1991T-Like Type Ia Supernovae as an Extension of the Normal Population

Type Ia supernovae (SNe) remain poorly understood despite decades of investigation. Massive computationally intensive hydrodynamic simulations have been developed and run to model an ever-growing number of proposed progenitor channels. Further complicating the matter, a large number of subtypes of Type Ia SNe have been identified in recent decades. Due to the massive computational load required, inference of the internal structure of Type Ia SNe ejecta directly from observations using simulations has previously been computationally intractable. However, deep-learning emulators for radiation transport simulations have alleviated such barriers. We perform abundance tomography on 40 Type Ia SNe from optical spectra using the radiative transfer code TARDIS accelerated by the probabilistic DALEK deep-learning emulator. We apply a parametric model of potential outer ejecta structures to comparatively investigate abundance distributions and internal ionization fractions of intermediate-mass elements (IMEs) between normal and 1991T-like Type Ia SNe in the early phases. Our inference shows that the outer ejecta of 1991T-like Type Ia SNe is underabundant in the typical intermediate mass elements that heavily contribute to the spectral line formation seen in normal Type Ia SNe at early times. Additionally, we find that the IMEs present in 1991T-like Type Ia SNe are highly ionized compared to those in the normal Type Ia population. Finally, we conclude that the transition between normal and 1991T-like Type Ia SNe appears to be continuous observationally and that the observed differences come out of a combination of both abundance and ionization fractions in these SNe populations.


INTRODUCTION
Type Ia supernovae (SNe Ia), the thermonuclear explosions of Carbon/Oxygen (C/O) white dwarfs (WD), are critical tools for understanding the evolution of the cosmos.SNe Ia populate galaxies with iron-group and Corresponding author: John T. O'Brien jobrien585@gmail.com,obrie278@msu.eduintermediate-mass elements (Kobayashi et al. 2020, see Figure 39) critical to the formation of planets and lategeneration stars.As cosmic distance indicators (Phillips 1993), SNe Ia have proved useful in both determining the size and age of the universe, as well as for probing the nature of dark energy (Branch 1992;Riess et al. 1998;Perlmutter et al. 1999).However, despite their success as tools for probing galactic and cosmological evolution, the mechanism(s) underlying their ignition remain poorly understood.
An ever-increasing number of progenitor models have been proposed in the literature to explain SNe Ia, usually involving some sort of mass transfer from a binary companion.For example, ignition of a C/O WD has been suggested to be the result of mergers with a binary companion (e.g.Nomoto 1982;Webbink 1984;Iben & Tutukov 1984;van Kerkwijk et al. 2010;Livio & Riess 2003;Kashi & Soker 2011), accretion from a companion star onto a near Chandrasekhar-mass (M Ch ) WD (e.g.Whelan & Iben 1973) resulting in a turbulent deflagration, or accretion onto a sub-M Ch WD resulting in a super-sonic detonation (e.g.Woosley & Weaver 1994;Fink et al. 2010a;Shen et al. 2018;Polin et al. 2019;Pakmor et al. 2022).Despite intensive work and an ever-increasing number of proposed models, secure progenitor identification from spectral and photometric observations remains elusive.
Further complicating the matter of progenitor identification is the large spectroscopic diversity of thermonuclear SNe that have been identified over the past few decades.A large number of objects within the class of SNe Ia with unique spectral and photometric properties have resulted in a variety of classification schemes (e.g.Branch et al. 2006;Taubenberger 2017).These objects range from the subluminous lowvelocity Type Iax/02cx-like thermonuclear supernovae (Foley et al. 2013) to super-luminous shallow-silicon (Branch et al. 2006) 1991T-like SNe Ia (Filippenko et al. 1992;Phillips et al. 1992).The variation in the properties of these objects leads us to consider the possibility of either distinct progenitor channels for these sub-types or a unified progenitor model that can describe massive variations in spectral properties.
We begin our investigation into the relationship between SNe Ia sub-types from the bright end of thermonuclear transients by focusing on the super-luminous 1991T-like SNe Ia.On the observational side, 1991T-like SNe Ia appear spectroscopically similar to the normal (Branch et al. 1993;Benetti et al. 2004;Branch et al. 2006) SNe Ia population after their light curves achieve maximum brightness (Phillips et al. 1992), however, in their early phases they are quite distinct.Their earlytime spectra contain strong absorption lines of highvelocity Fe II/Fe III and lack the characteristic strong Si II absorption features of normal SNe Ia (Filippenko et al. 1992;Filippenko 1997).Additionally, 1991T-like SNe Ia lie close to the normal SNe Ia in the space of the luminosity-decline rate relation, potentiality contaminating SNe Ia samples used for cosmic distance measurements due to Malmquist bias at high redshift (Sasdelli et al. 2014).On the theoretical side, Filippenko et al. (1992) originally proposed that 1991T-like supernovae may either be the results of either a double-detonation initiated at an intermediate layer in the progenitor WD, or a delayed-detonation model, in order to explain the large amount of the progenitor WD that is burned into 56 Ni and the apparent narrow region of IMEs present with the ejecta.Since then, many hypotheses have been proposed to explain the deviations in photometric and spectroscopic properties of 1991T-like SNe Ia from the normal SNe Ia population with mixed success (e.g.Ruiz-Lapuente et al. 1992;Mazzali et al. 1995;Liu et al. 1997;Marquardt et al. 2015;Seitenzahl et al. 2016).A definitive connection between the theoretical progenitor channels for 1991T-like SNe Ia and their observed spectral properties requires constraining the possible theoretical models to the observations directly.
In this paper, we present ejecta reconstructions from inference and a direct statistical comparison of the internal ejecta state between populations of 35 normal and five 1991T-like SNe Ia.The ejecta models are presented as probability distributions determined through Bayesian inference performed on single-epoch early-time optical spectra.Our parameterized ejecta model is based on hydrodynamical simulations of a variety of proposed progenitor systems from the Heidelberg Supernova Model Archive (HESMA Kromer et al. 2017).We use a radiative transport scheme based on the opensource radiative transfer code tardis (Kerzendorf & Sim 2014) accelerated by the probabilistic dalek deeplearning emulator (Kerzendorf et al. 2022) to generate predictions of synthetic spectra over our space of model parameters.We compare distributions of ejecta compositions and ionization states between the normal and 1991T-like SNe Ia populations and identify a relationship between their internal structure and observed spectral features.These results allow us to better understand the relationship between normal SNe Ia and 1991T-like SNe Ia.
In Section 2, we describe the selection criteria for the observed spectra samples of normal and 1991T-like SNe Ia that we chose to model.Section 3 describes the parametric ejecta model implemented to model these spectra as well as details of the radiative transfer simulation and its acceleration through emulation.Section 4 describes the inference framework for estimating the posterior distributions of our model parameters, including the form of the likelihood function and the priors placed on our parameters.Results of our modeling are presented in Section 5 along with a discussion of their physical implications.Finally, our conclusions and final discussion are summarized in Section 6.
1991T-Like Type Ia Supernovae as an Extension of the Normal Population

