# No Surviving SN Ia Companion In SNR 0509$-$67.5: Stellar Population
Characterization and Comparison To Models

Joshua V. Shields Department of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA<EMAIL_ADDRESS>Prasiddha
Arunachalam Department of Physics and Astronomy, Rutgers University, 136
Frelinghuysen Road, Piscataway, NJ 08854, USA  Wolfgang Kerzendorf Department
of Physics and Astronomy, Michigan State University, East Lansing, MI 48824,
USA  Department of Computational Mathematics, Science, and Engineering,
Michigan State University, East Lansing, MI 48824, USA  John P. Hughes
Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen
Road, Piscataway, NJ 08854, USA  Sofia Biriouk Department of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  Hayden Monk
Department of Physics and Astronomy, Michigan State University, East Lansing,
MI 48824, USA  Johannes Buchner Max-Planck-Institut fur extraterrestrische
Physik, Giessenbachstrasse 1, 85748 Garching bei Munchen, Germany

###### Abstract

The community agrees that Type Ia supernovae arise from Carbon/Oxygen white
dwarfs undergoing thermonuclear runaway. However, the full progenitor system
and the process that prompts the white dwarf to explode remain unknown. Most
current models suggest that the white dwarf explodes because of interaction
with a binary companion which may survive the process and remain within the
resulting remnant of the exploded star. Furthermore, both the pre-supernova
interaction process and the explosion of the primary are expected to imprint a
significant departure from ordinary stellar radii and temperatures onto the
secondary, making the star identifiable against the unrelated stellar
population. Identification of a surviving companion inside an SN Ia remnant
might confirm a specific corresponding SN Ia progenitor channel based on the
identity of the companion. We conducted a surviving companion search of the
Type Ia remnant SNR 0509$-$67.5based in the Large Magellanic Cloud. The well-
constrained distance to and foreground extinction of the Large Magellanic
Cloud allow for Bayesian inference of stellar parameters with low correlation
and uncertainties. We present a deep catalog of fully characterized stars
interior to SNR 0509$-$67.5 with radii, effective temperatures, and
metallicities inferred using combined Hubble Space Telescope photometric
observations across multiple visits. We then compile a list of surviving
companion models appropriate for the age of the remnant (roughly 400 years
after the explosion). We compare these predictions with the inferred stellar
parameters and conclude that none of the stars are consistent with the
predicted signatures of a surviving companion.

Type Ia supernovae (1728), Supernovae (1668), Supernova remnants (1667)

††software: Astropy (The Astropy Collaboration et al., 2013; Astropy
Collaboration et al., 2018), Scipy (Virtanen et al., 2020), Numpy (Harris et
al., 2020), pandas (Reback et al., 2022), Matplotlib (Hunter, 2007), corner
(Foreman-Mackey, 2016), StarKit (Kerzendorf & Do, 2015), wsynphot (Kerzendorf
& Singhal, 2022), APLpy (Robitaille & Bressert, 2012), UltraNest (Buchner,
2021).

tablenum SIXtablenum

##  1 Introduction

Type Ia supernovae (SNe Ia) play a critical role across astronomy. As
standardizable candles, they serve as distance indicators (e.g. Phillips,
1993; Phillips et al., 1999) that led to the discovery of the accelerating
expansion of the universe (Riess et al., 1998; Schmidt et al., 1998;
Perlmutter et al., 1999). They are also known to provide a substantial
fraction of the iron group elements in the Universe, driving galactic chemical
enrichment over cosmic time (Timmes et al., 1995; Nomoto et al., 2013;
Kobayashi et al., 2020). Despite the importance of these energetic events, we
have still not confirmed their progenitor system and explosion mechanism
(Livio, 2000; Wang & Han, 2012; Ruiz-Lapuente, 2019). It is widely accepted
that SNe Ia arises from the thermonuclear explosions of Carbon/Oxygen (C/O)
white dwarfs (Pankey, 1962; Colgate & McKee, 1969), but the process that
prompts the white dwarfs to explode is still uncertain. This major uncertainty
on the origins of SNe Ia propagates directly to their empirically calibrated
interpretations, introducing additional uncertainty or potential bias into our
understandings of galactic chemical enrichment and universal expansion.

