11institutetext:  Institut d’Astrophysique de Paris, CNRS-Sorbonne Université,
98 bis boulevard Arago, F-75014 Paris, France 22institutetext: Institut
d’Estudis Espacials de Catalunya (IEEC), Gran Capità, 2-4, Edifici Nexus,
Desp. 201, E-08034 Barcelona, Spain 33institutetext: Institute of Space
Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, E-08193
Barcelona, Spain 44institutetext: Argelander Institut für Astronomie, Auf dem
Hügel 71, DE-53121 Bonn, Germany 55institutetext: Max-Planck-Institut für
Radioastronomie, Auf dem Hfürgel 69, DE-53121 Bonn, Germany

# A sequence of Type Ib, IIb, II-L, and II-P supernovae from binary-star
progenitors of varying initial separation

Luc Dessart A sequence of Type Ib, IIb, II-L, and II-P supernovae from binary-
star progenitors of varying initial separationA sequence of Type Ib, IIb,
II-L, and II-P supernovae from binary-star progenitors of varying initial
separation Claudia P. Gutiérrez A sequence of Type Ib, IIb, II-L, and II-P
supernovae from binary-star progenitors of varying initial separationA
sequence of Type Ib, IIb, II-L, and II-P supernovae from binary-star
progenitors of varying initial separationA sequence of Type Ib, IIb, II-L, and
II-P supernovae from binary-star progenitors of varying initial separationA
sequence of Type Ib, IIb, II-L, and II-P supernovae from binary-star
progenitors of varying initial separation Andrea Ercolino A sequence of Type
Ib, IIb, II-L, and II-P supernovae from binary-star progenitors of varying
initial separationA sequence of Type Ib, IIb, II-L, and II-P supernovae from
binary-star progenitors of varying initial separation Harim Jin A sequence of
Type Ib, IIb, II-L, and II-P supernovae from binary-star progenitors of
varying initial separationA sequence of Type Ib, IIb, II-L, and II-P
supernovae from binary-star progenitors of varying initial separation Norbert
Langer A sequence of Type Ib, IIb, II-L, and II-P supernovae from binary-star
progenitors of varying initial separationA sequence of Type Ib, IIb, II-L, and
II-P supernovae from binary-star progenitors of varying initial separationA
sequence of Type Ib, IIb, II-L, and II-P supernovae from binary-star
progenitors of varying initial separationA sequence of Type Ib, IIb, II-L, and
II-P supernovae from binary-star progenitors of varying initial separation

(Received; accepted)

Over the last decade, evidence has accumulated that massive stars do not
typically evolve in isolation but instead follow a tumultuous journey with a
companion star on their way to core collapse. While Roche-lobe overflow
appears instrumental for the production of a large fraction of supernovae
(SNe) of Type Ib and Ic, variations in the initial orbital period $P_{\rm
init}$ of massive interacting binaries may also produce a wide diversity of
case B, BC, or C systems, with preSN stars endowed from minute to massive
H-rich envelopes. Focusing here on the explosion of the primary, donor star,
originally of 12.6 M⊙, we use radiation-hydrodynamics and nonlocal
thermodynamic equilibrium time-dependent radiative transfer to document the
gas and radiation properties of such SNe, covering from Type Ib, IIb, II-L to
II-P. Variations in $P_{\rm init}$ are the root cause behind the wide
diversity of our SN light curves, with single-peak, double-peak, fast-
declining or plateau-like morphologies in the $V$ band. The different ejecta
structures, expansion rates, and relative abundances (e.g., H, He,
${}^{56}\rm{N}$i) are conducive to much diversity in spectral line shapes
(absorption vs emission strength, width) and evolution. We emphasize that
H$\alpha$ is a key tracer of these modulations, and that He i 7065 Å is an
enduring optical diagnostic for the presence of He. Our grid of simulations
fare well against representative SNe Ib, IIb, and II-P SNe, but interaction
with circumstellar material, which is ignored in this work, is likely at the
origin of the tension between our Type II-L SN models and observations (e.g.,
of SN 2006Y). Remaining discrepancies in our model rise time to bolometric
maximum call for a proper account of both small-scale and large-scale
structures in core-collapse SN ejecta. Discrepant Type II-P SN models, with a
large plateau brightness but small line widths, may be cured by adopting more
compact red-supergiant star progenitors.

###### Key Words.:

radiative transfer – radiation hydrodynamics – supernovae: general – binaries:
general

##  1 Introduction

Over the last several decades, the community has assembled a large dataset of
core-collapse supernova (SN) light curves whose characteristic morphology
includes single peak, double peak, fast declining or plateau events (Anderson
et al., 2014b; Stritzinger et al., 2018; Modjaz et al., 2019).111These
morphologies generally refer to $V$-band and not bolometric light curves,
which differ when there is significant UV flux. Such variations have been
understood as arising from different evolutionary channels and in particular
single vs binary star evolution (e.g., Podsiadlowski et al. 1992; Yoon et al.
2010; Eldridge et al. 2018; Schneider et al. 2021; Laplace et al. 2021).
Roche-lobe overflow (RLOF) allows for huge mass loss rates in stars of modest
luminosity and weak winds, opening a channel for the production of Type IIb
and Ib SNe222Type Ic are unlikely to arise from lower-mass massive stars in
binary systems because, once stripped of the H-rich shell through RLOF, the
stripping of the progenitor He-rich shell must occur through wind mass loss,
which is strong enough only in higher mass Wolf-Rayet stars (see, for example,
Yoon 2017). from stars of moderate mass, which would have otherwise exploded
as Type II-P SNe had they been single. The consideration of binary-star
evolution has also become a necessity when investigating core-collapse SN
progenitors since a high fraction of massive stars reside in binary systems
with an initial orbital separation tight enough for interaction and RLOF at
some stage in their life (e.g., see Sana et al. 2012).

The strict segregation of events in separate SN types hides the complexity
inherent to SN light curves which tend to show a continuum in-between
morphological types. For example, the exact dichotomy between slow (aka, SNe
II-P) and fast decliners (aka, SNe II-L) is hard to define (Anderson et al.,
2014b) and the wealth of information encoded in spectra is typically reduced
to the presence or absence of certain lines or ions. The diversity in spectral
morphology is indeed considerable among Type II SNe (Gutiérrez et al., 2017),
even when considering a single line like H$\alpha$ (Gutiérrez et al., 2014).
This profile morphology is generally considered a feature, but it can provide
critical information on the processes controlling the SN radiation
characteristics and in particular in lifting degeneracies (Hillier & Dessart,
2019). Clear examples of this are the detection of short lived Type IIn
signatures, which provide robust evidence for ejecta interaction with
circumstellar material (CSM) in the early aftermath of shock breakout (Yaron
et al., 2017). Type II SNe in which H$\alpha$ develops a strong and broad
emission line with weak or no absorption likely interact with CSM, covering
from extreme cases like SN 1998S (Leonard et al., 2000; Fassia et al., 2000,
2001) to weaker ones like SN 2013ej (Bose et al., 2015; Yuan et al., 2016;
Hillier & Dessart, 2019).

Similarly, the dichotomy between Type IIb and Type Ib SNe rests upon the
residual H-rich envelope that survives at the progenitor surface at the time
of core collapse. Depending on the mass transferred to a companion in a binary
and the adopted wind mass loss rates, this extended and tenuous envelope may
range from as little as 0.001 M⊙ in tight binaries (Yoon et al., 2010) up to
several solar masses in the widest binaries that effectively evolve as single
stars (Yoon et al., 2017; Gilkis & Arcavi, 2022; Ercolino et al., 2023). The
exact threshold H mass separating Type IIb from Type Ib SNe is inferred from
observations to be around a few 0.01 M⊙ (Hachinger et al., 2012; Gilkis &
Arcavi, 2022), although theoretically, $M$(H) values as low as 0.001 M⊙ are
sufficient to produce a Type IIb SN (Dessart et al., 2011). Previous studies
have documented the influence of mass loss on a massive star, in particular in
terms of H-rich envelope mass at core collapse. Morozova et al. (2015) showed
the impact of an enhanced red-supergiant (RSG) mass loss on the final preSN
star and the corresponding Type II SN light curves, covering from Type II-P to
Type II-L SNe. Interaction with CSM lies behind the early-time luminosity
boost of Type II SNe (González-Gaitán et al., 2015; Moriya et al., 2017;
Morozova et al., 2017; Yaron et al., 2017; Förster et al., 2018). Hillier &
Dessart (2019) presented similar simulations describing both light curves and
spectra. They argued that the excess luminosity of fast-declining Type II as
well as the spectral morphologies required interaction — a low $M$(H) cannot
alone explain the shape of fast-declining Type II SNe and their large
luminosity. Eldridge et al. (2018) discussed the broad diversity of Type II SN
light curves that arise when including interacting binaries rather than single
stars alone. Hence, the impact of mass loss on the preSN star, and in
particular on the residual H-rich envelope, as well the potential presence of
that stripped material in the direct vicinity of the exploding star, play a
major role in determining the SN type and properties.

In this work, we present explosion and radiative-transfer calculations for
massive stars in a binary system with an initial orbital period varying from
562 to 2818 d, employing the binary-star evolution models of Ercolino et al.
(2023). Although similar work has been done by, for example, Gilkis & Arcavi
(2022), we document here the gas, photometric, and spectroscopic properties of
the resulting SNe, finding that this sample of models cover the whole range
from Type Ib, IIb, II-L (or fast-declining Type II)333Our models with such
fast declining light curves are qualitatively similar to Type II-L but
typically underluminous at peak relative to events like SN 1979C (Panagia et
al., 1980). The terminology should thus be taken loosely rather than strictly.
to Type II-P SNe. In particular, through this sample of progenitors, we reveal
how the progressive changes in progenitor H-rich envelope impact the
photometric and spectral properties during the photospheric phase.

In the next section, we present the numerical setup for our calculations. We
then present the results of our radiative transfer simulations, focusing first
on photometric properties (Section 3) and then on spectroscopic properties
(Section 4). In Section 5, we discuss in more detail the properties obtained
for H$\alpha$, in particular the evolution of its strength and width in our
set of models. Section 6 discusses the evolution of He i lines and in
particular the properties of He i 7065 Å, which is found to be present in all
models at late times and may thus offer an alternative to test for the
presence of He in Type Ic SNe. Section 7 then presents an extensive comparison
of our model results with prototypical SNe of Type Ib (Section 7.1), IIb
(Section 7.2 and 7.3), II-L (i.e., fast-declining fast-evolving SNe; Section
7.4) and II-P (Section 7.5).

##  2 Numerical approach

Our numerical exploration is a three-step process consisting of stellar
evolution models carried out until core collapse with MESA (Paxton et al.,
2011, 2013, 2015, 2018, 2019), followed by radiation hydrodynamics of the
explosion phase until homologous expansion with V1D (Livne, 1993; Dessart et
al., 2010b, a), and finally the remapping of the resulting SN ejecta into the
radiative transfer code CMFGEN (Hillier & Miller, 1998; Hillier & Dessart,
2012) to compute the evolution of the properties of the gas and the radiation
(bolometric and multi-band light curves as well as spectra covering from the
far-UV to the far-IR).

Table 1: Summary of preSN model properties.

Model | $M_{\rm f}$ | $L_{\star}$ | $T_{\rm eff}$ | $R_{\star}$ |  $M$(H) |  $M$(H-env) |  $M$(He) |  $M$(O) | $M_{\rm He,c}$ | $M_{\rm Fe,c}$ |  $X_{s}$(H) |  $X_{s}$(He)
---|---|---|---|---|---|---|---|---|---|---|---|---
| [M⊙] | [L⊙] | [K] | [R⊙] | [M⊙] | [M⊙] | [M⊙] | [M⊙] | [M⊙] | [M⊙] |  |
logP2p75∗ | 3.42 | 48823 | 24715 | 12.1 | 0.00 | 0.00 | 1.44 | 0.19 | 3.42 | 1.28 | 0.00 | 0.98
logP2p80 | 3.76 | 60789 | 4775 | 360.7 | 0.02 | 0.12 | 1.75 | 0.17 | 3.67 | 1.52 | 0.27 | 0.72
logP2p85 | 3.92 | 63983 | 3690 | 619.8 | 0.06 | 0.19 | 1.83 | 0.22 | 3.73 | 1.51 | 0.50 | 0.48
logP2p90 | 4.06 | 65103 | 3462 | 710.2 | 0.12 | 0.28 | 1.86 | 0.27 | 3.78 | 1.59 | 0.54 | 0.44
logP2p95∗ | 4.14 | 65102 | 3389 | 740.9 | 0.15 | 0.31 | 1.84 | 0.28 | 3.82 | 1.59 | 0.57 | 0.41
logP3p00∗ | 4.26 | 57528 | 3267 | 749.4 | 0.20 | 0.39 | 1.91 | 0.27 | 3.86 | 1.50 | 0.60 | 0.39
logP3p10∗ | 4.51 | 66203 | 3205 | 835.6 | 0.34 | 0.60 | 1.95 | 0.28 | 3.88 | 0.93 | 0.63 | 0.36
logP3p20 | 5.18 | 68434 | 3091 | 913.2 | 0.73 | 1.18 | 2.21 | 0.29 | 3.92 | 1.51 | 0.66 | 0.32
logP3p35 | 7.97 | 70136 | 3065 | 940.1 | 2.50 | 3.74 | 3.04 | 0.32 | 3.98 | 1.50 | 0.69 | 0.30
logP3p45 | 10.84 | 71080 | 3146 | 898.2 | 4.64 | 6.86 | 3.90 | 0.36 | 3.98 | 1.52 | 0.69 | 0.30

Notes: For each progenitor model (which all have an initial mass of 12.59 M⊙),
the table gives the final mass, the surface luminosity, the effective
temperature, the surface radius, the total hydrogen mass, the mass of the
H-rich envelope, the total mass of He and O, the He-core and Fe-core masses,
and finally the surface mass fraction of H and He. The “∗” symbol refers to
models that did not reach core collapse but terminated after core silicon
exhaustion (consequently, these models show a lower central density – see Fig.
1 – at the end of the MESA simulation). For historical reasons having to do
with the development of this work, the preSN models used here are not all
exactly identical to the preSN models described in Ercolino et al. (2023).

