# JWST Low-Resolution MIRI Spectral Observations of SN 2021aefx: High-density
Burning in a Type Ia Supernova

J. M. DerKacy Department of Physics, Virginia Tech, Blacksburg, VA 24061, USA
C. Ashall Department of Physics, Virginia Tech, Blacksburg, VA 24061, USA  P.
Hoeflich Department of Physics, Florida State University, 77 Chieftan Way,
Tallahassee, FL 32306, USA  E. Baron Homer L. Dodge Department of Physics and
Astronomy, University of Oklahoma, 440 W. Brooks, Rm 100, Norman, OK
73019-2061, USA  Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg,
Germany  B. J. Shappee Institute for Astronomy, University of Hawai’i at
Manoa, 2680 Woodlawn Dr., Hawai’i, HI 96822, USA  D. Baade European
Organization for Astronomical Research in the Southern Hemisphere (ESO), Karl-
Schwarzschild-Str. 2, 85748 Garching b. München, Germany  J. Andrews Gemini
Observatory/NSF’s NOIRLab, 670 North A‘ohoku Place, Hilo, HI 96720-2700, USA
K. A. Bostroem LSSTC Catalyst Fellow  Steward Observatory, University of
Arizona, 933 North Cherry Avenue, Tucson, AZ 85721-0065, USA  P. J. Brown
George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and
Astronomy, Texas A&M University, Department of Physics and Astronomy, College
Station, TX 77843, USA  C. R. Burns Observatories of the Carnegie Institution
for Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA  A. Burrow
Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma,
440 W. Brooks, Rm 100, Norman, OK 73019-2061, USA  A. Cikota Gemini
Observatory/NSF’s NOIRLab, Casilla 603, La Serena, Chile  T. de Jaeger
Institute for Astronomy, University of Hawai’i at Manoa, 2680 Woodlawn Dr.,
Hawai’i, HI 96822, USA  A. Do Institute for Astronomy, University of Hawai’i
at Manoa, 2680 Woodlawn Dr., Hawai’i, HI 96822, USA  Y. Dong Department of
Physics, University of California, 1 Shields Avenue, Davis, CA 95616-5270, USA
I. Dominguez Universidad de Granada, 18071, Granada, Spain  L. Galbany
Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans,
s/n, E-08193 Barcelona, Spain  Institut d’Estudis Espacials de Catalunya
(IEEC), E-08034 Barcelona, Spain  E. Y. Hsiao Department of Physics, Florida
State University, 77 Chieftan Way, Tallahassee, FL 32306, USA  E.
Karamehmetoglu Department of Physics and Astronomy, Aarhus University, Ny
Munkegade 120, DK-8000 Aarhus C, Denmark  K. Krisciunas George P. and Cynthia
Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M
University, Department of Physics and Astronomy, College Station, TX 77843,
USA  S. Kumar Department of Physics, Florida State University, 77 Chieftan
Way, Tallahassee, FL 32306, USA  J. Lu Department of Physics, Florida State
University, 77 Chieftan Way, Tallahassee, FL 32306, USA  T. B. Mera Evans
Department of Physics, Florida State University, 77 Chieftan Way, Tallahassee,
FL 32306, USA  J. R. Maund Department of Physics and Astronomy, University of
Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, U.K.  P. Mazzali
Astrophysics Research Institute, Liverpool John Moores University, UK  Max-
Planck Institute for Astrophysics, Garching, Germany  K. Medler Astrophysics
Research Institute, Liverpool John Moores University, UK  Max-Planck Institute
for Astrophysics, Garching, Germany  N. Morrell Las Campanas Observatory,
Carnegie Observatories, Casilla 601, La Serena, Chile  F. Patat European
Organization for Astronomical Research in the Southern Hemisphere (ESO), Karl-
Schwarzschild-Str. 2, 85748 Garching b. München, Germany  M. M. Phillips Las
Campanas Observatory, Carnegie Observatories, Casilla 601, La Serena, Chile
M. Shahbandeh Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218-2410, USA  S. Stangl Homer L. Dodge Department of Physics
and Astronomy, University of Oklahoma, 440 W. Brooks, Rm 100, Norman, OK
73019-2061, USA  C. P. Stevens Department of Physics, Virginia Tech,
Blacksburg, VA 24061, USA  M. D. Stritzinger Department of Physics and
Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark  N.
B. Suntzeff George P. and Cynthia Woods Mitchell Institute for Fundamental
Physics and Astronomy, Texas A&M University, Department of Physics and
Astronomy, College Station, TX 77843, USA  C. M. Telesco Department of
Astronomy, University of Florida, Gainesville, FL 32611 USA  M. A. Tucker
CCAPP Fellow  Center for Cosmology and AstroParticle Physics, The Ohio State
University, 191 W. Woodruff Ave., Columbus, OH 43210, USA  S. Valenti
Department of Physics, University of California, 1 Shields Avenue, Davis, CA
95616-5270, USA  L. Wang Department of Physics and Astronomy, Texas A&M
University, College Station, TX 77843, USA  Y. Yang Bengier-Winslow-Robertson
Postdoctoral Fellow  Department of Astronomy, University of California,
Berkeley, CA 94720-3411, USA  S. W. Jha Department of Physics and Astronomy,
Rutgers, the State University of New Jersey, 136 Frelinghuysen Road,
Piscataway, NJ 08854-8019, USA  L. A. Kwok Department of Physics and
Astronomy, Rutgers, the State University of New Jersey, 136 Frelinghuysen
Road, Piscataway, NJ 08854-8019, USA

(Received January 9, 2023; Revised February, 1, 2023; Accepted February 1,
2023)

###### Abstract

We present a JWST/MIRI low-resolution mid-infrared (MIR) spectroscopic
observation of the normal Type Ia supernova (SN Ia) SN 2021aefx at $+323$ days
past rest-frame $B$-band maximum light. The spectrum ranges from 4-14 $\mu$m,
and shows many unique qualities including a flat-topped [Ar III] $8.991$
$\mu$m profile, a strongly tilted [Co III] $11.888$ $\mu$m feature, and
multiple stable Ni lines. These features provide critical information about
the physics of the explosion. The observations are compared to synthetic
spectra from detailed NLTE multi-dimensional models. The results of the best-
fitting model are used to identify the components of the spectral blends and
provide a quantitative comparison to the explosion physics. Emission line
profiles and the presence of electron capture (EC) elements are used to
constrain the mass of the exploding white dwarf (WD) and the chemical
asymmetries in the ejecta. We show that the observations of SN 2021aefx are
consistent with an off-center delayed-detonation explosion of a near-
Chandrasekhar mass ($M_{\text{Ch}}$) WD at a viewing angle of $-30\arcdeg$
relative to the point of the deflagration-to-detonation transition. From the
strength of the stable Ni lines we determine that there is little to no mixing
in the central regions of the ejecta. Based on both the presence of stable Ni
and the Ar velocity distributions, we obtain a strict lower limit of $1.2$
$M_{\odot}$ the initial WD, implying that most sub-$M_{\text{Ch}}$ explosions
models are not viable models for SN 2021aefx. The analysis here shows the
crucial importance of MIR spectra for distinguishing between explosion
scenarios for SNe Ia.

supernovae: general - supernovae: individual (SN 2021aefx), JWST

††journal: ApJL††facilities: JWST (LRS/MIRI), MAST (JWST), The simulations
presented here were performed on the Beowulf system of the Astrophysics Group
at Florida State University.††software: jwst (Bushouse et al., 2022, ver.
1.8.1,), HYDRA (Höflich, 2003, 2009; Hoeflich et al., 2017), OpenDx (an open-
sourced visualization package developed by IBM), SNooPy (Burns et al., 2011,
2014), Astropy (Astropy Collaboration et al., 2013, 2018, 2022), NumPy (Harris
et al., 2020), SciPy (Virtanen et al., 2020), Matplotlib (Hunter, 2007).

##  1 Introduction

Type Ia supernovae (SNe Ia) arise from the thermonuclear explosion of at least
one carbon/oxygen (C/O) white dwarf (WD) in a binary system (Hoyle & Fowler,
1960). Despite being the most precise extra-galactic distance indicators in
the Universe (Phillips, 1993; Riess et al., 1998; Perlmutter et al., 1999;
Riess et al., 2016, 2018), the exact make-up of SNe Ia progenitor systems and
the mechanism of their explosions are still unknown (see Maoz et al., 2014;
Branch & Wheeler, 2017; Jha et al., 2019, for recent reviews).

There are multiple progenitor scenarios that may produce SNe Ia. These
include: the single-degenerate (SD) scenario where the companion is a main-
sequence star or an evolved, non-degenerate companion like a red giant or He-
star (Whelan & Iben, 1973); the double-degenerate (DD) scenario, where the
companion is also a WD (Iben & Tutukov, 1984; Webbink, 1984); or a triple
system where at least two of the bodies are C/O WDs (Thompson, 2011; Kushnir
et al., 2013). Additionally, a wide range of explosion mechanisms also exist.
Multiple mechanisms originate from the merger of both stars in the progenitor
system, including the dynamical merger of two WDs (Benz et al., 1990; García-
Berro et al., 2017), the violent merger of two WDs (Pakmor et al., 2012,
2013), and the collisions of two WDs within triple systems (Rosswog et al.,
2009a; Kushnir et al., 2013). Currently, two of the leading explosion models
are of SNe Ia arising from the explosion of a near-$M_{\text{Ch}}$ mass WD,
and the detonation of a sub-$M_{\text{Ch}}$ mass WD. In $M_{\text{Ch}}$
explosions H, He, or C material is accreted from a companion star (which can
be degenerate or non-degenerate) until the central density in the primary WD
is high enough to trigger a thermonuclear runaway (Iben & Tutukov, 1984;
Diamond et al., 2018). The flame can then propagate as a deflagration,
detonation or both via a deflagration-to-detonation transition (DDT)
(Khokhlov, 1991a; Hoeflich & Khokhlov, 1996; Gamezo et al., 2003; Poludnenko
et al., 2019). In contrast, a sub-$M_{\text{Ch}}$ explosion is triggered when
a surface He layer detonates and drives a shock-wave inwards, causing a
secondary detonation that disrupts the whole WD (Nomoto et al., 1984; Woosley
& Weaver, 1994; Livne & Arnett, 1995; Hoeflich & Khokhlov, 1996; Shen et al.,
2018). Similar to a $M_{\text{Ch}}$ explosion, a sub-$M_{\text{Ch}}$ explosion
can occur in both the single and double degenerate scenarios (Piersanti et
al., 2003a, b).

