Still Brighter than Pre-explosion, SN 2012Z Did Not Disappear: Comparing Hubble Space Telescope Observations a Decade Apart

Our late-time HST observations of SN 2012Z yielded several surprising results. In Figure 3 we show the light curve of SN 2012Z for nearly 1500 days. We show the early data from Stritzinger et al. (2015) taken in the BVri filters. For the last three epochs, we show our HST observations. The filters F435W, F555W, F625W, and F814W are similar to the ground-based BVri filters, respectively, so we do not apply a filter correction. Filter corrections require some estimate of the spectral energy distribution (SED) and are generally smaller (∼0.1 mag) than the effects we are interested in here.

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The light curves for V and I are the most complete so we focus on those. The final four epochs for both filters are fit well to within the errors by an exponential-decay model (in magnitude units) with an asymptotic magnitude of 26.70 and 26.77 for V and I, respectively. These fits are shown as dotted lines in Figure 3. For both filters, our latest observation is within 2σ of the asymptotic magnitudes. This does not imply that this trend will continue at later epochs when new energy sources may become important.

The blue bands show the photometry from the pre-explosion images from McCully et al. (2014b). The final epoch of photometry is taken with the same filters and instrument as the pre-explosion images, so these can be directly compared without any filter correction. We find that in all bands, even at nearly 1500 days past explosion, SN 2012Z is still brighter than our photometry from pre-explosion images. We thus consider it extremely unlikely that the source seen in the pre-explosion images was the star that exploded as SN 2012Z, as the source has not disappeared as has been observed for core-collapse supernovae. Disentangling the contributions to the late-time flux and whether the progenitor system remained unchanged is more complicated.

3.1.1. Radioactive Decay

3.1.2. Comparison to Other White Dwarf Supernovae

The light curves of SN 2012Z are compared to the Iax SN 2005hk and SN 2008A, the peculiar Iax SN 2008ha, and the normal Ia SN 2011fe in Figure 4. SN 2005hk and SN 2008A have observations out to ∼600 days past maximum light. At similar epochs, SN 2012Z was fainter than both SN 2005hk and SN 2008A, which is surprising given that SN 2012Z was one of the brightest SNe Iax at maximum light.

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SN 2011fe was ∼1 mag brighter than SN 2012Z at peak, but, around three years after peak, the light curves have crossed. At ∼1450 days past peak, SN 2012Z is ∼2 mag brighter than SN 2011fe. It appears that the light curve of SN 2012Z is leveling off above the detection in the pre-explosion images, whereas SN 2011fe is continuing to decline, roughly following radioactive decay of ⁵⁷Co and ⁵⁵Fe (see Kerzendorf et al. 2017).

We compare to observations of SN 2008ha near 1500 days past maximum from Foley et al. (2014). The source we detected that is coincident with the position of SN 2008ha is fainter and substantially redder (it was only detected in the reddest bands; Foley et al. 2014) than that for SN 2012Z.

At these late phases, the interpretation of the photometry becomes more complicated as there can now be contribution from multiple sources including the SN ejecta, the companion star, interaction with CSM if present, and possibly a bound remnant with a wind.

At these extremely late phases, spectroscopy is no longer possible. Instead, we rely on photometry and the evolution of the SED of SN 2012Z to constrain the physics of SNe Iax. We consider two main scenarios that should bracket the true behavior of the SN. The first assumes that the pre-explosion flux was dominated by accretion and therefore does not contribute to the late-time HST photometry. The other scenario assumes that the companion star was the main contributor to the pre-explosion flux and would therefore be unchanged after the SN explosion (or could even become brighter).

In Figure 5, we show the SED of SN 2012Z at the latest epochs taken with HST without removing any contamination from the pre-explosion source. At ∼500 days and ∼850 days, the source is blue and has similar colors to the pre-explosion photometry. These measurements are consistent with being on the Rayleigh–Jeans tail of a blackbody, implying that we can only really constrain the temperature to be ≳10,000 K. The blue colors at late times suggest that SN 2012Z did not undergo an "IR catastrophe" with a redistribution of energy to the far infrared (Sollerman et al. 2004; see discussion of the IR catastrophe in McCully et al. 2014a).