Figure 1: PreSN structure for our model set. We show the density versus mass
(top-left) and radius (top-right), the H mass fraction versus radius (bottom-
left), and the He mass fraction versus mass. [See Section 2.1 for discussion.]

###  2.1 PreSN evolution

Our work starts from a subset of the binary-star evolution models presented in
Ercolino et al. (2023), namely the models for a binary system with a primary
star mass of 12.6 M⊙, a system mass ratio of 0.95, and a range of initial
binary period from 562 d (logP2p75) up to 2818 d (logP3p45) – our nomenclature
is to refer to the models by the log of their initial period in days since our
models differ initially only in that parameter. A mixing-length parameter
$\alpha_{\rm MLT}$ of 1.5 was chosen to keep in line with previous stellar-
evolution simulations (see Section 7.5 for further discussion). Full details
about the MESA parameters used are given in Ercolino et al. (2023).

With the adopted range of initial orbital separations, mass transfer takes
place at different stages in the evolution of the primary star. For the
shortest initial periods (i.e., tightest initial orbits), the primary H-rich
envelope is severed early in the life of the primary star and leads to a case
B mass transfer. For the longest initial periods (i.e., widest initial
orbits), the primary never fills its Roche lobe and the star effectively
evolves as a single star. In between these two extremes, RLOF starts at
different ages and lasts different durations, producing a range of case B,
case BC, and case C systems. The ultimate result from this set of progenitors
are preSN stars with essentially the same core (the He-core masses for our set
covers from 3.42 to 3.98 M⊙, with most cluttering around 3.8 M⊙) but widely
different H-rich envelope masses covering from 0 (model logP2p75) up to 6.86
M⊙ (model logP3p45). As is well known (see, e.g., Woosley et al. 1994; Dessart
et al. 2010a; Morozova et al. 2015; Hillier & Dessart 2019) and already
discussed in Ercolino et al. (2023), the high-brightness phase of Type II SNe
being primarily controlled by the H-rich envelope mass of the progenitor (and
not of its metal-rich core; Dessart & Hillier 2019), one expects a wide
diversity of SN outcomes covering from Type Ib (model logP2p75) to Type IIb
(cases with $M$(H-env) of order 0.1 M⊙) to fast-declining Type II (cases with
$M$(H-env) of order 1 M⊙) and more standard Type II-P (cases with $M$(H-env)
of several solar masses).

Ercolino et al. (2023) also emphasize the large wind mass loss rates and mass
transfer rates for case BC and case C systems within O (10 000 yr) prior to
core collapse. These conditions are prime for producing interacting SNe.
However, in this study, we will ignore this circumstellar material (we thus
assume that all these preSN models explode successfully and in a vacuum) in
order to document the fundamental properties of the exploding stars alone.
This is a useful first step to consider before incorporating the extra
complexity associated with such CSM. We present various properties of our
selected sample of binary star models in Table. 1 and illustrate some of their
important properties at core collapse in Fig. 1.

Figure 2:  Initial ejecta structure for our CMFGEN simulations. We show the
density (left) and the temperature (right) versus velocity for the ejecta that
result from the explosion of the primary star in our set of binary progenitor
models. These profiles are used as initial conditions for the radiative
transfer calculations. The initial SN age, at which homologous expansion is
essentially reached, occurs earlier for more compact progenitors and covers
from 2.3 (model logP2p75) to 14.3 d (model logP3p45). The ejecta extend to
about 40 000 km s-1 for model logP2p75 (cut at 29 000 km s-1 here for better
visibility).  Figure 3:  Composition profile of model logP2p95 at 3.5 d used
as initial conditions for the CMFGEN calculations. In the case of Ni, we show
both the total mass fraction from all Ni isotopes (solid) and the mass
fraction of ${}^{56}\rm{N}$i alone (dashed). The right axis corresponds to the
Lagrangian mass (black dashed line).

###  2.2 Explosion phase and evolution to homologous expansion

The next stage was to model the explosion of the primary star once it had
reached its evolutionary endpoint. All models terminated after silicon core
exhaustion but not all reached the nominal endpoint with a maximum core infall
velocity of 1000 km s-1. This issue is not critical for our work since we
artificially trigger the explosion and do not focus on the exact post-shock
nucleosynthesis nor on the remnant mass. In practice, at a mass cut of 1.53 M⊙
(1.60 M⊙ for models logP2p90 and logP2p95),444For consistency with previous
similar simulations with CMFGEN, we choose our mass cut at the location where
the entropy jumps above 4 kB baryon-1 – other choices are possible, as long as
they remain reasonable (i.e., shifts of order 0.1 M⊙). The exact value of the
mass cut has little importance for the present study. we deposit, within a
narrow region of 0.05 M⊙, an energy corresponding to the binding energy of the
overlying layers (about $-2\times 10^{50}$ erg) and the desired kinetic energy
$E_{\rm kin}$ of the ejecta at infinity. Although V1D solves for the explosive
nucleosynthesis during the simulation (each progenitor yields a specific value
but with little scatter given the very similar core structures for all models
in our sample), we reset the ${}^{56}\rm{N}$i mass to be the same in all
models. Here, guided by the inferred values for the Type IIb SN 1993J (Woosley
et al., 1994), we adopt $M$(${}^{56}\rm{N}$i)$=$ 0.09 M⊙ and $E_{\rm kin}=$
1051 erg (the actual values in the final ejecta differ a little because of the
additional energy for nuclear burning as well as the various adjustments we
make to the ejecta structure – see below). The exact value is unimportant as
long as it is essentially the same one for all models in our sample – this
will facilitate the interpretation of photometric and spectroscopic
properties.

In all cases, the preSN structure was adjusted to ensure that the density at
the outermost grid point was low enough to allow for shock breakout under
optically-thin conditions (or at least close to that). Hence, progenitors were
extended with an atmosphere having a density scale height of 1% of the stellar
radius and going down to a minimum density of 10-12 g cm-3 (see top-right
panel in Fig. 1).555Other choices corresponding to a mass loaded atmosphere, a
slowly accelerating wind, or even enhanced mass loss rates are largely
irrelevant here since we focus on the long-term evolution of the SN ejecta and
radiation rather than on the immediate phase following shock breakout.
Although the V1D simulations were run until one year after explosion, we use
the V1D results for each model at the onset of homologous expansion, or at
about 2 d after explosion, whatever came first. The initial density and
temperature structures used for the CMFGEN calculations are shown in Fig. 2.
In contrast to the smooth density and temperature structure obtained for the
compact H-deficient logP2p75 model, most models in our sample exhibit strong
density variations with depth, with multiple dense shells. To reduce the sharp
density jumps obtained in a Lagrangian code like V1D, we apply a gaussian
smoothing before remapping in CMFGEN (Fig. 2 shows the profiles after
smoothing). These adjustments are mostly done for numerical convenience but
also to get rid of artifacts arising from the imposed spherical symmetry. For
a more extended discussion on shock propagation in progenitors with extended
envelopes, we refer the reader, for example, to Woosley et al. (1994) or
Dessart et al. (2018b) for the 1-D case and to Gabler et al. (2021) for the
multi-dimensional case.

Finally, to avoid having all the ${}^{56}\rm{N}$i present in the innermost
ejecta layers, we apply a boxcar smoothing (width of 0.1 M⊙, run once through
the model at 100 s after the explosion trigger). This leads to chemical mixing
between all shells and the presence of ${}^{56}\rm{N}$i out to velocities of a
few thousand km s-1 (see illustration of the composition for model logP2p95 in
Fig. 3). Table 2 summarizes the ejecta properties of our model set used as
initial conditions for the CMFGEN calculations.

Table 2: Summary of ejecta properties used as initial conditions for our
CMFGEN simulations.

Model | $M_{\rm ej}$ | $E_{\rm kin}$ |  $M$(${}^{56}\rm{N}$i) | $V_{99,{\rm H}}$ | $V_{99,{\rm He}}$ | $V_{99,^{56}{\rm Ni}}$ |  $X_{s}$(H) |  $X_{s}$(He)
---|---|---|---|---|---|---|---|---
| [M⊙] | [1051 erg] | [0.01 M⊙] | [1000 km s-1] | [1000 km s-1] | [1000 km s-1] |  |
logP2p75 | 1.90 | 1.02 | 8.97 | … | 1.79 | 6.47 | 0. | 0.98
logP2p80 | 2.25 | 1.07 | 8.96 | 7.12 | 2.10 | 6.74 | 0.13 | 0.86
logP2p85 | 2.43 | 1.17 | 8.81 | 6.43 | 2.06 | 6.73 | 0.33 | 0.65
logP2p90 | 2.49 | 1.15 | 8.79 | 5.93 | 2.31 | 7.05 | 0.48 | 0.51
logP2p95 | 2.56 | 1.17 | 8.78 | 5.85 | 2.00 | 6.86 | 0.53 | 0.46
logP3p00 | 2.75 | 1.09 | 8.76 | 4.96 | 2.39 | 6.76 | 0.57 | 0.42
logP3p10 | 3.03 | 1.13 | 8.57 | 4.37 | 1.92 | 6.21 | 0.62 | 0.37
logP3p20 | 3.72 | 1.19 | 8.55 | 2.92 | 2.13 | 6.54 | 0.66 | 0.33
logP3p35 | 6.49 | 0.98 | 8.76 | 1.57 | 1.39 | 5.70 | 0.68 | 0.30
logP3p45 | 9.45 | 1.09 | 8.84 | 0.78 | 0.64 | 5.45 | 0.68 | 0.30

Notes: The columns give in turn the ejecta mass, the kinetic energy, the
${}^{56}\rm{N}$i mass, the velocity bounding 99% of the mass of H, He, and
${}^{56}\rm{N}$i (integral performed inwards for H and He and outwards for
${}^{56}\rm{N}$i), and the surface mass fractions of H and He. These abundance
values slightly differ from those shown in Table 1 because of the adopted
chemical mixing (see discussion in Section 2.2).

###  2.3 Radiative transfer with CMFGEN

Starting from the ejecta models described in the previous section (see also
Table 2 and Fig. 2), we solve the nonlocal thermodynamic equilibrium (NLTE)
time-dependent radiative transfer with CMFGEN (Hillier & Dessart, 2012) and
compute the evolution of the gas and radiation until the nebular phase.
Species that have a relatively high abundance or have been understood to
impact SN radiation are included in our model atom. We treat H, He, C, N, O,
Ne, Na, Mg, Al, Si, S, Ar, Ca, Sc, Ti, Cr, Fe, Co, and Ni – species with
heavier nuclei than Ni are not included because they are not covered by our
nuclear network (the corresponding atomic data is also scarce or inexistent).
We use the updated atomic data described in Blondin et al. (2023) and include
the following ions: H i (26,36), He i (40,51), He ii (13,30), C i (14,26), C
ii (14,26), C iii (62,112), N i (44,104), N ii (23,41), N iii (25,53), O i
(21,51), O ii (54,123), O iii (44,86), Ne i (78,155), Ne ii (22,91), Ne iii
(32,80), Na i (22,71), Mg i (39,122), Mg ii (31,80), Mg iii (31,99), Al ii
(26,44), Al iii (17,45), Sc i (26,72), Sc ii (38,85), Sc iii (25,45), Si i
(100,187), Si ii (31,59), Si iii (33,61), S i (106,322), S ii (56,324), S iii
(48,98), Ar i (56,110), Ar ii (134,415), Ar ii (32,346), K i (25,44), Ca i
(76,98), Ca ii (21,77), Ca iii (16,40), Ti ii (37,152), Ti iii (33,206), Cr ii
(28,196), Cr iii (30,145), Cr iv (29,234), Fe i (44,136), Fe ii (228, 2696),
Fe iii (96,1001), Fe iv (100,1000), Fe v (47,191), Co ii (44,162), Co iii
(33,220), Co iv (37,314), Co v (32,387), Ni i (56,301), Ni ii (27,177), Ni iii
(20,107), Ni iv (36,200), and Ni v (46,183). The numbers in parenthesis
correspond to the number of super levels and full levels employed (for details
on the treatment of super levels, see Hillier & Miller 1998). With our model
atom, we treat 11 939 levels and a total of 830 000 bound-bound transitions.
These are mostly coming from iron-group elements, in particular Fe, Co, and Ni
(and of these three elements, Fe is the most important followed by Ni).