SN Ia progenitor models can be divided into two major channels distinguished
by the survival or destruction of the secondary in the binary progenitor
system that prompts the C/O white dwarf to explode. In the first channel, the
primary white dwarf violently merges with a secondary white dwarf, prompting
thermonuclear explosion (e.g. Webbink, 1984). In this scenario, the explosion
may fully unbind both stars leaving no stellar remnant behind (Pakmor et al.,
2012; Papish et al., 2015). In the second, the primary either stably or
unstably accretes material from a secondary which prompts thermonuclear
runaway in one of a variety of ways (Whelan & Iben, 1973; Iben & Tutukov,
1984). The companion in this broad progenitor channel has been proposed to be
either a helium star (Iben & Tutukov, 1994; Wang et al., 2009), a helium-rich
white dwarf (Bildsten et al., 2007), a post-main sequence giant star (Li & van
den Heuvel, 1997), an evolved sub-dwarf (Meng & Li, 2019), or a main sequence
star (Han, 2008; Meng et al., 2009). The majority of accretion scenarios
predict that the secondary survives the SN explosion and will remain near the
site of the explosion (Shappee et al., 2013). Crucially, this means that the
surviving companion to the exploded star will reside near the center of the
supernova remnant (SNR) that is produced by the event.

In most accretion scenarios, the accretion and explosion processes are
expected to impart identifiable signatures onto the companion that persist for
at least thousands of years: During mass transfer, the secondary may
experience tidal forces that may both heat the star (Shen & Schwab, 2017).
This process may also cause the secondary to become tidally locked with the
primary which will also cause the star to adopt an anomalously high rotation
rate (Kerzendorf et al., 2009). When the primary explodes, the secondary will
no longer be gravitationally bound and will be shot out of the system at its
pre-explosion orbital velocity (Shen et al., 2018), far above velocities
obtainable through normal processes of stellar evolution. Shortly after the
primary explodes, the companion will be impacted by the SN ejecta, which may
strip a significant amount of material from the star (Marietta et al., 2000),
or deposit energy into the stellar envelope, causing it to increase in
temperature or inflate (Liu et al., 2021). Any ejecta that is captured by the
companion will be rich in radioactive elements which can continue to inject
energy into the star (Shen & Schwab, 2017). The ejecta will also contain a
large fraction of iron group elements which can remain detectable in the
stellar photosphere (Ozaki & Shigeyama, 2006).

If a surviving companion can be identified inside an SNR Ia by a combination
of the signatures expected for such a star, that identification would directly
confirm a specific corresponding accretion scenario as a viable SN Ia
progenitor channel (Marietta et al., 2000; Pakmor et al., 2008). However,
decades of intense, focused searches of Galactic SNRs have failed to securely
identify even a single unambiguous SN Ia companion (see e.g. Ruiz-Lapuente et
al., 2004, 2018; Ruiz-Lapuente, 2019; Kerzendorf et al., 2013, 2018; Shields
et al., 2022). Unfortunately, it is difficult to extrapolate from these
results to make conclusive statements about the viability of SN Ia progenitor
channels. Galactic remnants are plagued with highly uncertain distances (see
e.g. Tycho’s SNR, Ihara et al., 2007) and unconstrained column densities of
foreground dust (see e.g. Kepler’s SNR, Kerzendorf et al., 2014) which leads
to generally narrow searches that are not sensitive to all viable progenitor
channels and the surviving companions they are expected to produce.

In direct contrast, the Large Magellanic Cloud (LMC) resides at a well-
constrained distance of $49.59\pm 0.63$ kpc (Pietrzyński et al., 2019), with
very little foreground extinction (Joshi & Panchal, 2019) due to its high
Galactic latitude and face-on orientation (van der Marel et al., 2002).
Additionally, the galaxy resides close enough for individual stars to be
resolved by the Hubble Space Telescope (HST). These properties make SNRs Ia
enclosed in the LMC uniquely well-suited for surviving companion searches that
are free from the major problems of remnants in the Milky Way (Li et al.,
2019).