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If the late-time photometry has no contamination from the pre-explosion source, it would imply that the late-time emission is consistent with a blackbody. The latest spectrum we have of SN 2012Z (Figure 1) is already nonthermal, so this could suggest that we are no longer measuring light from the SN ejecta, but are instead seeing some other component like the companion star or a bound remnant.

If we consider the case where the pre-explosion source is unchanged, we can take the difference of the fluxes from the pre-explosion images from our late-time observations of SN 2012Z. The SEDs are shown in Figure 6. The earlier epochs (+503 and +865 days) are basically unchanged from above. The final epoch has a significantly different SED than the previous case. The SED is peaked in the F555W band, which corresponds to a blackbody temperature of 5000 K. While the F435W data are consistent with this blackbody temperature, the F814W is more than a factor of two fainter than would be expected. This implies that if the pre-explosion source remained at constant brightness, then the radiation from the supernova is nonthermal.

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Based on the latest spectrum of SN 2012Z, we expect the spectrum from the SN ejecta to be line dominated, which could explain the excess of V-band flux. Previously we searched for evidence of [O i] 6300 Å (McCully et al. 2014a) from unburned oxygen predicted in pure-deflagration models (Kozma et al. 2005). We again see no evidence in any of our HST photometry for an excess due to this line for SN 2012Z.

Foley et al. (2013) suggest that SN Iax could arise from He star donor systems, so we consider emission from He i 5876 Å as a possible source of the excess V-band flux that could arise if He was stripped off of the donor star (see Zeng et al. 2020). We fit a blackbody with a single He emission line to our photometry. We follow Jacobson-Galán et al. (2019) using both their analytic model and results from Botyánszki et al. (2018) to estimate the helium mass needed to explain our best-fit line flux. Both models require more than a solar mass of He making it unlikely that He i is the sole source of this flux excess.

The SED after subtracting the pre-explosion flux requires such strong line flux that it is difficult to explain with any of the models we have tested. Given the unphysical amount of material needed to explain the excess V-band flux, we find that it is unlikely that the pre-explosion source is unchanged and therefore directly subtracting the pre-explosion flux is too simplistic.

We next compare the color evolution of SN 2012Z to other SNe Iax that have late-time observations and the canonical type Ia SN 2011fe. One of the primary difficulties with comparing the light curves of these SNe is that the observations were taken in a range of filters. SN 2011fe was typically observed using Johnson filters while SN 2012Z was observed with BVgri at early phases. While the HST filters are approximately the same as the ground filters, there are small differences for which we need to account.

To compare the colors across telescopes/filters, we model the SED of each supernova at each epoch for which we have more than single-band photometry. Our models are built by linearly interpolating between knots, which are chosen to be at the center of the filter passbands. The fluxes of the knots are optimized so that the synthetic photometry matches the observed photometry. The uncertainties in the models are estimated using Markov Chain Monte Carlo. We only consider colors for epochs that include observations in filters that have a central wavelength within 50 nm of the filters of interest. The color curves are shown in Figure 7. We have included estimates of both pre-explosion subtracted and unsubtracted photometry (unfilled and filled markers, respectively) for comparison.

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At early times, the colors of the SNe Iax are slightly redder but roughly follow the color evolution of SN 2011fe out to ∼75 days. Around a hundred days past peak, normal SNe Ia become nebular, but SNe Iax do not (Jha et al. 2006; Foley et al. 2013; McCully et al. 2014a). This key spectroscopic difference is also noticeable in the photometry. As SN 2011fe enters its nebular phase, it becomes bluer, while the SNe Iax remain red for several hundred days.

In the latest HST observations, SN 2012Z has become bluer again. Even by ∼500 days past maximum it is much bluer than SN 2005hk and SN 2008A. The colors of SN 2012Z are consistent with the colors of SN 2011fe at the latest phases of ∼1500 days past maximum.

