The HST Nondetection of SN Ia 2011fe 11.5 yr after Explosion Further Restricts Single-degenerate Progenitor Systems

We present deep Hubble Space Telescope imaging of the nearby Type Ia supernova (SN Ia) 2011fe obtained 11.5 yr after explosion. No emission is detected at the SN location to a 1σ (3σ) limit of F555W > 30.2 (29.0) mag, or equivalently M V > 1.2 (−0.1) mag, neglecting the distance uncertainty to M101. We constrain the presence of donor stars impacted by the SN ejecta with the strictest limits thus far on compact (i.e., logg≳4 ) companions. H-rich zero-age main-sequence companions with masses ≥2 M ⊙ are excluded, a significant improvement upon the preexplosion imaging limit of ≈5 M ⊙. Main-sequence He stars with masses ≥1.0 M ⊙ and subgiant He stars with masses ≤0.8 M ⊙ are also disfavored by our late-time imaging. Synthesizing our limits on postimpact donors with previous constraints from preexplosion imaging, early-time radio and X-ray observations, and nebular-phase spectroscopy, essentially all formation channels for SN 2011fe invoking a nondegenerate donor star at the time of explosion are unlikely.


INTRODUCTION
The single-degenerate scenario for producing Type Ia supernovae (SNe Ia) invokes a non-degenerate donor star undergoing Roche Lobe overflow (RLOF) to transfer mass onto the white dwarf (WD) until reaching the necessary central densities for carbon ignition (Whelan & Iben 1973;Nomoto 1982).Mass transfer via RLOF restricts the distance between the WD and the donor to a ≲ 3R ⋆ for semi-major axis a and companion radius R ⋆ (Eggleton 1983) resulting in the SN Ia ejecta impacting the companion within moments of the explosion (e.g., Wheeler et al. 1975; see Liu et al. 2023 for a recent review of observables).The impact deposits energy into the envelope of the companion (e.g., Marietta et al. 2000;Boehner et al. 2017), heating and expanding the outer layers and becoming overluminous for ∼ 10 3 yr (e.g., Podsiadlowski 2003;Shappee et al. 2013a).
tucker.957@osu.edu* CCAPP Fellow Searches for these post-impact donors have mostly been confined to nearby SN Ia remnants that are ≲ 1000 yr old when the donor is still expected to be significantly overluminous.Some tentative candidates have been reported for Galactic and Magellanic Clouds SN Ia remnants (e.g., Ruiz-Lapuente et al. 2004;Ihara et al. 2007;Li et al. 2019) but no unambiguous surviving donor stars have been identified thus far (e.g., Schaefer & Pagnotta 2012; Kerzendorf et al. 2013;Pagnotta & Schaefer 2015;Kerzendorf et al. 2018;Shields et al. 2023; see Ruiz-Lapuente 2019 for a recent review).However, this experiment is observationally difficult due to the cost of obtaining deep spectroscopic follow-up for many targets and a limited number of nearby and young SN Ia remnants.
An alternative method for identifying post-impact companion stars is to obtain deep imaging for nearby SNe Ia many years after explosion once the SN has sufficiently faded.However, this is only possible for the most nearby (≲ 10 Mpc) SNe Ia due to crowding and faintness constraints.Do et al. (2021) recently searched for a post-impact donor star for SN 1972E but did not find any candidates in HST imaging ≈ 33 yr after explosion.
In this Letter, we present deep Hubble Space Telescope (HST ) imaging of the nearby and well-studied SN Ia 2011fe (Nugent et al. 2011) ≈ 11.5 yr after explosion to constrain the presence of post-impact companions.We adopt a distance to M101 of 6.4 ± 0.4 Mpc (µ = 29.03± 0.14 mag; Shappee & Stanek 2011) to ease comparisons with previous studies of SN 2011fe.We correct for the small amount of Milky Way reddening (E(B − V ) MW = 0.008 mag; Schlafly & Finkbeiner 2011) but do not correct for any host-galaxy reddening toward SN 2011fe as it is negligible (Patat et al. 2013).The date of explosion is MJD 55797 (Pereira et al. 2013).