Due to the degenerate nature of C/O WDs, the central density ($\rho_{c}$) of
the star is directly correlated with its mass (Chandrasekhar, 1939).
Therefore, one of the key differences between $M_{\text{Ch}}$ and
sub-$M_{\text{Ch}}$ scenarios is the peak density of the burning. In
particular when $\rho_{c}>5\times 10^{8}$ g cm-3, significant amounts of
stable iron group elements (IGEs) such as 58Ni are produced (Hoeflich &
Khokhlov, 1996). These central densities correspond to WD masses of $\gtrsim
1.2$ $M_{\odot}$, where the thermonuclear runaway must start via compressional
heating in the center of the WD (Seitenzahl & Townsley, 2017).

Traditionally there have been fewer studies of SNe Ia in the longer near-
infrared (NIR) and mid-infrared (MIR) wavelengths compared to the optical.
However, recent efforts have shown that these longer wavelengths offer
additional, and sometimes better, information about the physics of SN
explosions (Meikle et al., 1993; Höflich et al., 2002; Marion et al., 2009;
Hsiao et al., 2013; Graham et al., 2017; Diamond et al., 2018; Wilk et al.,
2018; Hoeflich et al., 2021; Lu et al., 2022; Kumar et al., 2022; Hoeflich et
al., 2023). This is due, in part, to the fact that the location of the
photosphere is wavelength-dependent, and that different diagnostic spectral
lines are revealed at longer wavelengths (Hoeflich et al., 1991, 1995; Wheeler
et al., 1998; Kasen, 2006; Ashall et al., 2019a, b).

Prior to the launch of the James Webb Space Telescope (JWST), there were only
seven MIR ($\lambda>5$ $\mu$m) spectral observations of SNe Ia across four
different objects. Three spectra were obtained with the Spitzer Space
Telescope (SST); one of SN 2003hv at $\sim+375$ days (relative to estimated
explosion), one of SN 2005df at $\sim+135$ days (Gerardy et al., 2007), and
one of SN 2006ce at $+127$ days relative to $B$-band maximum light (Kwok et
al., 2022, GO-30292, PI: W.P. Meikle;). Four MIR spectra of SN 2014J were
obtained with CanariCam on the 10.4-m Gran Telescopio Canarias (GTC) between
$57-137$ days after explosion (Telesco et al., 2015). Despite the small sample
size it is apparent that the MIR contains many diagnostics to differentiate
between leading explosion scenarios. For example, nebular phase MIR spectral
observations, which probe the high-density central layers, can reveal the
presence and distribution of stable Ni. These lines are direct indicators of
high-density burning.

With the successful launch of JWST, high-S/N MIR spectral observations during
the nebular phase of SNe Ia are now possible. The first spectrum of a SN Ia
obtained with JWST was that of SN 2021aefx at $+255$ days after maximum light
(Kwok et al., 2022, MJD=59801.4;). Here we present and analyze a spectrum of
SN 2021aefx taken $+323$ days (MJD=59871.6) after maximum light. In contrast
to the work of Kwok et al. (2022), who focused primarily on line
identifications and determination of observed velocities, we interpret the
explosion physics of SN 2021aefx through comparisons to a self-consistent set
of non-local thermodynamic equilibrium (NLTE) radiation hydrodynamic models of
SNe Ia. This allows us to provide a set of line IDs specific to SN 2021aefx in
addition to a consistent picture of the explosion based on our newly observed
spectrum and models. In § 2 we describe our observations, and in § 3 the
details of our spectral reduction. Line identifications from full NLTE models
are performed in § 4, while an analysis of their velocities is presented in §
5. § 6 discusses the details of our chosen NLTE models and a comparison to the
observations. Alternative explosion scenarios are discussed in § 6.4. Finally,
we summarize our findings in § 7.

##  2 Observations

SN 2021aefx was discovered on 2021 Nov 11.3 (MJD=59529.5) by the Distance Less
Than 40 Mpc Survey (DLT40; Tartaglia et al., 2018) and classified as a young
SN Ia (Bostroem et al., 2021; Hosseinzadeh et al., 2022). SN 2021aefx was
subsequently followed by several groups, including a multi-band optical and
spectroscopic follow-up campaign by the Precision Observations of Infant
Supernova Explosions Collaboration (POISE, Burns et al., 2021; Ashall et al.,
2022). POISE’s detailed photometric observations revealed an early blue
excess, which may be explained by a rapid change in the velocities of spectral
lines (Ashall et al., 2022). An analysis of the complete POISE data set
reveals the basic light curve properties of SN 2021aefx, including a decline
rate of $\Delta{\rm m_{15}(B)}=1.01\pm 0.06$ mag, and a peak absolute
magnitude of $M_{B}=-19.28\pm 0.49$ mag, which places SN 2021aefx in the
normal part of the luminosity-width relation (Phillips, 1993; Ashall et al.,
2022; C. Stevens et al., in prep.). SN 2021aefx is located 105″.3 south, 37″.0
west from the center of its host NGC 1566 at a redshift of 0.005
($\alpha=04^{h}20^{m}00^{s}.42$, $\delta=-54\arcdeg 56\arcmin 16\arcsec.10$;
Allison et al., 2014). NGC 1566 is a face-on spiral galaxy with systemic
recessional velocity of 1500 km s-1, and a rotational velocity of $65\pm 60$
km s-1 at the location of the SN (Elagali et al., 2019). All figures showing
observed spectra of SN 2021aefx have been corrected for the combined
recessional and rational velocities of 1550 km s-1 at the location of the SN
in the host. This low rotational velocity implies that any observed off-center
lines (i.e. lines shifted relative to the line-of-sight velocity) are
intrinsic to the progenitor system itself, and not attributable to a peculiar
velocity within the host galaxy.

We present a MIR observation of SN 2021aefx obtained through program GO-
JWST-2114 (P.I. Ashall) from $\sim 4-14$ $\mu$m. The data were obtained using
JWST’s Mid-Infrared Instrument (MIRI) in its Low Resolution Spectroscopy (LRS)
configuration. In this mode, MIRI/LRS obtains slit spectroscopy of objects
with a spectral resolving power $(R=\lambda/\Delta\lambda)$ of $R\sim 100$ at
$7.5$ $\mu$m, varying from $R\sim 40$ at $5$ $\mu$m to $R\sim 160$ at $10$
$\mu$m (Kendrew et al., 2015, 2016; Rigby et al., 2022). The instrumental
configuration is identical to that of Kwok et al. (2022). The spectral
observations were performed with a 2-point dither strategy. For each grating
setting there were $134$ groups per integration, $2$ integrations per exposure
and $1$ exposure per dither. This results in an exposure of $734.5$ seconds at
each dither position, which are combined for a total exposure time of $1493$
seconds. Full details of our observational set-up are found in Table 1.

Figure 1: JWST/MIRI LRS spectrum of SN 2021aefx at $+323$ days relative to
$B$-band maximum. The ions responsible for the most prominent features in the
spectrum are labeled. A full set of line identifications is plotted in Figure
3 and shown in Table 2. Table 1: JWST/MIRI Observation Details

Parameter | Value
---|---
Acquisition Image |
Filter | F1000W
Exp Time [s] | 89
Readout Pattern | FASTGRPAVG8
SN 2021aefx Spectrum |
Mode | LRS
Exp Time [s] | 1493
$T_{\text{obs}}$ [MJD] | 59871.6
Epochaafootnotemark:  [days] | 322.71
Groups per Integration | 134
Integrations per Exp. | 2
Exposures per Dither | 1
Total Dithers | 2

Note. — aafootnotemark:  Rest frame days relative to $B$-band maximum of MJD
$=59547.25$ (C. Stevens et al., in prep.).

##  3 Data Reduction

The data were obtained on 2022 Oct 19.6 (MJD=59871.6) and reduced with the
JWST calibration pipeline111https://jwst-
pipeline.readthedocs.io/en/stable/jwst/introduction.html, version 1.8.1
(Bushouse et al., 2022). Both raw (Stage 1 calibrated) and fully reduced data
were retrieved from the Mikulski Archive for Space Telescopes
(MAST)222https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html. This
data can be accessed via: https://doi.org/10.17909/6fjc-sx91 (catalog DOI:
10.17909/6fjc-sx91). The raw data was processed with a local installation of
the version 1.8.1 pipeline for comparison to the fully reduced data from MAST,
using the spec_mode_stage_2 and spec_mode_stage_3 Jupyter notebooks as
templates for the reduction. Both reductions used the most up-to-date
wavelength (jwst_miri_specwcs_0005.fits) and flux calibration
(jwst_miri_photom_0085.fits) files. These calibration files produce a
wavelength solution accurate to $\sim 0.05-0.02$ $\mu$m, varying from short to
long wavelengths, and a flux calibration accurate to a $\sim 2$ – $5$% global
offset between 5 – 12 $\mu$m. (Gordon et al., 2022, S. Kendrew, private
communication). Furthermore, Kwok et al. (2022) found that the flux
calibration of their MIRI spectrum was accurate to 2%.

Using the LRS Optimal Spectral Extraction
notebook333https://spacetelescope.github.io/jdat_notebooks/notebooks/MIRI_LRS_spectral_extraction/miri_lrs_spectral_extraction.html,
the spectra were re-extracted using multiple techniques. This re-extraction
was necessary to properly center the position of the spectrum in the science
aperture, as the pipeline-derived aperture produced a poor extraction at long
wavelengths. After proper re-extraction with the Optimal Extraction notebook,
no significant differences were found between the locally reduced data and the
fully calibrated (but un-extracted) data available from MAST. Future updates
to the JWST calibration files are expected to further improve the accuracy of
the automated extractions (S. Kendrew, private communication).