Foley et al. (2016) suggest that a SN Iax that does not fully disrupt the white dwarf and could leave behind an observable remnant. Shen & Schwab (2017) model the observational signatures of such a remnant. The newly produced radioactive material would heat the remnant, driving a wind. This could explain why SNe Iax show P-Cygni lines more than a year after explosion. We compare these models to our data in Figure 7. Three of the four models from Shen & Schwab (2017) are too red to be consistent with our observations. However, the high-entropy model for a 0.5 M_⊙ remnant has similar colors to what we observe for SN 2012Z for the latest observation.

Another possibility to explain the late-time photometric behavior of SNe Iax is the donor star. We know this star must be present in the system, and Bulla et al. (2020) find that including its contributions near maximum can better match the spectropolarimetry observations of SN 2005hk. Pan et al. (2013) model the effects of the SN explosion on a He star companion. They find that the post-impact companion expands and goes through a luminous phase We compare our data to their models in Figure 8. We find that the companion models are too blue to explain our latest photometry, so the companion is likely not the dominant source of the flux at these epochs, which is also supported by our estimates of the luminosity below.

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If material was ejected from the binary system during its evolution to SN 2012Z, we would expect that CSM to eventually dominate the flux (Gerardy et al. 2004; Graham et al. 2019). CSM interaction models generally predict blue emission so if we assume the unsubtracted scenario, our latest color measurement is consistent with the CSM interpretation but more detailed modeling would be necessary to test if these models match in detail.

To estimate the optical luminosity, we use the SED models described above, integrating using the trapezoid rule. Similarly to McCully et al. (2014a), we integrate from 340 to 970 nm, where our data are best sampled. By only considering the optical range, we remove some of the systematics associated with extrapolating to get the full bolometric luminosity. We use the Monte Carlo samples to estimate the uncertainties in luminosity measurements. The results are shown in Figure 9.

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Near peak, SN 2012Z was brighter than SN 2005hk and SN 2008A. However, this reversed about 250 days past maximum: both SN 2008A and SN 2005hk were brighter than SN 2012Z at these epochs. All three SNe Iax (SNe 2012Z, 2008A, and 2005hk) have similar rise times, but SN 2012Z has slower decline post-peak.

SN 2011fe was (unsurprisingly) brighter than all of the SNe Iax by about a factor of two at peak. However, at ∼850 days past maximum the light curves of SN 2012Z and SN 2011fe crossed. SN 2012Z is approaching a constant luminosity while SN 2011fe continues to fade. At the latest epoch we have for SN 2012Z, nearly 1500 days after maximum, SN 2012Z is an order of magnitude brighter than SN 2011fe and is roughly at the Eddington luminosity for a mass of 0.5 M_⊙.

The models from Shen & Schwab (2017) are also shown on Figure 9 in the left panel. Between 1 and 3 yr after maximum, the models become so red that much of the flux has dropped out of the optical bands. It is not until our latest epochs that the models begin to heat and the flux moves back into the optical bands. The low-entropy remnant models are too faint for our observations, but the high-entropy models are similar to the final photometric observations for SN 2012Z.

An alternative explanation for the excess flux is that, instead of seeing a bound remnant, the flux is dominated by the shock-heated companion star. Pan et al. (2013), Shappee et al. (2013), and Liu et al. (2013) predict that when the ejecta collide with the companion star, they will strip some mass and shock-heat the envelope. Pan et al. (2013) calculated the properties of a surviving helium-star companion. They found that that the helium star would be hot (∼30,000 K) and bright (∼10,000 L_⊙). This corresponds to an absolute magnitude in V of −5.2, within a magnitude of what we observe at our latest epoch. This is also consistent with the blue SED we observe (without subtracting the pre-explosion flux).

We compare our observations to the companion models from Pan et al. (2013) in the right panel of Figure 9. We find that the models here are much fainter in the optical than we observe. The models do predict that the companion should become brighter at later epochs, so the companion may produce the dominant contribution of the flux in later observations, perhaps even causing a rebrightening of the source.