Besides the initially stored radiative energy, we account at all times for the
radioactive decay power from the two-step ${}^{56}\rm{N}$i decay chain – all
other isotopes are stable (the only exceptions are ${}^{44}\rm{T}$i and
${}^{57}\rm{N}$i but because of their low abundance or long lifetime, they are
irrelevant at the times considered here; see, for example, Dessart et al.
2023). We treat non-thermal processes for high-energy electrons as described
in Li et al. (2012). Nonlocal $\gamma$-ray energy deposition is computed by
solving the radiative-transfer equation using a grey, absorption-only opacity
equal to 0.06 $Y_{\rm e}$ cm2 g-1, where $Y_{\rm e}$ is the electron fraction.

The grid employs 80 to 100 grid points uniformly spaced on a logarithmic
optical-depth scale (the exact number depends on model and SN age). Remapping
the grid is necessary at the start of every timestep as well as during the
calculation in order to track recombination fronts, if present. To cover the
full evolution to the nebular phase, a total of 30 to 40 timesteps were
computed (differences arise because the start time is not the same for all
sequences and also because some ejecta take much longer to turn nebular). The
main CMFGEN output of interest for this study is the emergent flux, which is
calculated at each time step in the observer’s frame from the far-UV to the
far-IR. This spectrum can be shown directly or used to compute the bolometric
luminosity $L_{\rm bol}$ or the absolute magnitude in various filters.

In this work, to refer to the models in our set, we will repeatedly call them
as members of a sequence “from” logP2p75 “up” to logP3p45 because this forms a
sequence of increasing initial period for the binary system from which we
extracted the exploding primary star. This sequence is a natural one since it
is also one of increasing ejecta mass or H mass (see Table 1). This is a
convenient shorthand.

Figure 4: Photometric properties for our model set. We show the bolometric
light curves (top left) followed by the $UVW2$ (top right), $U$ (bottom left),
and $V$-band (bottom right) light curves. In the top-left panel, the dashed
line corresponds to the emitted power from 0.09 M⊙ of ${}^{56}\rm{N}$i. In the
bottom-right panel, the dashed curve gives the predicted decline rate for full
$\gamma$-ray trapping and constant color, which essentially holds in the more
massive ejecta models logP3p35 and logP3p45.

##  3 Results: Diversity of model light curves

Figure 4 presents the photometric evolution for our model set from 2.3$-$14.3
d until 92.2$-$159.5 d after explosion, essentially stopped when the ejecta
optical depth drops to near unity. The bolometric light curves (top-left
panel) exhibit different morphologies. Model logP2p75, whose progenitor has no
residual H-rich envelope, shows a single, ${}^{56}\rm{N}$i-powered luminosity
peak (we exclude here the shock breakout burst, modeled with V1D but not with
CMFGEN) followed by a steep decline from maximum, and eventually a quasilinear
decline at nebular times with a slope that is steeper than predicted for full
$\gamma$-ray trapping. Models logP2p80, logP2p85, logP2p90 show two separate
phases in their light curves, with a first high and slowly declining
luminosity down to a minimum at 10${}^{41.5}-10^{42.3}$ erg s-1, and a
subsequent evolution that lines up with that obtained for model
logP2p75.666SNe from He-giant star explosions also yield a double-peak light
curve in the $V$ band and this arises from the presence of an extended He-rich
H-deficient envelope (Dessart et al., 2018b). Models logP2p95, logP3p00,
logP3p10, and logP3p20 show a prolonged decline of the initial high, post-
breakout luminosity, with no clear separated peak, and eventually merge with
the light curve obtained for model logP2p75 at 50$-$70 d after explosion. The
late-time decline in those models is flatter for greater ejecta masses. Models
logP3p35 and logP3p45 exhibit a clear plateau in their light curve, which
lasts until the end of the optically-thick phase at 100$-$120 d after
explosion. At a qualitative level, this set of light curves thus covers that
obtained for Type Ib or Ic SNe (e.g., logP2p75) from stripped compact
progenitors, for Type IIb SNe from progenitors with an extended but low-mass
H-rich envelope (e.g., models logP2p80, logP2p85, logP2p90), for fast-
declining Type II-L SNe (e.g., models logP2p95, logP3p00, logP3p10, and
logP3p20), and for more standard Type II-P SNe (e.g., models logP3p35 and
logP3p45).

Such a diversity of light curves is not a new prediction of our work. Single-
peaked light curves are typical of stripped-envelope SNe and are well
understood in the context of moderate mass ejecta (say 3$-$5 M⊙) powered by
the radioactive decay of O (0.1 M⊙) of ${}^{56}\rm{N}$i (see., e.g., Ensman &
Woosley 1988, Dessart et al. 2011, Bersten et al. 2013). The extended high
luminosity phase prior to that main peak arises from progenitors with extended
O (0.1 M⊙) H-rich envelopes (see, .e.g, Woosley et al. 1994, Blinnikov et al.
1998, Bersten et al. 2012, Dessart et al. 2018b). Our results for higher but
still moderate, O (1 M⊙) H-rich envelopes have been obtained before in the
context of massive stars partially stripped of their envelope because of wind
mass loss (see, e.g., Blinnikov & Bartunov 1993; Morozova et al. 2015, Hillier
& Dessart 2019). Finally, standard RSG progenitors are notorious for producing
a plateau in their light curves, a feature known since the 70s (see, e.g.,
Grassberg et al. 1971). What is new though is that our model set based on the
same primary star but different initial system orbital separation can
reproduce the full sequence of light curves from Type Ib (or Ic), to Type IIb,
Type II-L, and Type II-P SNe. This property arises in part from the fact that
the residual H-rich envelope in our progenitors varies from zero to $\sim$ 7
M⊙ while the metal rich core remains essentially the same for the whole set,
leading to an explosion with the same ejecta kinetic energy and
${}^{56}\rm{N}$i mass (the adopted values for $E_{\rm kin}$ and $M_{\rm ej}$
could have been different, but these values should be the same for the whole
set). For a given explosion energy, the potential presence of a loosely bound
H-rich envelope (whose binding energy is about $-10^{47}$ erg) does not affect
the ejecta kinetic energy at infinity, although it strongly impacts the ejecta
structure, the SN light curves and the spectra.

Models that stand between logP2p75 (progenitor with no residual H-rich
envelope) and logP3p35/logP3p45 (standard RSG star progenitors with a massive
H-rich envelope) are hybrid cases in which the photospheric phase is powered
by the release of shock-deposited energy (whose original budget is essentially
set at the time of shock breakout) and by continuous radioactive decay. In
model logP2p85, the light curve is composed of two, essentially separate
components. The first one arises from the power released from the shocked
H-rich envelope, which lasts about 10 d, and the second one from the
${}^{56}\rm{N}$i heating of the underlying metal-rich ejecta (more diversity
could have been produced by varying the explosion energy, the ${}^{56}\rm{N}$i
mass, the chemical mixing etc). Because essentially the same ${}^{56}\rm{N}$i
mass is used (and expected for such progenitors) in our set, the model
sequence from logP2p75 to logP3p20 yields progressively more luminous light
curves since an increasing amount of shock-deposited power within the
increasingly massive progenitor envelope is added to the contribution from
radioactive decay power (which is comparable in all models; see Table 2). More
massive ejecta eventually break this luminosity sequence because this increase
in ejecta mass reduces the ejecta expansion rate ($E_{\rm kin}/M_{\rm ej}$ is
smaller) and increases the ejecta optical depth (which inhibits radiative
diffusion and the recession of the photosphere). In models logP3p35 and
logP3p45, the ${}^{56}\rm{N}$i is more deeply embedded and contributes to the
light curve at later times. The release of shock-deposited energy over the
first 30$-$50 d exceeds the decay power in all relevant models (i.e., those
whose preSN star has a massive H-rich envelope). Finally, the diversity in
late-time decline rate reflects the greater efficiency of higher mass ejecta
at trapping $\gamma$-rays. For example, at 50 d after explosion, model
logP2p75 absorbs only 88% of the emitted decay power whereas model logP3p45
absorbs 100% of that emitted power. In the same order, this fraction is 59%
and 99% at 92 d after explosion.

Figure 4 also shows the model light curves in the $UVW2$, $U$, and $V$ bands.
Each of these light curves differs significantly from the bolometric light
curves because of the evolution of the color, with the noticeable exception of
model logP2p75. Because of its small progenitor radius ($R_{\star}=$ 12.1 R⊙),
the ejecta model logP2p75 undergoes significant cooling so that the model
essentially evolves at constant photospheric, or equivalently color
temperature, at all times covered here (i.e., 2 d and beyond after explosion).
Model logP2p75 radiates predominantly at optical wavelengths at all times and
consequently its $V$-band light curve follows closely the bolometric light
curve. In all other models, the presence of a residual H-rich envelope in the
preSN star comes with a large progenitor radius of about 400 to 900 R⊙. All
these models first exhibit colors more typical of RSG star explosions (the
flux peaks in the UV; top-right panel of Fig. 4) before shifting to the
optical band as the outer H-rich ejecta layers become optically thin (and the
${}^{56}\rm{N}$i-powered ejecta dominates the radiative display) or until the
H-rich ejecta layers recombine. This transition occurs over a few days in
models logP2p80, over 10$-$20 d in models logP2p85$-$logP3p00 and even longer
in the rest of the model set. This hybrid powering source between early and
late times is what causes the double-peak $V$-band light curves in models
logP2p80 to logP2p90 (see also discussion about this process in Woosley et al.
1994; Bersten et al. 2012; Nakar & Piro 2014; Dessart et al. 2018b; Park et
al. 2023).

Another feature of interest in the models is the $V$-band rise time, which is
of order 20$-$50 d in models logP3p35 and logP3p45. This is a typical result
for explosions of RSG stars with a very large radius (see, e.g., Kasen &
Woosley 2009; Dessart & Hillier 2011; Morozova et al. 2015). The peak in the
$V$-band light curve occurs in those models when the spectral energy
distribution essentially peaks in the optical, hence at the onset of the
recombination phase. Prior to that, the bulk of the flux falls in the UV and
the optical brightness is small. We will return to this property in Section
7.5.

Figure 5: Evolution of photospheric properties for our model set. From top to
bottom, we show the evolution (the $x$-axis is shown in logarithmic scale to
better reveal the rapid changes at early times) of the radius (top), velocity
(middle), and gas temperature (bottom) at the location where the inward-
integrated electron scattering optical depth is equal to 2/3. The dashed lines
correspond to early epochs for models logP3p10 to logP3p45 in which we
computed single snapshots based on V1D inputs.

We can also connect these photometric properties with the evolution of
properties at the photosphere, which we show for all models in Fig. 5. At
early times, there is a marked dichotomy in photospheric temperature $T_{\rm
ph}$ with high values up to 20$-$25 kK in models with large radii and a
sizable H-rich envelope and much cooler temperatures of $\mathrel{\hbox{\hbox
to0.0pt{\hbox{\lower 4.0pt\hbox{$\sim$}}\hss}\hbox{$<$}}}$ 10 kK in those from
more compact progenitors (models logP2p75 and logP2p80) – this offset is the
cause lying behind the color offset between models (i.e., UV bright vs
optically bright at early times). This offset disappears after about 20 d when
the photosphere is at about 7 kK – in models logP3p45 and analogs, this
corresponds to the recombination phase (plateau-like in the $V$ band) of the
SN. In all models, the photospheric velocity $V_{\rm ph}$ decreases steadily
at all times. In the lighter ejecta models, the recession is fast so that
despite the relatively larger outer ejecta velocity (see Fig. 2), they have
relative low $V_{\rm ph}$ values at 5 d after explosion, comparable to values
obtained for more massive, slower moving ejecta – the offset in $E_{\rm
kin}/M_{\rm ej}$ is compensated by a greater ionization and optical depth.
Models with the highest photospheric velocities at early times (up to 16 000
km s-1) are those with intermediate-mass H-rich envelopes (i.e., logP2p85)
since they have a combination of a relatively high $E_{\rm kin}/M_{\rm ej}$
and a relatively high optical-depth from the outer H-rich ejecta. Models that
exhibit a steep density drop-off in their outer ejecta (e.g., logP3p45; see
Fig. 2) have a very slow evolving $V_{\rm ph}$ as long as the photosphere
remains in those external layers. This arises because that density cliff
represents a large jump in optical depth at a fixed velocity. This velocity
also gives the maximum velocity one may record from any spectral line in these
models (e.g., about 9 000 km s-1 in model logP3p45, which is much smaller than
typically observed in SNe II-P – see Section 7.5). Because of our assumption
of homologous expansion (which is warranted), the photospheric radii yield an
information equivalent to that of the velocity since $R_{\rm ph}$ is just
$V_{\rm ph}$ multiplied by the SN age. Not surprisingly, differentiating
between the models of our set (whose progenitors differ strongly in H-rich
envelope mass) is best done at early times, when the photosphere probes the
outer ejecta layers.