Figure 2: Comparison of $+323$ day spectrum of SN 2021aefx to other MIR
spectral observations of SNe Ia, including SNe 2005df (Gerardy et al., 2007),
2006ce (Kwok et al., 2022), 2014J (Telesco et al., 2015), and the $+255$ days
spectrum of 2021aefx (Kwok et al., 2022). The epoch relative to $B$-band
maximum light for each spectrum is shown. The primary difference between the
$+255$ and $+323$ day spectra of SN 2021aefx is the increased strength of
other features relative to the peak at $\sim 11.9$ $\mu$m.

##  4 Data comparison & Line Identifications

Figure 1 presents the spectrum of SN 2021aefx acquired on 2022 Oct 19.6
(corresponding to $+323$ days after $B$-band maximum light) from $4-14$
$\mu$m. At these phases, the ejecta are optically thin and dominated by
emission lines. The strongest of these lines are labeled in Figure 1. Figure 2
shows our spectrum of SN 2021aefx compared to the MIR spectra of SNe 2005df
(Gerardy et al., 2007), 2006ce (Kwok et al., 2022), 2014J (Telesco et al.,
2015), and the earlier spectrum of SN 2021aefx at +$255$ days (Kwok et al.,
2022). From Figure 2 it is clear that SN 2021aefx is similar to other
previously observed SNe Ia, but the size and sensitivity of JWST produces a
high S/N spectrum with a quality that was previously impossible to obtain.
Comparing the two JWST spectra of SN 2021aefx, the most noticeable difference
is the decrease in the relative strength of the $\sim 11.9$ $\mu$m profile
compared to the other features caused by the radioactive decay of 56Co.

To assist in line identifications, we use a suite of full NLTE radiation
transport models. These models reproduce both the early and late time
properties of SN 2021aefx, and an in-depth discussion of the models with
respect to the MIR observables can be found in § 6.

A detailed examination of the SN 2021aefx MIR spectrum reveals four prominent
wavelength regions of line formation, which are described individually in the
following subsections. Detailed line identifications in each of these regions
are plotted in Figure 3, while Table 2 lists the lines that contribute
significantly to the spectrum.

Table 2: Mid-Infrared Line Identifications from Model 25

S |  $\lambda$ [$\mu$m ] | Ion | S |  $\lambda$ [$\mu$m ] | Ion
---|---|---|---|---|---
$*\ *$ | $6.214$ | [Co II] |  | $8.555$ | [Fe III]
$*$ | $6.273$ | [Co I] | $*\ *$ | $8.611$ | [Fe III]
$*$ | $6.274$ | [Co II] | $*$ | $8.644$ | [Co II]
$*\ *$ | $6.383$ | [Ar III] | $*\ *$ | $8.733$ | [Fe II]
$*\ *\ *$ | $6.636$ | [Ni II] | $*\ *$ | $8.945$ | [Ni IV]
| $6.636$ | [Ni II] | $*\ *\ *$ | $8.991$ | [Ar III]
$*\ *$ | $6.920$ | [Ni II] | $*$ | $9.618$ | [Ni II]
$*\ *\ *$ | $6.985$ | [Ar II] | $*$ | $10.080$ | [Ni II]
| $6.985$ | [Ar II] | $*\ *\ *$ | $10.189$ | [Fe II]
| $6.985$ | [Ar II] | $*\ *$ | $10.203$ | [Fe III]
| $7.045$ | [Co I] | $*\ *\ *$ | $10.523$ | [Co II]
| $7.103$ | [Co III] | $*\ *\ *$ | $10.682$ | [Ni II]
| $7.147$ | [Fe III] | $*$ | $11.002$ | [Ni III]
| $7.272$ | [Fe III] | $*\ *$ | $11.130$ | [Ni IV]
$*\ *$ | $7.349$ | [Ni III] | $*\ *$ | $11.167$ | [Co II]
$*\ *\ *$ | $7.507$ | [Ni I] | $*\ *$ | $11.307$ | [Ni I]
| $7.773$ | [Co I] | $*\ *\ *\ *$ | $11.888$ | [Co III]
$*\ *\ *$ | $7.791$ | [Fe III] | $*$ | $11.978$ | [Fe III]
$*$ | $8.044$ | [Co II] | $*\ *$ | $12.001$ | [Ni I]
$*$ | $8.063$ | [Ni II] | $*\ *$ | $12.255$ | [Co I]
| $8.114$ | [Co I] | $*$ | $12.261$ | [Mn II]
$*\ *$ | $8.211$ | [Fe III] | $*\ *\ *$ | $12.642$ | [Fe II]
| $8.282$ | [Ni I] | $*\ *$ | $12.681$ | [Co III]
$*\ *\ *$ | $8.405$ | [Ni IV] | $*\ *\ *$ | $12.729$ | [Ni II]
$*\ *$ | $8.489$ | [Co III] |  | $13.058$ | [Co I]

Note. — For each transition, the markers correspond to dominant ($*\ *\ *\
*$), strong ($*\ *\ *$), moderate ($*\ *$), weak ($*$), and scarcely
detectable ( ) on top of the quasi-continuum formed by a large number of
lines. The relative strength S is estimated by the integral over the envelope,
$\int{A_{ij}n_{j}\,dV}$ where $n_{j}$ is the particle density of the upper
level. The list is based on the simulations described in § 6.

Figure 3: Detailed line identifications in the four prominent feature regions
based on the lines from Model 25 (Hoeflich, 2017) included in Table 2. The
color intensity of the vertical lines corresponds to the strength of the
spectral lines, with 4-star lines the most intense and 1-star lines being the
faintest. Dashed lines correspond to ground state ions, solid lines singly-
ionized species, dotted lines doubly-ionized species, and dash-dotted lines
triply-ionized species.

###  4.1 The $6.0-8.0$ $\mu$m Region

The $6.0-8.0$ $\mu$m region is dominated by emission lines of stable Ni, the
most prominent of which is a blend of [Ni III] $7.349$ $\mu$m and [Ni I]
$7.507$ $\mu$m that defines the red edge of the feature. The blue edge of this
peak is blended with several other weaker lines, creating a series of
shoulders, extending from $\sim 6.5$ $\mu$m to $\sim 7.2$ $\mu$m. Moving from
red to blue, these shoulders are comprised of [Ar II] $6.985$ $\mu$m, [Ni II]
$6.920$ $\mu$m, and [Ni II] $6.636$ $\mu$m. Finally, there is a small bump
associated with a combination of [Co II] $6.214$ $\mu$m, [Co I] $6.273$
$\mu$m, and [Co II] $6.274$ $\mu$m.

###  4.2 The $8.0-9.5$ $\mu$m Region

The $8.0-9.5$ $\mu$m region is dominated by two features whose edges are
blended with other weaker lines at $\sim 8.7$ $\mu$m. The bluer of the two is
due to the emission of [Ni IV] $8.405$ $\mu$m, while the redder feature is
dominated by the [Ar III] $8.991$ $\mu$m line. The [Ar III] line shows a
distinct flat-topped profile, which increases in flux moving from blue to red.
Tilted flat-topped profiles are connected to both an ion’s velocity
distribution in the ejecta and the viewing angle of the explosion (see § 5.1
and § 6.3.1, also Hoeflich et al. 2021). Small contributions from the weak [Fe
II] $8.733$ $\mu$m and [Ni IV] $8.945$ $\mu$m lines may also add to the
observed flux at the 10% level.

###  4.3 The $9.5-11.5$ $\mu$m Region

The $9.5-11.5$ $\mu$m region shows a structure reminiscent of the $6.0-8.0$
$\mu$m region; with one dominant blended feature and a series of smaller bumps
and shoulders blended into the wings. The strongest peak arises from a blend
of [Co II] $10.523$ $\mu$m and [Ni II] $10.682$ $\mu$m. A blend of [Fe II]
$10.189$ $\mu$m and [Fe III] $10.203$ $\mu$m forms a shoulder that is
partially blended into the blue wing of the [Co II]$+$[Ni II] blend. Blended
into the red wing is a series of three other weaker features. The first
feature, centered near $\sim 10.85$ $\mu$m is not associated with any strong
lines in our model. The next feature in the series arises from the
comparatively weak [Ni III] $11.002$ $\mu$m line, while a blend of [Ni IV]
$11.130$ $\mu$m and [Co II] $11.167$ $\mu$m forms a shoulder on the red wing
of the [Ni III] line. Finally, there may be a small contribution to the red
wing of the [Ni IV]$+$[Co II] shoulder from [Ni I] $11.307$ $\mu$m.

###  4.4 The $11.5-13.0$ $\mu$m Region

The $11.5-13.0$ $\mu$m region contains the only relatively isolated, un-
blended feature in the MIR spectrum, the [Co III] $11.888$ $\mu$m resonance
line which produces the strongest line in the entire MIR spectrum. Our model
shows weak contributions from [Fe III] $11.978$ $\mu$m and [Ni I] $12.001$
$\mu$m, however they only produce $\sim$1% of the flux and do not alter the
line profile in a significant manner (again see Table 2). A small shoulder at
the edge of the red wing of the [Co III] line is attributable to [Co I]
$12.255$ $\mu$m. A series of peaks between $12.5-13.0$ $\mu$m suggests the
presence of multiple weak lines, however the low S/N in this region prevents
us from unambiguously identifying any lines. We tentatively identify the first
peak with [Fe II] $12.642$ $\mu$m and [Co III] $12.681$ $\mu$m, and the second
peak with [Ni II] $12.729$ $\mu$m. Our model shows no strong lines in the
vicinity of the third and final peak in the series.

##  5 Velocity Distributions and Line Profiles

In this section, we discuss the velocity distributions and line profiles of
three important species in the ejecta: Ar, Co, and Ni. In discussing these
velocities and profiles we reiterate that the current wavelength calibration
of the MIRI/LRS observations is accurate to $0.05-0.02$ $\mu$m, with lower
errors at longer wavelengths. This corresponds to an error on the order of
$\sim 500$ km s-1 in the [Co III] $11.888$ $\mu$m line, and $\sim 1400$ km s-1
in the [Ni III] $7.349$ $\mu$m line. Future updates to the JWST pipeline
calibration files may increase the precision of these results.