In Figure 10, we compare our observations to the models from Zeng et al. (2020; evolution of the post-supernova companion will be presented in Y. Zeng et al. 2021. in preparation). Zeng et al. (2020) use the 3D smoothed particle hydrodynamics code Stellar GADGET (Pakmor et al. 2012). Their models use the results from Liu et al. (2013) as the initial state of the He star. Zeng et al. (2020) assume the N5def model from Kromer et al. (2013a) who find that model best explains the characteristic observations of SN 2005hk. The N5def is a weak deflagration of a Chandrasekhar-mass white dwarf that ejects 0.372 M_⊙ of material leaving a 1.03 M_⊙ bound remnant. After the supernova explosion, the evolution of the companion star is modeled using the 1D MESA stellar-evolution code (Paxton et al. 2011, 2015, 2018, 2019).

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The solid line shows the optical flux, which is too faint to contribute to our observations significantly. However, the bolometric luminosity from the models are comparable to our observed late-time flux. If there was material to redistribute the blue flux into the optical (e.g., from a wind from a bound remnant), the shock-heated companion could contribute to our late-time observations.

During the evolution of the binary leading up to SN 2012Z, material may have escaped the system. When the ejecta collides with this material, a shock is produced creating another possible source of luminosity. The flux produced by the CSM interaction depends on the velocity of the shell and the mass accumulated by the ejecta. Jacobson-Galán et al. (2019) find evidence for CSM interaction in some SNe Iax, so we estimate the order of magnitude properties of the CSM that would be necessary to explain the slow decline in our latest photometry.

We consider the constant-density CSM model from Gerardy et al. (2004). SN 2012Z has reached ∼ 5 × 10³⁷ erg s⁻¹ at the latest phases as shown in Figure 9. This is ∼6 orders of magnitude fainter than what Gerardy et al. (2004) considers for SN 2003du. If we assume that the luminosity scales linearly with density, this would imply a density of 1.66 × 10⁻²² g cm⁻³. At 1450 days of expansion at 8000 km s⁻¹, we would estimate a radius of 10¹⁷ cm. Integrating over the sphere, this would imply a total accumulated mass of 3.5 × 10⁻⁴ M_⊙.

Smith (2017) write

$$\begin{eqnarray}&&L=2\pi {R}^{2}\rho {v}_{\mathrm{shell}}^{3}.\end{eqnarray} \tag{ 1 }$$

Using the values above, this would imply a shell velocity of 1700 km s⁻¹, which is similar to the escape velocity of the progenitor system, making this a plausible explanation for the late-time flux we see for SN 2012Z. We note that if this is the source of the excess late-time luminosity of SN 2012Z, then even this small amount of material cannot be present in the normal SN Ia, SN 2011fe, as its light curve continues to decline following radioactive decay. More detailed modeling is necessary to distinguish whether the CSM interaction or a bound remnant dominates the luminosity at our latest observations.

There is significant evidence from our pre-explosion imaging of SN 2012Z (McCully et al. 2014b) and from late-time spectra (Foley et al. 2016) that SNe Iax arise from single-degenerate, Chandrasekhar-mass systems. The ejecta mass is more uncertain. Here we consider models to guide our interpretation of our latest photometry.

Using a simple Arnett's scaling relation (${M}_{\mathrm{ej}}\propto {{vt}}_{\mathrm{rise}}^{2}$) that is only based on the ejecta velocity and the rise time (Arnett 1982), we find that SN 2012Z has about a third of the ejecta mass of SN 2011fe, which would give ≈ 0.5 M_⊙. This would imply a 0.9 M_⊙ remnant if the white dwarf exploded at the Chandrasekhar mass.

However, while the light curve of SN 2012Z has a fast rise time, it is also broad after maximum (Δm_15,bol = 0.6 mag, Δm_40,bol = 1.6 mag), which would for a normal SN Ia suggest a super-Chandrasekhar ejecta mass, M_ej, of 1.7–2.0 M_⊙ (Scalzo et al. 2019). This is consistent with the estimates of Stritzinger et al. (2015) for SN 2012Z, who use a similar technique. However, this model does not take into account a bound remnant and may differ for SNe Iax given their density profile.

