharply
above $\sim$12000 km s-1. This results in a model that is very sensitive to
temperature changes, as with all of the Ti concentrated around the
photosphere, a shift in photospheric temperature will result in an ionisation
shift for almost all of the Ti present. The fiducial SN 2021rhu model from
Harvey et al. (2023) possesses a far more extended Ti distribution - as does
the N100 model - and is therefore, far less sensitive to changing photospheric
temperatures. Over the range 10500 - 12000 km s-1the SN 2021rhu model contains
$\sim$11 times as much Ti than the W7 model, similar to that of the model
investigated in Nugent et al. (1995).

It is well known that SNe Ia in elliptical early-type galaxies are found to be
intrinsically fainter with faster evolving light curves than SNe Ia in spiral
late-type galaxies (Hamuy et al., 1995; Gallagher et al., 2005; Sullivan et
al., 2006). While the host galaxy studies are not the scope of this paper, all
the ‘04gs-like’ faint normal events in our sample are from late-type, high-
mass host galaxies (log10 (${M}_{\star}$/${M}_{\odot}$) $\gtrsim$ 10) as is
also mainly seen for transitional and ‘91bg-like’ events. Hence, for faint
‘normal’ SNe Ia like SN 2004gs, our findings agree with the previous studies
showing faint normal SNe Ia preferring to explode in late-type galaxies.

Figure 10: The Si ii 6355 velocity plotted against SN light curves parameters
from SALT2, $x_{1}$ and $c$. Blue circles represent 66 HV SN Ia and red
circles represent 191 NV SN Ia. All SN Ia in this plot are ‘normal’ SNe Ia.
Figure 11: Si ii $\lambda 6355$ velocities plotted against the pEW ratio of Si
ii features, colour mapped with $x_{1}$ for normal SNe Ia in our sample. The
black dashed line at $v_{\mathrm{Si}}$ $=$ 12,000 km s-1 marks the boundary
between HV and NV SNe Ia on the plot. SNe Ia with velocities higher than
12,000 km s-1 are classified as HV SNe Ia, while those below are categorized
as NV SNe Ia. Filled and empty black diamond represents the weighted averages
of HV SNe Ia and NV SNe Ia, respectively.

###  4.4 Connection with light curve properties

In this section, we compare the spectral line measurements of our SN Ia sample
to those of their SALT2 light curve parameters ($x_{1}$, $c$). We present the
peak Si ii $\lambda 6355$ velocity, $v_{\mathrm{Si}}$ as a function of $x_{1}$
and $c$ for the ‘normal’ SN Ia sample in Fig. 10. We adopt the NV/HV
classification scheme of Wang et al. (2009a) for splitting the sample based on
their velocities. The weighted average of $x_{1}$ for the HV and NV SNe Ia in
our sample are $-$0.68$\pm$0.13 and $-$0.18$\pm$0.07, respectively, showing a
3.4$\sigma$ difference between the two samples. The two populations (NV/HV)
show similar distributions with the SALT2 $c$ parameter as seen in Dettman et
al. (2021), with mean $c$ for the NV and HV SNe Ia for our sample of $\sim$
0.04$\pm$0.01 and $\sim$ 0.10$\pm$0.02, respectively, showing a 2.7$\sigma$
difference between the two samples.

We also investigated the relation amongst Si ii $\lambda 6355$ velocity, Si ii
ratio, and light curve width, $x_{1}$ for normal SNe Ia (Fig. 11). A 3$\sigma$
difference is found with HV SNe Ia, on average, tending to have smaller pEW
ratios than NV SNe Ia, with weighted averages of the pEW of 0.117$\pm$0.008
and 0.148$\pm$0.005 for the HV and NV SNe Ia, respectively (shown as diamonds
in Fig. 11). The Si ii ratio is considered an indicator of the temperature of
the line-forming region (Nugent et al., 1995; Hachinger et al., 2008).  Harvey
et al. (subm.) estimated that around 40 per cent of SN Ia spectra between $-$5
d and peak have Si ii $\lambda 6355$ high-velocity features that are blended
with the photospheric components. While this will not change the photometric
properties of the SNe Ia, it will result in larger Si ii $\lambda 6355$ pEWs
and higher average velocities for the SNe Ia where a high-velocity feature is
present but not distinct from the photospheric component (also see Section
4.1.3).  Harvey et al. (subm.) did not however investigate the presence of Si
HVFs in the Si ii $\lambda 5972$ line and as such we cannot comment upon the
resulting impact upon the Si ii ratios. mdHarvey et al. (subm.) found that
high-velocity features in Si ii $\lambda 6355$ were more common in SNe Ia with
smaller $x_{1}$ values. This suggests that the trend we observed, where HV SNe
Ia tend to have smaller $x_{1}$ values compared to NV SNe Ia, may be
influenced by contributions from these high-velocity features.