###  5.1 [Ar III] $8.991$ $\mu$m

Ar traces the transition region between incomplete oxygen burning and nuclear
statistical equilibrium (NSE) in the ejecta; thereby providing details about
the chemical distribution between the 56Ni and Si-group layers. The [Ar III]
8.991 $\mu$m line profile is plotted in Figure 4 in velocity space. The
profile is flat-topped with an increasing tilt from blue to red wavelengths,
which we refer as a “flat-tilted” profile hereafter. Flat-topped profiles are
indicative of a central hole or void in the emitting material — that is, a
shell of line emitting material (Beals, 1929; Menzel, 1929; Struve, 1931). For
[Ar III] the flat-top component of the feature starts at $\sim-7000$ km s-1
and extends to $\sim 8000$ km s-1. The feature increases in flux by 10% across
the profile from the blue to red side, and the flat-topped component of the
profile indicates that there is a central hole in the ejecta of $\sim\pm 8000$
km s-1 which does not contain Ar. This is because Ar is destroyed in high
temperature regimes of the NSE where $T\geq 6\times 10^{9}$ K, and there is a
lack of strong mixing during the explosion, consistent with explosion models
of near $M_{\text{Ch}}$ WDs (see § 6 for details).

Figure 4: Line profiles of the [Ar III] (top) and [Co III] lines (bottom) in
velocity space. The blue boxed region around $v=0$ km s-1 in the rest frame
denote the 1$\sigma$ error in the rest wavelength for the given line. Red
vertical lines mark the left and right edges of the flat-tilted profiles in
both panels.

###  5.2 [Co III] $11.888$ $\mu$m

SNe Ia are powered by the nuclear decay chain of 56Ni to 56Co to 56Fe. Since
the [Co III] $11.888$ $\mu$m feature is a resonance line, most of the de-
excitation and recombination of Co passes through this transition, making it a
direct tracer of the distribution and amount of 56Ni in the ejecta. This
feature covers a width of $\sim\pm 10000$ km s-1. If the shape of the line is
assumed to be symmetric, and thus well described by a Gaussian profile, it
peaks at $740\pm 200$ km s-1 with a FWHM of $4840\pm 170$ km s-1 (see Figure
5). Combining the error in the line-of-sight velocity (recessional plus
rotational; $\sim 60$ km s-1) and the estimated error in the wavelength
calibration of $\sim 500$ km s-1 with that of the fit error yields a total
estimated error of $544$ km s-1. The fact that this resonance line is not
located at the kinematic center of the explosion indicates that the bulk of
the 56Ni is off-center, at the $1.4\sigma$ level. The [Co III] $11.888$ $\mu$m
profile also shows hints of a flat-tilted profile, peaking to the red at $\sim
2000$ km s-1 (see Figure 4), although the low resolution prevents a definitive
identification of this profile. Similarly, hints of this flat-tilted peak are
also seen in the spectrum at the earlier epoch of SN 2021aefx (see Kwok et
al., 2022). If real, this flat-tilted profile may extend from $\sim-1000$ km
s-1 to $\sim 2000$ km s-1. Similar to the [Ar III] $8.991$ $\mu$m line, the
flat-tilted profile of the [Co III] feature may imply a central hole of 56Ni
in the ejecta. This hole is smaller than that of Ar, and would only be a few
thousand km s-1 across (Telesco et al., 2015; Diamond et al., 2015). Note that
unlike Ar, which is produced by nuclear burning that has a steep temperature
dependence leading to a sharp cutoff in velocity extent and thus flat line
profiles, electron capture is nearly temperature independent, so its effects
follow the density profile leading to somewhat rounder line profiles. The
increase in flux across the [Co III] $11.888$ $\mu$m profile is 10%, the same
as that in the [Ar III] $8.991$ $\mu$m feature, implying the distribution of
the two elements are linked. Since Ar is produced at the edge of the 56Ni
region (see § 6), it is reasonable that Ar and Co have similar changes in flux
across their profiles. In § 6, we discuss the [Co III] $11.888$ $\mu$m line
profile in the context of off-center 56Ni distributions in the explosion.
However, in order to confirm that the [Co III] $11.888$ $\mu$m feature is
truly asymmetrical and off-center, higher resolution spectra are required
(such as those obtainable by the Medium Resolution Spectrograph (MRS) of
JWST/MIRI) and improved wavelength calibrations are also needed.

Figure 5: The [Co III] 11.866 $\mu$m line compared to a Gaussian fit. The
Gaussian peaks at $11.91\pm 0.01$ $\mu$m, $\sigma=0.19\pm 0.04$ $\mu$m, which
in velocity space corresponds to a peak at $740\pm 200$ km s-1 and
$\sigma=4840\pm 170$ km s-1.

###  5.3 Stable Ni

Figure 6: Velocity space profiles of the three spectral regions with prominent
Ni lines. Vertical lines indicate the ionization and line strength as in
Figure 3. The left panel shows the [Ni III] $7.349$ $\mu$m region is
contaminated by the [Ni I] $7.506$ $\mu$m feature. The right panel, centered
on the [Ni III] $11.002$ $\mu$m line, shows evidence for multiple stable Ni
lines contributing to the series of weak features and shoulders.

Multiple ionization states of Ni have forbidden emission lines which occur in
the MIR, making nebular phase MIR spectra an invaluable resource for probing
the explosion physics and corresponding nucleosynthesis of SNe Ia. Since the
56Ni that powers the early light curves of SNe Ia has a half life of $6.1$
days, any emission from Ni at these late phases comes from isotopes of stable
Ni (e.g. 58Ni) and not from radioactive isotopes like 56Ni. Figure 6 presents
three of these regions in velocity space. The left panel shows the [Ni III]
$7.349$ $\mu$m line, which appears to be red-shifted in velocity space with an
apparent maximum around $3000$ km s-1. However, this feature is blended with
[Ni I] $7.506$ $\mu$m, such that the velocity extent of [Ni III] $7.349$
$\mu$m appears to be larger than its true distribution. The middle panel shows
the [Ni III] $8.405$ $\mu$m line profile in velocity space, while the right
panel depicts the [Ni III] $11.002$ $\mu$m feature within a much larger series
of blended lines. At higher resolution these blends, including the $11.002$
$\mu$m line, are likely to be resolved.

##  6 Numerical Modeling and Implications for Explosion Scenarios

To explore the explosion physics of SN 2021aefx we turn to detailed
comparisons with NLTE radiation hydrodynamical models. The goals of these
comparisons are: (1) to demonstrate that MIR spectral features and line
profiles can be used as a critical tool to determine the explosion physics and
progenitor scenario of SNe Ia, (2) to show that JWST has opened up a new
frontier in MIR SN science and that there is a need to test and calculate
atomic models and processes, including cross sections to improve future
models. Specifically, we address how the data allows us to measure the mass of
the exploding WD, the chemical asymmetries in the initiation of the explosion,
and small-scale mixing processes in the ejecta. When taken in total, these
measurements allow us to determine the most likely explosion scenario of SN
2021aefx.

As discussed in § 5.3 and shown by Kwok et al. (2022), SN 2021aefx presents
many spectral lines of stable Ni (Figure 3). This Ni requires high-density
burning in the ejecta, above 5 $\times$ 108 g cm-3, which must originate from
a massive WD, making the explosion either a near-$M_{\text{Ch}}$ WD where the
explosion is triggered by compressional heating in the center of the
explosion, or the detonation of a high-mass, sub-$M_{\text{Ch}}$ larger than
1.15–1.2 $M_{\odot}$ (Hoeflich & Khokhlov, 1996; Höflich et al., 1998;
Seitenzahl & Townsley, 2017, but see also Blondin et al., 2022). Such massive
WDs can only be produced via accretion (Kippenhahn et al., 2013). Therefore,
we limit our comparisons to models within this region of parameter space.

###  6.1 Numerics

The simulations employ modules of the HYDrodynamical RAdiation (HYDRA) code.
HYDRA solves the time-dependent radiation transport equation (RTE) and
positron transport (Penney & Hoeflich, 2014), including the rate equations
that calculate the nuclear reactions based on a network with 211 isotopes and
statistical equations for the atomic level populations, the equation of state,
the matter opacities, and the hydrodynamic evolution as applied to SN 2020qxp
(Hoeflich et al., 2021; Hristov et al., 2021, and references therein).
Detailed atomic models and line lists are based on the database for bound-
bound transitions of van Hoof (2018)444Version v3.00b3,
https://www.pa.uky.edu/~peter/newpage/, supplemented by additional forbidden
lines from Diamond et al. (2015) and Telesco et al. (2015). For details on
modeling of nebular phase spectra with HYDRA, see Hoeflich et al. (2021), and
for more general discussions on modeling the nebular phase and downward
cascading of high-energy particles and photons by Monte Carlo, see also
Spencer & Fano (1954), Axelrod (1980), Kozma & Fransson (1992), Fransson
(1994), Mazzali et al. (2007), Mazzali et al. (2015), Fransson & Jerkstrand
(2015), Botyánszki & Kasen (2017), Wilk et al. (2018), Shingles et al. (2020),
and Wilk et al. (2020). The models include transitions for ionization stages
I-IV of C, O, Ne, Mg, Si, S, Cl, Ar, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, and Ni.
Though most of the prominent features in the MIR are caused by forbidden
lines, the underlying quasi-continuum is formed by allowed lines in the inner
layers well above the critical density. At these phases, the iron-rich layers
are still partially optically thick at UV wavelengths, meaning the inclusion
of permitted lines is important to fully characterize the ionization balance
via Rosseland cycles (Mihalas, 1978).