DATA
We select a sample of normal and 1991T-like SNe Ia with spectra between 7 and 14 days before the B-band maximum in the light curve as these observations are well into the photospheric phase (see Section 3.1.3)when the ejecta are still optically thick.This selection was designed to model spectral observations taken 8 to 12 days post-explosion given a rise-time of 19.5 days with a 2.5 day rise-time uncertainty.Some studies (e.g.Phillips et al. 2022) will discern between the transitional shallowsilicon 1999aa-like SNe Ia and the 1991T-like SNe Ia due to the presence of early-time Calcium features and larger Si II absorption features.For the purposes of this study, we group together 1999aa-like SNe Ia with 1991T-like SNe Ia and refer to the joint group as 1991T-like SNe Ia.
Our sample of selected SNe Ia is based on the sample investigated by Polin et al. (2021) as these objects are well studied.We queried WISeREP (Yaron & Gal-Yam 2012) for each selected SN, filtering to only objects labeled as either Ia or Ia-pec with spectra within our time interval, and found a total of 158 spectra covering 44 objects.For each object found, we select a single spectrum to model according to two criteria relating to the quality and coverage of the data.We first attempt to limit our sets of spectra to those with coverage of more than 90% of the wavelength range from 3400 Å to 7600 Å which corresponds to the wavelength range of our model.If no spectra for a single object fully encompass this range, we keep them for the next step of selection to maximize the number of objects we model.We then select the spectrum from each object with the highest average signal-to-noise ratio.If a spectrum does not include the flux error, we assume the signal-to-noise ratio for that spectrum is below that of all spectra containing a flux error column when making this cut.
We classify the spectra into two categories: 1991T-like SNe Ia and normal SNe Ia based on spectral template fitting.We use the Supernova Identification tool (SNID Blondin & Tonry 2007) to determine the sub-type, and all objects that are found to be 1991T-like objects are further investigated through a literature search (See footnotes of Table 1) in order to properly classify objects whose photospheric phase spectra can commonly be mistaken with 1991T-likes such as 02cx-likes/Type Iax (see e.g.Phillips et al. 2022).The final selection includes five 1991T-like SNe Ia and 35 normal SNe Ia spectra.The list of objects, with their phase from maximum light, classification, and references can be found in Table 1.