We further inspected the light-curve properties of all the objects (not just
normal events) in our sample. We compare the pEW of Si ii $\lambda 5972$ and
Si ii $\lambda 6355$ with the SALT2 light curve parameters, $x_{1}$ and $c$ in
Fig. 12. We see a clear relation, similar to that of previous studies such as
Nugent et al. (1995); Hachinger et al. (2008), between the pEW of the Si ii
$\lambda 5972$ features and the light-curve width parameter, $x_{1}$, where
the ‘91bg-like’, ‘86G-like’, and the ‘cool’ normal ‘04gs-like’ events, have on
average faster declining light curves ($x_{1}$ $\lesssim$ $-$2) than ‘normal’
SNe Ia. The ‘99a-like’ and ‘91T-like’ SNe Ia, populate the slower light curve
decline rate ($x_{1}$ $\gtrsim$ 0) regime with similar pEW of Si ii $\lambda
5972$ to normal SNe Ia. Within the ‘normal’ SNe Ia, a trend of SNe Ia with
narrower light curves being slightly cooler than those with a broader one is
also seen (visible also in Fig. 11). This trend is similar to what we already
see for ‘86G-like’ and ‘99aa-like’ SNe Ia on the extremes. This trend is now
also observed to be present as a gradient within the ‘normal’ SNe Ia.

A similar correlation can also be seen between $c$ and Si ii $\lambda 5972$
feature (top right panel of Fig. 12). The colour $c$, on average is larger for
‘91bg-like’ SNe (weighted average $c$ of 0.50$\pm$0.04 compared to the
‘86g-like’ SNe ($c$ of 0.35$\pm$0.04) and the ‘04gs-like’ SNe Ia ($c$ of
0.04$\pm$0.02). ‘91T-like’ SN Ia are slightly redder ($c$ of 0.14$\pm$0.07)
than ‘99a-like’ SN Ia ($c$ of 0.09$\pm$0.04) but the number of ‘91T-like’ SNe
Ia is low. No strong correlation between Si ii $\lambda 6355$ and either
$x_{1}$ or $c$ is seen (bottom panel of Fig. 12), apart from ‘99aa-like’ and
‘91T-like’ events having weaker pEW. This is likely due to be the temperature
having a more direct effect on the Si ii $\lambda 5972$ than Si ii $\lambda
6355$ line strengths (see Sec. 4.3). The absolute peak magnitudes from SALT2
(corrected for Milky Way extinction) in the ZTF g-band are plotted against the
pEW ratio of the Si ii 5972 to 6355 Å features in Fig. 13. Only for this plot,
we have removed ‘normal’ SNe Ia with $c$ values higher than 0.3 to remove
highly reddened normal SNe Ia. ‘04gs-like’ SNe Ia are seen to be on average
brighter ($-$18.55$\pm$0.06 mag) than the ‘86G-like’ ($-$17.96$\pm$0.11 mag)
and ‘91bg-like’ ($-$17.25$\pm$0.11 mag) events. As shown in Section 4.3 and in
previous studies such as Hachinger et al. (2008), the pEW ratio of the Si ii
features is a good temperature indicator, with the Si ii $\lambda 5972$
feature becoming more prominent when the temperature is lower. The absolute
magnitude of an event directly relates to the amount of ${}^{56}\rm Ni$
produced in the explosion. Therefore, Fig. 13 shows that there is a strong
relation between the mass of radioactive ${}^{56}\rm Ni$ and the temperature
of the ejecta, with SNe with more ${}^{56}\rm Ni$ having hotter ejecta.
However, from our tardis analysis in Sec. 4.3, temperature alone is
insufficient to produce the combination of features seen in the spectra of SN
2004gs of weaker Ti ii compared to ‘86G-like’ or ‘91bg-like’ events but a
similar pEW ratio of the Si ii 5972 to 6355 Å.