###  6.2 A Delayed-Detonation Model for SN 2021aefx

We compare SN 2021aefx to new simulations of off-center $M_{\text{Ch}}$ mass
explosion models, based upon the spherical model of the Model 25-series from
Hoeflich (2017), as it produces early light-curve properties and a maximum
light luminosity very similar to those of SN 2021aefx. These new simulations
are parameterized explosion models, using a spherical delayed-detonation to
constrain the global parameters of the explosion. Fine-tuning these models is
not necessary to achieve the goals of this study as we focus on spectra rather
than high-precision photometry. The model produces $\Delta m_{15}(V)=0.68$ mag
(for reference, $\Delta m_{15}(V)=0.64\pm 0.01$ mag for SN 2021aefx, which is
within the error of the model), and $\sim$0.6 $M_{\odot}$ of 56Ni.

The model originates from a C/O WD with a main-sequence progenitor mass of $5$
$M_{\odot}$, solar metallicity, and a central density $\rho_{c}=1.1\times
10^{9}$ g cm-3. We adopt this $\rho_{c}$ due to the line width and shape of
the [Co III] $11.888$ $\mu$m line and due to the strength of the stable Ni
lines in the MIR spectrum (see § 5.3). In this model, burning starts as a
deflagration front near the center and transitions to a detonation (Khokhlov,
1991b). The deflagration–detonation transition is triggered when the density
at the burning front drops below $2.5\times 10^{7}$ g cm-3, when $\sim 0.24$
$M_{\odot}$ of the material has been burned by the deflagration front, and is
induced by the mixing of unburned fuel and hot ashes (Khokhlov, 1991b). The
model has a magnetic field of B(WD) $=10^{6}$ G, which has been found in
magneto-hydrodynamical simulations, suggesting that turbulent magnetic fields
are produced during the deflagration phase (Diamond et al., 2018; Hristov et
al., 2021). The basic model parameters are given in Table 3.

Table 3: Model 25 Parameters  Parameter | Value
---|---
Mej |  $\sim$1.38 $M_{\odot}$
$\rho_{c}$ |  $1.1\times 10^{9}$ g cm-3
Mtr |  $0.24$ $M_{\odot}$
MDDT |  $0.5$ $M_{\odot}$
B(WD) |  $10^{6}$ G

####  6.2.1 Off-center 56Ni and Abundance Distributions

To investigate the line profiles and asymmetries, we consider the Model
25-series which includes off-center DDTs. For the construction of the off-
center DDT we follow the description of Livne (1999) that has also been
employed by Höflich et al. (2006), Fesen et al. (2015), Hoeflich et al.
(2021), and Hoeflich et al. (2023). The DDT is triggered at
$M_{\text{DDT}}=0.5$ $M_{\odot}$. Note that due to the buoyancy of flame
fronts in the explosion, the DDT can be triggered at a different mass
coordinate relative to the total integrated mass of the deflagration burning.
This leads to asymmetric abundance distributions of all elements produced
during the detonation phase (see Fig. 2 in Hoeflich et al., 2021).

In principle, the use of multiple resolved line profiles allows us to
determine the value of $M_{\text{DDT}}$ as well as the viewing angle. In the
case of SN 2021aefx we use the two strongest features: [Co III] $11.888$
$\mu$m and [Ar III] $8.991$ $\mu$m. As shown in Figure 4 we see a consistent
tilt in the [Ar III] and [Co III] lines. We can determine the viewing angle
from the tilt of these features. The value of $M_{\text{DDT}}$ determined here
was also consistent with the spectrophotmetric observations of the normal SN
Ia 2019np (Hoeflich et al., 2023). Most normal SNe Ia have very similar
polarization properties (Cikota et al., 2019).

####  6.2.2 Overall Abundance Distribution

The angle-averaged abundance structure and the 56Ni distribution of Model 25
are shown in Figure 7. In the model, the region of high electron capture is
spherical because we assume central ignition, no fragmentation during the 56Ni
decay over the first week after the explosion (e.g. Fesen et al., 2015), and
that Rayleigh-Taylor instabilities are largely suppressed by high magnetic
fields (Hristov et al., 2018). The most notable results in the abundance
distribution are: (1) $\sim 6\times 10^{-2}$ $M_{\odot}$ of 58Ni is produced
in the center of the ejecta, (2) the velocity extent of the central hole in
56Ni is $\sim 3200$ km s-1, (3) the velocity extent of the 56Ni region
produced in NSE ranges from $\sim 3200$ – $10000$ km s-1, and (4) the size of
the shell of the Ar region covering a range of $\sim 8000$ – $15000$ km s-1.
We note that simulating the point of the DDT in multi-dimensions does not lead
to a strong rarefaction wave (Gamezo et al., 2005; Fesen et al., 2015) as seen
in all spherical delayed-detonation models (Khokhlov, 1991b; Höflich et al.,
2002; Hoeflich et al., 2021).

The off-center DDT at a point in an already-expanding medium results in a run-
time effect which yields an asymmetric distribution of burning products. The
material closer to the DDT burns under higher density than the opposite side
because the front reaches the corresponding layer $0.5-1$ s later. The result
is a bulge of all elements that undergo only Si and O burning including Ca,
Ar, and 56Ni (see Figure 7). For a more complete depiction of this, see Fig. 7
of Fesen et al. (2007). These asymmetries are aligned along the axis defined
by the center and the DDT ignition point.

Figure 7: (Left:) The chemical composition of our best fit model, Model 25
from Hoeflich et al. (2017) and Hoeflich et al. (2023). The model has a
chemically stratified ejecta. EC elements (e.g. 58Ni with M(58Ni) $\approx
5.9\times 10^{-2}$ $M_{\odot}$) are located in the center of the ejecta,
followed by 56Ni further out in velocity space. The Ar distribution goes
between $8000$ – $15000$ km s-1 and the lightest elements (e.g. O and C) are
located in the outermost layers. For illustration, the thin red line at
expansion velocities larger than $3200$ km s-1 shows the EC distribution after
microscopic mixing applied (see text). (Right:) The distribution of the IGEs
of the off-center delayed detonation Model 25 at a point (black dot). The bulk
of the 56Ni is in a ring-like structure between $3000$ – $9500$ km s-1 as well
as a bulge produced at the point of the delayed detonation transition.
Depending upon the viewing angle, differently shaped line profiles will be
produced in the [Co III] feature. These profiles are shown in Figure 8.

###  6.3 Spectral Modeling

####  6.3.1 Determining the Inclination Angle

We begin our discussion of Model 25’s fit to the observations by illustrating
its ability to determine the inclination angle of the explosion relative to
our line of sight. Remember that to first order, the [Co III] profile can be
fit with a Gaussian of a half-width $\approx 4800$ km s-1, emission wings
ranging from $-10000$ – $+10000$ km s-1, and an offset from the rest
wavelength of $+740$ km s-1 (see § 5 and Figure 5). This is consistent with
the overall 56Ni distribution seen in the model (see Figure 7), but we note
that assuming an emission feature is a Gaussian makes an implicit assumption
about the underlying chemical distribution of an element within the ejecta,
and should be used with caution. As previously discussed, the host galaxy is
seen face on and has a very small projected rotation ($65\pm 60$ km s-1),
implying that host rotation plays a minor role in this offset. This leaves the
peculiar motion of the progenitor system and the orbital velocity of the
progenitor as remaining potential sources of this offset. However, if these
were the dominant factors, one would expect a consistent velocity offset in
all of the spectral lines, contrary to observations.

On the other hand, the observed flux in the [Co III] $11.888$ $\mu$m line
center changes by $\sim 10\%$ across the peak of the feature (see § 5),
consistent with expectations of flux arising from the asymmetric ejecta of an
off-center DDT model when viewed from a specific angle (Hoeflich et al.,
2021). As previously shown in § 5, the [Co III] $11.888$ $\mu$m feature
appears to show a flat-tilted profile, where the velocity extent of the
central tilted region corresponds to the region in velocity space of partial
burning in quasi-statistical equilibrium (QSE) ($\approx 1800$ km s-1 across
in the angle averaged spectrum). This flat-tilted profile is seen in both the
$+255$ and $+323$ day JWST spectra. In Model 25, the inner size of the
electron capture region and the distribution of 56Ni produce different line
profiles when viewed at different angles. Three specific viewing angles,
$-90^{\circ}$, $-30^{\circ}$ and $+30^{\circ}$ are shown in Figure 8. From the
bottom left panel, we see that the observations are well matched by a viewing
angle of $\approx-30^{\circ}$, including replicating the $\sim 10\%$ change in
flux across the peak seen in the observations. While the high signal-to-noise
(S/N $\approx 100$) of both JWST spectra of SN 2021aefx suggests that the
flat-tilted profile is real and significant, future planned observations with
JWST/MIRI MRS (JWST-GO-2114, PI: Ashall) will better resolve the line
profiles.

Figure 8: Top Left: Comparison of the [Co III] $11.888$ $\mu$m line profile at
$+255$ (dashed grey) and $+323$ days (solid black). Top Right: Dependence of
the [Co III] $11.888$ $\mu$m line profile as a function of inclination in
comparison with the $+323$ day spectrum (solid black). Note that the profile
and the red-shift of the observed peak are consistent with the off-center DDT
model seen at $-30^{\circ}$ (bottom left) and the $-30^{\circ}$ model is also
the best fit to both observations (bottom right).

####  6.3.2 Overall MIR Spectra

Figure 9: Comparison of the synthetic MIR spectrum of the off-center Model 25
seen from $-30^{\circ}$ without (blue) and with (red) mixing of the EC
elements (see Figure 6) and the JWST/MIRI LRS spectrum of SN 2021aefx at
$+255$ (dashed grey) and $+323$ (solid black) days relative to $B$-band
maximum. The angle-averaged spectra would look similar, but they would show a
flat-topped rather than a flat-tilted [Ar III] $8.991$ $\mu$m feature. Though
[Ni II] lines are present in both the synthetic spectra, the sensitivity to
microscopic mixing should be noted. In particular, the [Ni II] 6.6 $\mu$m line
shows a strong variation with mixing (see text).

Having determined the inclination angle, we now compare our full model
spectrum to our observations, as seen in Figure 9. Model spectra are shown
with and without mixing of electron capture elements on the scale of the
pressure scale height of the WD (Höflich & Stein, 2002). We examine
microscopic mixing (i.e. smaller than the mean free path of the positrons) in
the center of the explosion to constrain the position (e.g. central, off-
center, or multi-spot) of the thermonuclear runaway ignition (Niemeyer et al.,
1996; Höflich & Stein, 2002; Calder et al., 2004; Livne et al., 2005; Röpke et
al., 2007; Ma et al., 2013).

