The diversity of late-time interaction in Type II supernovae

Introduction

Most of the observations of core-collapse supernovae (SNe) are focused on their early phase of evolution when they are optically bright (see, for example, [3, 46, 43, 15]). Because of the exponential decline of radioactive decay power, SN ejecta become increasingly faint and eventually undetectable on timescales of months to years. SN 1987A is an exception in this respect as it continues to be observed today only because of its proximity (see, e.g., [1]) – it would be undetectable at any representative SN distance of 10 Mpc or more. Consequently, SNe may be detected at later times only if there is another power source, either from the compact remnant (e.g., the Type Ib SN 2012au; [59]) or from interaction with circumstellar material (CSM; e.g., the Type II-P SN 2017eaw; [76]). Such old SNe can thus shed light on the physics of young compact objects or on the progenitor mass loss history. Furthermore, injected power is probed by the material reprocessing that power (e.g. progenitor composition), providing different constraints from early time observations. There is thus much interest in studying SNe at late times, on year timescales or more, as they transition to a young supernova remnant.

For the current sample of late-time detections in core-collapse SNe, and nearly exclusively in Type II SNe (there are rare cases such as the Type Ib SN 2014C; [58, 54]), the power source seems to be interaction with CSM. In events initially classified as Type IIn SNe, the objects continue to be detected until late times suggesting the presence of a large reservoir of CSM out to large distances. One such example is SN 1998S which was interacting from first light ([51, 31]) and for years afterwards ([36, 71]). In some other events, the signatures of interaction with CSM are evident at first light (i.e., presence of narrow lines with electron-scattering broadened wings) but ebb after a few days. The transient then evolves with what appears to be a noninteracting SN for months until clear signs of interaction emerge again after 1–2 years. One such event is SN 2023ixf, which showed IIn signatures for about a week (see, e.g., [48, 6]), followed by a photospheric evolution in which the signatures of interaction were limited to a slight excess in the UV and some excess flux in H$\alpha$ ([7]). And it is only later on in the nebular phase that the UV flux came to dominate the spectral energy distribution (i.e., the CSM interaction came to dominate the radioactive decay), with a morphing of line profiles in the optical from narrow to broad and boxy [50, 34, 47, 80, 8]. Other events show no signs of interaction until about two years. However, the optical brightness then switches from an exponential decline to a plateau while the spectra exhibit a morphological change from narrow emission lines powered by radioactive decay in the inner ejecta to broad and boxy emission profiles arising from the outer ejecta (e.g., SN 2004et, Kotak et al. 2009; SN 2013ej, Mauerhan et al. 2017; SN 2017eaw, Weil et al. 2020).

The picture described above is, however, strongly sensitive to the wavelength range where the observations are undertaken. The UV is thought to dominate the escaping radiation of year-old SNe with interaction [10, 20, 18], and thus optical observations alone may not be conclusive. Furthermore, dust is thought to form both in the inner, metal-rich ejecta as well as in the outer ejecta (or the cold dense shell – CDS – that forms at the interface with the CSM), causing both absorption in the optical and thermal emission in the IR [e.g. 52, 67, 68, 69].

Numerical modeling of the radiation arising from Type II SNe interacting with CSM on a 1–10 yr timescale have been carried out since the 1990s. Chevalier & Fransson [10] modeled the evolution of UV-optical-IR line fluxes for the first decades following the explosion of a standard red-supergiant star and the interaction of the ejecta with the progenitor wind. Chevalier [9] studied the radio and X-ray emission properties of Type II SNe [for a review see 11], with specific studies of nearby events like SN 1993J [37]. Fransson et al. [36] presented UV and optical observations of SNe 1993J and 1998S extending out to a few years and found evidence for CNO processing from UV emission line ratios. But most of these studies focused on the properties of the high-energy radiation that escapes, and much less on the UV and optical properties of the associated transients. In particular, none of these works provide a complete modeling of the spectra of the low-energy radiation, from UV to optical and infrared.

Our approach differs in that it leaves aside the details of the power injection and focuses instead on the reprocessing of the shock power by the ejecta and CDS and how this shapes the SN spectrum from the UV to the IR. The method was presented in Dessart & Hillier [20] and Dessart et al. [18] and recently applied to SN 2023ixf [26 a]. One motivation for using this approach is that late-time SNe II with interaction exhibit mostly emission lines in the UV and optical from material of modest ionization, suggesting that the shock power at the origin of the UV and optical radiation is efficiently thermalized. Consequently, this approach makes no prediction for the escaping X-ray radiation.

The majority of massive stars are born in binaries that will interact during their evolution (e.g., see Sana et al. 2012, 2025), leading to a transfer of mass to the companion (or mass loss by the binary system) that far exceeds the impact of wind mass loss in stars of moderate mass, or to the merger of the two stars [e.g. 78]. Thus, to extend our previous work on a generic 15 M$_\odot$ single star that exploded as a massive red supergiant [20, 18], we here employed progenitor models that evolved in a binary system and reached core collapse with different levels of stripping, yielding final H-rich envelope masses that span from about 0.1 to 7 M$_\odot$ [30]. In the absence of any CSM, these exploding stars produce a range of SN photometric and spectroscopic properties that mimic the trend from SNe IIb, to II-L and II-P [17] – see also, for example, Eldridge et al. [29] or Hiramatzu et al. (2021). In this work, we explore how these different SNe evolve from 1.5 to 3–6 years under the influence of interaction with CSM, varying for that purpose the CDS mass and velocity, or the power injected. We thus document the broad diversity of UV and optical signatures of ejecta interaction with CSM for the full range of Type II SNe and their associated supergiant-star progenitors.

This paper is structured as follows. In Section 2 we present the numerical setup. Section 3 describes the spectral evolution from 1.5 year (i.e., 500 d) to about 6 years for one representative model. In Section 4, we use one of our models to explore the impact of varying the CDS mass at a given epoch. In Section 5, we explore how these results differ when the mass of the progenitor H-rich envelope is varied. The subsequent sections present specific comparisons to contemporaneous UV and optical observations of SN 1993J (Section 6.1), SN 1998S (Section 6.2), SN 2013ej (Section 6.3; optical data only), and SN 2023ixf (Section 6.4). In Section 7, we present our conclusions. Additional illustrations are provided in the appendix in Section B.

Numerical setup

The numerical approach used for the present radiative-transfer simulations is identical to that presented in Dessart et al. (2026b,a) for the modeling of SN 2023ixf at photospheric and nebular epochs, and given in more details in Dessart & Hillier [20] and Dessart et al. [18]. The treatment of shock power injection is either in the form of high-energy electrons deposited with a prescribed spatial distribution (as in Dessart & Hillier 2022; Dessart et al. 2023) or in the form of X-rays (for details, see Appendix A of Dessart 2024, as well as Section 4 of Dessart et al. 2026a) – the former is used by default and the latter invoked to cure specific discrepancies of the former (e.g., the presence of Ly$\alpha$ at early times in the nebular phase of SN 2023ixf [25] or the presence of [O III] $\lambda\lambda$ 4958.9, 5006.8) or to gauge the uncertainties associated with the treatment of power injection. In this work, the spatial distribution of the X-ray power injection has a gaussian profile, which by default was centered on the CDS and with a standard deviation of 35 km s$^{-1}$. This centroid was sometimes shifted away from the CDS (typically by a few 10 km s$^{-1}$) to bias the power injection in favor of the reverse shock or of the forward shock. Such modulations were carried out in § 6 to test the sensitivity of our results and exploring possible ways of improving the agreement with observations. We thus constrain the nature, magnitude, and distribution of the injected power by confronting to UV and optical observations.