Figure 12: Top left: Light curve parameter $x_{1}$ from SALT2 is plotted
against pEW of Si ii $\lambda 5972$ feature. Upper limits represent where
actual calculations for Si ii $\lambda 6355$ exist but 5927 does not. Top
right: Same plot as left but for the light curve parameter $c$ from SALT2.
Bottom left: $x_{1}$ plotted against pEW of Si ii $\lambda 6355$ feature.
Bottom right: Same plot as bottom left but for $c$. Figure 13: Absolute g-band
magnitudes of the volume limited ZTF DR2 SN Ia sample from SALT2 as function
of Si ii ratios. All magnitudes are corrected for MW extinction. In this plot,
‘normal’ SNe Ia with a colour parameter ($c$) higher than 0.3 are excluded to
remove highly reddened SNe Ia.

##  5 Conclusions

In this work, we presented a sub-sample of maximum-light spectra of 482 SNe Ia
from the ZTF DR2 sample up to a redshift of 0.06. We have investigated the
spectral profiles of Si ii $\lambda 6355$ and Si ii $\lambda 5972$, as well as
tested the template-matching accuracy of the DR2 spectral classifications. We
provide a summary of our conclusions:

  1. 1.

We investigated the accuracy of the spectral-template matching and initial
classifications and methods used for typing in 482 SNe Ia. After this manual
inspection, we re-classified one SNe Ia with no sub-class (typed as “Ia-
unclear”) as ‘91T-like’, 12 “Ia-unclear” as ‘99a-like’ and 10 “Ia-unclear” as
‘normal’. We also re-classified 9 ‘91T-like’ SNe Ia as ‘99a-like’ and 2
‘91T-like’ SNe Ia as ‘normal’. Our classifications of ‘91T-like’ and ‘99aa-
like’ SNe Ia are consistent with Phillips et al. (2022). While ‘91T-like’ and
‘99aa-like’ SNe Ia are generally included in cosmology samples, there are
studies (Scalzo et al., 2012; Yang et al., 2022; Chakraborty et al., 2023)
suggesting that inclusion of these event might introduce a systematic bias. It
is important to have a more accurate sub-class identification to help keep
these cosmological samples of SNe Ia more homogeneous.

  2. 2.

Host galaxy contamination in the SN Ia spectra is seen to have a considerable
impact on sub-typing and spectral features, such as pseudo equivalent widths.
No significant change in the velocities is seen. The galaxy contribution makes
the SN Ia spectra appear redder and the strength of the features can become
weaker. However, the minimum of the feature used to calculate the velocities
is less affected.

  3. 3.

Spectral template matching, such as snid, still provides fast and reliable
results for normal SN Ia. The rarer sub-types, on the other hand, need more
detailed analysis and constraints from many spectral features such as Si ii
ratios, Ti ii , O i, and Ca ii NIR. These rarer sub-types are also less
represented in training sets for spectral classifications codes.

  4. 4.

Transitional ‘04gs-like’ events have a relatively high Si ii ratio (suggesting
cooler temperatures than normal SNe Ia) and weak Ti ii absorption features.
Using tardis modelling, we demonstrated that decreasing the temperature alone
produces a good match to the S ii ratio but not to the Ti ii feature. An
increase in the Ti ii abundance is also required to match its spectra. These
events appear to sit between normal and sub-luminous SNe Ia but brighter than
the standard transitional ‘86G-like’ events.

  5. 5.

We assigned Branch sub-types to all SNe in our sample and studied the observed
diversity from the spectral features. The ‘normal’ to ‘91T-like’ transition,
where ‘99aa-like’ SNe Ia bridging the gap is seen in terms of the pEW of Si ii
$\lambda 6355$. True ‘91T-like’ SNe Ia in our sample remain very rare.

  6. 6.

We observed a strong correlation between $x_{1}$ and the pEW of Si ii $\lambda
5972$, with a clear transition in properties at $\sim$30Å and $x_{1}$ of
around $-$2\. Other than all true ‘91T-like’ SNe Ia showing positive $x_{1}$
values, no other significant correlation is seen between Si ii $\lambda 6355$
feature and $x_{1}$ and $c$. Especially for fainter objects, this is due to
the Si ii $\lambda 6355$ feature becoming saturated, while the Si ii $\lambda
5972$ feature becomes more prominent due to the ionisation balance.

  7. 7.

We found a trend among Si ii $\lambda 6355$ velocity, Si ii ratio and $x_{1}$
within the ‘normal’ SNe Ia, showing HV SNe Ia with lower pEW ratios tend to
have faster declining light curves.