Figure 6: Spectral properties of our model set at about 5 (top-left), 15 (top-
right), 30 (bottom-left), and 85 d (bottom-right) after explosion. We stack
our ten models from top to bottom in order of increasing H content, using the
same color coding as before. For the montage at 5 d, we show the quantity
$\lambda^{2}F_{\lambda}$ in order to reduce the contrast between UV and
optical ranges. We also shade the flux associated with bound-bound transitions
of H i (light shade) and He i (dark shade).

##  4 Results: Diversity of evolution of model spectra

A richer information is conveyed by the spectral evolution since it contains
information on photometry (and in particular color) as well as on the
temperature, ionization, composition, and kinematics of the ejecta. In Fig. 6,
we show the spectra for our model set at about 5, 15, 30, and 85 d after
explosion.777For the models logP3p10, logP3p20, logP3p35, and logP3p45 at 5 d
(top-left panel of Fig. 6), we computed the spectra assuming steady state and
fixing the temperature to the value obtained in the V1D calculation. This is
not ideal but is used nonetheless to illustrate the spectral properties for
these models prior to the phase of homologous expansion – the outer ejecta
layers are in fact close to homologous expansion at that time. There are
numerous differences between models and between epochs which reflect the
different ejecta structure and composition.

At 5 d after explosion (top-left panel of Fig. 6), the first striking spectral
difference is that models logP2p75 and logP2p80 are optically bright and UV
faint whereas all other models have the bulk of their flux emerging in the UV,
and the more so the bigger the progenitor radius (which covers from about 600
to 900 R⊙). The luminosity in those bluer models is much greater (see top-left
panel of Fig. 4). The other striking difference is the change in H i (e.g.,
H$\alpha$) or He i (e.g., He i 10830 Å) line widths and strengths, which are
large in models logP2p75 (H-free model) and logP2p80, and weak in models with
a greater H content. In the absence of a sizable H-rich envelope, the outer
ejecta layers expand much faster and become much more transparent and cold,
causing this red color, as well as the broader and stronger lines. In models
from progenitors with a sizable H-rich envelope, a greater shock-deposited
energy is radiated away and less turned into kinetic energy so the lines are
systematically narrower. The weakness of the lines arises from the steep
density profile in the outer ejecta (where the spectrum forms at such times;
see Fig. 2) as well as the relatively high ionization. Most optical lines are
from the H i Balmer series. In addition, SN ejecta from more compact RSG
progenitors show spectra with stronger He i lines whereas those from more
extended RSG stars show stronger He ii lines (e.g., He ii 4686 Å in the
optical). This reflects a shift to higher temperature and ionization at the
photosphere, rooted in the difference in progenitor radius. In the optical,
these spectra exhibit weak lines but are not featureless (they might appear so
in observations with low quality signal). Most strong lines reside in the UV.
This includes resonant transitions from CNO elements, Al, as well as Fe (in
particular the forest of lines from Fe iii; see for example the discussion of
models tailored to the observations of the Type II-P SN 2022acko at $\sim$ 5 d
after explosion; Bostroem et al. 2023).

At 15 d after explosion (top-right panel of Fig. 6), our model set shows a
clear trend towards a bluer optical color as we progress to ejecta from
progenitors with more massive and more extented H-rich envelopes. In model
logP2p75, the spectrum has hardly changed (it already had a red color at 5 d;
see also top-left panel of Fig. 14) except for slightly stronger He i lines
and narrower line profiles (the photosphere has receded from $\sim$ 9000 km
s-1 to $\sim$ 7000 km s-1. In the rest of the model set, these He i lines are
progressively weaker. In lighter ejecta, He i lines are influenced by non-
thermal excitation by high-energy, Compton-scattered electrons (Lucy, 1991;
Swartz, 1991), while in heavier ejecta, the higher gas temperature and
stronger photoionization are the main processes controlling their strength
(the weakness of the lines in massive ejecta also results from the steeper
density profile; Fig. 2). Cooler ejecta in which the spectral energy
distribution peaks around 4000 Å show clear signs of metal line blanketing in
the optical (primarily associated with Ti ii and Fe ii), while the
recombination phase has not yet started in bluer models ($T_{\rm ph}$ is about
10 kK in model logP3p45 at that time). The most striking feature in our model
set at this epoch is the strong decrease in H$\alpha$ absorption and emission
strength, as well as in line width, as $M$(H) increases from models
logP2p80/logP2p85 to logP3p45 – this reflects the decrease in the volume over
which the spectrum forms and little the actual H/He abundance ratio (the
models with the stronger H$\alpha$ line here are those that are the more He
enriched – see Fig. 1). The more massive ejecta (with more H), have a lower
$E_{\rm kin}/M_{\rm ej}$ and therefore yield narrower lines (best seen in H i
lines and in particular H$\alpha$).

At 30 d after explosion (bottom-left panel of Fig. 6), all models exhibit a
similar spectral morphology, with a spectral energy distribution peaking in
the optical, which reflects their similar photospheric temperature of about
7000 K. All models show signs of metal-line blanketing in the optical. He i
lines are strongest in model logP2p75 and decrease in strength for models with
higher ejecta mass – He i lines are absent beyond model logP3p00 because the
influence of ${}^{56}\rm{N}$i is too weak and the He mass fraction smaller
(even though the total He mass is greater in more massive ejecta). H i lines
(of which H$\alpha$ is the most visible Balmer transition) are present in
models logP2p80 to lopP3p45 but in lighter models the lower H content yields a
weaker feature. H$\alpha$ is strongest at this phase in intermediate models
like logP2p90 and logP2p95. We also see a trend of decreasing strength for O i
7774 Å (likely a composition effect since the O-rich layers are revealed at
this time in lighter ejecta) or the Ca ii NIR triplet (reflecting the lower
ionization and more extended ejecta in lighter models).

At 85 d after explosion (bottom-right panel of Fig. 6), the physical
conditions prevailing for the different models differ fundamentally since
lighter ones are optically thin (e.g., logP2p75) while others are optically
thick (e.g., logP3p45). With their greater He and ${}^{56}\rm{N}$i content
(i.e., relative to $M_{\rm ej}$), lighter models are slightly bluer in the
optical although strong signs of metal-line blanketing are present in all
models. The He i 10830 Å shows a clear trend of decreasing strength from
logP2p75 to logP3p45. In the optical, the strongest He i line is due to the
transition at 7065 Å (see further discussion in Section 6). H$\alpha$ is
strongly affected by overlapping lines (e.g., due to Fe ii) in lighter models.
In heavier models, H$\alpha$ is weaker and narrower, primarily because of the
steeper density gradient and slower velocity at the photosphere.

To summarize, the evolution of each model and the differences between models
reflect the differences in $M_{\rm ej}$ (all models in our set have
essentially the same $E_{\rm kin}$ so the ejecta density is typically greater
and the expansion rate smaller in higher mass ejecta), in the relative H
abundance (i.e., $M$(H)/$M_{\rm ej}$), which also determines how external in
the ejecta H is present, in the relative He abundance (i.e., $M$(He)/ $M_{\rm
ej}$), and in the relative ${}^{56}\rm{N}$i abundance (i.e.,
$M$(${}^{56}\rm{N}$i)/$M_{\rm ej}$), which determines how strong non-thermal
processes can impact elements like He. We show the more complete spectral
evolution of all ten models in Figs. 14$-$16.

Figure 7: Evolution of the flux ratio associated with the absorption and
emission parts of H$\alpha$. This ratio is computed by integrating the flux
over the absorption and emission parts of the H$\alpha$ profiles (see Fig. 17
for time sequences of these profiles).

##  5 Results: H$\alpha$ properties

Much discussion surrounds the H$\alpha$ transition in core-collapse SNe. It is
the strongest line in optical spectra of SNe II at most epochs and is also the
diagnostic line used to differentiate Type IIb from Type Ib SNe. There is a
consensus that not much residual H is needed to produce a clear H$\alpha$
line, with values ranging from as low as 0.001 M⊙ (Dessart et al., 2011),
around 0.01 M⊙ (Hachinger et al., 2012), all the way to a few 0.1 M⊙ (Ben-Ami
et al., 2015; Dessart et al., 2018b). Objects with double-peak $V$-band light
curves or with a large bolometric luminosity for days after shock breakout
(e.g., SN 1993J; Richmond et al. 1994) are understood to arise from
progenitors with an extended, H-rich envelope with a mass of order 0.1 M⊙
(Blinnikov et al., 1998; Nomoto et al., 1993; Podsiadlowski et al., 1993;
Woosley et al., 1994; Nakar & Piro, 2014; Dessart et al., 2018b). The
photometric signature is much more elusive, or even absent if the H-rich
envelope mass is lower (see, e.g., Dessart et al. 2011; Bersten et al. 2012).

In binary progenitors, the amount of residual hydrogen of the primary star at
core collapse is a function of the post-RLOF stellar wind mass loss. It also
strongly depends on the initial orbital separation. For example, very low
values of $M$(H) were obtained for the short-period, tight binary systems
studied by Yoon et al. (2010, that work also employed weak mass loss rates
that facilitated the survival of H at the progenitor surface until core
collapse). SN radiative-transfer simulations based on such progenitors
indicated that H$\alpha$ would be present, although only for a few days after
shock breakout (Dessart et al., 2011). Other studies that included wider
orbits yielded a broader range of residual H (see, for example, Yoon et al.
2017, Gilkis & Arcavi 2022, Ercolino et al. 2023).

The radiative-transfer simulations in this work are based on a subset of ten
binary progenitor models from Ercolino et al. (2023). Although limited to a
primary star of 12.6 M⊙ with an initial binary mass ratio of 0.95, they cover
initial periods ranging from 562 up to 2818 d and final $M$(H) of 0, 0.02,
0.06, 0.12, 0.15, 0.22, 0.37, 0.80, 2.68, and 4.64 (these values correspond to
about 40 to 70 % of the progenitor H-rich envelope mass since the H/He mass-
fraction ratio covers 0.69/0.30 in model logP3p45 down to 0.27/0.72 in model
logP2p80). With our fixed explosion energy of 1051 erg and moderate, ad-hoc
chemical mixing, this preSN chemical stratification in mass leads to a
stratification in velocity space. As indicated in Table 2, the minimum
velocity bounding 99 % of the H decreases from 7120 (model logP2p80) to 781 km
s-1 (model logP3p45). This implies that no absorption or emission can occur in
H$\alpha$ below that threshold (in the emergent H$\alpha$ profile, absorption
and emission can be seen below this velocity because of the change in
projected velocity for non-zero impact parameters and this may be aggravated
by departures from spherical symmetry; see Section 5 of Dessart & Hillier
2005a). In those models, the depth at which H is present depends also on the
adopted mixing whose exact magnitude is not robustly known and probably varies
a great deal in nature.

Figure 6 and Figs. 14$-$16 show that H$\alpha$ is visible until about 50 d in
model logP2p80, until about 70 d in model logP2p85, and at least until 90 d in
all other models with a higher $M$(H). In models logP3p35 and logP3p45,
H$\alpha$ is visible throughout the nebular phase, as in typical RSG star
explosions since in those events, H is mixed inwards while ${}^{56}\rm{N}$i is
mixed outwards, so that H and ${}^{56}\rm{N}$i overlap in velocity space (see
Table 2 and specifically the values for $V_{99,{\rm H}}$ and $V_{99,^{56}{\rm
Ni}}$). This means that in all models (except H-deficient model logP2p75),
H$\alpha$ is visible until the nebular phase.

Figure 7 shows in more detail the evolution of the H$\alpha$ profile
characteristics by comparing the flux ratio of the absorption and emission
parts. To make these measurements on the H$\alpha$ profile, we computed the
spectrum accounting for all bound-bound transitions and subtracting from it
the spectrum obtained when all but H i transitions are included. Over the
H$\alpha$ profile region (shown for all H-rich models in Fig. 17), the flux is
zero far away from the line (at Doppler velocities exceeding the maximum
ejecta velocity), negative in the blue-shifted part (corresponding to the
P-Cygni trough), and positive as we move closer to line center and into the
so-called “red-wing”. Besides the notorious blue-shift of peak emission
(Dessart & Hillier, 2005b; Anderson et al., 2014a), we see that both emission
and absorption persist at all epochs in all cases. The absorption component is
typically weaker than the emission part. This is related to complicated
radiative transfer effects (i.e., how the line and continuum source functions
compare, how the ionization varies with depth above the photosphere), but it
is also the result of a simple geometric effect since the emission arises
potentially from a large volume (this volume is greater for flatter density
profiles) while the absorption is fundamentally limited to the column of
material falling onto the radiating disk (roughly limited by an impact
parameter equal to the photospheric radius). This geometric effect dominates
at late times in models like logP3p45. In model logP2p85 or logP2p90, the
H$\alpha$ absorption extends from about 10 000km s-1 out to 25 000 km s-1,
hence essentially from the photosphere out to the outermost ejecta layers at
large velocity. The maximum range of velocities is much more limited in more
massive H-rich ejecta (see Fig. 2) so there is little space between the
photosphere and the outermost ejecta layers to accommodate a broad absorption.