To explore this, we reexamine the hierarchical Bayesian model of Scalzo et al. (2014a, 2014b, 2019). The model includes a semianalytic prediction of radioactive energy deposition within a spherically symmetric, homologously expanding SN Ia ejecta with a user-defined radial density profile and ⁵⁶Ni distribution (Jeffery 1999). The ejecta expansion velocity is determined by energy balance, subtracting the binding energy of the white dwarf (Yoon & Langer 2005) from the nuclear energy released in conversion of carbon and oxygen to the final ejecta composition (Maeda & Iwamoto 2009). These models are similar to those from Arnett, but use model-driven priors and marginalize over unknown parameter values rather than assuming a simple scaling as we did above. The Arnett scaling relation for estimating the ejecta mass is based on photospheric-phase behavior, relying on measurements of the rise time and the velocity of the Si ii absorption feature at maximum light. In contrast, the Scalzo parametric model relies on bolometric measurements made at later phases when the ejecta have become optically thin to ⁵⁶Co gamma rays (from +40 –+100 days).

The potential for a bound remnant complicates this interpretation, and so the semianalytic explosion model must be updated to account for this in some way. We incorporate into the framework a schematic treatment of the mass of a bound remnant. The remnant mass contributes to the progenitor binding energy but is not part of the ejecta mass available for scattering of ⁵⁶Co gamma rays from the ejecta. The binding energy of the remnant cannot be turned into the kinetic energy of the ejecta so the remnant thus acts as a drag on the expanding ejecta, lowering the expansion velocity. Since numerical simulations indicate a puffed-up remnant relative to a normal white dwarf (Kromer et al. 2013b, 2013a; Zhang et al. 2019), we approximate the final remnant binding energy as being negligible for our estimate. The effect of the remnant on this simplified explosion is thus to lower the expansion velocity of the ejecta, producing a flatter bolometric light curve past peak. We produce simulations using both ejecta radial density profiles used in Scalzo et al. (2014a): a profile that is exponential in velocity and a power-law density profile tuned to match 3D simulations of SNe Ia (Kromer et al. 2010; Pakmor et al. 2012; Seitenzahl et al. 2013).

The ratio of the observed bolometric luminosity to the modeled luminosity from radioactive decay (α) is a nuisance parameter in our analysis, but is expected to be close to 1 (Branch 1992; Stritzinger et al. 2006; Howell et al. 2006, 2009). In the semianalytic models of Arnett (1982), α = 1 identically. We consider two priors for alpha, as in Scalzo et al. (2014a): a Gaussian prior α = 1.00 ± 0.01, corresponding to the ideal Arnett case, and a Gaussian prior α = 1.2 ± 0.2, corresponding to the range seen in the numerical models of Hoeflich & Khokhlov (1996).

The presence of an unknown amount of material with gravitational influence but no effect on gamma-ray opacities requires additional priors to constrain meaningfully. In contrast to previous analyses of normal SNe Ia (Scalzo et al. 2014a, 2019), we introduce a Gaussian prior on the bulk kinetic energy velocity based on the Si ii 6355 line velocity at maximum light with a standard deviation of 500 km s⁻¹. We adopt the following silicon velocity priors: SN 2011fe: 10,400 km s⁻¹ (Zhang et al. 2016); SN 2012Z: 7500 km s⁻¹ (Stritzinger et al. 2015); SN 2008A: 7000 km s⁻¹ (McCully et al. 2014a); SN 2008ha: 3700 km s⁻¹ (Foley et al. 2010); and SN 2005hk: 5500 km s⁻¹ (Phillips et al. 2007).