SUPERNOVA MODEL
We present a condensed parametric ejecta model designed to fit a wide variety of predicted SNe Ia spectra corresponding to different progenitor systems.In Section 3.1 we introduce the hydrodynamic models upon which these parameters and their ranges are based.Section 3.1.1introduces the way that the density structure of the ejecta is parameterized in the regime of the photospheric outer ejecta.Section 3.1.2describes the method by which we parameterize the relative abundances according to the masses of individual elements present throughout the ejecta and how these masses are folded into a general multi-zone model for SNe Ia ejecta.Sections 3.1.3and 3.2 describe the physical assumptions made when performing spectral synthesis for comparison between model parameters and observed spectra.Finally, Section 3.2.1 describes the deep-learning framework implemented to perform the acceleration of our spectral synthesis over our space of model parameters.

Parameterized Ejecta Model
We develop a parametric model of the ejecta of SNe Ia based on the structure of spherically averaged ejecta profiles taken from HESMA.HESMA contains a database of a wide range of simulations of a variety of proposed SNe Ia progenitor scenarios (Fink et al. 2014;Noebauer et al. 2017;Kromer et al. 2013Kromer et al. , 2015;;Sim et al. 2010;Noebauer et al. 2017;Fink et al. 2018;Marquardt et al. 2015;Fink et al. 2010b;Kromer et al. 2010;Sim et al. 2012;Gronow et al. 2020) which provide an approximation to the space of potential ejecta structures that describe SNe Ia observations at various times.A visualization of a randomly generated ejecta profile from a set of model parameters drawn from our space is presented in Figure 1.The ejecta model is parameterized by density and abundance profiles, described in the next two sections.

Density Profile
We adopt a velocity-dependent power-law density profile in homologous expansion to model the outer ejecta of the supernova (Equation 1).The outer ejecta of HESMA models can be well fit by power-law at early times.A power-law index, α ρ is left as a free parameter which allows the model to cover the full range of outerejecta density profiles present in the HESMA models (see Section 4.2 for a description).A reference velocity for our density profile, v 0 = 8000 km s −1 , is statically set for all models as a reference density, ρ 0 , is solved to constrain the density of the model.The constructed density profile extends from v 0 to an outer boundary velocity, v outer , set such that the density at the outer-boundary velocity is ρ(v outer , t = t 0 ) = 10 −14 g cm 3 which is the cutoff value of the density profiles present in the HESMA models at t 0 = 2 days.The value of v 0 is an arbitrary choice as a reference coordinate from where we define  2018) classifies these as a 1999aa-like SNe Ia Table 1.Table of selected SNe with photospheric phase spectra.The phase of the spectrum represents the time before maximum B-band magnitude that the spectrum was taken.Classification of the SNe Ia sub-types was performed with SNID for all models and further classification of those initially labeled as 91T-likes is determined through a literature search to avoid possible contamination.
our model, so the value was selected as the lower bound of the inner boundary velocity prior (Section 4.2) for simplicity.
We constrain the values for v outer and ρ 0 from a given total ejecta mass above v 0 , M tot , and a given α ρ by integrating Equation 1 at a time t = t 0 by applying the substitution v t 0 = r from homologous expansion.
The value for M tot is determined from the total of the masses of the individual elements contributing to the ejecta above v 0 .