A fundamental difference with our previous work on late-time SNe II interacting with CSM is that we now broaden the range of envelope stripping of the progenitors. For a given explosion energy, this leads to a different ejecta structure and composition, including the mean expansion rate, the velocity of the H-rich material, or the He and N abundance in the H-rich material. Observationally, it covers from SNe of Type IIb to those of Type II-P and thus the broadest possible range in H-rich envelope mass for Type II SNe. Specifically, we used the models of Dessart et al. [17], which originate from a subset of binary massive star evolution models presented in Ercolino et al. [30]. Our sample is differentiated in terms of initial binary period, which in days and in the log have the value of 2.85, 2.90, 2.95, 3.0, 3.1, 3.2, 3.35, and 3.45 (these models are thus named logP2p85 etc).

To allow for a flexible, parameterized approach, we make a number of simplifications. First, to avoid the sharp variations in density that arise from 1D radiation-hydrodynamics of red-

supergiant star explosions (see Fig. 2 of Dessart et al. [17], we reset their density structure using the procedure of Chugai et al. [13]. That is, adopting the $M_{\rm ej}$ and $E_{\rm kin}$ of the original model, a new ejecta density structure is calculated, and the original composition is then remapped in Lagrangian mass space onto that new structure – the procedure is then repeated for all ejecta models in our sample. The ${}^{56}\mathrm{Ni}$ abundance profile was reset to enforce strong mixing for the same mass of 0.08 M$_\odot$, followed by a renormalization to maintain the sum of mass fractions at unity. Only the ${}^{56}\mathrm{Ni}$ radioactive decay chain is considered here and associated isotopes were decayed to the start time of 500 d used in this work for all simulations. These simplifications were motivated by the fact that the model of Dessart et al. [18] computed at an age of 1000 d took one full month to converge because of the complex shuffled-shell composition structure (for details see Dessart & Hillier [19], which requires about 350 grid points, as well as the numerical difficulties arising from the Notes: The table gives some details about the progenitor star, the ejecta, and the CDS parameters used in our simulations. From left to right, the columns first give the final mass, the H-rich envelope mass, and the surface He mass fraction of the progenitor stars at core collapse, followed by the CDS velocity and mass, and finally the epochs at which the radiative transfer calculations were carried out together with the range of powers adopted (either in the form of high-energy, nonthermal electrons or as X-rays). In all cases, the original ejecta (i.e., without a CDS) contains 0.08 $M_{\odot}$ of $^{56}\mathrm{Ni}$ and have a kinetic energy of $10^{51}$ erg.

outer CDS where shock power is injected. Here, with the smooth composition and density structure of our ejecta, only 70 points are necessary (leaving aside for now the CDS) and numerical convergence is greatly facilitated, allowing us to explore a broad parameter space.

All these models were then augmented with a CDS, with mass $M_{\mathrm{CDS}}$ and velocity $V_{\mathrm{CDS}}$. Rather than running radiation-hydrodynamics simulations from shock breakout out to late times, we approximated the structure at the time of 500 d. Based on results from previous radiation-hydrodynamics simulations of SNe II with CSM (see Figure 1 here, or the Fig. 2 of Dessart & Jacobson-Galán [24]), we assumed here that a given CSM mass would decelerate the same amount of ejecta material, and that the CDS would be centered at a velocity corresponding to that Lagrangian mass in the ejecta (i.e., $M_{\mathrm{ej}} - 0.5M_{\mathrm{CDS}}$). Hence, half the CDS is composed from the CSM and the other half from the ejecta. All else being the same, a greater CDS mass corresponds to a deeper CDS location (i.e., a greater deceleration of the outer ejecta) and a closer proximity to the metal-rich ejecta regions. Obviously, this effect is exacerbated in progenitors with a lower $M(\mathrm{H\text{-}env})$. In this work, the bare ejecta models of Dessart et al. [17] were augmented by a CDS with a mass that covers from 0.1 up to 2.0 $M_{\odot}$. Not all combinations were considered.

The CDS density profile was set to have a gaussian shape with a centroid at $V_{\mathrm{CDS}}$ and a standard deviation of 70 $\mathrm{km\ s^{-1}}$. The material within the CDS was also clumped such that the volume filling factor was given by $1 - (1-a)\exp(-X^2)$, with $X=(V-V_{\mathrm{CDS}})/dV_{\mathrm{CDS}}$, $dV_{\mathrm{CDS}}=100\ \mathrm{km\ s^{-1}}$, and $a=0.01$ – this ensures strong clumping within the CDS and none exterior to it. From models logP2p85 to logP3p45 (thus spanning $M(\mathrm{H\text{-}env})$ from 0.19 to 6.86 $M_{\odot}$) and augmented with a 0.2 $M_{\odot}$ CDS, the velocity of the CDS decreases from 10643 to 6390 $\mathrm{km\ s^{-1}}$. For model logP3p35 augmented with an increasing CDS mass from 0.1 to 2.0 $M_{\odot}$, the centroid velocity of the CDS decreases from

7627 to 5002 $\mathrm{km\ s^{-1}}$. Our present simulations are not meant to be perfectly hydrodynamically consistent (it is obviously possible to compute large grids of simulations for many configurations, as done for one progenitor star in Dessart & Jacobson-Galán [24], but this is unnecessary for the present conceptual study – none of our results rest, for example, on the claim that the CDS moves at $X\ \mathrm{km\ s^{-1}}$ or 5% faster or slower etc) nor do they reflect consistently the progenitor mass loss history, which is never known accurately anyway.

Figure 2 illustrates the properties of model logP3p35 for a variety of CDS masses, as well as the impact of going from the 1D hydrodynamical model of Dessart et al. [17] to the smooth, analytical counterpart with the same $M_{\mathrm{ej}}$, $E_{\mathrm{kin}}$, and abundance profiles in mass space. Figure 3 shows how the different progenitors differ in structure and composition for the same adopted CDS mass of 0.2 $M_{\odot}$. For the same adopted $E_{\mathrm{kin}}$ and $M_{\mathrm{CDS}}$, the CDS velocity is systematically greater for lower $M_{\mathrm{ej}}$ (enhanced progenitor stripping). The abundances of He and N are also notably greater in the CDS for more stripped progenitors.

We typically used a constant power injection inside the CDS at all times, with a representative value of $10^{40}\ \mathrm{erg\ s^{-1}}$. Additional models were done with different power magnitudes, changing the nature of that power (i.e., injection of high-energy electrons or X-rays), or changing the injection profile. The choice of a constant power is a convenience. It overestimates the power in the case of a decreasing CSM density (see, e.g., Chevalier & Fransson [10]) but the CSM density profile is not known a priori. Ultimately, this model set is a solid base to compare to observations and adjust the adopted properties of the injection power as suggested by the data.