The most dominant lines produced by the models are shown in Table 2, and have
been successfully identified in Figure 3. For NIR lines outside the observed
range, see Appendix A. Identification of weaker lines within the spectrum will
be possible after the acquisition of MIRI/MRS data.

The model reproduces the observations overall, including all four regions of
prominent spectral lines and does especially well in reproducing the blends of
the $6.0-8.0$ $\mu$m and $8.0-9.5$ $\mu$m regions in addition to the [Co III]
$11.888$ $\mu$m line. While the exact contribution of each ion may vary with
the underlying explosion model, the synthetic spectra have been obtained
without further tuning and in general are in good agreement with the
observations. The similarity between the mixed and unmixed model shows the
stability of the synthetic spectral features.

Most of the Ni features are in blends with other iron-group elements of
similar strengths. In light of uncertainties in the atomic models and cross
sections, the photons at a given wavelength may couple to elements other than
Ni (through fluorescence; Morrison & Sartori, 1966). Thus, many of the line
IDs of weaker features in low resolution spectra are model dependent. The
easiest way to separate the elements is by comparing the mixed and unmixed
models. In the unmixed models, the electron capture elements are effectively
shielded from non-thermal excitations from radioactive decay, thus the
electron capture features will be weaker. Features dominated by Ni show
variations in the region between $6.4$ – $8.5$ $\mu$m and weak variation at
longer wavelengths, for example at $10.5$ $\mu$m.

One major effect of mixing can be seen in the $6.5$ – $7.4$ $\mu$m region. In
the unmixed models, EC and radioactive elements are mostly separate, leading
to weak spectral features. This due to the locally trapped positrons
dominating the excitation in the EC region, with $\gamma$-rays responsible for
$\sim 10\%$ of the excited ions (Penney & Hoeflich, 2014). In turn,
microscopic mixing produces narrow features, for example, [Ni II] at $6.636$
$\mu$m has a half-width of $\approx 4000$ km s-1 determined by the numerical
resolution. In contrast, the observed broad features suggest a central
ignition of the WD.

The broad feature at $\sim 9.0$ $\mu$m dominated by Ar is a strong diagnostic
of the point of the transition from the deflagration to the detonation. Ar is
located in a shell with a large central hole because it is destroyed in
moderately high density burning environments ($\rho\gtrsim 1-2\times 10^{7}$ g
cm-3). Our model (Figure 8) is consistent with the estimates for the minimum
Ar velocity, strongly suggesting a high mass WD. The [Ar III] $8.991$ $\mu$m
feature shows the same slope as the [Co III] $11.888$ $\mu$m, providing
evidence of an off-center DDT.

Line profiles are strongly affected by the ionization balance. Typically for
normal SNe Ia at this phase, iron group elements are dominated by doubly
ionized ions, and the ionization fraction decreases with increasing density
because the recombination rate scales with the square of the density. Only in
the center do we see effects at the 10% level of singly ionized iron group
elements that produce a strong resonance [Ni I] feature at $\approx 3$ $\mu$m
(Kwok et al., 2022; Fisher, 2022). In the line forming regions, the ionization
balance hardly changes. Therefore, our results are insensitive to the
differences in the ionization structure. More detailed discussions are given
in Hoeflich et al. (2021), Wilk et al. (2020), and § 6.1.

In the synthetic spectrum, the feature at $\sim 11.9$ $\mu$m agrees well with
the observations, it is dominated by [Co III] $11.888$ $\mu$m and has minor
line blends of [Ni I] $12.001$ $\mu$m and [Co I] $12.255$ $\mu$m in the red
wing at the 1% level relative to the [Co III] peak (see the line strengths
given in Table 2).

However, our models tend to show features from singly ionized elements that
are too strong by about $10-20$% as can be seen from the ratio of the [Co III]
$11.888$ $\mu$m and the [Co II] $10.523$ $\mu$m plus [Ni II] $10.682$ $\mu$m
blend. The discrepancies in the ionization balance are not unexpected, due to
uncertainties in the atomic data and the $\sim 2-5$% accuracy of the flux
calibration of the observed spectrum (see § 3). Uncertain ionization and
excitation by non-thermal leptons and uncertainties in the recombination rates
lead to ionization balance uncertainties. Though we treat the cascades in
energy within our Monte-Carlo scheme, missing and uncertain atomic levels are
likely responsible for some of the discrepancies (Wilk et al., 2018; Shingles
et al., 2020, and see Appendix A of Hoeflich et al., 2021).

Finally, we discuss other observables obtainable at a higher spectral
resolution that may support our interpretation. Off-center delayed-detonation
models predict an offset between electron capture elements (e.g., 58Ni)
produced during the deflagration phase and elements (e.g., 56Ni, Fe, Co, Si,
S, Ar) synthesized during the detonation. The former are created in a subsonic
deflagration resulting in a slow pre-expansion phase of the WD with an almost
spherical density structure, whereas the latter are formed in a weak
detonation with a burning speed close to the speed of sound. This offset may
be seen with higher-resolution spectra.

Note that the unresolved small flux variations near 11 $\mu$m and in the
wavelength range $12-14$ $\mu$m seen in MIR spectra are at a $1\sigma$ level
which, if confirmed by MRS spectra, have important implications. The
computational results indicate that these small variations signal the presence
of a caustic structure in density and abundance of the inner electron-capture
core as has been observed by Fesen et al. (2007) and Fesen et al. (2015). At
this epoch, positrons remain local for the high $B$-field required (Penney &
Hoeflich, 2014; Hristov et al., 2021; Mera Evans et al., 2022).

###  6.4 Alternative Explosion Scenarios

A detailed discussion of explosion scenarios and progenitor systems of SNe Ia
is beyond the scope of this work. For reviews, we refer to Alsabti & Murdin
(2017) and Hoeflich et al. (2021). The total mass of the exploding WD is one
of the parameters separating different explosion scenarios such as He-
triggered detonations of sub-$M_{\text{Ch}}$, dynamical mergers, violent
mergers, collisions of two WDs in a triple system, and $M_{\text{Ch}}$
explosions. Dynamical mergers go through a loosely bound hydrostatic WD state
and are unlikely to synthesize EC elements because the peak density during
merging is too low (Benz et al., 1990; García-Berro et al., 2017). Collisions
of two WDs may result in high density burning, high masses, and may produce EC
elements; but also produce large polarization signatures and a $90^{\circ}$
flip in the polarization angle (Höflich, 1995; Bulla et al., 2016), both of
which are not observed in any SNe Ia (Cikota et al., 2019). Similarly, violent
mergers would be expected to yield high continuum polarization ($\sim 1$%) at
$\sim 10$ days before the $B-$band maximum light (Bulla et al., 2016), which
is also not seen in observations (Yang et al., 2020; Patra et al., 2022).

Therefore, we focus on sub-$M_{\text{Ch}}$ He-triggered detonations of C/O WDs
as an alternative viable candidate to produce SN 2021aefx. For normal SNe Ia
sub-$M_{\text{Ch}}$ models have WD masses of $1$ – $1.05$ $M_{\odot}$ and for
bright SNe Ia they have WD masses up to 1.1 $M_{\odot}$ (Shen et al., 2018;
Blondin et al., 2022).

Stable Ni has been identified in observations of several SN Ia based upon
heavily blended optical and NIR features (e.g. Maguire et al., 2018; Mazzali
et al., 2020); however, the Ni in these features is never the dominant line.
The 1.94 $\mu$m [Ni II] line may also be present in some SNe Ia (Friesen et
al., 2014; Dhawan et al., 2018; Hoeflich et al., 2021). However, this line is
located at the edge of a telluric region, and with different reductions of the
same data it has not been seen (see e.g. Dhawan et al. 2018; Diamond et al.
2018). Stable Ni has also been identified in the MIR spectra of some SNe Ia
(Gerardy et al., 2007; Telesco et al., 2015), albeit at low S/N. However, JWST
spectra firmly establish the presence of stable Ni in SN 2021aefx through
multiple ionization states which are the dominant ions in their features; thus
affirming that stable Ni exists in at least some SNe Ia (Kwok et al., 2022).
The presence of EC elements strongly suggest a high mass progenitor even
within He-triggered detonations.

In the absence of detailed spectral models, we use as guide the 58Ni mass,
$\approx 5.9\times 10^{-2}$ $M_{\odot}$ obtained in our simulations. Although
the overall abundance and density structures of various scenarios are similar,
we note that the actual value of 58Ni depends on details of the structure and,
possibly, microscopic mixing. For a $M_{\text{Ch}}$ progenitor, strong
microscopic mixing can be excluded because it destroys the spectral fits
(Figure 9). We note that even larger uncertainties in M(58Ni) can be expected
in 1-zone models (Flörs et al., 2020) because they do not take into account
variations in the chemical or density distributions in the inner layers and
assume that each ion has a free density, meaning that the ionization balance
and level populations are not calculated self-consistently. Homogeneous
abundances are unlike typical explosion models for SNe Ia, and would require
artificial mixing not to be expected in pure detonations. For a
sub-$M_{\text{Ch}}$ explosion, the EC and 56Ni region are produced in-situ,
and show boosted stable Ni line strengths but would not produce the asymmetric
line [Ar III] and [Co III] profiles nor the correct width of [Co III] feature.
All three of these considerations point to a high likelihood of SN 2021aefx
originating from a $M_{\text{Ch}}$ explosion.