SNR 0509$-$67.5 is a young LMC remnant confirmed to be of SN Ia origin by
light echoes of the original SN spectrum (Rest et al., 2005, 2008). Schaefer &
Pagnotta (2012) conducted a tight search near the geometric center of the
remnant, with a search region large enough to discover stars ejected from the
progenitor system at speeds of up to 390 km s-1. That work found no objects in
their search region other than a diffuse source that was later identified to
be a background galaxy (Litke et al., 2017), suggesting that no surviving
companion exists within the remnant. However, recent works allow for surviving
companions traveling significantly faster (see e.g. Shen et al., 2018, up to
2500 km s-1), suggesting that a companion has not been conclusively ruled out.
Recently, Arunachalam et al. (2022, hereafter A22) used accurate proper motion
and location measurements of the remnant’s forward shock to determine a
precise dynamical explosion center. We decided to revisit this remnant with
these new constraints to conduct a thorough surviving companion search.

Prop. ID | MJD | Prop. PI | Filter | Exp. Time (s) | Limiting Mag (AB)
---|---|---|---|---|---
12326 | 55504 | Noll | F475W | 1010 | 26.08
12326 | 55504 | Noll | F555W | 696 | 26.05
12326 | 55504 | Noll | F814W | 800 | 25.17
13282 | 56559 | Chu | F814W | 1465 | 25.49
13282 | 56559 | Chu | F110W | 298 | 25.53
13282 | 56559 | Chu | F160W | 798 | 25.03
Table 1: The six observations combined to create our stellar catalogs.
Limiting magnitudes were estimated based on the faintest star observed in the
observation.

In this work, we present a characterized catalog of the stellar population
inside SNR 0509$-$67.5 to discover a surviving Ia companion. We synthesized
six HST observations of the remnant in five broad filters to construct
detailed spectral energy distributions (SEDs) of the enclosed stars. We fit
the observations of each star with backward physical modeling using Bayesian
Inference to move from SEDs to distributions of stellar astrophysical
parameters that could produce each set of photometric observations.

In Section 2, we describe the data and synthesis methods we used to construct
SEDs of the interior stellar population to SNR 0509$-$67.5. In Section 3, we
describe our models and astrophysical parameter inference methods. In Section
4, we present the results of our inference and compare them to the expected
parameters of surviving companions in the literature. In Section 5, we discuss
the constraints our results place on allowed surviving companions in the SNR
0509$-$67.5 remnant. We conclude in Section 6 by highlighting the parameter
space ruled out for surviving companions as well as discussing further
implementations of the techniques in this paper.

##  2 Observations

Figure 1: Error on magnitude as a function of magnitude for the full set of
characterized stars in the larger sample, by filter. These data show the
observational uncertainties used for our Bayesian inference fitting.

We needed to construct a well-sampled SED of each star inside SNR 0509$-$67.5
to characterize the interior stellar population and search for the existence
of a surviving companion. To measure stellar radii and temperatures, we
fundamentally needed to constrain the peak and shape of each stellar blackbody
curve. SNR 0509$-$67.5 has been well observed by the HST in eight different
filters. In this work, we chose to restrict ourselves to five wide-band HST
filters (see Table 1) for ease of methodological development. A larger set of
filters would more powerfully constrain stellar astrophysical parameters but
is beyond the scope of this work.

###  2.1 HST Catalogs

We set out to create a catalog of the interior stellar population to the SNR
0509$-$67.5 using a large enough sample of HST observations to construct well-
sampled SEDs. However, individual archival HST observations have been shown to
suffer from misaligned WCS with errors on the order of an arcsec, which has
previously prohibited the creation of stellar catalogs with straightforward
coordinate-based source matching. However, the recent HST Astrometry Project
has re-derived WCS for archival observations by cross-identifying bright stars
Gaia DR2 for alignment and reduced astrometric errors to approximately 10 mas
(Hoffmann et al., 2021), published in the Hubble Source Catalog (HSC). We
queried updated stellar sky positions and matched sources in the HSC available
through the CasJobs database (Whitmore et al., 2016) for cross-visit matching
to construct SEDs for stellar characterization. The resulting individual,
unmatched observations are shown in Figure 1.

