A Rapid Ionization Change in the Nebular-Phase Spectra of the Type Ia SN 2011fe

Type Ia supernovae (SNe Ia) are the thermonuclear explosions of carbon/oxygen (C/O) white dwarfs (WDs; Hoyle & Fowler, 1960) and produce the majority of iron-group elements in the Universe (e.g., Iwamoto et al., 1999). These stellar explosions attracted much attention due their use as standardizable candles (Phillips, 1993) but we still lack a genuine understanding of how and why some WDs explode as SNe Ia.

SN 2011fe was discovered $\approx 11$ hours after explosion by the Palomar Transient Facility (PTF; Law et al., 2009) in M101 at a mere $6.4~\rm{Mpc}$ (e.g., Shappee & Stanek, 2011) and became the brightest SN Ia in several decades. Additionally, SN 2011fe is the quintessential SN Ia (Pereira et al., 2013), making it an ideal object for testing SN Ia progenitor and explosion models (e.g., Röpke et al., 2012). This is especially important for nebular-phase observations when the ejecta becomes optically-thin to optical and NIR photons to provide a direct view to the inner ejecta.

Several studies have already analyzed spectra of SN 2011fe as it transitioned into the nebular phase. Shappee et al. (2013) and Lundqvist et al. (2015) searched for H$\alpha$ emission indicative of a nearby donor star at the time of explosion and found none. McClelland et al. (2013) showed that the nebular-phase mid-infrared (MIR) decay is correlated with the nucleosynthetic yield. Mazzali et al. (2015) modeled a suite of photospheric- and nebular-phase spectra and claimed the existence of a stable iron core, although this remains debated (e.g., Botyánszki & Kasen, 2017). Finally, Taubenberger et al. (2015) and Graham et al. (2015a) analyzed spectra acquired $\approx 1000$ days after maximum light, the latest spectra of a SN Ia to-date. They found that the emission characteristics were drastically different from the previous spectra at $\approx 300$ days. Models by Fransson & Jerkstrand (2015) show that the 1000-day spectrum is dominated by Fe I emission lines with minor contributions from Fe II and Ca. However, the spectroscopic evolution between $\sim 400-1000$ days after explosion remains poorly understood. Friesen et al. (2017) briefly attempted to model the +576-day spectrum from Graham et al. (2015a) obtained by the Berkeley SuperNova Identification Program (BSNIP; Silverman et al., 2012) but the results were unsatisfactory and they focused on modeling earlier-phase spectra.

In this Letter we analyze new nebular-phase spectra of SN 2011fe acquired $\approx 480-850$ days after peak-light. Details about the data reduction and calibration are provided in §2. §3 presents the temporal evolution including a distinct change in the iron blends at $4000-6000$ Å and the appearance of [Ca II]. Constraints on the progenitor system and explosion mechanism are described in §4. Finally, we discuss the rapid ionization change in the context of SN Ia models and the use of [Ca II] as an ejecta diagnostic in §5. For our analysis we adopt the time of maximum-light in the $B$-band of $t_{\rm{max}}=\rm{MJD}~55813.98\pm 0.03$ from Zhang et al. (2016). This is interchangeable with the time of explosion using the $\approx 18$-day rise-time of SN 2011fe from Pereira et al. (2013). We use the distance to M101 of $6.4~\rm{Mpc}$ (Shappee & Stanek, 2011) as in previous studies and all phases are given relative to $t_{\rm{max}}$ in the SN rest-frame.

We obtained new spectroscopic observations of SN 2011fe $\approx 480-850$ days after maximum light with the Multi-Object Double Spectrograph (MODS; Pogge et al., 2010) on the Large Binocular Telescope (LBT). Details about the spectroscopic data reduction are described in Shappee et al. (2013). In brief, each frame is bias-subtracted and flat-fielded before detecting and removing cosmic rays with lacosmic (van Dokkum, 2001). Then, we extract the 1D spectrum with iraf and derive the wavelength calibration with arc-lamp frames. Finally, each spectrum is corrected for instrumental response and placed on a relative flux scale with standard star observations. Table 1 summarizes the observations.