Stable Ni is produced in NSE by shifting the ratio $Y_{e}$ from $\approx 0.5$
to a lower value either by electron-capture under high density burning or in a
WD with super-solar metallicities, as a result of an initial high 22Ne
abundance (see, for example, Brachwitz et al., 2000; Timmes et al., 2003;
Thielemann et al., 2018). Gronow et al. (2021) simulate a variety of He-
detonation explosions at various metallicities, with various He-shell masses.
They find that super-solar metallicities produce EC elements due to the
decrease $Y_{e}$ from the presence of neutron-rich 22Ne. Gronow et al. (2021)
find that WDs with masses of $\sim 1.1$ $M_{\odot}$ and primordial metallicity
3$Z_{\odot}$ produce $0.046$ $M_{\odot}$ of stable Ni, and the amount of 58Ni
sufficient to produce the strong Ni features observed in SN 2021aefx. However,
since this result is due to the primordial metallicity of the WD, which
reduced the $Y_{e}$ uniformly throughout the WD — the full half-width of the
[Co III] line and of the Ni features should be comparable because both 56Ni
and 58Ni are formed in the same NSE region and constant $Y_{e}$ results in a
constant isotopic ratio. Future MIRI/MRS observations will be able to resolve
the Ni lines and accurately measure its elemental distribution. In particular,
in these sub-$M_{\text{Ch}}$ models the [Ni IV] should be broad as the high
ionization stage will occur in the low-density, high-velocity region of the
envelope because the recombination rates scale with the density squared
(Osterbrock & Ferland, 2006). Moreover, the model that produces the large 58Ni
abundance requires of a He shell of $0.02$ $M_{\odot}$. Finally, if large
stable Ni abundances are ubiquitous to all SNe Ia, within the
sub-$M_{\text{Ch}}$ paradigm it would require all of them to have super-solar
metallicity, which is unlikely.

Based on recent 3D simulations for solar metallicities, Boos et al. (2021)
showed that a thin He-triggered detonation in a $1.1$ $M_{\odot}$ C/O WD may
produce $0.02$ $M_{\odot}$ of stable Ni, an amount that is insufficient to
explain the observed NIR features from stable Ni (see Wilk et al., 2020).555
Blondin et al. (2022) claim that sub-$M_{\text{Ch}}$ models with $M>1$
$M_{\odot}$ can produce the NIR [Ni II] lines at late times. They argue that
the lack of [Ni II] in the NIR at earlier times can be simply an ionization
effect, with the mixing of radioactive products into the EC region
dramatically reducing the strength of [Ni II], thus, providing an option for
the absence of the observed NIR [Ni II] feature. This explanation is, however,
inconsistent with the fact that in SN 2021aefx many ionization stages of Ni
are observed.

For both sets of He-det simulations discussed above, the mass of the outer He
layers may also be inconsistent with recent limits from other early-time
normal SNe Ia spectra that show carbon in the outer $2-5\times 10^{-3}$
$M_{\odot}$ (Yang et al., 2020; Hoeflich et al., 2023). Furthermore, thin He-
detonation models have nearly spherical 56Ni distributions (Fesen et al.,
2007; Hoeflich et al., 2023), which contradict the observation of SN 2021aefx.

Lacking advanced He-triggered detonation models, we focus on spherical
explosion models with sub-$M_{\text{Ch}}$ cores such as DET2 (Hoeflich &
Khokhlov, 1996). This model has a pure C/O WD without a He surface layer. It
originates from a WD whose mass is 1.2 $M_{\odot}$, and produces a sufficient
amount of EC material. Strict limits on the WD mass and the density of the
central region can be obtained from both the [Ar III] $8.991$ $\mu$m and [Co
III] $11.888$ $\mu$m features. In particular, a tight mass limit on the WD can
be obtained via the width of the flat-top component of the [Ar III] $8.991$
$\mu$m feature. The observed edge of the Ar profiles implies a central hole of
Ar between $\sim 0-8000$ km s-1 (see Figure 4). However, DET2 produces an
inner hole of Ar of $6000$ km s-1. This is $2000$ km s-1 lower than observed.
To produce a wider flat-topped Ar feature requires a higher mass WD. In a high
mass model (such as a near $M_{\text{Ch}}$ explosion), the Ar hole extends
further out in velocity space.

We note that, as an upper limit, detonating a WD with an ejecta mass of 1.38
$M_{\odot}$ would mostly produce 56Ni and few QSE elements, resulting in a SN
that produced too much 56Ni, is too bright at maximum light, and has spectra
that are inconsistent with a typical SN Ia (Hoeflich et al., 1996; Marquardt
et al., 2015).

The velocity extent of the Ar hole would require a C/O WD of $\approx 1.24$
$M_{\odot}$ from HYDRA simulations. From stellar evolution (Straniero et al.,
2016), a maximum mass of a C/O core of 1.2 $M_{\odot}$ is produced by stars
with a main sequence mass of $\approx 8$ $M_{\odot}$. For more massive
progenitors, burning continues beyond He, resulting in O/Ne/Mg WDs and a core
collapse SN (see, for example Woosley & Baron, 1992). Alternatively, O/Ne/Mg
WDs that accrete material from a companion end their lives in accretion-
induced collapse (AIC) to a neutron star (Woosley & Baron, 1992; Wasserburg et
al., 1996) because compression will not reach temperatures in excess of
$\approx 3\times 10^{9}$ K needed to trigger explosive O-burning. In the case
of C/O detonation produced via an external trigger (Rosswog et al., 2009b,
i.e. disruption by a black hole;), thermonuclear burning would result in a
low-velocity explosion with expansion velocities smaller by a factor of $2-3$
compared to typical SNe Ia (Hoeflich, 2017). Thus, such C/O WDs can only be
produced via accretion over a long time (Kippenhahn et al., 2013). This is,
however, inconsistent with the progenitor evolution channel commonly assumed
for He-shell detonations (Woosley et al., 1980; Nomoto, 1982; Hoeflich &
Khokhlov, 1996; Shen et al., 2018).

##  7 Conclusion

The successful launch of JWST heralds a new era in our understanding of the
physics of thermonuclear supernovae. Late nebular phase MIR studies of SNe Ia
are now possible thanks to JWST’s impressive sensitivity, obtaining spectra
with higher S/N and higher resolution than any prior MIR observatory capable
of observing SNe Ia.

Here, we present a JWST/MIRI LRS spectrum of SN 2021aefx at $+323$ days after
maximum light obtained through JWST program GO-JWST-2114 (P.I: C. Ashall). We
show how a single spectrum can be used to extract previously unavailable
information about SNe Ia. We demonstrate how by combining JWST data with
spectral models the nature of these important astrophysical objects can be
determined. Below, we highlight our most important results:

  * •

The observed spectrum of SN 2021aefx is linked to the physics of SNe Ia
through the construction of multi-dimensional radiation hydrodynamical NLTE
models. We show that the spectrum and line profiles can be understood within
the context of a delayed-detonation $M_{\text{Ch}}$ model that produced an
asymmetric 56Ni distribution originating from a WD with a central density of
$\rho_{c}\approx 1.1\times 10^{9}$ g cm-3. Although it is at the brighter end
of the distribution, the model for SN 2021aefx fits within the model series,
which reproduces the light curves, the luminosity-width relation, and spectra
of typical SNe Ia (§ 6.2).

  * •

These models are used to identify the spectral lines which comprise the main
features seen in the observed spectrum. The main lines we identify include:
[Co III] $11.888$ $\mu$m, [Ar III] $8.991$ $\mu$m, [Ni IV] $8.945$ $\mu$m, [Ni
I] $7.507$ $\mu$m, and [Ni III] $7.349$ $\mu$m. Weaker identifiable blends
include lines of: [Ar II], [Fe II], [Fe III], [Co II], and [Ni II] (see § 2).

  * •

The presence of multiple Ni lines in the observed spectrum demonstrates that
electron capture elements (e.g. 58Ni) are present in the inner region of SN
2021aefx. Significant amounts of these elements can only be produced by high-
density burning (above $5\times 10^{8}$ g cm-3). These densities are found in
C/O WDs with masses above $\sim$ 1.2 $M_{\odot}$. Such massive WDs must be
produced via accretion (see § 5).

  * •

We find evidence for no, or very limited, mixing on microscopic scales between
the electron capture elements and the 56Ni region in the ejecta. In the
context of near $M_{\text{Ch}}$ models this suggests a central point of
ignition (see § 6.3.2). Our simulations of SN 2021aefx suggest that $\sim
0.06$ $M_{\odot}$ of stable Ni was produced in the explosion. In fact, since
the synthetic Ni lines appear slightly too weak (Figure 9), we may need
slightly more stable Ni than our simulations imply. The inclusion of mixing
would not result in better agreement between the model and observations, as it
would alter the ionization balance of the Ni lines.

  * •

Both the [Co III] $11.888$ $\mu$m and [Ar III] $8.991$ $\mu$m features show
flat-tilted profiles, which vary by 10% in flux across their peaks (see § 5).
These profiles are consistent with a central hole in the corresponding element
distributions. The profiles also indicate that the explosion is seen at an
inclination of $-30^{\circ}$ relative to the point of the deflagration to
detonation transition (see § 6.3.1).

  * •

We demonstrate how a flat-tilted profile can be used as a tool to determine
the electron capture element and Ar distribution within the ejecta. The length
of the flat-top component corresponds to the Doppler shift of the inner hole
in the element distribution and the measured velocity extent corresponds to
the average projected expansion velocity of the hole (see § 5.1).

  * •

By combining information on both the strength and profiles of the Ar and
stable Ni features, we show that SN 2021aefx was most likely produced from a
C/O WD with a mass $>1.2$ $M_{\odot}$. This makes a He-detonation
sub-$M_{\text{Ch}}$ explosion an unlikely candidate for this SN. SN 2021aefx
appears to be a normal SN Ia with typical light curves and spectra. We cannot
rule out supersolar metallicity in sub-$M_{\text{Ch}}$ WDs as an alternative
option to produce EC elements in SN 2021aefx, but such models would not
produce a large enough hole in the Ar region or the line profiles to reproduce
the observations of SN 2021aefx. Furthermore, we regard a He-detonation as
unlikely, due to the fact that they produce spherical cores (e.g. 56Ni
distributions) which are not seen in SN 2021aefx, and are also inconsistent
with the carbon-rich surfaces commonly seen in normal SNe Ia (see § 6.4).