The model nomenclature is such that logP3p35/mcds0p2/pwr1e40 corresponds to the progenitor logP3p35 (i.e., a primary star in a system with an original binary period of $10^{3.35}$ or 2238 d) from Dessart et al. [17], augmented with a CDS mass of 0.2 M$_\odot$ and with an injected power (in the form of high-energy electrons) of $10^{40}$ erg s$^{-1}$. Were this power injected in the form of X-rays, the name would be logP3p35/mcds0p2/xray1e40. When the power was injected away from the CDS centroid, the model name is appended with “vlocX” where $X$ is the new adopted velocity centroid (in km s$^{-1}$). All simulations started at 500 d but the end time was often dictated by numerical difficulties (e.g., models with a lighter CDS were harder to converge at late times), and thus covers from $\sim1000$ to $\sim2000$ d. Table 1 summarizes the set of simulations we carried out in this work.

Progenitor	$M_{\mathrm{f}}$	$M(\mathrm{H\text{-}env})$	$X_{\mathrm{s}}(\mathrm{He})$	$V_{\mathrm{CDS}}$	$M_{\mathrm{CDS}}$	Epochs	Power
	[$M_{\odot}$]	[$M_{\odot}$]		[$\mathrm{km\ s^{-1}}$]	[$M_{\odot}$]	[d]	[$\mathrm{erg\ s^{-1}}$]
logP2p85	3.92	0.19	0.48	10643	0.2	550 $\to$ 976	1e40, 3e39
logP2p90	4.06	0.28	0.44	10492	0.2	550 $\to$ 976	1e40, 3e39
logP2p95	4.14	0.31	0.41	10476	0.2	550 $\to$ 1181	1e40, 3e39
logP3p00	4.26	0.39	0.39	9834	0.2	550 $\to$ 1074	1e40, 1e39
logP3p10	4.51	0.60	0.36	9670	0.2	550 $\to$ 1299	1e40, 3e39
logP3p20	5.18	1.18	0.32	9231	0.2	550 $\to$ 1299	1e40, 3e39, 5e38
logP3p35	7.97	3.74	0.30	6966	0.2	550 $\to$ 1429	1e40, 3e39
logP3p45	10.84	6.86	0.30	6390	0.2	550 $\to$ 2000	1e40, 3e39
logP3p35	7.97	3.74	0.30	7627	0.1	550 $\to$ 887	1e40
logP3p35	7.97	3.74	0.30	6966	0.2	550 $\to$ 1429	1e40, 3e39
logP3p35	7.97	3.74	0.30	6325	0.4	550 $\to$ 1902	1e40, 3e39
logP3p35	7.97	3.74	0.30	5984	0.6	550 $\to$ 1074	1e40, 3e39
logP3p35	7.97	3.74	0.30	5743	0.8	550 $\to$ 1729	1e40, 3e39
logP3p35	7.97	3.74	0.30	5563	1.0	550 $\to$ 1902	1e40, 3e39
logP3p35	7.97	3.74	0.30	5222	1.5	550 $\to$ 1729	1e40, 3e39
logP3p35	7.97	3.74	0.30	5002	2.0	550 $\to$ 1902	1e40, 3e39

As stated at the start of this section, the radiative transfer modeling was done using the same approach as in Dessart et al. [25]. However, our model atom, which is identical for all simulations, includes higher ionization stages (specifically with stages iii and iv for CNO and intermediate mass elements) as well as a very large number of levels for iron-group elements. More ionization stages ensure that the gas can cool over a wide range of densities and temperature, which is essential at late times when the densities are low and when the gas is potentially energized by X-rays. A large model atom for iron-group element ensures that we are not underestimating the gas opacity, again for a wide range of densities and temperatures. Details on the model atom are given in Appendix § 8.

Finally, when comparing our models to observations, we sometimes invoke dust. The treatment of dust was adopted from Dessart et al. [27] using a C-rich and Si-rich dust mixture as in the modeling of SN 2023ixf (Dessart et al. [25]). Dust properties (i.e., spatial distribution and amount) were given in the corresponding sections where dust is introduced, with the same nomenclature as in Dessart et al. [25]. For example, in the section describing a specific SN and a model, the dust characteristics labelled as “ej/2em4/0p035/cds/1em4/0p035” would refer to dust in the inner, metal-rich ejecta (typically below 2500 km s$^{-1}$) with a temperature of 350 K and a mass of $2 \times10^{-4}$ M$_\odot$, together with dust in the CDS with a temperature of 350 K and a mass of $10^{-4}$ M$_\odot$. At present, the dust is made of the same grain composition and size in a given calculation (only the spatial distribution and temperature can be modified).

Dependence on time

Figure 4 shows the evolution of the spectra as well as individual line fluxes for model logP3p35/mcds0p4/pwr1e40 from 550 until 1902 d after explosion. Throughout most of the UV and optical, iron is the main element that sculpts the spectral appearance with only localized emission of stronger individual, generally forbidden lines. These lines are typically broad and boxy in the optical and infrared with a full Doppler width corresponding to twice the CDS velocity ($V_{\rm CDS}$ is 6325 km s$^{-1}$ in this model). In the UV, all lines suffer strong optical depth effects and appear with a flux deficit that increases from the blue edge to the red edge. In some cases, this is caused by the intrinsically large optical depth of the line (e.g., Ly $\alpha$), but it also stems from the optical depth arising from other lines (e.g., forests of lines from Fe ii and Fe iii – see also Figure 2 of Dessart et al. [25]). The Lyman continuum is highly optically thick across the CDS but the Balmer continuum is optically thin at 550 d. Hence, in Figure 4, the noticeable narrowing of emission lines towards smaller wavelengths arises not only because Doppler broadening scales linearly with wavelength but also because of the increased profile skewness.

In the bottom panel of Figure 4, we show the fractional power radiated in individual emission lines. For the strong Ly $\alpha$ line, this is measured from the total flux spectrum, but for weaker lines, this is measured from the model spectrum computed by accounting only for the associated species. This is necessary because of the severe optical depth effects, which prevent a simple calculation of those fluxes. Consequently, the line fluxes are indicative (this problem applies as well to real data from which the evaluation of line fluxes are very uncertain, in particular for emission lines in the UV where Fe absorption and emission impacts all lines). In this model at 550 d, the strongest line in the spectrum is Mg ii $\lambda\lambda$ 2795, 2802, followed by H$\alpha$ and [Ca ii] $\lambda\lambda$ 7291.5, 7323.9, and a myriad of other lines than carry one percent or less of the bolometric luminosity – Ly $\alpha$ carries only 0.73 %. As time passes, Mg ii $\lambda\lambda$ 2795, 2802 remains roughly constant and the spectral energy distribution pivots around it as it shifts from optical to UV dominated. At 1902 d, Ly $\alpha$ has become the strongest line (i.e., 47.3 %) followed by Mg ii $\lambda\lambda$ 2795, 2802 (10.1 %), H$\alpha$ (1.1 %), [O i] $\lambda\lambda$ 6300.3, 6363.8 (0.9 %) and a myriad of other lines at 0.5 % or less. The strongest coolants in the CDS that carry away the injected power are therefore Ly $\alpha$ and Mg ii $\lambda\lambda$ 2795, 2802. However, 74 % (34 %) of the flux is carried away by iron lines at 550 d (1902 d) so these iron lines are amongst the top coolants of the CDS (in this model the decay power represents only about a third of the shock power at 500 d, about a tenth at 600 d, and about a hundredth at 800 d – see also Dessart et al. [18]).