Archival spectra from Shappee et al. (2013); Graham et al. (2015b, a); Taubenberger et al. (2015); Mazzali et al. (2015) and Zhang et al. (2016) are included in our analysis to increase the temporal coverage. We also use photometric observations from Munari et al. (2013), Tsvetkov et al. (2013), Zhang et al. (2016), and Shappee et al. (2017) to place the spectra on an absolute flux scale. We restrict the photometry to the $BVR$ filters because 1) our spectral analysis is focused on the wavelength range covered by these filters, and 2) data from these filters are available for the spectral epochs used in our analysis (e.g., Fig. 1 from Tucker et al., 2021a). We fit the light curves with low-order splines over the range of $200-1000$ days. We added Gaussian deviates of the estimated noise and refit the data multiple times to estimate the uncertainties in the spline model. To account for minor differences in the filter throughputs between the photometric setups we include a conservative $0.05$ mag ($\sim 5\%$) systematic uncertainty in the final spline fit.

To flux-calibrate each spectrum, we interpolate the $BVR$ magnitudes and uncertainties using the spline fits. The synthetic $BVR$ filter magnitude is calculated from the spectrum using Eq. 7 from Fukugita et al. (1996) and the spectrum is linearly scaled to match the observed $BVR$ magnitudes. Nebular-phase photometry in other optical filters ($gri$, Firth et al., 2015; Kerzendorf et al., 2014, 2017) is used to check that the spectroscopic flux calibration is correct given the measurement measurement uncertainties.

Line identification at $\lesssim 300~$days after maximum light is well-established due to the increasing number of nebular spectra obtained in recent years (e.g., Graham et al., 2017; Maguire et al., 2018; Sand et al., 2018; Tucker et al., 2020) and improvements in modeling these phases (e.g., Mazzali et al., 2015; Flörs et al., 2018; Wilk et al., 2018; Flörs et al., 2020; Wilk et al., 2020; Shingles et al., 2020; Polin et al., 2021). Optical spectra $\sim 200-300$ days after $t_{\rm{max}}$ are dominated by [Fe III] with contributions from [Fe II], [Ni II], and [Co III]. Fig. 1 shows the flux-calibrated spectral evolution at $>200$ days after $t_{\rm{max}}$ and Fig. 2 shows the normalized spectra at various epochs. We discuss the evolution of the $4000-6000$ Å and $\approx 7300$ Å regions in §3.1 and §3.2, respectively.

The nebular spectra also provide constraints on the progenitor system of SN 2011fe. We discuss scenarios involving mass-transfer from non-degenerate companions (i.e., the “single-degenerate” scenario) in §4.1 and discuss double WD systems (i.e., the “double-degenerate” scenario) in 4.2.

Our new spectra reveal a hitherto unseen transition in the ejecta $\sim 500$ days after explosion. This epoch also corresponds to the decades-old prediction of Axelrod (1980) who proposed that an infrared catastrophe occurs when the ejecta temperature and density are too low to populate the $\sim 3~\rm{eV}$ [Fe III] transitions. However, Axelrod (1980) predicted that all emission will be shifted into the mid-IR (MIR) regime as the only remaining cooling mechanism would be by exciting fine-structure transitions.

High-energy ($\sim 1~\rm{MeV}$) ⁵⁶Co positrons dominate the energy input at $\lesssim 1200$ days explosion (e.g., Tucker et al., 2021a). Some of these positrons heat the ejecta directly but the majority of the positrons produce non-thermal excitations and ionizations (e.g., Kozma & Fransson, 1992; Jerkstrand et al., 2011; Li et al., 2012; Shingles et al., 2020), either directly or via downgraded electrons. UV photons are produced upon recombination which are transferred to optical and NIR wavelengths though multiple scatterings and fluorescence due to the optically-thick forest of Fe transitions in the UV (e.g., Pinto & Eastman, 2000; Jerkstrand et al., 2011; Fransson & Jerkstrand, 2015). This scenario is consistent with the failure to detect SN 2011fe at $<4000$ Å during the nebular phase (Kerzendorf et al., 2017).

Non-local radiative transfer effects explain the continued presence of optical emission at these epochs (Fransson & Jerkstrand, 2015), but it does not account for the observed change in emission properties at $\sim 500$ days after explosion. The shift from Fe II+Fe III to Fe I+Fe II suggests a “recombination wave” propagating through the ⁵⁶Ni region (Graur et al., 2020). However, we observe the transition at $\sim 500$ days after explosion rather than $\sim 600$ days predicted by the models of Fransson & Jerkstrand (2015, see their Fig. 1). This discrepancy may seem minor but for spherically-symmetric expansion, this changes the density at the transition by a factor of $\approx 1.5-2$ which has important ramifications for energy deposition (c.f., Axelrod, 1980).