  8. 8.

Absolute magnitude of SNe Ia follows a sequence as a function of Si ii pEW
ratio for the subtypes. By investigating the faint normal SNe Ia, we show that
this is likely caused by the different initial abundance profiles and
temperature settings, which more directly correlates with the subtypes.

We emphasize that regardless of the underlying explosion mechanism and/or
binary configuration, the continuity seen in both bright and faint SNe Ia
persists and is encouraged to be further quantified. Since only the peak
spectra are investigated in this work, there is a possibility that even if
there are several explosion mechanisms, they may all be showing similar
properties due to all being highly driven by ${}^{56}\rm Ni$ near the peak.
Therefore, it is encouraged to obtain more early time spectra to investigate
the ejecta properties that are more directly related to the explosion and late
time spectra to investigate progenitor channels since the materials at this
phase get optically thin. A forthcoming paper will present any effect coming
from the host galaxies and their impact on our findings in current
cosmological studies.

###### Acknowledgements.

Based on observations obtained with the Samuel Oschin Telescope 48-inch and
the 60-inch Telescope at the Palomar Observatory as part of the Zwicky
Transient Facility project. ZTF is supported by the National Science
Foundation under Grants No. AST-1440341 and AST-2034437 and a collaboration
including current partners Caltech, IPAC, the Weizmann Institute of Science,
the Oskar Klein Center at Stockholm University, the University of Maryland,
Deutsches Elektronen-Synchrotron and Humboldt University, the TANGO Consortium
of Taiwan, the University of Wisconsin at Milwaukee, Trinity College Dublin,
Lawrence Livermore National Laboratories, IN2P3, University of Warwick, Ruhr
University Bochum, Northwestern University and former partners the University
of Washington, Los Alamos National Laboratories, and Lawrence Berkeley
National Laboratories. Operations are conducted by COO, IPAC, and UW. SED
Machine is based upon work supported by the National Science Foundation under
Grant No. 1106171. The ZTF forced-photometry service was funded under the
Heising-Simons Foundation grant #12540303 (PI: Graham). This work was
supported by the GROWTH project funded by the National Science Foundation
under Grant No 1545949 (Kasliwal et al., 2019). Fritz (van der Walt et al.,
2019; Coughlin et al., 2023) is used in this work. The Gordon and Betty Moore
Foundation, through both the Data-Driven Investigator Program and a dedicated
grant, provided critical funding for SkyPortal. UB, KM, GD, RS, MD, and JHT
are supported by the H2020 European Research Council grant no. 758638. LH is
funded by the Irish Research Council under grant number GOIPG/2020/1387.
Y.-L.K. has received funding from the Science and Technology Facilities
Council [grant number ST/V000713/1]. L.G. acknowledges financial support from
the Spanish Ministerio de Ciencia e Innovación (MCIN) and the Agencia Estatal
de Investigación (AEI) 10.13039/501100011033 under the PID2020-115253GA-I00
HOSTFLOWS project, from Centro Superior de Investigaciones Científicas (CSIC)
under the PIE project 20215AT016 and the program Unidad de Excelencia María de
Maeztu CEX2020-001058-M, and from the Departament de Recerca i Universitats de
la Generalitat de Catalunya through the 2021-SGR-01270 grant. This project has
received funding from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (grant agreement no
759194 - USNAC). This work has been supported by the research project grant
”Understanding the Dynamic Universe” funded by the Knut and Alice Wallenberg
Foundation under Dnr KAW 2018.0067. AG acknowledges support from
Vetenskapsrådet, the Swedish Research Council, project 2020-03444. SD
acknowledges support from the Marie Curie Individual Fellowship under grant ID
890695 and a Junior Research Fellowship at Lucy Cavendish College. T.E.M.B.
acknowledges financial support from the Spanish Ministerio de Ciencia e
Innovación (MCIN), the Agencia Estatal de Investigación (AEI)
10.13039/501100011033, and the European Union Next Generation EU/PRTR funds
under the 2021 Juan de la Cierva program FJC2021-047124-I and the
PID2020-115253GA-I00 HOSTFLOWS project, from Centro Superior de
Investigaciones Científicas (CSIC) under the PIE project 20215AT016, and the
program Unidad de Excelencia María de Maeztu CEX2020-001058-M. This work has
been supported by the Agence Nationale de la Recherche of the French
government through the program ANR-21-CE31-0016-03.