Figure 4 includes numerous weak lines. There is generally a strengthening of forbidden lines by a factor of a few from 550 to 1902 d but these remain subdominant relative to Ly $\alpha$, Mg ii $\lambda\lambda$ 2795, 2802 and the forest of Fe lines. There is also a shift to higher ionization, illustrated for example by the strengthening of the contribution from [O ii] $\lambda\lambda$ 7319.5, 7330.2 in the 7300 Å region relative to [Ca ii] $\lambda\lambda$ 7291.5, 7323.9. [N ii] $\lambda\lambda$ 6548.0, 6583.5 and [N ii] $\lambda$ 5755 are both present at all times, the former contributing a sizable fraction of the emission around 6550 Å and the latter overlapping with Na i $\lambda\lambda$ 5896, 5890.

In the red part of the optical, the model shows a complex evolution from a mix of decay-powered (relatively narrow lines emitted from the inner ejecta) and shock-powered (relatively broad lines emitted from the CDS) emission lines to lines arising exclusively from the CDS. This includes [Ca ii] $\lambda\lambda$ 7291.5, 7323.9 which becomes increasingly broad and contaminated by [O ii] $\lambda\lambda$ 7319.5, 7330.2 at late times. At 550 d and at longer wavelengths, the strong emission from He i $\lambda$ 10830.2 overlaps with several lines of Si i and S ii as well as Pa $\gamma$, but this region becomes dominated at later times by a mix of broad boxy emission from Mg ii 9231.2 Å, [S ii] $\lambda\lambda$ 10286.7, 10370.5, [S iii] $\lambda$ 9530.62, He i $\lambda$ 10830.2, and Mg ii 10914.2 Å.

Dependence on CDS mass

Figure 5 shows the evolution of the spectra as well as individual line fluxes when the CDS mass is increased from 0.1 to 2.0 M$_\odot$ – we use model logP3p35 at 976 d with the same power injection of $10^{40}$ erg s$^{-1}$ for this comparison. This change in CDS mass also comes with a change in CDS velocity, since the more massive it is the slower it is (see Table 1). Hence, for higher CDS mass, the conditions in the CDS are denser, cooler, more optically thick, and the associated emission is less Doppler broadened. This is most strongly seen in the plunging of the Ly $\alpha$ emission from the strongest line for $M_{\rm CDS}$ of 0.1 M$_\odot$ to a negligible coolant for $M_{\rm CDS}$ of 2.0 M$_\odot$ (in which case 71 % of the total cooling occurs through Fe emission). This drop is caused by the large CDS optical depth in Ly $\alpha$ itself but also from the influence of overlapping Fe lines. Mg ii $\lambda\lambda$ 2795, 2802 remains essentially constant across these values of $M_{\mathrm{CDS}}$.

The lower CDS ionization at higher $M_{\mathrm{CDS}}$ leads to stronger lines from neutral species (e.g., [O i] $\lambda\lambda$ 6300.3, 6363.8 versus [O ii] $\lambda\lambda$ 7319.5, 7330.2) and a weakening of transitions arising from higher excited states (e.g., Mg ii 9218.2 Å). In the models with the larger CDS velocity (i.e., lower $M_{\mathrm{CDS}}$), H$\alpha$ and [O i] $\lambda\lambda$ 6300.3, 6363.8 overlap. This leads to an excess emission on the blue side of H$\alpha$ although this excess is commensurate to the strength of [O i] $\lambda\lambda$ 6300.3, 6363.8 (specifically the red component of the doublet) – this overlap is also clearly visible in the breakdown of species contributions in the model spectra shown in the appendix, for example those used for the comparison to SN 2013ej. Overall, there is a relatively weak sensitivity of most of the lines to $M_{\mathrm{CDS}}$ (the most sensitive line being Ly $\alpha$), which suggests that our results should not be overly compromised by the simplicity of our model setup.

Dependence on progenitor H-rich envelope mass

Figure 6 shows the results for the set of progenitors endowed with an H-rich envelope between 0.1 and 6.86 $M_{\odot}$ at the time of explosion (i.e., models logP2p85 to logP3p45). The time is 976d after explosion, the shock power is $10^{40}$ erg s$^{-1}$, and the CDS mass is 0.2 $M_{\odot}$ for the whole set. As in the case of a varying $M_{\mathrm{CDS}}$, the lower is $M$(H-env) the higher is the expansion rate of the ejecta and by extension that of the CDS (see Table 1). Hence, for the same $M_{\mathrm{CDS}}$, the CDS is of a lower density, which leads in our simulations to more ionized conditions in the CDS (for a fixed injected power). Furthermore, the gas is more He and N rich for lower $M$(H-env) (see also Table 1 and Figure 3) – it covers a range of a factor of three at the progenitor surface in the set logP2p85 to logP3p45. Altogether, these variations affect the coolants, although mostly for the lowest values of $M$(H-env) (i.e., less than 0.3 $M_{\odot}$).

We find that Ly $\alpha$ and Mg ii $\lambda\lambda$ 2795, 2802 are the strongest coolants at all times (in competition with the bulk cooling effect of Fe lines) but their importance is modulated at low $M$(H-env) because of an increased contribution from N lines (e.g., N iii] 1749.2 Å or [N ii] $\lambda\lambda$ 6548.0, 6583.5). The higher ionization at lower $M$(H-env) also boosts the strength of [O ii] $\lambda\lambda$ 7319.5, 7330.2 and also leads to the clear presence of [O iii] $\lambda\lambda$ 4958.9, 5006.8 and [Ne iii] $\lambda$ 3868.8 (which overlap with Fe lines as well as [S ii] $\lambda$ 4068.6) in model logP2p85. In the red part of the spectrum, there is a broad blend of

Notes: a: Matheson et al. [55]; b: Fransson et al. [36]; c: Fassia et al. [32]; d: Leonard et al. [51]; e: Yuan et al. [77]; f: Mauerhan et al. [56]; g: Jacobson-Galán et al. [48]; h: Bostroem et al. [8]; i: Dessart et al. [25].

[S II] $\lambda\lambda$ 10286.7, 10370.5, He I $\lambda$ 10830.2, and Mg II 10914.2 Å. In all models, H$\alpha$ and [O I] $\lambda\lambda$ 6300.3, 6363.8 remain strong in the optical.