HST OBSERVATIONS
We obtain deep imaging of SN 2011fe using the HST Wide Field Camera 3 (WFC3) UVIS module.Imaging was only conducted in the F 555W filter due to the expected faintness of SN 2011fe at these epochs.Six images were obtained on UT 2023-03-04 (MJD 60007.55 1 ) corresponding to 4208 d (11.5 yr) after explosion with a total exposure time of 8400 s.To characterize the long-term evolution of SN 2011fe we include previous HST observations published by Shappee et al. (2017) and Tucker et al. (2022b) spanning ≈ 1100 − 2400 d after explosion.
Individual images were aligned with TweakReg and combined with AstroDrizzle (Avila et al. 2015) before performing point spread function (PSF) fitting photometry with Dolphot (Dolphin 2000(Dolphin , 2016)).Timedependent filter zeropoints are taken from the WFC3 headers (Calamida et al. 2022).All images are analyzed simultaneously to ensure the location of SN 2011fe remains consistent across images.SN 2011fe is for-1 Weighted by the exposure time for each observation.
mally undetected in the last epoch of HST imaging obtained 11.5 yr after the explosion so we validate the reported uncertainties by checking the photometry of nearby sources.The F 555W light curve of SN 2011fe is provided in Table 1.Non-detection limits are computed via m > −2.5 log 10 (3σ f ) + z for a given flux uncertainty σ f in counts/s and image zeropoint z in magnitudes.Fig. 1 shows cutouts around SN 2011fe for several HST epochs and the long-term F 555W evolution is shown in Fig. 2.

NON-DETECTION OF A POST-IMPACT COMPANION
We compare the F 555W light curve of SN 2011fe to models of post-impact He ( §3.1) and H-rich ( §3.2) companions.The stsynphot software (STScI Development Team 2020) is used to impute synthetic HST F 555W magnitudes (in the Vega system) using the T eff and L ⋆ values taken from the models.When referring to the stellar properties of different models throughout the following sections, we always report the values at the moment of SN explosion (i.e., after mass transfer but before the ejecta impact) to avoid confusion.

He-star Donors
Models of the post-impact evolution for He-burning donors are taken from Pan et al. (2013, models HeWDad; see also Pan et al. 2010Pan et al. , 2012) ) and Liu et al. (2022, models He01r and He02r; see also Liu et al. 2013) which use the binary evolution results of Wang et al. (2009) to construct their initial binary systems.We also include the simulations of Liu et al. (2021) for a doubledetonation explosion triggered by accretion from a lowmass MS He-star (models A, B, and C).
Fig. 3 shows that most He-star models are incompatible with the observed F 555W light curve of SN 2011fe.The three lowest-mass He donors (0.30 M ⊙ , 0.40 M ⊙ , 0.50 M ⊙ ) from Liu et al. (2021) would not be detected.Thus, we disfavor MS He-burning donors with masses ≳ 1.0 M ⊙ because the thermal timescale decreases with increasing mass.The inverse is true for the subgiant (SG) models, where more massive donors produce more extended envelopes and thus increase the thermalization timescale.The 1.0 M ⊙ model from Liu et al. (2022) would not be detected in our HST observations so we disfavor ≤ 0.8 M ⊙ SG He-stars.

H-rich Donors
Unlike He-stars, most H-burning MS donors remain undetectable (F 555W ≳ 32 mag) over the observational baseline (Pan et al. 2012;Rau & Pan 2022).This is attributed to H-rich stars having larger radii at a given   1.The red dashed line shows a simple power-law fit with f ∝ t −5 highlighting the steadily declining flux.The last observation is not included when fitting the power-law model.
mass compared to He stars and thus respond slower and reach lower maximum luminosities (e.g., Pan et al. 2012Pan et al. , 2013)).However, there are a few cases where H-rich donors can be assessed with the HST non-detection.
Rau & Pan (2022) compute models for zero-age mainsequence (ZAMS) companions assuming RLOF and extend the simulations to binary systems with companions beyond the canonical RLOF separation.While such systems are somewhat contrived due to fine-tuning the mass transfer and time of ignition for the C/O WD, the larger separations produce shallower energy deposition which, in turn, corresponds to increased post-impact luminosities and shorter thermalization timescales (e.g., Fig. 8 in Rau & Pan 2022).2022) assume ZAMS stars to facilitate parameter exploration and dependencies on SN properties.These differences will be discussed further below.