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##  Appendix A Tables

Table 4: Classification and spectroscopic properties of SNe Ia from the volume
limited ZTF DR2 sample.

ZTF Name | SN Name | Phase | Subtype | Wang Type | Branch Type |  v${}_{\text{{Si {ii}}}}$(6355) | pEW(6355) |  v${}_{\text{{Si {ii}}}}$(5972) | pEW(5972)
---|---|---|---|---|---|---|---|---|---
|  | (d) |  |  |  |  (x10${}^{\text{4}}$ km s-1) | $(\mbox{\AA})$ |  (x10${}^{\text{4}}$ km s-1) | $(\mbox{\AA})$
dDLR $>$ 0.2 |
ZTF18aabtiph | 2018yq | 2.2 | normal | NV | SS |  1.18$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  61.99$\pm$${}^{\text{0.56}}_{\text{0.39}}$ |  1.16$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  9.57$\pm$${}^{\text{0.27}}_{\text{0.22}}$
ZTF18aahfgsk | 2018aqk | 2.3 | normal | NV | CN |  1.07$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  79.23$\pm$${}^{\text{1.44}}_{\text{1.83}}$ |  1.15$\pm$${}^{\text{0.03}}_{\text{0.02}}$ |  15.31$\pm$${}^{\text{1.35}}_{\text{1.79}}$
ZTF18aahfzea | 2018aqh |  $-$4.2 | normal | NV | CN |  1.10$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  73.93$\pm$${}^{\text{0.92}}_{\text{0.66}}$ |  1.10$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  4.92$\pm$${}^{\text{0.28}}_{\text{0.53}}$
ZTF18aahheaj | 2018avp | 2.7 | normal | HV | BL |  1.25$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  109.65$\pm$${}^{\text{2.4}}_{\text{1.25}}$ |  0.95$\pm$${}^{\text{0.07}}_{\text{0.02}}$ |  13.68$\pm$${}^{\text{1.73}}_{\text{4.90}}$
ZTF18aahjaxz | 2018avg |  $-$0.2 | 91bg-like | 91bg | CL |  1.04$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  110.46$\pm$${}^{\text{4.3}}_{\text{4.35}}$ |  1.06$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  48.68$\pm$${}^{\text{1.07}}_{\text{0.85}}$
ZTF18aahtjsc | 2019cdd |  $-$2.3 | Ia-unclear | $-$ | SS |  0.96$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  28.41$\pm$${}^{\text{1.05}}_{\text{0.52}}$ | $-$ |  10.88∗
ZTF18aaimxdx | 2018bay | 1.6 | 91bg-like | 91bg | CL |  1.05$\pm$${}^{\text{0.06}}_{\text{0.06}}$ |  107.04$\pm$${}^{\text{2.3}}_{\text{1.36}}$ |  0.94$\pm$${}^{\text{0.06}}_{\text{0.06}}$ |  39.12$\pm$${}^{\text{2.48}}_{\text{2.64}}$
ZTF18aajivpr | 2020gaa | 0.5 | normal | NV | CN |  1.06$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  79.88$\pm$${}^{\text{0.51}}_{\text{0.53}}$ |  1.02$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  10.64$\pm$${}^{\text{0.86}}_{\text{0.87}}$
ZTF18aajtlbf | 2018bbz |  $-$0.1 | 86G-like | $-$ | CL |  1.03$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  122.62$\pm$${}^{\text{1.3}}_{\text{2.33}}$ |  0.92$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  46.88$\pm$${}^{\text{2.80}}_{\text{1.41}}$
ZTF18aakglgw | 2018aoy |  $-$0.2 | normal | HV | BL |  1.33$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  118.66$\pm$${}^{\text{1.0}}_{\text{0.70}}$ |  1.13$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  7.92$\pm$${}^{\text{0.87}}_{\text{0.54}}$
ZTF18aaklpdo | 2018hvf |  $-$2.6 | normal | NV | SS |  1.13$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  67.16$\pm$${}^{\text{1.16}}_{\text{1.05}}$ |  1.08$\pm$${}^{\text{0.03}}_{\text{0.03}}$ |  11.97$\pm$${}^{\text{1.11}}_{\text{1.34}}$
ZTF18aalurka | 2018awj |  $-$3.9 | normal | NV | CN |  1.01$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  104.26$\pm$${}^{\text{4.4}}_{\text{1.91}}$ |  0.88$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  27.09$\pm$${}^{\text{1.06}}_{\text{0.59}}$