Figure 17 also reveals the intrinsic morphology and characteristics of the
H$\alpha$ profile. For example, in model logP2p80, the line covers from $-$ 25
000 to $+$ 20 000 km s-1 at early times and eventually narrows down to exhibit
at late times a narrow absorption at about $-$ 11 000 km s-1 together with a
weak flat-topped emission bounded by a similar velocity. This velocity of 11
000 km s-1 is where the H mass fraction drops to about 0.1 as we progress
inwards from the outermost ejecta layers (the absorption exhibits two minima
at 11 000 and 13 000 km s-1, which correspond to the location of two maxima in
the density profile; see Fig. 2). In model logP2p85, the morphology is
analogous but the velocities are smaller, the peak blueshift even more marked
at early times, the flat-topped profile at late times is narrower, and the
P-Cygni absorption exhibits multiple minima reflecting the presence of density
extrema at about 8000, 10 000, and 16 000 km s-1. Such extended troughs are
present at late times in models with $M$(H) between 0.06 and 0.37 M⊙
(progenitors with a H-rich envelope mass between 0.14 and 0.59 M⊙). These
troughs are narrow and weak at late times in models logP3p20, logP3p35, and
logP3p45 because of the limited range in ejecta velocity and the large
emitting volume of the H-rich ejecta (this emission fills in the absorption
part).

##  6 Results: Evolution of Helium lines

Our set of simulations also exhibit interesting features and paradoxes in
relation to He lines. As shown earlier in Fig. 6 and in Figs. 14$-$16, He
lines are present in all models at early times. Models logP2p75 and logP2p80
have cool and partially ionized photospheres at essentially all epochs past 2
d so that the excitation of He i lines is caused by collisions with high-
energy electrons themselves produced through scattering with $\gamma$-rays
emitted by decaying ${}^{56}\rm{N}$i and ${}^{56}\rm{C}$o isotopes. In these
models, He i lines (e.g., He i 5875, 6678, 7075, and 10830 Å) persist through
this process throughout the evolution (i.e., thus out to at least 90 d). In
models whose progenitors have a residual H-rich envelope greater than 0.1 M⊙,
the presence of He lines at early times is caused by the large photospheric
temperature and photoionizing flux. That temperature is large enough to
produce He ii lines (in particular He ii 4686 Å; this line is obvious in all
models beyond logP2p90) or only He i lines (e.g., at 5875 Å; model logP2p85 at
$\sim$ 5 d). In models with intermediate $M$(H) values, the transition from
photoionization to non-thermal excitation as the process behind the production
of He i lines occurs after about 20 d. In more massive ejecta, the He i lines
are essentially absent in the optical after the onset of the recombination
phase, apart from He i 10830 Å in the NIR, which persists until late times. It
is thus paradoxical, though not surprising, that the ejecta with the largest
amount of He are those that show weaker and only short-lived He lines.

Surprisingly, the He i 7065 Å line is predicted in all models once they turn
nebular – it strengthens as the continuum optical depth drops. This line is
present earlier on (i.e., during the photospheric phase) as we progress from
model logP3p45 to logP2p75 (i.e., in order of increasing $M$(He)/$M_{\rm
ej}$). It is much more obvious than the weak He i 6678 Å but also He i 5875 Å,
which overlaps with Na i D. Although not the main focus of this work, this He
i 7065 Å line offers an interesting diagnostic to test for the presence of He
in the ejecta. The detection of He i lines is the sole criterion for
differentiating Type Ib from Type Ic SN and this task is trivial when such He
i lines are strong. However, if they are weak, one is often limited to
searching absorptions related to those He i transitions (see, e.g., Liu et al.
2016 or Williamson et al. 2019), and such absorptions only probe for the
presence of He within the column of material falling onto the photodisk.888The
alternative is to use the NIR and in particular search for the unblended He i
20581 Å line; see, for example, Shahbandeh et al. (2022). In an aspherical
explosion where most of the He may reside along other lines of sight, this
absorption may be weak or even absent, complicating the identification of He i
lines. In contrast, when searching for signs of He at later times, after
bolometric maximum and as the ejecta become optically thin, a line like He i
7065 Å would be ideal since it does not suffer from overlap with Na i D or Fe
ii lines, and it is also predicted as a strong emission line.

Table 3: Characteristics of the selected sample of observations, ranked in
order of increasing of $M$(H).

SN | Type | Redshift | $\mu$ | $E(B-V)_{{\rm tot}}$ | Explosion date | Refs (spectra) | Refs (photometry)
---|---|---|---|---|---|---|---
|  |  | (mag) | (mag) | (MJD) |  |
iPTF13bvn | Ib | 0.00449 | 31.76 | 0.071 | 56459 | [1]; [2]; [3] | [1]; [4]; [5]
SN 2011dh | IIb | 0.00168 | 29.42 | 0.07 | 55713 | [6] | [6]
SN 1993J | IIb | 0.000113 | 27.82 | 0.2 | 49074 | [7]; [8] | [7]; [9]; [10]
SN 2006Y | II-L | 0.03358 | 35.73 | 0.115 | 53766 | [11] | [12]; [13]
SN 2017eaw | II-P | 0.002192 | 29.47 | 0.30 | 57885 | [14] | [15]; [16]

  * Data downloaded from http://wiserep.weizmann.ac.il/home (Yaron & Gal-Yam, 2012).

  * References: [1] Cao et al. 2013; [2] Fremling et al. 2014; [3] Fremling et al. 2016; [4] Srivastav et al. 2014; [5] Zheng et al. 2022; [6] Ergon et al. 2014; [7] Barbon et al. 1995; [8] Matheson et al. 2000; [9] Richmond et al. 1994; [10] Richmond et al. 1996; [11] Gutiérrez et al. 2017; [12] Anderson et al. 2014b; [13] Hiramatsu et al. 2021; [14] Szalai et al. 2019; [15] Tsvetkov et al. 2018; [16] Van Dyk et al. 2019.

##  7 Comparison to observations

In this section, we compare a few models (using both light curves and
multiepoch spectra) from our set to well observed, prototypical core-collapse
SNe of various kinds, that is of Type Ib (i.e., iPTF13bvn; Section 7.1), Type
IIb (i.e., SNe 2011dh and 1993J; Section 7.2 and 7.3), Type II-L (aka fast
decliners; i.e., SN 2006Y; Section 7.4), and Type II-P (i.e., SN 2017eaw;
Section 7.5). The origin of the photometric and spectroscopic data that we use
together with some of their inferred characteristics (i.e., redshift, distance
modulus, extinction, and explosion date) are presented in Table 3. This
comparison is mostly qualitative and focused on assessing whether the models
are fundamentally compatible with observations (e.g., if a slight shift in
kinetic energy could resolve a discrepancy) or whether there is something
fundamentally inadequate about the model (e.g., there is a missing physics,
process, or “ingredient” in the model). The comparison is also limited to
photospheric epochs (or at most the onset of the nebular phase). At later
times, a different approach is used in CMFGEN simulations in order to treat
chemical mixing in the ejecta (Dessart & Hillier, 2020), and this approach has
been applied to Type II SNe from 9 to 29 M⊙ single-star progenitors (Dessart
et al., 2021b, specifically, 9.0, 9.5, 10.0, 10.5, 11.0, 12., 12.5, 13.5,
14.5, 15.2, 15.7, 16.5, 17.5, 18.5, 20.1, 21.5, 25.2, and 26.5 M⊙) as well as
from 2.6 to 12 M⊙ He-star progenitors (Dessart et al., 2021a, corresponding to
a zero-age main sequence mass between 13.85 up to 35.74 M⊙; the specific He-
star models have masses of 2.6, 2.9, 3.3, 3.5, 4.0, 4.5, 5.0, 6.0, 7.0, 8.0,
and 12.0 M⊙, including progenitor models evolved with different mass loss
prescriptions).

To address some of the mismatches and to give a sense of how ejecta properties
impact the observables, we also include models computed in previous work using
a similar numerical approach with MESA, V1D, and CMFGEN. Namely, we
additionally include :

  1. 1.

The Type Ib model he4 from Dessart et al. (2020), with $M_{\rm ej}=$ 1.49 M⊙,
$E_{\rm kin}=$ 0.75 $\times$1051 erg, $M$(${}^{56}\rm{N}$i)$=$ 0.08 M⊙, and
$M$(He)$=$ 1.13 M⊙. Strong chemical mixing was enforced in this model, as well
as all others in that work. This model is used in Section 7.1.

  2. 2.

The Type IIb model 3p65Ax1 from Dessart et al. (2015), characterized by
moderate chemical mixing, and with $M_{\rm ej}=$ 2.22 M⊙, $E_{\rm kin}=$ 1.24
$\times$1051 erg, $M$(H)$=$ 0.005 M⊙, $M$(He)$=$ 1.49 M⊙, and
$M$(${}^{56}\rm{N}$i)$=$ 0.074 M⊙. This model is used in Section 7.2.

  3. 3.

The Type II-L/II-P model x2p0 from (Hillier & Dessart, 2019). This model
corresponds to a solar-metallicity single-star model for a 15 M⊙ progenitor on
the zero-age main sequence but evolved with a twice greater RSG mass loss rate
relative to the nominal value in MESA (as adopted in the corresponding version
– see Hillier & Dessart 2019 for details). The preSN progenitor has an H-rich
envelope mass of 9.24 M⊙. The corresponding ejecta have $E_{\rm kin}=$
1.2$\times$ 1051 erg, and $M$(${}^{56}\rm{N}$i)$=$ 0.036 M⊙. This model is
used in Section 7.5.

Figure 8: Comparison of model light curves and spectra with the observations
of iPTF13bvn. Top: we show the photometric data (black symbols) shifted in
time by $+8$ d and in magnitude by $-0.5$ mag as well as the results for model
logP2p75 (solid line). With such shifts, data and model are in close agreement
at $V$-band maximum. Middle: Same as top but for the model he4 of Dessart et
al. (2020), now with a shift in time of $+6$ d. Bottom: Comparison of
multiepoch spectra at about 5, 15, 30, and 85 d after explosion between the
observations of SN iPTF13bvn and models logP2p75 and he4 (no time shift has
been applied to the observed spectra).

###  7.1 Type Ib SN iPTF13bvn and model logP2p75

The top panel of Fig. 8 compares the multiband optical light curves of type Ib
SN iPTF13bvn with the results obtained for model logP2p75 whose H-deficient
progenitor had a surface radius of 12 R⊙. The model rises one week too slowly
and is 0.5 mag brighter than iPTF13bvn (both shifts were applied to the data
in Fig. 8). The model stays too bright after maximum (i.e., it declines too
slowly) and at late times in all bands except in the $U$ band. However, the
overall shape of the observed light curves is reproduced, including the
shorter rise time to maximum in bluer bands. The color at most epochs is also
well matched (with the global magnitude shift of $-0.5$ mag) although there is
a marked offset in the $U$ band by about 1 mag at all times (model is too
faint early on and too bright later on).

The bottom panel of Fig. 8 compares the multiepoch spectra of type Ib SN
iPTF13bvn with the results obtained for model logP2p75, specifically at about
5, 15, 30, and 85 d. The model predicts essentially all observed lines.
Overall, the model line widths are too small, with the exception of Ca ii
$\lambda\lambda\,8498-8662$. The ejecta density of the model is also too high
at late times because the model exhibits essentially no [Ca ii]
$\lambda\lambda$ $7291,\,7323$, which only appears when the material density
is low enough for forbidden-line formation. In the optical spectrum at 85 d,
all model lines appear much narrower than observed.

Some of these discrepancies are reduced by using model he4 ($E_{\rm kin}=$
0.75 $\times$ 1051 erg, $M_{\rm ej}=$ 1.49 M⊙, $M$(${}^{56}\rm{N}$i)$=$ 0.08
M⊙) from Dessart et al. (2020) – see middle and bottom panels of Fig. 8. The
rise time is shorter by 2 d, and this slight gain arises because of the lower
ejecta mass and the 5% higher $E_{\rm kin}/M_{\rm ej}$. The stronger chemical
mixing causes a faster brightening (more ${}^{56}\rm{N}$i at large velocities)
and the faster decline (more $\gamma$-ray escape at late times), but the light
curve is now too broad. The He i lines are too broad at early times (which
would argue against the adopted, strong mixing of ${}^{56}\rm{N}$i), but well
matched after 30 d. Another way to reduce the discrepancy is to increase the
explosion energy. This would shorten the rise time, brighten the peak, and
steepen the fading at late times due to the enhanced $\gamma$-ray escape. The
${}^{56}\rm{N}$i mass would need to be reduced since the peak would be too
bright, but this might bring the late-time brightness too low. We leave this
to future work.