DISCUSSION
The compressibility of the stellar envelope determines the thermal response timescale (Pan et al. 2012).Stars with high surface gravities confine the energy deposition to the outermost layers whereas the energy is deposited deeper into the stellar interior for low log g donors (cf.50% 2 , our results restrict MS He donors to ≲ 1.1 M ⊙ at the onset of RLOF.While such systems are observed in the Milky Way (i.e., AM CVn binaries) they are likely the progenitors of faint and spectroscopically peculiar 2 The adopted 50% accretion efficiency is purely instructive as the true accretion efficiency depends sensitively on the mass transfer rate (e.g., Piersanti et al. 2014;Wu et al. 2017).He shells with masses ≳ 0.05 M ⊙ produce distinct early-time signatures (e.g., Polin et al. 2019;Collins et al. 2022) that are not observed in SN 2011fe.
The SG He donors follow an opposing trend, with more massive companions being harder to detect due to the increasing mass of the envelope which increases the heating depth and thermalization timescale.SG He donors with masses ≳ 0.9 M ⊙ (again assuming the mass of the He shell is ≲ 0.05 M ⊙ and an accretion efficiency of 50%) are disfavored by our late-time imaging.Highermass SG He donors are inconsistent with pre-explosion imaging (Li et al. 2011;Graur et al. 2014) so binaries with SG He stars are disfavored for SN 2011fe.
H-rich donors are less constrained by our latest epoch of HST imaging but complement existing non-detections of H-rich companions.All ZAMS H-rich donors with masses ≳ 2 M ⊙ are disfavored, representing a distinct improvement on the pre-explosion limit of ≈ 5 M ⊙ (Li et al. 2011).1.5 M ⊙ donors beyond 4 R ⋆ are also disfavored but smaller separations would not be detected, and ≤ 1 M ⊙ donors at < 5 R ⋆ are unconstrained by the late-time HST imaging due to their low post-impact luminosity (≲ 10 L ⊙ ).
However, these same H-rich ZAMS donors are already disfavored along separate lines of evidence.The impacting ejecta will strip or ablate material off the surface of the donor and heating from the radioactively-decaying ejecta will produce strong H emission lines in the nebular phase (Mattila et al. 2005;Botyánszki et al. 2018;Dessart et al. 2020).H emission is not seen in the spectra of SN 2011fe (Shappee et al. 2013b) out to 1000 d after explosion (Graham et al. 2015;Taubenberger et al. 2015) and the formal limits on unbound donor material are ≲ 10 −3 M ⊙ (e.g., Fig. 6 in Tucker et al. 2022a).All post-impact ZAMS donors not excluded by our HST observations produce ≳ 0.05 M ⊙ of unbound material, inconsistent with nebular-phase observations (Shappee et al. 2013b;Lundqvist et al. 2015).Our results also restrict 'spin-up/spin-down' scenarios (e.g., Justham 2011;Di Stefano et al. 2011) due to smaller companion radii increasing the surface gravity, decreasing the heating depth, and producing brighter companions after impact (see Fig. 4 and Rau & Pan 2022).Thus, H-rich donors are also disfavored for SN 2011fe.
One potential caveat for future observational and theoretical work on post-impact donor stars is the effect of the donor star structure.We qualitatively compare the H-rich 2 M ⊙ ZAMS model at RLOF from Rau & Pan (2022) to Model B from Pan et al. (2012) with a mass of 1.92 M ⊙ at the time of the explosion.While the right panel of Fig. 4 shows the former is disfavored by our observations, the latter is unconstrained by our observations (F 555W > 32 mag).The difference between these models is the density profile of the companion at the moment of impact, as the models of Pan et al. (2012) include mass transfer prior to explosion instead of adopting a ZAMS density profile.The mass transfer reduces the envelope density compared to a ZAMS star with identical mass.This is supported by the higher amount of unbound mass in the Pan et al. (2012) evolved model (≈ 15%) compared to the Rau & Pan (2022) ZAMS model (≈ 10%).This qualitative comparison highlights the differences in post-impact evolution with and with-out including the effects of mass loss on the donor star structure.
The ≈ 1 mag difference between the 1.2 M ⊙ MS Hestar models of Pan et al. (2013) and Liu et al. (2022) seen in Fig. 3 further highlights the effect of mass-transfer on the donor structure.Despite the donors having similar mass at the moment the WD explodes, they began with different masses 3 and experienced different masstransfer histories.The observed difference in synthetic F 555W (and the underlying L ⋆ estimates) are driven by inherent differences in the donor's internal density profile.Thus, all constraints on post-impact companions depend on the underlying assumptions used to construct the density profile of the companion.We encourage future simulation efforts to explore the dependence on different density profiles produced by realistic masstransfer histories.
It is worth noting that some constraints on a doubledegenerate system can be derived, assuming a companion WD survives the explosion as in the 'D6' scenario (Shen et al. 2018).Shen & Schwab (2017) show that winds can be driven from the WD surface by pollution from radioactive species in the SN ejecta.However, the primary issue with this constraining these models with the HST observations of SN 2011fe is the high temperatures (T eff > 10 5 K) shifting the majority of the emission to UV wavelengths.The UV photons likely cannot escape the Fe-rich SN ejecta due to extensive neutral and singly-ionized Fe transitions at these wavelengths (e.g., Pradhan et al. 1996;Bautista 1997).This will likely cause the observed radiation to deviate strongly from a blackbody and complicates reliable comparison to observations.Additionally, the excess luminosity from the polluted WD fades on similar timescales as the radioactively-decaying ejecta.Thus, one must simultaneously fit the isotopic ratios produced during the explosion (e.g., Tucker et al. 2022b) and the emission contribution from the surviving WD.This should be possible once radiative-transfer calculations can be incorporated into the Shen & Schwab (2017) models.
SN 2011fe has been a boon for understanding the complex physics governing SN Ia explosions.These observations, at 11.5 yr after explosion, provide the strongest limits on He-rich donors in addition to further disfavoring H-rich donors.Assessing our new imaging in conjunction with prior limits on the progenitor system of SN 2011fe (Li et al. 2011;Nugent et al. 2011;Bloom et al. 2012;Margutti et al. 2012;Chomiuk et al. 2012;Brown et al. 2012), almost all non-degenerate donor stars are observationally disfavored.The remaining scenarios that cannot be formally excluded, such as very low-mass (≲ 0.6 M ⊙ ) He donors, are disfavored by rate arguments (e.g., Bildsten et al. 2007;Neunteufel et al. 2019) given that SN 2011fe is a quintessential example of the SN Ia population.