ZTF18aamlhee | 2018zs | 1.2 | normal | NV | CN |  1.06$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  87.75$\pm$${}^{\text{0.88}}_{\text{0.39}}$ |  0.96$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  21.58$\pm$${}^{\text{0.57}}_{\text{0.01}}$
ZTF18aaodrgt | 2018bfd | 1.5 | normal | NV | BL |  1.15$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  125.11$\pm$${}^{\text{0.5}}_{\text{0.54}}$ |  1.04$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  25.19$\pm$${}^{\text{0.99}}_{\text{1.05}}$
ZTF18aaoufjt | 2019fyi | 1.4 | 99aa-like | $-$ | SS |  1.36$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  31.50$\pm$${}^{\text{0.70}}_{\text{0.48}}$ | $-$ |  6.15∗
ZTF18aaqfziz | 2018bhp | 4.2 | normal | NV | BL |  1.09$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  122.68$\pm$${}^{\text{2.0}}_{\text{1.94}}$ |  1.03$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  24.07$\pm$${}^{\text{0.66}}_{\text{1.25}}$
ZTF18aaroihe | 2018bio |  $-$0.3 | 04gs-like | $-$ | CL |  1.15$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  96.61$\pm$${}^{\text{2.30}}_{\text{2.07}}$ |  1.10$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  30.55$\pm$${}^{\text{2.75}}_{\text{2.97}}$
ZTF18aarymnz | 2018azu | 0.1 | normal | HV | CN |  1.24$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  94.59$\pm$${}^{\text{1.84}}_{\text{0.81}}$ |  1.22$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  4.88$\pm$${}^{\text{0.08}}_{\text{0.31}}$
ZTF18aaslhxt | 2018btk |  $-$2.3 | normal | NV | CN |  1.06$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  99.43$\pm$${}^{\text{1.97}}_{\text{2.55}}$ |  0.96$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  15.13$\pm$${}^{\text{0.72}}_{\text{1.32}}$
ZTF18aasprui | 2018euz | 0.4 | 04gs-like | $-$ | CL |  1.02$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  107.13$\pm$${}^{\text{0.4}}_{\text{0.42}}$ |  0.97$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  34.20$\pm$${}^{\text{0.45}}_{\text{0.19}}$
. |
. |
. |
dDLRa $\leq$ 0.2 |
ZTF18aagstdc | 2018apn | 3.4 | normal | NV | CN |  1.19$\pm$${}^{\text{0.06}}_{\text{0.06}}$ |  98.35$\pm$${}^{\text{0.74}}_{\text{0.55}}$ |  1.20$\pm$${}^{\text{0.06}}_{\text{0.06}}$ |  18.69$\pm$${}^{\text{0.28}}_{\text{0.31}}$
ZTF18aagtcxj | 2018aqm | 3.9 | normal | NV | SS |  1.09$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  69.86$\pm$${}^{\text{1.26}}_{\text{1.08}}$ |  1.10$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  18.13$\pm$${}^{\text{0.67}}_{\text{0.72}}$
ZTF18aahfbqp | 2020acua | -1.8 | Ia-unclear | $-$ | SS |  0.99$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  29.94$\pm$${}^{\text{1.02}}_{\text{0.63}}$ | $-$ |  2.83∗
ZTF18aahjafd | 2018loz | -1.5 | normal | HV | CN |  1.28$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  88.77$\pm$${}^{\text{2.86}}_{\text{1.01}}$ |  1.30$\pm$${}^{\text{0.04}}_{\text{0.05}}$ |  9.98$\pm$${}^{\text{1.48}}_{\text{0.86}}$
ZTF18aahshhp | 2020dln | -0.3 | Ia-unclear | $-$ | SS |  0.83$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  14.23$\pm$${}^{\text{0.49}}_{\text{0.65}}$ | $-$ |  3.43∗
ZTF18aaifxvz | 2020lyo | 4.8 | Ia-unclear | $-$ | SS |  1.05$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  48.24$\pm$${}^{\text{0.96}}_{\text{0.75}}$ |  1.00$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  4.03$\pm$${}^{\text{0.33}}_{\text{0.47}}$