###  2.2 Search Region

We obtained observations of each star within a 4.2 arcsec (1.00 pc at 49.27
kpc) radius of the dynamical center of the SNR 0509$-$67.5 as determined by
A22. This radius corresponds to the distance that a 2500 km s-1 object (the
fastest surviving companion velocity predicted in our considered models) could
have traveled at the distance of the LMC, over a highly conservative age
estimate for the remnant of 400 years (a strong upper limit from models of the
remnant’s expansion, see A22 for further discussion).

In addition, we obtained observations of the surrounding stellar population
within 10 arcsec of the dynamical center of SNR 0509$-$67.5 in order to have a
control sample of stars that could not be the surviving companion. We used
this sample to better understand the sensitivity of our search and how the
individual limiting magnitudes of the observations translate to limits on
inferred astrophysical parameters.

In Figure 2, we show a composite image of SNR 0509$-$67.5 created with APLPY
(Robitaille & Bressert, 2012) using two of the six observations analyzed in
this work (F814W and F555W), as well as F656N to clearly show the remnant. We
show the search region of potential surviving companions, the control sample,
as well as each of the identified interior stars.

Figure 2: A composite image of SNR 0509$-$67.5 from archival photometry. The
red channel is the F814W filter, green is F555W, and blue is F656N. The red
circle shows our search region where stars are close enough to the center to
be the surviving companion, and the green region shows the larger control
sample of characterized stars we used to better understand the unrelated
stellar population and the uncertainties of our technique. The white circles
show the individual stars that were modeled and characterized. The two large
stars we discuss in Subsection 4.2 are circled in pink.

##  3 Methodology & Analysis

Our goal was to be sensitive to the entire range of predicted surviving
companions which we gathered and show in Table 2. In designing this study, we
chose to propagate the most conservative case for each parameter across all
other parameters to be certain that we were sensitive to any potential type of
surviving companion. As a result, certain portions of our combined parameter
space are not realizable for a surviving companion (e.g. a non-degenerate
companion cannot reside far away from the center of the remnant due to a lower
maximum ejection speed). However, we decided that this approach was necessary
to safeguard against potentially missing a surviving companion.

###  3.1 Stars Identified in A22

We note the presence of three stars identified in A22 as potential surviving
companion candidates that reside very near the dynamical center of SNR
0509$-$67.5, within 1.4 arcsec, the angular distance that an object in the LMC
moving at 1000 km s-1 could have traveled in 317 years. These three stars are
too faint to be detected by the automated aperture photometry that created the
HSC. For completeness, we decided to include these stars in our search using
HST magnitudes from Hovey (2016), but we note that their photometry was
obtained inconsistently with the rest of the stellar population. We discuss
these stars further in Subsection 4.4.

###  3.2 Synthetic Spectra and Photometry

Source Work | Model | Surviving Companion Type | Temperature ($10^{4}$ K) | Radius (R${}_{\odot})$
---|---|---|---|---
Liu et al. 2021 | DDet∗ Kepler Model | He Star | 1 | 3
Liu et al. 2021 | DDet∗ Mesa Model | He Star | 1.1 | 0.5
Liu et al. 2022 | SD Accretion‡ | He Star | 4.6 | 0.5
Shappee et al. 2013 | SD Accretion‡ | MS Star | 0.52 | 10
Pan et al. 2013 | SD Accretion‡ | He Star | 4 | 0.6
Pan et al. 2014 | SD Accretion‡ | MS Star | 0.75 | 3.42
Pan et al. 2014 | DDet∗ | He WD | 5.5 | 0.39
Rau & Pan 2022 | SD Accretion‡ | MS Star | 0.4 | 2.5
Shen & Schwab 2017 | DDet∗ | He WD | 10 | 0.05†
Table 2:  A summary of predicted temperatures and radii from different
surviving companion models at the age of the remnant $\leq 1000$ yrs. Many of
these works tested a variety of models. In such cases, we show the resulting
temperature and radius that is the most difficult to detect, i.e. the
smallest, coolest model. We show two models from works where the smallest
model is not also the coolest. All combinations of temperature and radius are
clearly distinguishable from the surviving companion candidates inside SNR
0509$-$67.5with the exception of Shen & Schwab (2017) which is too faint to
detect.
∗ DDet refers to the Double Detonation model, also known as the Dynamically
Driven Double-Degenerate Double-Detonation (D6) model (Shen et al., 2018).
‡ SD Accretion refers to the single degenerate accretion scenario, in which
the companion has exhausted fusion energy.
†Shen & Schwab (2017) did not directly present an evolving radius of the
surviving companion over time. We calculated a radius using the provided
luminosity and effective temperature using the Stefan-Boltzmann law.