These models require the bolometric light curve rather than the integrated optical that we presented above. SN 2012Z has both UV and IR observations enabling a bolometric correction, but several of the other SNe Iax presented here do not. To account for this, we use IR observations from Yamanaka et al. (2015) and Swift observations from Brown et al. (2014) to estimate the bolometric correction for SN 2012Z (using the same method to convert from photometry to luminosity as above). To interpolate our observations onto a uniform grid, we fit the light curve in each band to a series of light-curve functions from Bazin et al. (2009). Using the light-curve fits, we integrate over wavelengths to get the luminosity using the pivot wavelengths as the filter centers. We then fit a pre-peak and post-peak stretch to the SN Iax-integrated optical light curves and apply a stretched bolometric correction accordingly. We implement the same procedure using data from Matheson et al. (2012) in the IR and Swift observations from Brown et al. (2014) for the normal Ia SN 2011fe. Our estimated UV and IR contributions are shown in Figure 11.

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The results of the exponential density profile models are shown Figure 12. The results for SN 2011fe are shown in the top row. We have explicitly included a prior that SN 2011fe did not leave behind a remnant. The nickel mass we obtain is consistent with previous works (e.g., Pereira et al. 2013). The ejecta mass and therefore total mass are both sub-Chandrasekhar. This is qualitatively consistent with Scalzo et al. (2014a), who find that SN 2011fe favored a sub-Chandra explosion at 1.08 M_⊙ for comparable models. More discussion of the reanalysis of SN 2011fe is in the Appendix. The models here favor a lower ejecta mass of 0.95 M_⊙. Here we are showing the exponential density distributions; the power-law density models favor a 0.1 M_⊙ higher ejecta mass implying a ∼ 0.1 M_⊙ systematic uncertainty in our ejecta-mass estimates, which must be accounted for in our interpretation of the models. Our estimates of the ejecta mass of SN 2011fe are consistent with those from the models of Shen et al. (2021) within systematics.

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We find that for these models of the SNe Iax, all of the total mass estimates are centered around the Chandrasekhar mass. There were no explicit constraints on the models to enforce this, so it is noteworthy that all of our models peak at this value. The power-law density models have total masses that are consistent with the Chandrasekhar mass but favor higher, super-Chandra total mass estimates similar to the findings of Stritzinger et al. (2015) for SN 2012Z. Chandrasekhar white dwarf masses are consistent with Foley et al. (2016), who find that SNe Iax produce a significant amount of stable Ni which requires high-density burning. The material would need to burn near the center of the white dwarf but then also escape as part of the ejecta. For example, Blondin et al. (2021) and Leung & Nomoto (2020) show that deflagrations of Chandrasekhar-mass white dwarfs can produce a significant amount of stable Ni in the ejecta. In Leung & Nomoto (2020), 2D simulations show that their models can produce both a remnant and stable Ni. Synthetic observables of their models are necessary to test if they can reproduce the layered spectral evolution seen in Stritzinger et al. (2015), to see if they are viable models for SNe Iax.

The exponential density profile models shown have probability distributions that peak with SN 2012Z with the smallest remnant mass of ${0.5}_{-0.18}^{+0.21}\,{M}_{\odot }$ and the highest remnant masses for SN 2005hk. The low velocities of SN 2005hk favor high remnant masses in our models. Given the systematics of at least a 0.1 M_⊙, our models do not require a bound remnant but are consistent with one for SN 2012Z. However, the models for both power-law and exponential density profiles favor a nonzero remnant mass for SN 2005hk at higher than 95% confidence.

Our models are not able to fit the light curve from SN 2008ha adequately to draw conclusions. SN 2008ha is the most extreme object in our sample and has the least data coverage because it was so faint. The models that converged (and are shown in Figure 12) require a large value of α, implying less-efficient conversion of radioactive decay to SN luminosity. The peak of the total mass is consistent with the Chandrasekhar mass, but the other parameters are multimodal and have broad tails of their distributions. In the high-mass, low-56Ni tail of parameter samples for SN 2008ha, the inferred timescale for passing into the optically thin regime for 56Co gamma rays far exceeds the range of available data, breaking the main assumption used to derive our light-curve model. We therefore do not consider our model reliable for SN 2008ha, and further constraints or different methods are needed to draw any significant conclusions.