Abundance Profile
We model the abundances of the same elements explored by O'Brien et al. ( 2021) in our ejecta model as these elements account for the majority of line formation in the resulting spectrum as well as trace the general nucleosynthetic products of the supernova (see e.g.Filippenko 1997).We parameterize these elements in terms of total masses above v 0 in order to better constrain the total ejecta mass as well as simplify the sampling procedure.Masses for Carbon (M C ), Oxygen (M O ), Magnesium (M Mg ), Silicon (M Si ), Sulfur (M S ), Calcium (M Ca ), Chromium (M Cr ), Titanium (M Ti ), stable Iron (M Fe ), and initial 56 Ni at t 0 , M56 Ni , are aggregated into three quantities corresponding to the mass of Iron Group Elements (IGEs, M IGE = M56 Ni + M Cr + M Ti + M Fe ), Intermediate Mass Elements (IMEs, M IME = M Si + M S + M Mg + M Ca ), and Unburned Elements (UBEs, M UBE = M C + M O ), as well as a total ejecta mass (M tot = M IGE + M IME + M UBE ).We place these three categories of elements into three distinct regions of the ejecta corresponding to a general structure seen in the HESMA abundance profiles as well as tomography results presented by Aouad et al. (2022, Figure 18) in which IGEs resulting from complete nuclear burning are placed below a layer of IMEs resulting from incomplete burning, with UBEs placed in the outer-most regions (see Figure 1).The fractional abundance of each region is parameterized by a set of functions, , where the sum of the profiles at each velocity adds up to unity.A modified Gaussian is used to represent the distribution of IMEs which is parameterized by a width, w, and a centroid, v c , in velocity space.The form of this profile was selected to allow for the model to parameterize various amounts of mixing between regions of the ejecta as well as explore the depth at which the properties of the ejecta are changing.The model results in a mass-fraction profile that follows a Gaussian bubble of IMEs over the ejecta velocity and serves as an approximation to the profiles present in the HESMA dataset.
Where A 0 is a normalization constant set to the inverse of the maximum value of The velocity corresponding to the distribution's maximum value is determined from v c and w through the relation The values for v max and w are then determined from the relative masses of each region of elements by numerically solving the following system of equations which results in a complete ejecta profile.

Explosion Model
Our analysis of early-phase spectra relies on the photospheric approximation in which the rapidly increasing optical depth of the ejecta towards the center is approximated as a hard inner boundary in velocity space, v inner .Thermalized radiation is injected into the ejecta above from a black-body distribution at a given temperature, T inner .A parameter representing the time since the explosion, t exp , scales the density profile (Equation 1) as well as sets the abundances of decay products of 56 Ni in the final ejecta profile.

Radiative Transfer
We calculate synthetic spectra from our ejecta model using the open-source Monte Carlo radiative transfer code tardis (Kerzendorf & Sim 2014;Kerzendorf et al. 2021).Tardis is a 1D steady-state code that iteratively solves for the excitation and ionization state of the plasma.tardis uses an inner boundary photosphere approximation that injects radiative packets into a homologously expanding ejecta.Ionization populations are solved using the "nebular" approximation (Equation 3 in Kerzendorf & Sim 2014) and excitation populations are solved using the "dilutelte" prescription (Equation 5 in Kerzendorf & Sim 2014;Equation 4 in Lucy 1999).Line interactions are handled using a macro-atom model (Lucy 2002).Models were generated using 40 shells of ejecta and run until plasma state convergence with 10 5 packets per Monte Carlo iteration.Further configuration information for tardis including links to a reproducible setup and the atomic data file created with carsus can be found in Appendix A.

Emulator
Spectral synthesis with tardis is too computationally expensive to be used directly for fitting.For example, a single tardis simulation takes approximately 30 CPU minutes, which would require hundreds of years to effectively sample a posterior distribution which requires over a million sequential simulation runs.
In recent years emulation of radiative transfer models has served as a powerful tool for directly probing the properties of a variety of supernovae and other astrophysical objects (see e.g.Vogl et al. 2020;O'Brien et al. 2021;Fullard et al. 2022).To expedite model evaluation we employ an emulator for tardis which performs spectral synthesis from model input parameters through an analytic approximation.O'Brien et al. ( 2021) applied a deep-learning emulator for tardis based on Kerzendorf et al. ( 2021) to simulate single-zone ejecta models for normal SNe Ia which, for the first time, allowed for fully-probabilistic reconstructions of the outer ejecta of a SN Ia.Kerzendorf et al. (2022) expanded upon the utility of such emulators by incorporating a probabilistic deep-learning architecture for emulated SNe Ia spectral synthesis which includes the added functionality of providing uncertainties in the emulated spectra.
We combine our ejecta model with the probabilistic emulator architecture to rapidly generate synthetic spectra from our model's parameters with improved uncertainty estimates.We train a deep ensemble (Lakshminarayanan et al. 2017) of 12 probabilistic emulators to emulate our spectral synthesis.Model evaluation is performed by aggregating the resulting spectra from each emulator with their associated uncertainty.Scripts and data files containing the emulator and its training data can be found in Appendix A.