We generated synthetic spectra by interpolating a spectral grid generated with
the PHOENIX stellar atmosphere code (Husser et al., 2013) using
StarKit111https://github.com/starkit/starkit (Kerzendorf & Do, 2015). The
PHOENIX spectra to be interpolated were sampled over effective temperature
$T_{\textrm{eff}}$, logarithmic surface gravity log$(g)$, and metallicity
relative to solar $[\frac{M}{H}]$. We then scaled the spectrum by stellar
radius as a free parameter to obtain a model intrinsic stellar spectrum.

We attributed all extinction to Galactic foreground dust, which is the
dominant source of extinction for objects contained in the LMC (Choi et al.,
2018). We reddened our stellar spectrum with a standard Galactic extinction
law of $R_{V}=3.1$ following Fitzpatrick (1999) with the
dust_extinction222https://github.com/karllark/dust_extinction package. We note
that, because of the modest cumulative amount of foreground extinction
(A${}_{V}\approx 0.28$, Joshi & Panchal 2019), the exact choice of reddening
model had little effect on synthetic magnitudes generated and resulting
extracted stellar parameters (roughly a maximum difference of 0.01 mags in
F475W and F814W, with smaller effects in other bands). Finally, we convolved
the spectrum with each HST filter curve in which a given star was observed
(shown in Figure 3) using wsynphot333https://github.com/starkit/wsynphot
(Kerzendorf & Singhal, 2022), and integrated the resulting flux to obtain a
photometric magnitude that we compared directly to each observation.

###  3.3 Bayesian Parameter Inference

We derived a multidimensional posterior probability distribution for the set
of astrophysical parameters for each star with the nested sampling Monte Carlo
algorithm MLFriends (Buchner, 2016, 2018) implemented in the
UltraNest444https://johannesbuchner.github.io/UltraNest/ package (Buchner,
2021) by comparing the observations to synthetic magnitudes generated with a
given set of parameters. Our priors are presented in Table 3. We fixed
log$(g)$ at 3.0 as our observations were generally insensitive to variation in
this space. Additionally, we fixed each star to be at a distance of 49.27 kpc,
the distance of the remnant following A22, noting that any variation in
distance for a given star in the LMC is small compared to other sources of
uncertainty, and any variation or uncertainty here translates directly to a
corresponding variation or uncertainty in radius. An uncertainty on distance
of 1 kpc (2%) typical for the LMC, would translate directly to an uncertainty
in radius of 2%.

We begin with a standard $\chi^{2}$ likelihood assuming Gaussian distributed
errors for our observations given by

$\chi^{2}=\sum_{i=1}^{n}\left(\frac{m_{i,obs}-m_{i,model}}{\sigma_{i,obs}}\right)^{2}$

over the observations for a given star. We adopt the log-likelihood function
$ln\mathcal{L}=\chi^{2}/2$ for fitting.

We show an example of a single set of observations and the resulting fit in
Figure 3. The distribution of spectra in this figure is generated by randomly
sampling the posterior parameter distribution and generating model spectra as
examples to show the constraints of the input observations.

###  3.4 SED Requirements

Stars only detected in the infrared F110W and F160W bands did not have
sufficient observational constraints to allow for strong astrophysical
characterization. As a result, we only present characterizations of stars with
observations in at least two non-infrared bands. This generally required that
stars be brighter than 25th magnitude, seen in the limiting magnitude
estimation reported in Table 1.