Our ejecta masses shown here are more similar to the lower ejecta masses predicted by only using the rise of the light curves of SNe Iax. We find a correlation for the four objects modeled here between the ejecta mass and the radioactive nickel mass. This is in line with the naive expectation that a more powerful explosion will produce more ejecta and produce more radioactive nickel. If the rise times are better indicators of the ejecta mass, this could explain the correlation between rise time and luminosity found by Magee et al. (2016).

Further theoretical/explosion simulations are necessary to confirm these results but are beyond the scope of this work.

At this point, we have at least three possible sources for the brightness at our latest observation of SN 2012Z: long half-life radioactive decay, CSM interaction, and a bound remnant. Here we further consider other signatures that could differentiate a bound remnant from the other models. If the flux of the remnant was substantial at phases > 60 days, it would make the light curve appear broader than it actually systematically biases our ejecta model above. To estimate the contribution of a remnant to supernova photometry, we use SN 2011fe as a template light curve. We shift, scale, and stretch the optical light curve of SN 2011fe to match the SNe Iax at peak, and then subtract the resulting light curve as an estimate of the flux from the SN ejecta.

Our results are shown in Figure 13. Before 50 days after peak, the error bars are large because the data near peak were not as deep as observations taken later. Therefore, we do not draw any conclusions from this data. At later epochs, there is an excess for both SN 2005hk and SN 2012Z. SN 2005hk has by far the best sampling at these intermediate phases and qualitatively follows the prediction of remnant models. This "ejecta + remnant" model is the only one we have tested that can explain the entire evolution of the bolometric light curve. More realistic models of the light curve from the ejecta that explore Ni distribution and density profile effects are necessary to confirm the robustness of this explanation.

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We conclude that models that rely on data at phases later than 50 days can be potentially contaminated by a remnant and will bring down the estimates of ejecta mass from these models.

One model that can produce a remnant is the pure deflagration of a white dwarf (e.g., Kromer et al. 2013a). However, these models are not without their issues. While the peak of the light curves from Kromer et al. (2013a) and Kromer et al. (2015) match SN 2005hk well, just 30 days past peak they underpredict the flux. Based on our analysis shown in Figure 13, one possibility is that the light curve of SN 2005hk is already starting to be contaminated by the remnant at these phases. There are other open questions about the pure-deflagration models, such as if they can produce the layered ejecta seen in SN 2012Z (Stritzinger et al. 2014; Barna et al. 2018), but this is beyond the scope of this work.

A general feature of the remnant models from Shen & Schwab (2017) is that from about 300 days until 1000–2000 days the remnant is very red with most of its flux emitted in the IR. The higher-mass remnants (lower ejecta masses assuming Chandrasekhar mass) tend to stay red until later epochs than lower-mass remnants. It is therefore possible that the source that we found to be coincident with SN 2008ha in Foley et al. (2014) is a remnant still in the red phase before it reheats, though detailed modeling would be necessary to confirm this hypothesis.

The light curve of SN 2012Z (as well as of other SNe Iax) is roughly an order of magnitude brighter than the remnant models a few hundred days past maximum. This is a significant issue for the remnant models given that we would expect the remnant brightness to be comparable to the ejecta at ∼300 days past maximum if the spectra are a composite of forbidden emission features from the ejecta and P-Cygni lines from the remnant wind. This may be less of a problem for SN 2012Z if the ejecta is simply brighter than that of SN 2005hk, but the velocities of SN 2012Z are much higher than for SN 2005hk (Foley et al. 2016) making it difficult to distinguish if the Fe P-Cygni features identified in SN 2005hk (McCully et al. 2014a) are faint or are just blended. It is possible the continuum estimations in the existing remnant models are too simplistic and the emission lines are stronger than expected, but detailed radiative transfer would be needed to test this idea and is beyond the scope of this work.

We encourage others to use our observations as constraints on their simulations to better understand the physical mechanisms that produce SNe Iax.