Both models have roughly the same brightness as observed at the earliest times
(i.e., without applying a time shift of the data by six or eight days) so the
luminosity of the outermost ejecta layers is compatible with observations – it
is the rate at which radiation leaks from within the ejecta that is too small.
In other words, the brightening rate is too slow. The simulations of stripped-
envelope SNe with CMFGEN always yield rise times in excess of 20 d unless the
explosion energy is enhanced considerably, bringing in discrepancies with line
width or late-time decline rates (Dessart et al., 2015, 2016b) – reducing the
ejecta mass shortens the rise time but low-mass He-rich ejecta no longer match
the nebular-phase spectra of typical SNe Ib, which systematically show strong
[O i] $\lambda\lambda$ $6300,\,6364$ (see how weak [O i] $\lambda\lambda$
$6300,\,6364$ is in model he3p3 of Dessart et al. 2021a). Results from 1D
grey, flux-limited diffusion, lagrangian, radiation hydrodynamics simulations
yield a good match to the rise time and peak luminosity of iPTF13bvn with
ejecta parameters similar to those employed here (Bersten et al., 2014). This
suggests that different methods yield different diffusion models for the
ejecta. There may be concerns that the opacities, and therefore the diffusion
time, are overestimated in CMFGEN (e.g., because of the adoption of a
turbulent velocity of 50 km s-1), but a similar concern holds for radiation
hydrodynamics calculations since they use approximate opacity means that
typically hold in the dense interior of stars (i.e., these codes might
underestimate the opacities and the diffusion time).

A source of physical error in our CMFGEN simulations comes from the assumption
of a smooth and spherically symmetric ejecta. In reality, the ${}^{56}\rm{N}$i
bubble effect (Woosley, 1988) should lead to a strong expansion and
rarefaction of the ${}^{56}\rm{N}$i-rich regions and a compression of the
surrounding gas, causing clumping on small scales and large voids, as
predicted by long-term simulations of the neutrino-driven explosions (Gabler
et al., 2021) and also directly inferred from observations of SN remnants like
Cas A (see., e.g., Milisavljevic & Fesen 2015). Small scale clumping can
hasten the recombination of the ejecta material and speed up the recession of
the photospheric layers, thereby releasing the energy stored from optically-
thick layers (Dessart et al., 2018a). In addition, larger scale
inhomogeneities, arising in part from the ${}^{56}\rm{N}$i-bubble effect, can
also reduce the effective optical depth of the ejecta and contribute to
further enhance the release of stored energy from the ejecta (Dessart & Audit,
2019). Both effects have been confirmed to reduce the rise time and enhance
the peak brightness of stripped-envelope SNe (Ergon & Fransson, 2022; Ergon et
al., 2023).

Figure 9: Comparison of model light curves and spectra with the observations
of SN 2011dh. Top: we show the photometric data (black symbols) shifted in
time by $+7$ d and in magnitude by $-0.2$ mag as well as the results for model
logP2p80 (solid line). Middle: Same as top but for the model 3p65Ax1 of
Dessart et al. (2015), now with a shift in time of $+$6 d. Bottom: Comparison
of multiepoch spectra at about 5, 15, 30, and 85 d after explosion for SN
2011dh and models logP2p80 and 3p65Ax1.

###  7.2 Type IIb SN 2011dh and model logP2p80

The top panel of Fig. 9 compares the multiband optical light curves of type
IIb SN 2011dh with the results obtained for model logP2p80, whose progenitor
had a surface radius of 361 R⊙ and a H-rich envelope mass of 0.05 M⊙. The
disagreements between model and observations are similar to those discussed in
the previous section, namely that the model rises too slowly by about 7 d and
the model is too blue at late times. Here too the model and the observations
have initially the same brightness so it is the brightening rate of the model
on the rise to photometric maximum that is too slow. The model predicts a
clear inflection in all bands at 5$-$10 d, which is not obviously observed.
Hence, the progenitor H-rich envelope is a little too massive and extended,
yielding a luminosity that is too large during the first five to ten days
after explosion. Omitting this brightness offset at early times and the rise
time, the $R$-band light curve is very well reproduced by the model – this
good match would be degraded in the absence of the time shift applied to the
data (i.e., it would require adjusting the ejecta kinetic energy and
${}^{56}\rm{N}$i mass).

The bottom panel of Fig. 9 compares the multiepoch spectra of type IIb SN
2011dh with the results obtained for model logP2p80 (thick line). Overall, the
spectral evolution is well matched by the model but there are offsets. The
model is bluer at 5 d and after maximum, but not blue enough around peak
(though not by much). The H$\alpha$ line is too broad early on but too narrow
at 15 d, likely because we overestimated the amount of H mixed inwards to
lower velocity (likely in addition to overestimating $M$(H-env)). The He i
lines are well matched in width and strength at all times, which suggests that
the model has an adequate stratification of helium (and of ${}^{56}\rm{N}$i,
which is the source of excitation of He i lines). Ca ii
$\lambda\lambda\,8498-8662$ is too broad at all times. Either the outer ejecta
stretch out too much to large velocity or something quenches the ionization in
those outer layers, or both.

In the middle and bottom panels of Fig. 9, we also show the photometric and
spectroscopic results for model 3p65Ax1 of Dessart et al. (2015). The smaller
and lighter progenitor H-rich envelope lead to an ejecta with a faster drop in
post-breakout luminosity. The weaker chemical mixing leads to a short post-
breakout plateau before a brightening that is also too slow. However, this
model reproduces better the spectral evolution of SN 2011dh than model
logP2p80, in particular concerning the width, strength, and survival time of
H$\alpha$.

Most deficiencies of both models may be related to the ejecta clumping and
porosity related to the ${}^{56}\rm{N}$i bubble effect, which were both taken
into consideration, and found to be important, in the study of Ergon &
Fransson (2022) – see also Jerkstrand et al. (2015) for models supporting
similar structure from nebular phase spectra. An interesting mismatch of our
spectral models relative to SN 2011dh at late times is that both [O i]
$\lambda\lambda$ $6300,\,6364$ and [Ca ii] $\lambda\lambda$ $7291,\,7323$
appear too weak. The [O i] $\lambda\lambda$ $6300,\,6364$ would strengthen by
lowering the ionization, as could occur if the O-rich material was clumped by
the surrounding expanding ${}^{56}\rm{N}$i-rich material, while that lower-
density ${}^{56}\rm{N}$i-rich material may facilitate the early emergence of
the forbidden [Ca ii] $\lambda\lambda$ $7291,\,7323$. This needs further
study.

Figure 10: Same as Fig. 9 but now for model logP2p85 and the observations of
SN 1993J.

###  7.3 Type IIb SN 1993J and model logP2p85

For the Type IIb SN 1993J, we use for comparison the model logP2p85 whose
progenitor had an H-rich envelope of 0.14 M⊙ and a surface radius of 620 R⊙.
The model matches the two-peak light curve in all bands but only the timing of
the first peak is well matched while the second peak occurs one week too late
(the opposite impression is given in the top panel of Fig. 10 because the data
was shifted by $+7$ d to match the main ${}^{56}\rm{N}$i-powered peak). The
drop in brightness between the two peaks is too small, which suggests that the
power released from the shocked envelope lasts for too long. The envelope may
be too massive, too extended, perhaps both. As for the comparison to SN
2011dh, the model matches well the (shifted) $R$-band light curve of SN 1993J.

The spectral comparison shown in the bottom panel of Fig. 10 shows a good
overall agreement for most lines of H i, He i, Ca ii or Fe ii. There are
noticeable offsets at early times when the model does not match the observed
quasi featureless optical spectrum. The model overpredicts the absorption
strength of most lines (particularly for H$\alpha$). This may be caused by
asphericity (see, for example, evidence of this from light-echo spectra of Cas
A; Rest et al. 2011) or from interaction with a wind, which would occasion
flux dilution from excess continuum radiation in the optical (see, for
example, Dessart et al. 2023).

The overall agreement of model logP2p85 with SN 1993J supports, but is also
confirmed by, former modeling work of SN 1993J for which similar parameters
were inferred (Blinnikov et al., 1998; Nomoto et al., 1993; Podsiadlowski et
al., 1993; Woosley et al., 1994). However, when looking into the details of
our mismatches, we argue that there is evidence here too for the effect of
clumping and porosity, which were not taken into account in those older works
nor in the present one.

###  7.4 Type II-L SNe and models with intermediate $M$(H) values

There does not appear to be any clear observational counterpart to our models
with $M$(H) between 0.15 and 0.80 M⊙ (models logP2p95 to logP3p20). They
exhibit a fast-declining bolometric light curve, in principle qualitatively
analogous to those of Type II-L SNe, but their $V$-band light curve exhibits
two bright peaks that may even merge into a short-lived plateau of $\sim$ 50 d
before turning nebular. The first $V$-band peak is brighter than the main
${}^{56}\rm{N}$i-powered peak, although the relative brightness of each peak
could be modulated by varying the progenitor radius and the ${}^{56}\rm{N}$i
mass.

In the sample of Anderson et al. (2014b), some Type II SNe exhibit short-lived
plateau of about 50 d, such as SN 2006Y but this SN exhibits a very different
spectral evolution from that of our models (see the comparison with model
logP3p20 in the bottom panel of Fig. 11). Indeed, SN 2006Y shows nearly
featureless spectra early on, turning into a nearly-unchanging spectrum out to
100 d, with weak signs of metal-line blanketing and a strong and broad
H$\alpha$ line with little or no absorption – the H$\alpha$ line in SN 2006Y
even broadens in time. Such spectral features in SN 2006Y are indicative of
ejecta interaction with CSM (Dessart et al., 2016a; Dessart & Hillier, 2022),
as was observed even more conspicuously in events like SN 1998S (Leonard et
al., 2000; Fassia et al., 2000, 2001). The Type IIb SNe 2011fu and 2013df also
exhibited a double-peak $V$-band light curve, with the first peak brighter
than the second, ${}^{56}\rm{N}$i-powered peak and a spectral evolution
clearly suggestive of interaction, which also persisted until late times as is
evidenced by the broad, and eventually boxy H$\alpha$ profile (Morales-
Garoffolo et al., 2014, 2015). Other evidence that interaction may take place
at various levels in some Type IIb SNe comes from excess emission in the blue
part of the optical or in the UV (Ben-Ami et al., 2015). This interaction may
not swamp the radiation of the underlying SN, but it can considerably alter
the ejecta structure and the SN spectral properties and evolution, and this is
what complicates the comparison to the present set of models in which
interaction was ignored.

It is interesting that the observational sample contains no obvious cases of
Type II SNe with a short photospheric phase and no sign of interaction, like
in our model logP3p20. This suggests that the main sequence and RSG mass loss
is strong enough to strip entirely the progenitor H-rich envelope and lead to
a compact, H-deficient star at core collapse (then producing a stripped-
envelope SN or a failed SN with no luminous radiative display and black-hole
formation). Or such partially stripped stars (i.e., $M$(H) of order 1 M⊙) are
systematically connected to Case C systems that transfer mass to the companion
at or soon before core collapse (Ercolino et al., 2023) and produce peculiar
Type II SNe more closely connected to interacting SNe.

Figure 11: Same as Fig. 10 but now for model logP3p20 and the observations of
SN 2006Y.

###  7.5 Type II-P SN 2017eaw and model logP3p45

In this final comparison to observations, we consider model logP3p45 whose
progenitor evolved as a single star, never experiencing RLOF. The progenitor
lost mass nearly exclusively during the RSG phase through wind mass loss,
dying as a RSG star with a massive H-rich envelope mass of 6.81 M⊙ and
external radius of 898 R⊙. In Fig. 12, we compare the multi-band light curves
and spectra of model logP3p45 with the data from SN 2017eaw – no shift has
been applied in this figure, neither in time nor in magnitude.

The agreement between model logP3p45 and SN 2017eaw is relatively good but
there are several discrepancies in the light curves and spectra. The plateau
brightness matches but the plateau duration is too long and the nebular
luminosity is too large. Both could be resolved by having employed a lower
${}^{56}\rm{N}$i mass (i.e., instead of the adopted value of 0.09 M⊙, a lower
value of 0.045 M⊙ should be used; Szalai et al. 2019). The early-time
brightness is too faint in all bands and could be remedied by adding in some
CSM in the direct environment of the SN (Morozova et al., 2017; Moriya et al.,
2017; Dessart et al., 2017). Since no Type IIn signatures were observed at
early times (Szalai et al., 2019), it suggests dense and confined CSM directly
at the progenitor surface, but it is unclear whether this material implies a
boost to the progenitor mass loss immediately before core collapse (see, e.g.,
Morozova et al. 2017 or Moriya et al. 2017) or whether this is indicative of
material “stagnating” in the atmosphere of the RSG, in the transition zone
between the hydrostatic surface and the accelerating regions at the base of
the RSG wind (Dessart et al., 2017; Soker, 2021; Ercolino et al., 2023). An
extra ingredient, not present in off-the-shelf stellar evolution models of
Type II-P SN progenitors, is clearly needed to bring the $V$-band rise time of
“bare” RSG star progenitors from 20$-$30 d (as obtained here for model
logP3p45 or long ago in Dessart & Hillier 2011) to less than a week (see also
the sample of $V$-band rise times of González-Gaitán et al. 2015 or the
results from the HITS survey of Förster et al. 2018).