Comparison to observations

In this section, we use the grid of models described above to compare to UV (if available) and optical spectra of a sample of Type II SNe at late times of 1.5–3 years after explosion. We consider here in a chronological manner the SNe 1993J (§ 6.1), 1998S (§ 6.2), 2013ej (§ 6.3), and 2023ixf (§ 6.4). The SN characteristics used for each are given in Table 2. In all comparisons, we corrected the observations for redshift and reddening and scaled the model to the SN distance. We generally plotted the flux $F_{\nu}$ rather than $F_{\lambda}$ because it yields a flatter flux distribution across the UV and optical and thus improves the visibility. A log scale was, however, used for the flux because of the large contrast in line strengths.

SN name	$t_{\mathrm{expl}}$ [MJD]	$cz$ [km s$^{-1}$]	$D$ [Mpc]	$E(B-V)$ [mag]	Ref.
SN 1993J	49074.0	33.9	3.63	0.2	a, b
SN 1998S	50875.2	905.4	17.0	0.22	b, c, d
SN 2013ej	56497.5	659.5	9.0	0.06	e, f
SN 2023ixf	60082.8	241.0	6.85	0.041	g, h, i

Comparison to SN 1993J at 976–1063 d

The Type IIb SN 1993J has been extensively analyzed and modeled over the years. The light curve supports a heavily stripped progenitor with an extended $\sim0.1\,M_{\odot}$ H-rich envelope at the time of explosion (Filippenko et al. [33]; Blinkov et al. 1998; Nomoto et al. [61]; Dessart et al. [17]), compatible with a preSN evolution in an interacting binary (Podsiadlowski et al. [63]). This was independently confirmed by the identification of both the progenitor star as a K-type supergiant (Aldering et al. [2]; Van Dyk et al. [75]) and the existence of a companion star (Maund et al. [57]; Fox et al. [35]). At late times, interaction of the ejecta with CSM was inferred, for example, from the flattening of the SN optical brightness after about a year (Zhang et al. [79]) but also from the sustained emission in the optical producing broad boxy line profiles (Matheson et al. [55]; Houck & Fransson [45]), or from X-ray emission (Uno et al. [72]; Nymark et al. [62]). UV observations of SN 1993J at late times revealed the presence of strong Ly$\alpha$, Mg II $\lambda\lambda$ 2795, 2802, as well as a myriad of weaker emission lines from CNO suggesting N enrichment (Fransson et al. [36]).

In this section, we compare some of our models to the observations of SN 1993J. We used an epoch around three years after explosion when both UV and optical data were collected. From our model set, we took a heavily stripped progenitor and selected a model with a CDS mass (and thus velocity) suitable to match the emission line widths observed in SN 1993J. Figure 7 compares the UV data of Fransson et al. [36] at 1063 d² and the optical data of Matheson et al. [55] at 976 d with a couple of models based on the progenitor logP2p90 with a CDS mass of $0.2\,M_{\odot}$, an age of 976 d and an injected power of $10^{40}$ erg s$^{-1}$. To test the sensitivity of the power injection and go beyond the set of models presented in earlier sections, we treated this power in the form of high-energy electrons (model pwr1e40) or in the form of X-rays (model xray1e40). In both cases, the power was injected with the same spatial distribution given by a gaussian with a centroid at 10492 km s$^{-1}$ (coinciding with the center of the CDS where the density is maximum) and a standard deviation of 35 km s$^{-1}$. Because there is little evidence for dust in these observations, dust was ignored in the two models shown.

Figure 7 suggests a broad overall agreement of both models, driven by the fact that the bulk of the power is absorbed within the densest parts of the CDS which in both cases remains cool and partially ionized (i.e., $\sim10\,000$ K; H, He, O neutral; Ca and Fe once ionized). However, in the X-ray case, the small fraction of X-rays that escape from the CDS and are absorbed above and below it cause a surge in temperature and ionization in those regions (i.e., 20–50 000 K; H fully ionized; He once and twice ionized; O three to four times ionized; Ca four times ionized; Fe five times ionized). In the model with a prescribed profile for the deposition of high-energy electrons, only the resulting radiation may photoionize the surrounding medium. This does not occur in the present case and the two models deviate consequently in a number of ways. In particular, the model with X-rays exhibits a number of high-ionization lines lacking in the pwr1e40 model, such as the O iv multiplet around 1400 Å, N iv 1486.5 Å, C iv 1550 Å, [Ne iii] $\lambda$ 3868.8 or [O iii] $\lambda\lambda$ 4958.9, 5006.8. The flux in Ly $\alpha$ and Mg ii $\lambda\lambda$ 2795, 2802 are the strongest emission lines in SN 1993J as well as in both models. A specificity of SN 1993J are the strong N lines, in particular [N ii] $\lambda$ 5755 and [N ii] $\lambda\lambda$ 6548.0, 6583.5 (which is nearly as strong as H$\alpha$ in both models), which arises both from the relatively high ionization in the CDS (nitrogen is once ionized) and the N enrichment in this progenitor (see also § 5 and Figure 6). Another specificity of SN 1993J is the broad and boxy appearance of many lines, not only in the optical but also in the UV (e.g., N ii] 2142.8 Å, Mg ii $\lambda\lambda$ 2795, 2802). The optical range provides a good alternative to assess N enrichment relative to the UV (Fransson et al. [36]), which is unobservable from the ground and strongly affected by metal line blanketing even at late times.

Comparison to SN1998S at 485–494d.

We now turn to SN 1998S and its long lived and multiple signatures of interaction with CSM. The presence of CSM in the immediate proximity of the exploding star led to the formation of emission lines with symmetric, electron-scattering broadened lines that survived for about a week (Leonard et al. [51]; Chugai [12]; Fassia et al. [31]; Shivvers et al. (2015); Dessart et al. [21, 28]). A percent-level polarization was also observed during this early interaction phase (Leonard et al. [51]) and is compatible with an axisymmetric, extended, ionized, optically-thick CSM with a pole-to-equator density contrast of a few (Dessart et al. [28]). Interaction with CSM continued during the photospheric phase, as evidenced from the peculiar H$\alpha$ line profile morphology with a strong and broad emission and a lack of P-Cygni absorption typical of standard Type II SNe (Dessart et al. [21]; Hillier & Dessart [41]). Nebular times saw the formation of molecules and dust, most likely in the CDS (Gerardy et al. [39]; Pozzo et al. [64]; Dessart et al. [27]).

(2025a). UV observations also indicated persisting interaction at late times, with strong Ly $\alpha$ and Mg ii $\lambda\lambda$ 2795, 2802 emission as well as emission lines from CNO elements from which Fransson et al. [36] inferred an elevated N enrichment.

In this section, we revisit these previous works, including our previous studies, and used our set of models to produce a rough description of SN 1998S at about 490 d when both UV and optical data are available. We used the optical data at 494 d from Leonard et al. [51] and the UV data at 485 d from Fransson et al. [36]. For the models, we selected one of the logP3p35 models with a CDS velocity that matched that of SN 1998S, which is around 5000 km s$^{-1}$. This meant using a CDS mass of 2.0 $M_{\odot}$, which may be on the heavy side but as we found in § 4 the sensitivity to CDS mass is not large. We then adjusted the power injected to produce a model in line with the SN brightness, although it is mitigated by dust attenuation in this SN. Indeed, Dessart et al. [27] found that the amount of dust needed to reproduce the optical line profile asymmetries in SN 1998S also caused a $\sim2$ mag extinction in the optical range. We employed a power injection of $2 \times10^{41}$ erg s$^{-1}$ and in the form of X-rays.