Figure 1 .
Figure 1.Image cutouts centered on SN 2011fe for several HST epochs.The time between explosion and observation is denoted in the lower-right corner of each panel.

Figure 2 .
Figure2.F 555W light curve of SN 2011fe provided in Table1.The red dashed line shows a simple power-law fit with f ∝ t −5 highlighting the steadily declining flux.The last observation is not included when fitting the power-law model.

Fig. 4
Fig.4shows that the 2 M ⊙ donor fromRau & Pan (2022) is disfavored for all binary separations.The 1.5 M ⊙ model would have been marginally detected (≈ 2σ) at a ≳ 3R ⋆ and undetected if the system was in RLOF.The two lower-mass models from Rau & Pan (2022), 0.8 M ⊙ and 1 M ⊙ , are not constrained by our observations regardless of separation due to their low peak luminosities (≲ 10 L ⊙ ).The MS models computed by Pan et al. (2012) with masses of ≈ 1.2 − 1.9 M ⊙ remain undetectable for another century or more.The differences between these models and the similar-mass models computed byRau & Pan (2022) are attributed to the density structure of the donor star at the time of impact.Pan et al. (2012)   model the full binary evolution, including mass transfer, when constructing their donor stars whereasRau & Pan (2022) assume ZAMS stars to facilitate parameter exploration and dependencies on SN properties.These differences will be discussed further below.

Fig. 5 Figure 3 .Figure 4 .
Figure 3.Comparison between the light curve of SN 2011fe (black squares) with models of post-impact He-star companions (colored lines).The inverted triangles show the 1σ (open triangle) and 3σ (filled triangle) non-detection limits.The uncertainty in the distance modulus is ≈ 0.14 mag.Left: Main-sequence He-star companions from Pan et al. (2013, P13), Liu et al. (2021, L21), and Liu et al. (2022, L22).Right: Similar to the left panel except for SG He-star companions.