Another discrepancy of model logP3p45 is the underestimate of line widths
relative to SN 2017eaw. The model has narrower lines than observed, in
particular at early times when the spectrum forms in the fastest moving layers
of the ejecta. However, because the plateau brightness of the model is already
well matched, one cannot increase $E_{\rm kin}$ since that would not just
increase the line widths but also the plateau brightness. This is a recurrent
problem of employing RSG star progenitors with a very large radius (Dessart &
Hillier, 2011) and a solution to this problem was found by invoking a larger
mixing length parameter (Dessart et al., 2013; Paxton et al., 2018; Goldberg
et al., 2019). There is independent evidence that RSG star radii may be
smaller than typically assumed (Davies et al., 2013) and models of convective
RSG star envelopes also support a greater mixing length parameter (see, e.g.,
Goldberg et al. 2022, and more recently Chun et al. 2018). In Fig. 12, we show
the results for the model x2p0 of Hillier & Dessart (2019) whose RSG
progenitor radius was 582 R⊙ (rather than 898 R⊙ for model logP3p45). Model
x2p0 would match better the plateau brightness with a slightly higher $E_{\rm
kin}/M_{\rm ej}$ and $M$(${}^{56}\rm{N}$i) but this model is close to SN
2017eaw in terms of brightness, line widths, and spectral evolution, while
model logP3p45 is too bright for its expansion rate.

Figure 12: Same as Fig. 11 but now for models logP3p45 and x2p0 and the
observations of SN 2017eaw.

##  8 Conclusion

We have investigated the final fate as a SN for the primary stars, initially
of 12.6 M⊙, in the large grid of binary-star evolution models computed by
Ercolino et al. (2023). Focusing on systems with an initial mass ratio of 0.95
and initial orbital periods from 562 to 2818 d, we simulated the explosion
with radiation hydrodynamics and solved the NLTE time-dependent radiative
transfer for the corresponding SN ejecta from a few days after explosion to
the nebular phase. Since the He-core properties of all models were essentially
the same, a unique explosion energy of 1051 erg and ${}^{56}\rm{N}$i mass
(i.e., $\sim$ 0.09 M⊙) was adopted for the whole set to be on par with the
inferred properties of the Type IIb SN 1993J. However, because of the wide
range in residual H-rich envelope mass at the time of explosion, the SN models
yielded widely different SN light curves and multiepoch spectra.

With our grid of models varying initially only in orbital separation, we
recover a continuum of $V$-band light-curve morphologies from single- or
double-peak to plateau-like, reflecting the observed types associated with
stripped-envelope SNe (case B mass transfer systems), the fast-declining Type
II-L SNe (case BC and case C mass transfer systems) and Type II-P SNe (primary
stars without RLOF). This diversity reflects the range in preSN H mass (or
H-rich envelope mass), from zero to several solar masses. Namely, the shortest
period system produces a Type Ib SN with a single-peak
${}^{56}\rm{N}$i-powered $V$-band light curve and spectra exhibiting
unambiguous He i lines (as observed for example in SN iPTF13bvn). Progenitors
with intermediate $M$(H) values produce ejecta with double-peak light curves
or light curves in which these two peaks merge into a short high-brightness
plateau, with spectra exhibiting long-lived H i and He i lines (at the low
$M$(H) end, these explosions capture the essence of events like Type IIb SNe
2011dh or 1993J). And finally, progenitors with a massive H-rich envelope that
evolve essentially in isolation and produce a plateau light curve typical of
SNe II-P, with spectra exhibiting H i lines at all epochs (as observed for
Type II-P SNe like 2017eaw).

Although all case BC and case C systems in the study of Ercolino et al. (2023)
underwent a major mass-transfer event shortly before, or were transferring
mass at core collapse, we ignored ejecta interaction with CSM but find that it
may be the dominant process affecting SNe from progenitors with intermediate
H-rich envelope masses. Indeed, we found essentially no observed counterpart
having the properties of models logP2p95 to logP3p20 (i.e., with $M$(H)
between 0.15 to 0.8 M⊙), characterized by luminous double-peaked light curves
or short plateaus and broad-lined spectra (relative to SNe II-P). Events like
SN 2006Y shows similar light curves but its spectral evolution suggest
interaction dominates the whole evolution and such ejecta/CSM interaction is
ignored in our work. Lacking observational counterparts to our intermediate
$M$(H) models, we surmise that a large fraction of these case-BC and case-C
systems are at the origin of interacting SNe like SN 1979C or 1998S.

Figure 13: Comparison of the bolometric light curves for model logP2p80
(solid; smooth ejecta) and model logP2p80fcl (dashed; clumped ejecta). For the
clumped model, we adopt the same ejecta as for model logP2p80 but introduce a
volume filling factor for the material, with a value of 10% up to about 12 000
km s-1 and rising steeply to asymptote at 100% beyond.

Our grid of models also reveal a number of intrinsic properties of core-
collapse SN progenitors and ejecta. As before in Dessart et al. (2013), we
find that a RSG progenitor with a moderate radius of order 500 R⊙ yields a
better match to the plateau brightness, the timing for the onset of
recombination, and the line widths of Type II-P SNe. A larger radius as
employed in logP3p45 (i.e., $\sim$ 900 R⊙) yields a greater luminosity but a
smaller expansion rate, making it difficult to match the $V$-band brightness
during the plateau at the same time as the spectral line widths. This arises
from the fact that the bigger the star, the greater the amount of energy
channeled into radiation at the expense of kinetic energy. Other works
employing large RSG radii (i.e., stellar evolution models in which the mixing
length parameter is around 1.4 rather than 2 or 3) alleviate this problem by
invoking, for example low and non-standard explosion energies for Type II-P
SNe (e.g., Morozova et al. 2018).

The models discussed in this paper represent only the mass donor in binary
systems. For each donor in a stable mass transfer binary, we can expect one
mass gainer, which will likely explode as a RSG. Furthermore, of the order of
50% of the massive binaries are expected to merge (Podsiadlowski et al., 1992;
Langer et al., 2020). In either case, the product is expected to produce a RSG
progenitor at core collapse, with a hydrogen-rich envelope mass that exceeds
that of single stars with the same He-core mass, and that may be significantly
more helium enriched than corresponding single stars (Justham et al., 2014;
Menon et al., 2023). The RSGs from mass-gaining binary products could even
outnumber the RSGs produced by true single stars, and determine the appearance
of typical Type II-P SNe. The effects of more massive and/or helium-enriched
envelopes on the preSN star and associated SN explosion will be the subject of
a future study.

A discrepancy that has been plaguing CMFGEN simulations for Type IIb, Ib, and
Ic SNe since 2011 is the systematic overestimate of the rise time to the main,
${}^{56}\rm{N}$i-powered peak, with a delay of about a week relative to the
observations. Such offsets with data are typically not present in our
simulations for Type Ia SNe although the same power source and diffusion
process lies behind these light curves (see, e.g., rise times in Blondin et
al. 2017). Modulations in chemical mixing is often invoked (see, e.g., Bersten
et al. 2013, Dessart et al. 2015, or more recently Park et al. 2023), but this
seems to be contradicted by the strong impact it has on He i line profiles at
early times (i.e., stronger mixing yields broader He i lines, all else being
the same and in particular the explosion energy) and the values inferred from
neutrino-driven explosions (Wongwathanarat et al., 2015). What we are most
likely lacking here is a proper description of the ejecta structure, which is
not smooth and spherically symmetric (as assumed here), but instead clumped
and structured on small and large scales due to the physics of neutrino-driven
explosions and the action of the ${}^{56}\rm{N}$i-bubble effect over time
(Woosley, 1988; Gabler et al., 2021). Clumping is known to hasten
recombination and the recession of the photosphere towards the inner ejecta,
thereby releasing on a shorter time scale the energy stored in the optically-
thick layers of the ejecta (Dessart et al., 2018a). To illustrate this effect
here for a stripped-envelope SN, we show in Fig. 13 the bolometric light curve
obtained for model logP2p80 without clumping (same model as described earlier)
and with clumping (model logP2p80fcl), confirming the effect obtained for BSG
star explosions in Dessart et al. (2018a). The ${}^{56}\rm{N}$i-bubble effect
also creates large cavities surrounded by denser, shell-like structures
through which radiation can escape more easily because of the reduced
effective opacity (Dessart & Audit, 2019). These effects should be present in
essentially all core-collapse SNe because they derive from the same explosion
mechanism. Ergon & Fransson (2022) and Ergon et al. (2023) have demonstrated
that such inhomogeneous ejecta structure can shorten the rise time and also
boost the luminosity at maximum.

###### Acknowledgements.

CPG acknowledges financial support from the Secretary of Universities and
Research (Government of Catalonia) and by the Horizon 2020 Research and
Innovation Programme of the European Union under the Marie Skłodowska-Curie
and the Beatriu de Pinós 2021 BP 00168 programme, from the Spanish Ministerio
de Ciencia e Innovación (MCIN) and the Agencia Estatal de Investigación (AEI)
10.13039/501100011033 under the PID2020-115253GA-I00 HOSTFLOWS project, and
the program Unidad de Excelencia María de Maeztu CEX2020-001058-M. This work
was granted access to the HPC resources of TGCC under the allocation 2022 –
A0130410554 made by GENCI, France. This research has made use of NASA’s
Astrophysics Data System Bibliographic Services.