MODEL INFERENCE
We perform Bayesian inference in order to find the posterior distribution of model parameters given our observed spectra.In order to model the posterior distribution we require a method of likelihood estimation, presented in Section 4.1, to effectively compare simulated spectra to observed spectra in the context of physical and systematic uncertainties and biases.The constraints we place on the parameters of our model are discussed in Section 4.2 and the method of sampling the posterior distribution is discussed in Section 4.3.A short discussion of our method of lowering the emulation uncertainty for regions of parameter space that are both high in likelihood and under-sampled in our emulator's training data is presented in Section 4.3.2.
1991T-Like Type Ia Supernovae as an Extension of the Normal Population

Likelihood Estimation
We apply an extended form of the likelihood function used by O'Brien et al. (2021) to incorporate emulator uncertainties determined by the probabilistic Dalek emulator by adding them in quadrature to the other sources of uncertainty.We aim to best reconstruct the composition of the ejecta, so we remove the continuum when determining the quality of a fit in order to maximize contributions from line formation.We incorporate a spectral continuum removal process, C( Fλ ( ⃗ θ)) which normalizes the synthetic spectrum estimate, Fλ ( ⃗ θ) to the continuum of the observed spectrum, F λ .This continuum removal process fits a 3rd order polynomial to the ratio between the observed spectrum and the simulated spectrum then multiplies the simulated spectrum by the polynomial.Such removal is necessary to remove the effects of the continuum, distance, and reddening from the observation to ensure our fits are driven by the line features.The total form of the log-likelihood is where where f σ represents an inferred fractional uncertainty (Hogg et al. 2010) over our spectrum and σ obs,λ is the observational uncertainty of the spectrum we are fitting.Observational uncertainties are taken from the spectra data source if available, otherwise, a constant uncertainty of 1% of the mean of the spectrum is assumed.σ emu,λ is the estimate of the emulator's uncertainty (Equation 4 in Kerzendorf et al. 2022) in the region corresponding to the fit.

Prior Bounds
Table 2 lists our prior distributions of model parameters.Multiple constraints are placed on the prior distribution of model parameters in order to accurately reflect the limits of currently explored hydrodynamic simulations of progenitor scenarios for SNe Ia.A large variety of hydrodynamical simulations of various SNe Ia progenitor systems are found in the HESMA models and offer information about the expected general properties of the ejecta structure such as the relative typical ratios of nucleosynthetic products present within the ejecta as well as full density profiles.We generate a prior space for total elemental masses by integrating models taken from HESMA above v 0 so that the final masses of each element follow the same general correlation structure as the Prior distributions for T inner , v inner and texp are further constrained by the condition that the luminosity estimated from the Stephan-Boltzmann law 8 × 10 40 erg s −1 < 4πσ SB v 2 inner t 2 rise T 4 inner < 5 × 10 43 erg s −1 based on the estimated range of SNe Ia luminosities computed from Figure 1  Prior centroid is dependent on the phase of the spectrum from maximum light reported in Table 1 e Mean of the prior distribution in linear space.The centroid of the log-normal distribution is the log 10 of this values.f 1D standard deviation of the log 10 of each mass distribution.It is important to note that there exists a non-zero covariance between each mass term.
Table 2.The prior distributions from which our model parameters are sampled during posterior inference.Parameters are sampled over different distributions according to their range of physical applicability determined from hydrodynamical models in the HESMA data set.
sum of all hydrodynamic models, ensuring a reasonable estimate of the distribution of likely supernovae ejecta profiles.The prior distribution of elemental masses is drawn from a multivariate Gaussian distribution whose covariance is set as the covariance of the log of elemental masses taken from the HESMA models with a centroid taken as the log of the mean of HESMA masses in linear space as to not bias the distribution towards models with little or no mass of certain elements.Drawing from this distribution offers a good balance between tracing the general covariance structure of the models found in the HESMA while also permitting nearly any parameter combination to be tested, albeit with a smaller probability.
We set a uniform prior on the distribution of values of α ρ by fitting linear models to the HESMA density profiles above v 0 and taking the minimum and maximum value to the nearest integer.Velocity and temperature distributions are initially sampled uniformly over the ranges specified in Table 2, with cuts placed on the luminosity of the supernovae under homologous expansion with an assumed rise time of 19.5 days (Riess et al. 1999) according to the Stephan-Boltzmann law as an estimate for the range of realistic maximum light luminosities.The prior distribution for the time since the explosion, t exp , is determined on a spectrum-by-spectrum basis.The distribution is always represented by a Gaussian distribution centered at a time of 19.5 days plus the phase of the spectrum from maximum light (see Table 1) with a standard deviation of 2.5 days to account for risetime uncertainty based on the spread of rise-times between normal and 1991T-like SNe Ia (see Figure 6 in Ganeshalingam et al. 2011).