###  3.5 Validation, Sensitivity, and Precision of Parameter Extraction

We examine the constraining power of our parameter extraction and find robust
validation of our ability to recover known temperatures and radii. In Appendix
A, we fit the sun as an example and show the posterior parameter distribution.
We find that the precision of our metallicity constraint is highly dependent
on the temperature of the star, and in some cases virtually no information is
gained and the prior is recovered. In principle, a star enriched by over an
order of magnitude in metallicity, a potential signature of a surviving SN Ia
companion, could be constrained and detected with HST photometry. However, no
star in our sample showed an obvious metallic enhancement signature (See
appendix B for further discussion). For this reason, we show the maximum
likelihood metallicities that result from our fitting process in Figures 4 and
5, but do not further probe this parameter space for the signature of a
surviving companion. Similarly, while we fit for foreground extinction and
thus allow the variation in the parameter to inform the posterior, in almost
all cases we recovered our extinction prior.

In this work, we did not attempt to characterize a systematic uncertainty
floor for our parameter constraints. We note that the brightest stars in our
sample show unrealistically small estimated temperature uncertainties, smaller
than our models are truly able to constrain tracing back to uncertainty in our
model PHOENIX spectra. We report these values as they were produced and note
that they do not influence our search for a surviving companion, but suggest
caution when interpreting these uncertainties for other purposes.

Our various limiting magnitudes in the original observations do not easily map
onto uncorrelated temperature and radius sensitivities. We estimate the
sensitivity of our HSC search in the dependent parameter space as the
smallest, coolest stars in our sample. For a 5000 K star this results in a
sensitivity to stars larger than half a solar radius, scaling with
temperature. A 10000 K star in line with the predictions of Liu et al. (2022)
would need to be smaller than 0.2 R⊙ to remain undetected.

Figure 3: An example outcome of the fitting process for one of the stars in
the search region. The blue crosses show the photometric observations with the
vertical spread showing observational uncertainty, and the horizontal spread
shows the width of the filter used for the observation, corresponding to the
rough portion of the spectrum probed by the observation. The transmission
curve of each filters is shown in dashed purple. The black and grey regions
show a distribution of spectra created by sampling the posterior distribution
of constrained stellar parameters.

##  4 Results

Figure 4: Radius vs. Effective Temperature and metallicity fits of stars in a
10 arcsec radius, excluding those close enough to the center of SNR
0509$-$67.5 to be the surviving companion. We used this sample to estimate the
underlying main sequence distribution of stars in the local LMC. We note the
presence of two anomalous large radius stars that we do not support belonging
to the local main sequence population, and thus do not include in our
distribution estimation in figure 5. We discuss these stars further in
Subsection 4.2.  Figure 5: Radius vs. Effective Temperature and metallicity
fits of stars within 4.2 arcsec of the hydrodynamic center of SNR 0509$-$67.5,
the sample of potential surviving companion stars. The gray crosses show the
surrounding control sample from Figure 4 which we used to estimate the
underlying temperature-radius distribution of the local stellar population,
shown by the contours. The purple crosses show the three stars identified in
A22. The red X markers show surviving companion models from Table 2 close
enough to be compared, with the other models too high in temperature or large
in radius to be placed within the bounds of the figure.

###  4.1 Characterized Stellar Astrophysical Parameters

We modeled the interior stellar population of SNR 0509$-$67.5 to extract
stellar parameters and search for a surviving companion in line with those
predicted by the surviving companion models shown in Table 2. We extracted the
parameters of each star within a 10 arcsec radius of the dynamical center, too
far from the center of the remnant to be the surviving companion to the
exploded star, to serve as a control sample of the local stellar population,
shown in Figure 4. We then analyzed and extracted the parameters of each star
within a conservative 4.2 arcsec search region, the maximum distance a
surviving companion could have traveled from the center of the remnant. This
is the sample of viable surviving companion candidates, shown in Figure 5. In
this sample, we do not detect a star substantially different from the local
temperature-radius main sequence or in line with any of the models shown in
Table 2.