When that power in the form of X-rays is injected within the CDS (i.e., with a gaussian profile centered at 5002 km s$^{-1}$ on the CDS and with a standard deviation of 35 km s$^{-1}$), the Ly $\alpha$ flux is essentially zero. Shifting the X-ray injection to regions below the CDS leads to even greater reduction, not just of Ly $\alpha$ but of the entire UV flux, and in disagreement with the observations of SN 1998S (Figure 8). This UV attenuation is caused by the large optical depth of the CDS, which is great in the UV and huge in Ly $\alpha$. Only models with an X-ray power injection exterior to the CDS produced a sizable Ly $\alpha$ emission. In practice, to match the observations of SN 1998S, we had to shift the centroid of the X-ray injection to 5052 km s$^{-1}$, thus 50 km s$^{-1}$ faster than the CDS centroid. With this choice, the outer parts of the CDS produce the entire emission from the SN. This arises mostly from the fact that the column density is smaller from such regions, leading to reduced optical depth. But it also arises from the enhanced ionization in those regions, which shuts off blanketing effects from Fe II or Fe III (see also discussion in Dessart et al. [25]). Indeed, the outer regions of the CDS are then dominated by ions like He$^{+}$, O$^{2+}$, or Fe$^{3+}$. With our assumption of homologous expansion, the model thus predicts broad emission lines from such ionized species – these predicted lines are also blueshifted because of optical-depth effects. In the observations, there is clear emission from N IV 1486.5 Å, C IV 1550 Å or He II 1640 Å, but the lines are narrow and indicates their formation in the unshocked CSM. There is thus some physical basis in the model predictions in terms of power injection and ionization stratification, the main limitation of the code in this sector being the inadequate assumption of homology which leads to the prediction of broad emission when sometimes it is instead narrow.

Figure 9 compares the observations of SN 1998S at 485 d (UV; Fransson et al. [36]) and 494 d (optical; Leonard et al. [51]) with the model exhibiting strong Ly $\alpha$, Mg II $\lambda\lambda$ 2795, 2802, and H$\alpha$, namely model logP3p35/mcds2p0/xray2e41/550d/vloc5052. The figure includes both the model without dust (blue) and with dust (red: ej/2em4/0p035/cds/1em4/0p035). The agreement is good for Ly $\alpha$, Mg II $\lambda\lambda$ 2795, 2802, and H$\alpha$, in particular with a good match to the peak flux of these three landmarks. There is however significant offsets for the weaker features although most of the observed emission lines are also present in the model. In the optical, He I lines at 5875 and 7065 Å are predicted, together with [Ca II] $\lambda\lambda$ 7291.5, 7323.9 ([O I] $\lambda\lambda$ 7319.5, 7330.2 is very weak in the model) – the skewness of the profiles caused by dust complicates the identification. The Ca II NIR triplet is contaminated by a strong O I 8446.5 Å, which is unusual at such late epochs but arises from the high density in the CDS. What is lacking is the presence of extended emission from Fe II in the optical, which is very strong in the model not just in the optical but also in the UV – the entire spectrum is essentially an iron spectrum if one ignores the three strongest lines (Ly $\alpha$, Mg II $\lambda\lambda$ 2795, 2802, and H$\alpha$).

The model with dust reproduces roughly the blue-red asymmetry of H$\alpha$ with $2 \times10^{-4} M_{\odot}$ of dust in the inner ejecta and $10^{-4} M_{\odot}$ of dust in the CDS – this is a lower dust mass than obtained in Dessart et al. [27] because we adopted here a mixture of C-rich and Si-rich dust (same choice as in Dessart et al. [25]) whereas we used Silicate dust only in Dessart et al. [27]. Invoking dust to explain the H$\alpha$ profile asymmetry may be an oversimplification since a reversed profile skewness is observed in the interacting SN PTFl 11iqb (Smith et al. [71]) – both dust and asymmetry (of either or both ejecta and CSM) may be involved. The introduction of dust has little impact on the UV in this matching model for SN 1998S (Figure 9).

Comparison to SN2013ej at 807d.

The Type II SN 2013ej is characterized by a long rise time, a short photospheric phase, and a steep decline during the photospheric phase (Valenti et al. [74]; Bose et al. [5]). Utrobin & Chugai [73] proposed a large ejecta mass of 23–25 $M_{\odot}$ with a standard $E_{\rm kin}$ but high-velocity $^{56}$Ni. Interaction with CSM is, however, likely at the origin of a number of peculiarities observed in SN 2013ej. The presence of CSM in the immediate environment of the progenitor improves the match to the light curve during the photospheric phase (Morozova et al. [60]). Using a $1.2\times10^{51}$ erg $\sim11\,M_{\odot}$ ejecta with early CSM interaction, Hillier & Dessart [41] could match the multi-band light curves and spectra of SN 2013ej during the photospheric phase, including the peculiar line profile shapes (e.g., H$\alpha$) – the weak absorption relative to the emission is one signature of previous or ongoing interaction with CSM in SNe II (see also [40, 20, 14]). Interaction with CSM was independently supported from X-ray detection (Margutti et al. [53]). Modeling of nebular-phase observations suggest a 12–15 $M_{\odot}$ progenitor ([77, 22]), also compatible with inferences based on pre-explosion photometry (Fraser et al. [38]). Remarkably, SN 2013ej continued to be detectable at very late times of a few years, indicative of ongoing interaction with CSM, together with infrared thermal emission associated with dust formation (Mauerhan et al. [56]).

Figure 10 compares the observations of SN 2013ej at 807 d (black; Mauerhan et al. [56]) and the model logP3p20 at 887 d with $M_{\mathrm{CDS}}=0.2\,M_{\odot}$ and an injection of X-rays with a total power of $5\times10^{38}$ erg s$^{-1}$ either centered at 9231 km s$^{-1}$ (blue curve; this corresponds to the maximum density in the CDS) or below the CDS at 9000 km s$^{-1}$ (red curve; model whose name contains vloc9e3). In both cases, the power injection follows a gaussian profile with a standard deviation of 35 km s$^{-1}$. A mixture of 350 K Si-rich and C-rich 1.0 $\mu$m dust grains is used in both models with $5\times10^{-3}\,M_{\odot}$ uniformly distributed below 2500 km s$^{-1}$ and $4\times10^{-3}\,M_{\odot}$ within the dense shell at 9231 km s$^{-1}$. Neither model matches all features but each matches well a subset of features.