UltraNest
The posterior inference was performed with nested sampling (Skilling 2004;Buchner 2021) with the ML-Friends Monte Carlo algorithm (Buchner 2014(Buchner , 2017)).Nested sampling is ideal for generating posterior samples from complex high-dimensional distributions.We used the nested sampling package UltraNest1 (Buchner 2021) to sample the posterior distribution for each observed spectrum.Each spectrum returned between 10 000 and 30 000 effective posterior samples which are presented in Figures 4 and 5.

Active Learning
The high dimensionality of the parameter space and unknown apriori parameter constraints required to effectively model individual spectra observations create difficulty in selecting an optimal training set for our emulator.We resolve this issue by iteratively selecting new training points that are predicted to best improve emulator accuracy in the regions of the parameter space that are most likely to model the spectra we are attempting to model.
We apply Active Learning (AL Cohn et al. 1996;Beluch et al. 2018) iterations to the emulator training to improve accuracy in regions of high importance.After an initial draw of 250 000 random samples, the emulator is trained to reproduce the results of tardis (see Section 3.2.1).We sample the posterior distribution, us-ing this emulator, of parameters best matching our observed spectra using a modified AL likelihood function, L AL ( ⃗ θ).This likelihood function weighs the likelihood of a proposed ⃗ θ by the relative fraction of emulator uncertainty to total uncertainty, encouraging exploration into regions of the parameter space where the emulator has less information.The AL likelihood function is computed as An equal number of posterior samples are selected for each observed spectrum and are evaluated by tardis.Synthetic tardis spectra are then appended to the original training data to provide the emulator with more information around areas that are simultaneously high in likelihood while also high in emulation uncertainty.Each acquisition process yields approximately 200 000 additional samples per iteration.Two iterations of active learning were performed on the data.

RESULTS
The posterior probability distribution of spectra for the five 1991T-like SNe Ia in our samples along with their maximum likelihood estimate and total uncertainty is presented in Figure 2.For comparison, a selection of five of the normal SNe Ia from our sampled are shown in Figure 3.Our fits accurately reproduce major line features that distinguish 1991T-like SNe Ia from the normal SNe Ia population.Specifically, our models generate the high-velocity Fe III features around 4250 Å and 4950 Å as well as the Si II feature near 6150 Å.