ZTF18aansqun | 2018dyp | -1.9 | normal | NV | CN |  1.08$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  79.03$\pm$${}^{\text{1.08}}_{\text{0.54}}$ |  0.95$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  10.92$\pm$${}^{\text{1.00}}_{\text{0.40}}$
ZTF18aaoxrup | 2020hdw | -1.3 | 04gs-like | $-$ | CL |  1.09$\pm$${}^{\text{0.06}}_{\text{0.06}}$ |  93.76$\pm$${}^{\text{0.61}}_{\text{0.41}}$ |  0.96$\pm$${}^{\text{0.06}}_{\text{0.06}}$ |  30.76$\pm$${}^{\text{1.10}}_{\text{0.81}}$
ZTF18aapqwyv | 2018bhc | 4.5 | Ia-unclear | $-$ | SS |  1.02$\pm$${}^{\text{0.04}}_{\text{0.04}}$ |  54.39$\pm$${}^{\text{3.07}}_{\text{3.01}}$ |  1.10$\pm$${}^{\text{0.06}}_{\text{0.06}}$ |  14.02$\pm$${}^{\text{2.62}}_{\text{2.97}}$
ZTF18aaqqhis | 2018ccy | -1.6 | Ia-unclear | $-$ | SS |  1.13$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  15.04$\pm$${}^{\text{0.30}}_{\text{0.50}}$ | $-$ |  3.91∗
ZTF18aarbaba | 2020mnu | 1.4 | normal | NV | CN |  1.15$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  98.25$\pm$${}^{\text{1.85}}_{\text{0.75}}$ | $-$ |  5.97∗
ZTF18aarcypa | 2018bil | 1.5 | Ia-unclear | $-$ | CN |  0.96$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  78.21$\pm$${}^{\text{1.95}}_{\text{0.35}}$ |  0.82$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  22.31$\pm$${}^{\text{0.52}}_{\text{0.10}}$
ZTF18aarikzk | 2020hll | -1.3 | 99aa-like | $-$ | SS |  1.08$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  49.92$\pm$${}^{\text{0.99}}_{\text{0.37}}$ | $-$ |  19.77∗
ZTF18aaupmks | 2018bsr | -4.8 | 99aa-like | $-$ | SS |  1.24$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  51.18$\pm$${}^{\text{1.37}}_{\text{0.81}}$ | $-$ |  7.18∗
ZTF18aavsilo | 2020jje | 3.9 | Ia-unclear | $-$ | SS |  1.11$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  18.78$\pm$${}^{\text{0.39}}_{\text{0.46}}$ | $-$ |  5.77∗
ZTF18aawmxdx | 2018jti | -3.4 | normal | HV | CN |  1.29$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  91.93$\pm$${}^{\text{0.64}}_{\text{0.32}}$ |  1.23$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  9.11$\pm$${}^{\text{0.58}}_{\text{0.95}}$
ZTF18abbikrz | 2020pwn | -2.0 | Ia-unclear | $-$ | SS |  0.94$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  33.62$\pm$${}^{\text{1.92}}_{\text{1.50}}$ | $-$ |  20.32∗
ZTF18abespgb | 2018dyg | -4.0 | normal | NV | CN |  1.16$\pm$${}^{\text{0.06}}_{\text{0.06}}$ |  83.29$\pm$${}^{\text{1.72}}_{\text{0.82}}$ |  1.16$\pm$${}^{\text{0.06}}_{\text{0.06}}$ |  5.82$\pm$${}^{\text{0.53}}_{\text{0.10}}$
ZTF18abhbqbh | 2020kwk | 3.5 | Ia-unclear | $-$ | SS |  1.09$\pm$${}^{\text{0.02}}_{\text{0.02}}$ |  35.38$\pm$${}^{\text{1.28}}_{\text{0.94}}$ |  1.24$\pm$${}^{\text{0.02}}_{\text{0.03}}$ |  7.92$\pm$${}^{\text{0.82}}_{\text{0.36}}$
ZTF18abjhack | 2018crv | 0.5 | normal | NV | CN |  1.08$\pm$${}^{\text{0.06}}_{\text{0.06}}$ |  92.67$\pm$${}^{\text{1.05}}_{\text{0.45}}$ | $-$ |  5.33∗
. |
. |
. |

(a) In this study only SNe Ia with a value of dDLR higher than 0.2 is used.
However the results from lower dDLR values are also listed here.

(∗) estimated pEW values for Si ii $\lambda 5972$ features as upper limits.

The complete table is accessible within the online journal. Here, a section is
displayed to offer direction on its structure and information included.