Although the data presented in this work have larger errors in wavelength
calibration than anticipated, most aspects of the physical interpretation
present here are insensitive to this error. For example, the off-center nature
of the DDT is driven by the shape of the line profiles. Moving forward,
improved wavelength calibration from the JWST pipeline, additional MIRI/LRS
data (from program 2072; P.I: S. Jha), and future MIRI/MRS data (from program
2114; P.I: C. Ashall) will allow us to further constrain the physics of SN
2021aefx and other SNe Ia, and can validate our interpretation. In particular,
MIRI/MRS observations will improve the precision of the data by probing the SN
ejecta to scales smaller than $\sim 100$ km s-1 which is essential. This MRS
data will also extend to longer wavelengths ($\sim 20$ $\mu$m) revealing
different lines and ions, as well as allowing us to identify weaker features
by resolving many of the blends seen in the LRS spectra. It will also open a
new window to probe for smaller-scale effects such as mixing and positron
transport within the ejecta at later times.

Overall, this work demonstrates the ability and potential that JWST MIR
spectral observations have to provide previously inaccessible information to
the scientific community. This new information will allow us to determine the
progenitor scenario and explosion mechanism(s) of SNe Ia. As the sample size
of MIR spectra grows over the coming years we will be able to look for
diversity within the SNe Ia population.

JD, CA, PH, and EB acknowledge support by NASA grant JWST-GO-02114.032-A.
Support for program #2114 was provided by NASA through a grant from the Space
Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127.
PH acknowledges support by the National Science Foundation (NSF) through grant
AST-1715133. EB acknowledges support by NASA grant 80NSSC20K0538. This
publication was made possible through the support of an LSSTC Catalyst
Fellowship to KAB funded through Grant 62192 from the John Templeton
Foundation to LSST Corporation. The opinions expressed in this publication are
those of the author(s) and do not necessarily reflect the views of LSSTC or
the John Templeton Foundation. ID acknowledges partial support by the Spanish
project PID2021-123110NB-100 financed by
MCIN/AEI/10.13039/501100011033/FEDER/UE. LG acknowledges financial support
from the Spanish Ministerio de Ciencia e Innovación (MCIN), the Agencia
Estatal de Investigación (AEI) 10.13039/501100011033, and the European Social
Fund (ESF) "Investing in your future" under the 2019 Ramón y Cajal program
RYC2019-027683-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. The research of YY is supported through a Bengier-Winslow-
Robertson Fellowship. SWJ and LAK acknowledge support by NASA grant JWST-
GO-02072.001 and NASA FINESST fellowship 80NSSC22K1599. This work is based on
observations made with the NASA/ESA/CSA James Webb Space Telescope. The data
were obtained from the Mikulski Archive for Space Telescopes at the Space
Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127
for JWST. These observations are associated with program #2114. The specific
observations analyzed in this work can be accessed via
https://doi.org/10.17909/6fjc-sx91 (catalog DOI: 10.17909/6fjc-sx91).

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##  Appendix A Near-Infrared Line Identifications from Model 25

Table 4: Near-Infrared Model Line Identifications

S |  $\lambda$ [$\mu$m ] | Ion | S |  $\lambda$ [$\mu$m ] | Ion | S |  $\lambda$ [$\mu$m ] | Ion | S |  $\lambda$ [$\mu$m ] | Ion | S |  $\lambda$ [$\mu$m ] | Ion
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
$*\ *$ | $2.211$ | [Fe II] | $*\ *\ *$ | $2.478$ | [Fe II] | $*$ | $2.935$ | [Co II] |  | $3.169$ | [Fe III] | $*\ *\ *$ | $4.076$ | [Fe II]
$*\ *\ *$ | $2.219$ | [Fe III] | $*$ | $2.479$ | [Ni II] | $*$ | $2.954$ | [Co I] |  | $3.185$ | [Fe III] | $*$ | $4.077$ | [Fe III]
$*$ | $2.219$ | [Fe III] |  | $2.481$ | [Co I] | $*\ *$ | $2.961$ | [Fe II] | $*$ | $3.187$ | [Co II] | $*\ *$ | $4.082$ | [Fe II]
$*\ *\ *$ | $2.243$ | [Fe III] |  | $2.493$ | [Fe III] |  | $2.963$ | [Fe III] | $*\ *\ *$ | $3.230$ | [Fe III] |  | $4.108$ | [Co I]
$*$ | $2.243$ | [Fe III] |  | $2.506$ | [Co I] |  | $2.965$ | [Fe III] |  | $3.230$ | [Fe III] | $*\ *\ *$ | $4.115$ | [Fe II]
$*\ *\ *$ | $2.244$ | [Fe II] | $*\ *$ | $2.515$ | [Fe II] |  | $2.966$ | [Fe III] | $*$ | $3.239$ | [Co II] | $*$ | $4.307$ | [Co II]
$*\ *$ | $2.257$ | [Fe II] | $*$ | $2.526$ | [Co I] |  | $2.987$ | [Fe III] |  | $3.242$ | [Fe III] |  | $4.340$ | [Co I]
$*\ *$ | $2.267$ | [Fe II] | $*$ | $2.531$ | [Co II] |  | $3.006$ | [Co I] |  | $3.286$ | [Co II] |  | $4.357$ | [Fe III]
$*\ *$ | $2.281$ | [Co III] |  | $2.570$ | [Fe III] |  | $3.012$ | [Co II] |  | $3.332$ | [Co I] |  | $4.357$ | [Fe III]
$*$ | $2.282$ | [Co II] |  | $2.581$ | [Co I] | $*$ | $3.014$ | [Co III] |  | $3.353$ | [Co I] | $*$ | $4.410$ | [Co II]
| $2.284$ | [Co I] | $*$ | $2.601$ | [Co II] | $*$ | $3.014$ | [Co II] | $*$ | $3.394$ | [Ni III] | $*\ *$ | $4.435$ | [Fe II]
| $2.285$ | [Co I] | $*$ | $2.652$ | [Co I] |  | $3.017$ | [Fe III] |  | $3.471$ | [Co I] | $*$ | $4.520$ | [Ni I]
| $2.297$ | [Co I] |  | $2.686$ | [Co I] |  | $3.018$ | [Fe III] | $*$ | $3.492$ | [Co III] | $*\ *\ *$ | $4.608$ | [Fe II]
$*\ *$ | $2.309$ | [Ni II] | $*$ | $2.692$ | [Co II] | $*$ | $3.031$ | [Co I] |  | $3.498$ | [Fe III] | $*$ | $4.672$ | [Fe II]
| $2.316$ | [Co I] | $*\ *$ | $2.717$ | [Fe III] | $*\ *\ *$ | $3.044$ | [Fe III] | $*$ | $3.630$ | [Co II] | $*$ | $4.788$ | [Ni I]
$*$ | $2.335$ | [Ni II] |  | $2.717$ | [Fe III] |  | $3.044$ | [Fe III] | $*$ | $3.633$ | [Co I] |  | $4.860$ | [Fe III]
| $2.348$ | [Co I] |  | $2.726$ | [Co I] |  | $3.046$ | [Co I] |  | $3.647$ | [Co I] | $*\ *\ *$ | $4.889$ | [Fe II]
$*\ *\ *$ | $2.349$ | [Fe III] | $*$ | $2.767$ | [Co II] |  | $3.061$ | [Co I] |  | $3.655$ | [Co I] |  | $5.054$ | [Co I]
$*$ | $2.349$ | [Fe III] |  | $2.833$ | [Co I] |  | $3.063$ | [Fe III] | $*$ | $3.659$ | [Co II] | $*\ *$ | $5.062$ | [Fe II]
$*$ | $2.361$ | [Ni II] | $*$ | $2.839$ | [Co II] |  | $3.085$ | [Fe III] | $*$ | $3.705$ | [Co II] |  | $5.164$ | [Co I]
$*\ *$ | $2.370$ | [Ni II] | $*$ | $2.848$ | [Co II] |  | $3.085$ | [Fe III] |  | $3.738$ | [Co I] | $*$ | $5.180$ | [Co II]
$*\ *\ *$ | $2.371$ | [Fe II] | $*$ | $2.871$ | [Co I] |  | $3.095$ | [Fe III] |  | $3.750$ | [Co I] | $*\ *$ | $5.187$ | [Ni II]
| $2.411$ | [Fe III] | $*\ *\ *$ | $2.874$ | [Fe III] |  | $3.097$ | [Fe III] | $*$ | $3.752$ | [Co II] |  | $5.211$ | [Co I]
$*$ | $2.414$ | [Co I] |  | $2.874$ | [Fe III] |  | $3.100$ | [Fe III] |  | $3.771$ | [Co I] | $*\ *\ *$ | $5.340$ | [Fe II]
| $2.447$ | [Fe III] | $*$ | $2.889$ | [Co II] | $*$ | $3.100$ | [Co II] | $*$ | $3.802$ | [Ni III] | $*\ *$ | $5.674$ | [Fe II]
$*$ | $2.453$ | [Fe III] | $*\ *\ *$ | $2.905$ | [Fe III] |  | $3.120$ | [Co I] |  | $3.823$ | [Co I] | $*\ *$ | $5.704$ | [Co II]
| $2.453$ | [Fe III] |  | $2.905$ | [Fe III] | $*\ *\ *$ | $3.120$ | [Ni I] | $*$ | $3.849$ | [Co II] | $*\ *$ | $5.893$ | [Ni I]
$*\ *$ | $2.474$ | [Co III] | $*\ *$ | $2.911$ | [Ni II] |  | $3.129$ | [Fe III] |  | $3.877$ | [Co I] | $*$ | $5.940$ | [Co II]
$*$ | $2.477$ | [Co II] | $*$ | $2.933$ | [Co II] | $*$ | $3.151$ | [Co II] | $*\ *$ | $3.952$ | [Ni I] | $*$ | $5.953$ | [Ni II]

Note. — For each transition, the markers correspond to strong ($*\ *\ *$),
moderate ($*\ *$), weak ($*$), and scarcely detectable ( ) on top of the
quasi-continuum formed by a large number of lines. The relative strength S is
estimated by the integral over the envelope, $\int{A_{ij}n_{j}\,dV}$ where
$n_{j}$ is the particle density of the upper level.