Ejecta Properties
The peculiar nature of early-time 1991T-like spectra has been well identified, but their origin remains unclear.1991T-like spectra show the presence of highvelocity Fe III emission and lack the strong characteristic Si II and Ca H&K absorption commonly seen in Branch-normal SNe Ia (see e.g.Filippenko 1997).After maximum light, 1991T-like spectra begin to behave similarly to normal Type Ia spectra, with Si II features reappearing in the spectra (see e.g.Taubenberger 2017).There have been two suggested causes behind the lack of singly-ionized IME absorption at early times.Namely, a lack of total IME production and higher ionization states of IMEs produced in the ejecta (e.g.Jeffery et al. 1992;Ruiz-Lapuente et al. 1992;Sasdelli et al. 2014) .
We find a variety of parameters that indicate the differences between 1991T-like and Normal SNe Ia.The distribution of inner boundary temperatures for 1991Tlike SNe Ia does not substantially differ from those of normal SNe Ia (Figure 4) indicating that high-ionization states of IMEs, in particular Silicon, are not due to a difference in temperature of the ejecta alone.This leads us then to investigate two other possible causes for the lack of Si II formation in the photospheric phase: a decrease in the electron density at the primary location of IME composition or a decrease in the total mass of IMEs contributing to the line features seen in the ejecta.
The material below the photosphere, parameterized through the inner boundary velocity, does not contribute to features in the resultant spectra.Therefore, constraints of physical properties of the ejecta must rely strictly upon material above the inner boundary photosphere.We determine the total mass of each con- tributing element above the photosphere by integrating Equations 5, 6, and 7 with their lower bounds set to the inner boundary velocity, v inner .We compute the mass fraction of each element as the integrated mass of each element above the photosphere divided by the total mass above the photosphere.The mass fraction offers a direct probe of the nucleosynthetic products that are visible in the photospheric phase and which can be directly compared to hydrodynamic models without a need to convert abundance fractions into total masses.
Figure 5 shows the posterior probability distributions of the IME fractions from 1991T-like SNe Ia demonstrating a clear deficit compared to that of normal SNe Ia coupled with a small increase of IGEs as a fraction of the total ejecta.The marginal distribution of the fraction of unburned elements does not demonstrate a discernible difference between 1991T-likes and Normal  SNe Ia, though the joint distribution between IGEs and unburned elements shows an interesting correlation in 1991T-likes in which the fraction of unburned elements in the ejecta is slightly higher for 1991T-like SNe Ia compared to Normal SNe Ia given the same iron-group element fraction.The consistent lack of IME mass fractions changing with respect to UBE fractions along with the correlation between UBE and IME fractions in 1991Tlike SNe Ia implies a rapid and consistent drop-off in the rate of production of nucleosynthetic products with respect to depth into the explosion.
While many 1991T-like SNe Ia show generally lower mass fractions of IMEs compared to the normal Ia population, there are cases of overlap (see Figures 4, 5) where low mass fractions alone are not enough to explain the observed lack of IME features, such as the Si II 6150 Å doublet, in the resulting spectra.Additionally, we note that the 1991T-like SNe Ia population has  generally lower ejecta densities at the location of the peak of the fractional abundance of IMEs in our model implying a lower electron density and therefore a higher ionization state.The combination of low IME mass fraction and higher ionization states leads to a dual effect where the observed properties of 1991T-like SNe Ia in comparison to the normal Ia population is not due to a single underlying mechanism, but a combination of different physical processes which result in similar looking spectra observationally.
We selected the maximum likelihood sample for each spectrum and simulated the ejecta radiation field using tardis.The ionization fraction of Si III to Si II was determined at the shell containing the velocity v max providing a look into the ionization state of the plasma at the location with the maximum abundance of intermediate-mass elements.1991T-like supernovae were found to have overall higher ionization fractions than the vast majority of normal SNe Ia, though some overlap was found within the normal SNe Ia population (Figure 6).The normal SNe Ia with comparable ionization fractions to 1991T-like SNe Ia all had a higher mass fraction of IMEs than 1991T-like SNe Ia at the same ionization fraction.Additionally, 1991T-like SNe Ia with lower ionization fractions among the 1991T-like population also had a lower mass fraction of intermediate-mass elements within their ejecta.The suppressed Si II absorption features observed in 1991T-like SNe Ia, therefore, is a result of a combination of low IME fraction and high ionization state, creating a region of space where there is a turnover in the classification between the spectral types.

CONCLUSION
We have performed single-epoch ejecta reconstructions for 35 normal SNe Ia and five 1991T-like SNe Ia.Elemental abundance distributions and their ionization fractions have provided a picture linking the internal properties of the ejecta to the observational properties of their spectra.Comparison between the ejecta properties between the two populations provides insight into the relationship between normal SNe Ia and 1991T-like SNe Ia.
We find 1991T-like SNe Ia both under-produce IMEs relative to the normal SNe Ia population and these IMEs exist in higher ionization states than the IMEs in the normal SNe Ia population.The cause of the higher ion-ization fractions is primarily driven by a lower overall electron density in the ejecta.The lower overall electron density may be a result of a relative overabundance of IGEs relative to the abundance of IMEs in the ejecta of 1991T-like SNe Ia resulting in an ejecta composition dominated by high-neutron number elements, while normal SNe Ia with depleted IMEs may have the remainder of the ejecta filled with unburned Carbon and Oxygen.
Neither the low abundance fraction of IMEs nor the high ionization states of IMEs alone are enough to explain the peculiar properties of 1991T-like SNe Ia; instead, a combination of the two effects drives their unique spectral signatures at early times.We have found 1991T-like SNe Ia that contain a similar IME fraction to some of the normal SNe Ia in our sample, but these 1991T-like SNe Ia have a higher overall IME ionization than a normal SNe Ia at a similar IME mass fraction.Conversely, we have found 1991T-like SNe Ia with similar IME ionization fractions to the normal SNe Ia but these objects have a lower mass fraction of IMEs than the normal SNe Ia given their ionization state.
Our findings suggest that normal SNe Ia and 1991Tlike SNe Ia might arise from a similar population or progenitor system.The observational spectral properties that traditionally separate the two groups result from a sharp change in the amplitude of spectral features corresponding to IMEs over small changes in both composition and ionization state.This results in small deviations in ejecta composition leading to a sharp contrast in observed spectral features.