We propose that clumping may explain this discrepancy. Clumping in the ejecta of SNe Ia has been suggested by both observational (e.g., Black et al., 2016; Mazzali et al., 2020) and theoretical (e.g., Wilk et al., 2020) studies, but confirmation is difficult. Clumping determines where energy deposition occurs as clumps will retain energy input from radioactive decays more efficiently than the lower-density regions between them. However, the higher electron density in the clumps also increases the recombination rate and lowers the average ionization state (e.g., Mazzali et al., 2020). Wilk et al. (2020) show that varying the level of clumping, parameterized as a “filling factor”, has a profound impact on the observed spectra. Increased clumping diminishes the strong [Fe III] blend at $\sim 4600$ Å while increasing the strength of the [Ca II] lines. Both signatures qualitatively match the spectral transition we observe $\sim 500$ days after explosion.

However, it is unclear if these simple comparisons match the true physical evolution of the ejecta, as the interpretation of [Ca II] is also dependent on the adopted explosion model. The $\rm M_{\rm{Ch}}$ and sub-$\rm M_{\rm{Ch}}$ explosions models from Wilk et al. (2020) differ in Ca production by a factor of $\sim 2$. The sub-$\rm M_{\rm{Ch}}$ double-detonation explosion models of Polin et al. (2021) also predict nebular-phase [Ca II]. The off-center $\rm M_{\rm{Ch}}$ delayed-detonation models of Hoeflich et al. (2021), designed to replicate a low-luminosity SN Ia, predict strong and asymmetric nebular-phase [Ca II] emission. Thus, it remains unclear which model(s) accurately predict [Ca II] emission after the nebular-phase ionization change without introducing new discrepancies with other observations of SN 2011fe.

Observationally, [Ca II] is absent in spectra of SNe Ia obtained $\lesssim 500$ days after explosion (e.g., Graham et al., 2017; Maguire et al., 2018; Flörs et al., 2018, 2020). However, [Ca II] is observed in the underluminous 91bg-like (e.g., SNe 1991bg, Turatto et al., 1996; 1999by, Blondin et al., 2018; 2006mr, Stritzinger et al., 2010) and 02es-like (e.g., SNe 2010lp, Taubenberger et al., 2013; 2019yvq, Siebert et al., 2020; Tucker et al., 2021b; Burke et al., 2021) subclasses of SNe Ia at $\lesssim 200$ days after explosion. Considering that [Ca II] is an effective coolant and a resonant transition, it is perhaps unsurprising that the time-dependence of [Ca II] emission is related to the temperature and density in the ejecta. However, the [Ca II] lines in the underluminous SNe Ia are also flat-topped and symmetric, similar to SN 2011fe (Fig. 4). If [Ca II] is indeed a reliable probe of the ejecta geometry, it is interesting that the [Ca II] line profiles are so similar. However, interpreting symmetric [Ca II] emission as evidence for symmetric ejecta introduces new tensions with the complex elemental distributions seen in some SN Ia remnants (e.g., Stone et al., 2021).

SN 2011fe presented a rare opportunity to study SNe Ia physics in unprecedented detail and it remains one of the best-studied astronomical objects to-date (e.g., Tucker et al., 2021a). If the sharp ionization change is related to the infrared catastrophe predicted by Axelrod (1980), this transition should produce a distinct increase in the MIR flux due to fine-structure cooling. Nebular-phase Spitzer and Herschel observations of SN 2011fe (Johansson et al., 2013, 2017) did not cover the wavelength range ($20-40~\mu\rm m$; e.g., Fransson & Jerkstrand, 2015) expected for fine-structure emission lines but the upcoming James Webb Space Telescope should provide a direct test of this theory (e.g., Ashall et al., 2021).

We thank Peter Hoeflich, Zach Claytor, Connor Auge, and Michelle Togami for useful discussions.

M.A.T. acknowledges support from the DOE CSGF through grant DE-SC0019323. CSK and KZS are supported by NSF grants AST-1814440 and AST-1907570.

The LBT is an international collaboration among institutions in the United States, Italy and Germany. LBT Corporation partners are: The University of Arizona on behalf of the Arizona Board of Regents; Istituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, The Leibniz Institute for Astrophysics Potsdam, and Heidelberg University; The Ohio State University, representing OSU, University of Notre Dame, University of Minnesota and University of Virginia.