The model with X-ray injection within the CDS overestimates the strength of [O I] $\lambda\lambda$6300, 6363, 6838 and H$\alpha$ but yields a satisfactory match to most other regions, including those around [S II] $\lambda$4068.6, [Ne III] $\lambda$3868.8, [O III] $\lambda\lambda$4958.9, 5006.8, He I 7065 Å, or [Ca II] $\lambda\lambda$7291.5, 7323.9. The model with the deeper X-ray injection matches better the [O I] $\lambda\lambda$6300, 6363.8 and H$\alpha$ but yields a worse match of the [Ne III] $\lambda$3868.8 and [O III] $\lambda\lambda$4958.9, 5006.8 region. These differences arise from the different impact of the dust located in the CDS relative to power injection within the CDS or below. If dust is external to the emission, it produces no blue-red asymmetry in the associated emission line profiles. So, while the intrinsic [O III] $\lambda\lambda$4958.9, 5006.8 emissivity is comparable in both models, the dusty model with X-ray injection within the CDS yields a better match of that feature because the blue-red asymmetry arises from the optically-thick dust in the CDS. The other model shows a flat emission around 5000 Å (a large part of this emission comes from Fe, as for the 4300 Å bump) because this emission comes from below the dust-rich CDS. This exercise shows how difficult it is to match the whole spectrum consistently and indicates that inferences of dust properties from individual profiles can be problematic since unblended lines are rare below 5500 Å.

Comparison to SN2023ixf at 723–998d

Previous work on nebular phase observations of SN 2023ixf clearly indicated that the SN was essentially entirely powered by interaction after about two years. This arose from the progressive strengthening of the UV relative to the optical ([47, 8, 25]), but also from the dominance of broad-boxy emission lines in the optical at later times relative to the dominance of narrow emission lines from the decay-powered inner ejecta ([50, 80, 25] (FolatelI et al. 2025)), in close correspondence to predictions (Dessart et al. [18]).

In this section, we extend the previous work of Dessart et al. [25] and present simulations based on model logP3p35 with a CDS mass of $0.2\,M_{\odot}$ and velocity of 6966 km s$^{-1}$ (which is more suitable to match the widths of emission lines like H$\alpha$ than the fixed value of 8000 km s$^{-1}$ used for all nebular epochs in Dessart et al. [25]). Using this model as a reference, numerous attempts were carried out by varying the interaction power (its magnitude, location, as well as its nature as high-energy electrons or X-rays) and the dust properties. For the latter, the amount of dust in the inner ejecta is largely irrelevant for the UV and optical range since most of that radiation at $\gtrsim2$ yr arises from the outermost ejecta regions (i.e., around the CDS). So, as far as the UV and optical are concerned, there can be as much inner-ejecta dust as one wishes – we adopted here $5\times10^{-4}\,M_{\odot}$ uniformly distributed below 2500 km s$^{-1}$.

Figure 11 shows a comparison between the UV (at 723 d) and optical (at 998 d) observations of SN 2023ixf and the model logP3p35/mcds0p2/pwr5e39 at 1074 d with and without dust – the slow evolution in the UV at those late times justifies merging data with such a large time offset (Jacobson-Galán et al., in prep.). The dust in the CDS at 6970 km s$^{-1}$ corresponds to $2\times10^{-4}\,M_{\odot}$ of a mixture of 350 K Si-rich and C-rich 0.1 $\mu$m grains. As before ([27, 25]), we find that the dust has a moderate impact on the UV because it forms in the outer parts of the CDS and thus largely external to the dust-rich regions – this impact is less obvious in the UV because UV lines exhibit a blue-red asymmetry even in the absence of dust. But it impacts the optical significantly (where most lines are optically thin in the absence of dust), with a blue-red asymmetry as well as a central dip in emission lines that arises from a greater attenuation from the limbs of the CDS (this feature is in part an artefact of the assumed spherical symmetry). The inset indicates that most of the spectrum is shaped by iron emission and absorption. Exceptions are Ly $\alpha$, N ii] 2142.8 Å, Mg ii $\lambda\lambda$ 2795, 2802, [S ii] $\lambda$ 4068.6, [Ne iii] $\lambda$ 3868.8 (underestimated by the model, although the data show no evidence for [O iii] $\lambda\lambda$ 4958.9, 5006.8), [N ii] $\lambda$ 5755, Na i $\lambda\lambda$ 5896, 5890, [O i] $\lambda\lambda$ 6300.3, 6363.8, H$\alpha$, [Fe ii] $\lambda$ 7155.2, [Ca ii] $\lambda\lambda$ 7291.5, 7323.9, [O ii] $\lambda\lambda$ 7319.5, 7330.2, and [Ni ii] $\lambda\lambda$ 7377.8, 7411.6. The match of the dusty model is somewhat superior to that presented in Dessart et al. [25] mostly because of the reduced CDS velocity (in that paper, the optical observations at 998 d were analyzed on their own).

Conclusions

In this work, we revisited our previous late-time radiative-transfer studies of ejecta interaction with CSM ([20, 18]) by considering a wide range of red-supergiant progenitors endowed with an H-rich envelope mass spanning from 0.19 to 6.86 $M_\odot$ as a result of binary mass exchange. In the absence of CSM, such explosions would produce SNe with properties typical of Type IIb or Type II with various decline rates from II-L to II-P ([17]). The main motivation for this work was to produce models capable of reproducing the UV and optical data of emblematic, well-observed, nearby SNe past the age of one year, which is the representative epoch for nebular phase observations or models for Type II SNe, and extend this to several years. Such (published and public) data exist for our selected sample, which includes SNe 1993J, 1998S, 2013ej, and 2023ixf.

To alleviate the difficulty of modeling such ejecta at late times of 500 to 2000 d, we made a number of simplifications by adopting ejecta with a smooth density structure, a mixed composition, and a fixed $^{56}$Ni mass of 0.08 $M_\odot$. These ejecta were augmented with a CDS covering a range of masses (0.1 to 2.0 $M_\odot$) and velocities (5002 to 10643 km s$^{-1}$) suitable for weak to strong interactions in this progenitor set. The shock power was treated in the form of high-energy electrons or X-rays injected with a gaussian profile in or around the CDS. The emerging radiation from such interacting ejecta encodes the complexity inherent to core-collapse SN ejecta (i.e., progenitor mass and composition, explosive nucleosynthesis, chemical mixing), ejecta interaction with CSM (mass, velocity, as well as small and large-scale structure of the CDS), but also the influence of dust that may be both intrinsic (forming in the inner metal-rich ejecta as well as in the CDS) and external. Obtaining a good match to observations throughout the UV and optical is thus a considerable challenge.

Our late-time spectra are generally dominated by Ly $\alpha$, Mg ii $\lambda\lambda$ 2795, 2802, and H$\alpha$. As a fraction of the total flux, Mg ii $\lambda\lambda$ 2795, 2802, changes little over time. Because of optical depth effects, Ly $\alpha$ strengthens considerably with increasing time or with decreasing $M_{\mathrm{CDS}}$. With increasing time, we tend to see a strengthening of forbidden lines and an increase in ionization. Conditions in the CDS are typically warm and partially ionized, but any energy injection above or below the CDS produces emission from high-ionization lines, with for example [O iii] $\lambda\lambda$ 4958.9, 5006.8. Although Fe contributes only few strong isolated lines (e.g., [Fe ii] $\lambda$ 7155.2), it contributes a large share of the total flux, in particular below 5500 Å where most of the flux resides at these late times. Overall, lines appear broad and boxy in the optical, but tend to show a strong red deficit in the UV, even in the absence of dust.