ACKNOWLEDGMENTS
This work was supported in part through computational resources and services provided by the Institute for Cyber-Enabled Research at Michigan State University.This work made use of the Heidelberg Supernova Model Archive (HESMA), https://hesma.h-its.orgThis research made use of tardis, a communitydeveloped software package for spectral synthesis in supernovae (Kerzendorf & Sim 2014;Kerzendorf et al. 2021)

Figure 1 .
Figure1.Visualization of a random realization of an abundance profile produced from our model in our prior space.Elemental abundances are presented as stacked histograms.The diagonally hatched regions correspond to the inner irongroup elements, the central unhatched region corresponds to the abundance of IMEs, and the vertically hatched region corresponds to the unburned elements in the outer layers of the ejecta.A red dashed vertical line represents the inner boundary velocity from which thermalized radiative packets are injected into the ejecta above.The solid black line represents the density of the ejecta through velocity space and the value of the density if provided by the right-hand axis.

b
Mean of the normal distribution in linear space.c Standard deviation of the normal distribution d

Figure 2 .
Figure 2. Posterior spectra of 1991T-like SNe Ia scaled and offset for visualization.The mean of the posterior is represented in black with the best fit (maximum likelihood sample) in orange dashed and the shaded orange region representing the total uncertainty of the best-fit sample at 1-σ.

Figure 3 .
Figure 3. Same as Figure 2 for a selection of five normal SNe Ia for comparison.

Figure 4 .
Figure 4. Posterior contours of SNe Ia probed in this study.Normal SNe Ia are shown with blue contours and 1991Tlike SNe Ia are shown in orange.The contours cover 68%, 95%, and 99.5% quantiles.The posterior means for each object are shown as stars.The plots show the joint distributions between ejecta density at v = vmax, inner boundary temperature Tinner, and integrated UVOIR luminosity from the model spectrum.While 1991T-like SNe Ia are generally brighter than the Normal SNe Ia population, the increase in brightness does not seem to be driven by substantially higher photospheric temperatures.The lower ejecta density in the region of highest intermediate mass element abundance shows that higher ionization fractions in 1991T-like SNe Ia are influenced by the lower electron density.

Figure 5 .
Figure 5. Posterior contours of SNe Ia probed in this study.Normal SNe Ia are shown with blue contours and 1991T-like SNe Ia are shown in orange.The contours cover 68%, 95%, and 99.5% quantiles.The posterior means for each object are shown as stars.Each plot shows the marginal distribution of mass fractions of the various ejecta compositions above the inner boundary velocity by integrating equations 6, 5, and 7.It can clearly be seen that 1991T-like SNe Ia lie on the edge of IME mass fraction distribution describing normal SNe Ia.

Figure 6 .
Figure 6.Ratio of Si III to Si II ion density at the shell encompassing vmax versus the fraction of intermediate-mass elements in the ejecta above the inner boundary.Samples are taken from the maximum likelihood parameters of each SNe Ia in our sample run through tardis to calculate the properties of the radiation field.Normal SNe Ia are shown in blue and 1991T-like SNe Ia are shown in orange.A clear turnover between normal SNe Ia and 1991T-like SNe Ia is evident in the regions of low intermediate mass element fraction and high ionization state of silicon.The combination of the lack of material coupled with high ionization states creates a boundary between the spectral types.
Zheng et al. (2018)reports this object as a normal SNe Ia but our results from SNID classify this as a 1991T-like SNe Ia which we keep based on the high-brightness and low Si II velocity.
SNPhase (d) λmin ( Å) λmax ( Å) Date (MJD) a b Zheng et al. ( . The development of tardis received support from the Google Summer of Code initiative, from ESA's Summer of Code in Space program, and from Num-FOCUS's Small Development Grant.tardis makes extensive use of Astropy 2 (Astropy Collaboration et al. 2013, 2018) C.V. was supported for this work by the Excellence Cluster ORIGINS, which is funded by the Deutsche