## References

  * Anderson et al. (2014a) Anderson, J. P., Dessart, L., Gutierrez, C. P., et al. 2014a, MNRAS, 441, 671
  * Anderson et al. (2014b) Anderson, J. P., González-Gaitán, S., Hamuy, M., et al. 2014b, ApJ, 786, 67
  * Barbon et al. (1995) Barbon, R., Benetti, S., Cappellaro, E., et al. 1995, A&AS, 110, 513
  * Ben-Ami et al. (2015) Ben-Ami, S., Hachinger, S., Gal-Yam, A., et al. 2015, ApJ, 803, 40
  * Bersten et al. (2014) Bersten, M. C., Benvenuto, O. G., Folatelli, G., et al. 2014, AJ, 148, 68
  * Bersten et al. (2012) Bersten, M. C., Benvenuto, O. G., Nomoto, K., et al. 2012, ApJ, 757, 31
  * Bersten et al. (2013) Bersten, M. C., Tanaka, M., Tominaga, N., Benvenuto, O. G., & Nomoto, K. 2013, ApJ, 767, 143
  * Blinnikov & Bartunov (1993) Blinnikov, S. I. & Bartunov, O. S. 1993, A&A, 273, 106
  * Blinnikov et al. (1998) Blinnikov, S. I., Eastman, R., Bartunov, O. S., Popolitov, V. A., & Woosley, S. E. 1998, ApJ, 496, 454
  * Blondin et al. (2017) Blondin, S., Dessart, L., Hillier, D. J., & Khokhlov, A. M. 2017, MNRAS, 470, 157
  * Blondin et al. (2023) Blondin, S., Dessart, L., Hillier, D. J., Ramsbottom, C. A., & Storey, P. J. 2023, A&A, 678, A170
  * Bose et al. (2015) Bose, S., Sutaria, F., Kumar, B., et al. 2015, ApJ, 806, 160
  * Bostroem et al. (2023) Bostroem, K. A., Dessart, L., Hillier, D. J., et al. 2023, ApJL, 953, L18
  * Cao et al. (2013) Cao, Y., Kasliwal, M. M., Arcavi, I., et al. 2013, ApJL, 775, L7
  * Chun et al. (2018) Chun, S.-H., Yoon, S.-C., Jung, M.-K., Kim, D. U., & Kim, J. 2018, ApJ, 853, 79
  * Davies et al. (2013) Davies, B., Kudritzki, R.-P., Plez, B., et al. 2013, ApJ, 767, 3
  * Dessart & Audit (2019) Dessart, L. & Audit, E. 2019, A&A, 629, A17
  * Dessart et al. (2023) Dessart, L., Gutiérrez, C. P., Kuncarayakti, H., Fox, O. D., & Filippenko, A. V. 2023, A&A, 675, A33
  * Dessart & Hillier (2005a) Dessart, L. & Hillier, D. J. 2005a, A&A, 439, 671
  * Dessart & Hillier (2005b) Dessart, L. & Hillier, D. J. 2005b, A&A, 437, 667
  * Dessart & Hillier (2011) Dessart, L. & Hillier, D. J. 2011, MNRAS, 410, 1739
  * Dessart & Hillier (2019) Dessart, L. & Hillier, D. J. 2019, A&A, 625, A9
  * Dessart & Hillier (2020) Dessart, L. & Hillier, D. J. 2020, A&A, 643, L13
  * Dessart & Hillier (2022) Dessart, L. & Hillier, D. J. 2022, A&A, 660, L9
  * Dessart et al. (2017) Dessart, L., Hillier, D. J., & Audit, E. 2017, A&A, 605, A83
  * Dessart et al. (2016a) Dessart, L., Hillier, D. J., Audit, E., Livne, E., & Waldman, R. 2016a, MNRAS, 458, 2094
  * Dessart et al. (2011) Dessart, L., Hillier, D. J., Livne, E., et al. 2011, MNRAS, 414, 2985
  * Dessart et al. (2021a) Dessart, L., Hillier, D. J., Sukhbold, T., Woosley, S. E., & Janka, H. T. 2021a, A&A, 656, A61
  * Dessart et al. (2013) Dessart, L., Hillier, D. J., Waldman, R., & Livne, E. 2013, MNRAS, 433, 1745
  * Dessart et al. (2018a) Dessart, L., Hillier, D. J., & Wilk, K. D. 2018a, A&A, 619, A30
  * Dessart et al. (2015) Dessart, L., Hillier, D. J., Woosley, S., et al. 2015, MNRAS, 453, 2189
  * Dessart et al. (2016b) Dessart, L., Hillier, D. J., Woosley, S., et al. 2016b, MNRAS, 458, 1618
  * Dessart et al. (2021b) Dessart, L., John Hillier, D., Sukhbold, T., Woosley, S. E., & Janka, H. T. 2021b, A&A, 652, A64
  * Dessart et al. (2010a) Dessart, L., Livne, E., & Waldman, R. 2010a, MNRAS, 408, 827
  * Dessart et al. (2010b) Dessart, L., Livne, E., & Waldman, R. 2010b, MNRAS, 405, 2113
  * Dessart et al. (2020) Dessart, L., Yoon, S.-C., Aguilera-Dena, D. R., & Langer, N. 2020, A&A, 642, A106
  * Dessart et al. (2018b) Dessart, L., Yoon, S.-C., Livne, E., & Waldman, R. 2018b, A&A, 612, A61
  * Eldridge et al. (2018) Eldridge, J. J., Xiao, L., Stanway, E. R., Rodrigues, N., & Guo, N. Y. 2018, PASA, 35, e049
  * Ensman & Woosley (1988) Ensman, L. M. & Woosley, S. E. 1988, ApJ, 333, 754
  * Ercolino et al. (2023) Ercolino, A., Jin, H., Langer, N., & Dessart, L. 2023, arXiv e-prints, arXiv:2308.01819
  * Ergon & Fransson (2022) Ergon, M. & Fransson, C. 2022, A&A, 666, A104
  * Ergon et al. (2023) Ergon, M., Lundqvist, P., Fransson, C., et al. 2023, arXiv e-prints, arXiv:2308.07158
  * Ergon et al. (2014) Ergon, M., Sollerman, J., Fraser, M., et al. 2014, A&A, 562, A17
  * Fassia et al. (2001) Fassia, A., Meikle, W. P. S., Chugai, N., et al. 2001, MNRAS, 325, 907
  * Fassia et al. (2000) Fassia, A., Meikle, W. P. S., Vacca, W. D., et al. 2000, MNRAS, 318, 1093
  * Förster et al. (2018) Förster, F., Moriya, T. J., Maureira, J. C., et al. 2018, Nature Astronomy, 2, 808
  * Fremling et al. (2016) Fremling, C., Sollerman, J., Taddia, F., et al. 2016, A&A, 593, A68
  * Fremling et al. (2014) Fremling, C., Sollerman, J., Taddia, F., et al. 2014, A&A, 565, A114
  * Gabler et al. (2021) Gabler, M., Wongwathanarat, A., & Janka, H.-T. 2021, MNRAS, 502, 3264
  * Gilkis & Arcavi (2022) Gilkis, A. & Arcavi, I. 2022, MNRAS, 511, 691
  * Goldberg et al. (2019) Goldberg, J. A., Bildsten, L., & Paxton, B. 2019, ApJ, 879, 3
  * Goldberg et al. (2022) Goldberg, J. A., Jiang, Y.-F., & Bildsten, L. 2022, ApJ, 929, 156
  * González-Gaitán et al. (2015) González-Gaitán, S., Tominaga, N., Molina, J., et al. 2015, MNRAS, 451, 2212
  * Grassberg et al. (1971) Grassberg, E. K., Imshennik, V. S., & Nadyozhin, D. K. 1971, Astrophysics and Space Science, 10, 28
  * Gutiérrez et al. (2014) Gutiérrez, C. P., Anderson, J. P., Hamuy, M., et al. 2014, ApJL, 786, L15
  * Gutiérrez et al. (2017) Gutiérrez, C. P., Anderson, J. P., Hamuy, M., et al. 2017, ApJ, 850, 89
  * Hachinger et al. (2012) Hachinger, S., Mazzali, P. A., Taubenberger, S., et al. 2012, MNRAS, 422, 70
  * Hillier & Dessart (2012) Hillier, D. J. & Dessart, L. 2012, MNRAS, 424, 252
  * Hillier & Dessart (2019) Hillier, D. J. & Dessart, L. 2019, A&A, 631, A8
  * Hillier & Miller (1998) Hillier, D. J. & Miller, D. L. 1998, ApJ, 496, 407
  * Hiramatsu et al. (2021) Hiramatsu, D., Howell, D. A., Moriya, T. J., et al. 2021, ApJ, 913, 55
  * Jerkstrand et al. (2015) Jerkstrand, A., Ergon, M., Smartt, S. J., et al. 2015, A&A, 573, A12
  * Justham et al. (2014) Justham, S., Podsiadlowski, P., & Vink, J. S. 2014, ApJ, 796, 121
  * Kasen & Woosley (2009) Kasen, D. & Woosley, S. E. 2009, ApJ, 703, 2205
  * Langer et al. (2020) Langer, N., Schürmann, C., Stoll, K., et al. 2020, A&A, 638, A39
  * Laplace et al. (2021) Laplace, E., Justham, S., Renzo, M., et al. 2021, A&A, 656, A58
  * Leonard et al. (2000) Leonard, D. C., Filippenko, A. V., Barth, A. J., & Matheson, T. 2000, ApJ, 536, 239
  * Li et al. (2012) Li, C., Hillier, D. J., & Dessart, L. 2012, MNRAS, 426, 1671
  * Liu et al. (2016) Liu, Y.-Q., Modjaz, M., Bianco, F. B., & Graur, O. 2016, ApJ, 827, 90
  * Livne (1993) Livne, E. 1993, ApJ, 412, 634
  * Lucy (1991) Lucy, L. B. 1991, ApJ, 383, 308
  * Matheson et al. (2000) Matheson, T., Filippenko, A. V., Barth, A. J., et al. 2000, AJ, 120, 1487
  * Menon et al. (2023) Menon, A., Ercolino, A., Urbaneja, M. A., et al. 2023, arXiv e-prints, arXiv:2311.05581
  * Milisavljevic & Fesen (2015) Milisavljevic, D. & Fesen, R. A. 2015, Science, 347, 526
  * Modjaz et al. (2019) Modjaz, M., Gutiérrez, C. P., & Arcavi, I. 2019, Nature Astronomy, 3, 717
  * Morales-Garoffolo et al. (2014) Morales-Garoffolo, A., Elias-Rosa, N., Benetti, S., et al. 2014, MNRAS, 445, 1647
  * Morales-Garoffolo et al. (2015) Morales-Garoffolo, A., Elias-Rosa, N., Bersten, M., et al. 2015, MNRAS, 454, 95
  * Moriya et al. (2017) Moriya, T. J., Yoon, S.-C., Gräfener, G., & Blinnikov, S. I. 2017, MNRAS, 469, L108
  * Morozova et al. (2015) Morozova, V., Piro, A. L., Renzo, M., et al. 2015, ApJ, 814, 63
  * Morozova et al. (2017) Morozova, V., Piro, A. L., & Valenti, S. 2017, ApJ, 838, 28
  * Morozova et al. (2018) Morozova, V., Piro, A. L., & Valenti, S. 2018, ApJ, 858, 15
  * Nakar & Piro (2014) Nakar, E. & Piro, A. L. 2014, ApJ, 788, 193
  * Nomoto et al. (1993) Nomoto, K., Suzuki, T., Shigeyama, T., et al. 1993, Nature, 364, 507
  * Panagia et al. (1980) Panagia, N., Vettolani, G., Boksenberg, A., et al. 1980, MNRAS, 192, 861
  * Park et al. (2023) Park, S. H., Yoon, S.-C., & Blinnikov, S. 2023, arXiv e-prints, arXiv:2310.16328
  * Paxton et al. (2011) Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192, 3
  * Paxton et al. (2013) Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4
  * Paxton et al. (2015) Paxton, B., Marchant, P., Schwab, J., et al. 2015, ApJS, 220, 15
  * Paxton et al. (2018) Paxton, B., Schwab, J., Bauer, E. B., et al. 2018, ApJS, 234, 34
  * Paxton et al. (2019) Paxton, B., Smolec, R., Schwab, J., et al. 2019, ApJS, 243, 10
  * Podsiadlowski et al. (1993) Podsiadlowski, P., Hsu, J. J. L., Joss, P. C., & Ross, R. R. 1993, Nature, 364, 509
  * Podsiadlowski et al. (1992) Podsiadlowski, P., Joss, P. C., & Hsu, J. J. L. 1992, ApJ, 391, 246
  * Rest et al. (2011) Rest, A., Foley, R. J., Sinnott, B., et al. 2011, ApJ, 732, 3
  * Richmond et al. (1996) Richmond, M. W., Treffers, R. R., Filippenko, A. V., & Paik, Y. 1996, AJ, 112, 732
  * Richmond et al. (1994) Richmond, M. W., Treffers, R. R., Filippenko, A. V., et al. 1994, AJ, 107, 1022
  * Sana et al. (2012) Sana, H., de Mink, S. E., de Koter, A., et al. 2012, Science, 337, 444
  * Schneider et al. (2021) Schneider, F. R. N., Podsiadlowski, P., & Müller, B. 2021, A&A, 645, A5
  * Shahbandeh et al. (2022) Shahbandeh, M., Hsiao, E. Y., Ashall, C., et al. 2022, ApJ, 925, 175
  * Soker (2021) Soker, N. 2021, ApJ, 906, 1
  * Srivastav et al. (2014) Srivastav, S., Anupama, G. C., & Sahu, D. K. 2014, MNRAS, 445, 1932
  * Stritzinger et al. (2018) Stritzinger, M. D., Anderson, J. P., Contreras, C., et al. 2018, A&A, 609, A134
  * Swartz (1991) Swartz, D. A. 1991, ApJ, 373, 604
  * Szalai et al. (2019) Szalai, T., Vinkó, J., Könyves-Tóth, R., et al. 2019, ApJ, 876, 19
  * Tsvetkov et al. (2018) Tsvetkov, D. Y., Shugarov, S. Y., Volkov, I. M., et al. 2018, Astronomy Letters, 44, 315
  * Van Dyk et al. (2019) Van Dyk, S. D., Zheng, W., Maund, J. R., et al. 2019, ApJ, 875, 136
  * Williamson et al. (2019) Williamson, M., Modjaz, M., & Bianco, F. B. 2019, ApJL, 880, L22
  * Wongwathanarat et al. (2015) Wongwathanarat, A., Mueller, E., & Janka, H.-T. 2015, A&A, 577, A48
  * Woosley (1988) Woosley, S. E. 1988, ApJ, 330, 218
  * Woosley et al. (1994) Woosley, S. E., Eastman, R. G., Weaver, T. A., & Pinto, P. A. 1994, ApJ, 429, 300
  * Yaron & Gal-Yam (2012) Yaron, O. & Gal-Yam, A. 2012, PASP, 124, 668
  * Yaron et al. (2017) Yaron, O., Perley, D. A., Gal-Yam, A., et al. 2017, Nature Physics, 13, 510
  * Yoon (2017) Yoon, S.-C. 2017, MNRAS, 470, 3970
  * Yoon et al. (2017) Yoon, S.-C., Dessart, L., & Clocchiatti, A. 2017, ApJ, 840, 10
  * Yoon et al. (2010) Yoon, S.-C., Woosley, S. E., & Langer, N. 2010, ApJ, 725, 940
  * Yuan et al. (2016) Yuan, F., Jerkstrand, A., Valenti, S., et al. 2016, MNRAS, 461, 2003
  * Zheng et al. (2022) Zheng, W., Stahl, B. E., de Jaeger, T., et al. 2022, MNRAS, 512, 3195

##  Appendix A Additional figures for all models

Figure 14: Spectral evolution of models logP2p75, logP2p80, logP2p85, and
logP2p90. The CMFGEN time sequences are computed at time steps $t_{i}$ such
that $t_{i+1}/t_{i}=$ 1.1. Here, we show fewer time steps for better
visibility so that $t_{iplot+1}/t_{iplot}\sim$ 1.3. As for Fig. 6, we
illustrate the flux associated with He i lines (dark shade) and H i lines
(light shade).

Figure 15: Same as Fig. 14 but now for models logP2p95, logP3p00, logP3p10,
and logP3p20.

Figure 16: Same as Fig. 14 but now for models logP3p35 and logP3p45.

Figure 17: Evolution of the H$\alpha$ profile for our set of models. We show
the flux obtained by accounting for all bound-bound transitions subtracted
from the flux obtained by ignoring those associated with H i. The fluxes are
normalized by the peak H$\alpha$ flux in the “full” model. These profiles are
used to compute the ratio of the absorption to the emission flux in H$\alpha$
(see Fig. 7).