Ly $\alpha$ is present in observations of a wide range of interacting transients ([8]), even at relatively early times (e.g., SN 1998S; [36]), whereas in models this line shows a strong sensitivity to the CDS mass and velocity. This sensitivity arises from the large background opacity brought in by metal lines and in particular from Fe but also from the huge optical depth in Ly $\alpha$ itself. Hence, we find that any Ly $\alpha$ emission from below and within the CDS is strongly attenuated (even in the absence of dust), and that instead Ly$\alpha$ emission arises from the outer parts of the CDS. In events in which dust is identified in the optical from a blue-red asymmetry in lines like H$\alpha$, Ly$\alpha$ is still present and well matched by a dust-free model (e.g., SN 1998S; § 6.2). This is thus independent evidence that the UV flux only forms and escapes from the outer parts of the CDS, even in the absence of dust, and not from regions underneath the CDS and influenced by the reverse shock. This finding is based on the models presented here, which cover a limited range in post-explosion epochs (at most 500 to 1900 d) and the few SN observations these models were confronted to. At later times of decades post-explosion, this situation will likely differ.

Our models with a higher He and N abundance in the H-rich material (models with lower $M(\mathrm{H\text{-}env})$) exhibit stronger N lines relative to C and O lines, in particular with the most stripped progenitor (model logP2p85). This is seen in the UV with, for example, N II] 2142.8 Å and N III 1749.7 Å, but also in the optical with the enhanced flux in [N II] $\lambda$ 5755 and [N II] $\lambda\lambda$ 6548.0, 6583.5. The latter overlaps and sometimes rivals with H$\alpha$ in our models. Such N lines are observed in SN 1993J and also roughly matched with our model logP2p90 (progenitor with a 0.28 M$_\odot$ H-rich envelope) augmented with a CDS of 0.2 M$_\odot$.

O III lines arise in our simulations when some shock power is absorbed either above or below the CDS. Such lines do not form in the dense shell at those epochs because of its relatively high density and low ionization. If such lines form below the CDS (i.e., in the ejecta), any dust in the CDS yields a globally attenuated line emission and no profile skewness results. If it forms outside the CDS, dust absorption within the CDS skews the profile with a flux deficit redward of line center. The identification of these effects is challenged by the overlap of such lines with the background flux from Fe, which sometimes dominates in the given spectral region. Our dusty models yield a good match to those features in SN 2013ej.

The two nearby SNe 2023ixf and 2024ggi offer an opportunity to study the long-term evolution of ejecta interaction with CSM across the electromagnetic spectrum. Arising from progenitors endowed with a larger mass at core collapse, they will offer an instructive contrast to other well observed events like SN 1993J.

Acknowledgements. We acknowledge fruitful discussions with Norbert Langer and Andrea Ercolino. This work was granted access to the HPC resources of TGCC under the allocation 2025 – A0190416871 made by GENCI, France. This research has made use of NASA’s Astrophysics Data System Bibliographic Services.

Model atom

The species (atoms and ions) included in all calculations are $\mathrm{H\,I}$ (26,36), $\mathrm{He\,I}$ (40,51), $\mathrm{He\,II}$ (13,30), $\mathrm{C\,I}$ (14,26), $\mathrm{C\,II}$ (14,26), $\mathrm{C\,III}$ (62,112), $\mathrm{C\,IV}$ (59,64), $\mathrm{N\,I}$ (44,104), $\mathrm{N\,II}$ (23,41), $\mathrm{N\,III}$ (25,53), $\mathrm{N\,IV}$ (56,92), $\mathrm{O\,I}$ (21,51), $\mathrm{O\,II}$ (54,123), $\mathrm{O\,III}$ (44,86), $\mathrm{O\,IV}$ (76,152), $\mathrm{Ne\,II}$ (22,91), $\mathrm{Ne\,III}$ (32,80), $\mathrm{Ne\,IV}$ (30,67), $\mathrm{Na\,I}$ (22,71), $\mathrm{Mg\,I}$ (39,122), $\mathrm{Mg\,II}$ (31,80), $\mathrm{Mg\,III}$ (31,99), $\mathrm{Mg\,IV}$ (18,100), $\mathrm{Al\,II}$ (26,44), $\mathrm{Al\,III}$ (27,60), $\mathrm{Si\,I}$ (100,187), $\mathrm{Si\,II}$ (31,59), $\mathrm{Si\,III}$ (33,61), $\mathrm{Si\,IV}$ (37,48), $\mathrm{S\,I}$ (106,322), $\mathrm{S\,II}$ (56,324), $\mathrm{S\,III}$ (48,98), $\mathrm{S\,IV}$ (27,67), $\mathrm{Ar\,I}$ (56,110), $\mathrm{Ar\,II}$ (134,415), $\mathrm{Ar\,III}$ (32,346), $\mathrm{K\,I}$ (25,44), $\mathrm{Ca\,II}$ (21,77), $\mathrm{Ca\,III}$ (16,40), $\mathrm{Ca\,IV}$ (18,69), $\mathrm{Sc\,II}$ (38,85), $\mathrm{Sc\,III}$ (25,45), $\mathrm{Ti\,II}$ (37,152), $\mathrm{Ti\,III}$ (33,206), $\mathrm{Cr\,II}$ (28,196), $\mathrm{Cr\,III}$ (30,145), $\mathrm{Cr\,IV}$ (29,234), $\mathrm{Fe\,I}$ (413,1142), $\mathrm{Fe\,II}$ (228,2698), $\mathrm{Fe\,III}$ (96,1001), $\mathrm{Fe\,IV}$ (100,1000), $\mathrm{Fe\,V}$ (139,1000), $\mathrm{Co\,II}$ (112,1005), $\mathrm{Co\,III}$ (88,1075), $\mathrm{Co\,IV}$ (56,1000), $\mathrm{Ni\,I}$ (56,301), $\mathrm{Ni\,II}$ (59,1000), $\mathrm{Ni\,III}$ (47,1000), and $\mathrm{Ni\,IV}$ (54,1000). The numbers in parenthesis correspond to the number of super-levels and full levels – for details see [42].

Additional illustrations

Figures B.1–B.4 show the individual species contributions in the best-fitting models to the observed SNe 1993J, 1998S, 2013ej, and 2023ixf discussed in § 6. In these illustrations, only the bound-bound transitions are included in the spectrum calculation, one species at a time. This is illustrative in the sense that the total flux is not the simple addition of all individual contributions. Figures B.5–B.7 give some ejecta and CDS properties for these same models (except for the model used for SN 2023ixf, whose modeling was described in detail in Dessart et al. [25]). These figures allow one to assess the impact on the ionization (temperature, density of free electrons, species ionization) obtained under different conditions for the ejecta or CDS.