Parameter | Prior Distribution | Source
---|---|---
Effective Temperature (K) | $\mathcal{U}(2300-12000)$ | Phoenix Grid Boundaries
Radius (R⊙) | $\mathcal{U}(0.05-10)$ | Chosen Physical Boundaries
V band Absorption (mags) |  $\mathcal{N}(0.28,0.15)$ bounded at 0 | Joshi & Panchal,2019
Metallicity ($[\frac{M}{H}]$) | $\mathcal{N}(-0.34,0.15)$ | Luck et al.,1998
Distance (kpc) | 49.27 | Arunachalam et al.,2022
Table 3: A compilation of the priors used for stellar parameter inference, as
well as sources where appropriate. $\mathcal{U}$ is Uniform (Lower boundary -
Upper boundary), $\mathcal{N}$ is Normal($\mu,\sigma$), where $\mu$ is the
mean and $\sigma$ is the standard deviation. See subsection 3.3 for discussion
of the choice of priors.

###  4.2 Large Radius Stars in the Control Sample

We note the presence of two anomalously large stars in our greater control
sample of 10 arcsec around the dynamical center of SNR 0509$-$67.5 denoted
separately in Figure 4. An inflated star could be a tracer of a surviving
companion, however neither of these stars lie close enough to the dynamical
center of the remnant to be associated with the Type Ia event. We highlight
that a large radius here is not necessarily physical because radius is
degenerate with distance and all stars were assumed to be at the distance of
the SNR 0509$-$67.5 for fitting. We favor the explanation that stars with
anomalously large radii here are either foreground Galactic halo stars or red
giants.

We examined the Besancon Galaxy model (Robin et al., 2012) to investigate the
possibility of observing a foreground Galactic halo star in our sample. We
sampled 10 arcsec cones oriented towards the LMC and found a stellar surface
number density of $1.1\times 10^{-3}$ arcsec-2, or 0.359 stars in a 10 arcsec
radius circle on average. Assuming star counts are Poisson distributed, we
calculate a $30.2\%$ chance to observe one or more Galactic halo stars, and a
$5.1\%$ chance to observe 2 or more. Assuming the 3000 K star in Figure 4 is
in the foreground, scaling its radius appropriately by roughly a factor of 10
for a halo star would place it firmly on the main sequence, making this a
likely explanation. Additionally, A22 identified this star (also known as star
M in Schaefer & Pagnotta 2012) as possessing the largest proper motion in and
around the remnant, consistent with it residing in the foreground and further
strengthening this identification.

The star that we measured to have a radius of 9.5 R⊙ and a temperature of 5000
K resides in a portion of temperature-radius space occupied by evolved red
giants in the LMC, and we support this identification as well. We emphasize
that neither of these two stars lie close enough to the center of the remnant
to be a surviving companion to the exploded star, so we prefer these
alternative explanations. We do not include either of the two stars discussed
here in our Kernel Density Estimation that we use to compare to the population
of surviving companion candidates due to their likely non-LMC main sequence
identities.

###  4.3 Comparison To Surviving Companion Models

We have gathered a compilation of models that make concrete predictions about
the effective temperature and radius of a surviving SN Ia companion on
timescales appropriate for the SNR 0509$-$67.5($10^{2}-10^{3}$ yrs), shown in
Table 2. The considered surviving companion models shown predict that the star
will either be hotter than $10000$ K or inflated to larger than 2.5 R⊙. Our
set of observations is sensitive to stars hotter than 5000 K or larger than
0.6 R⊙. Therefore, we rule out this set of surviving companions from existing
within SNR 0509$-$67.5 , as each model would be distinguishable from the
sample of potential surviving companions in Figure 5.

Other surviving companion models not considered here can be easily tested and
sought out in this remnant by comparing to our characterized stellar catalog.
We show examples of our fit parameters in Table 4, and provide the full
characterized catalog online.

MatchID | MatchRA | MatchDec | teff | teff_err | rad | rad_err | mh | mh_err | av | av_err | Near_center
---|---|---|---|---|---|---|---|---|---|---|---
1105108 | 77.37689 | -67.52006 | 5658.51 | 352.269 | 0.533 | 0.064 | -0.33 | 0.153 | 0.285 | 0.134 | False
1240861 | 77.3773 | -67.52317 | 5414.569 | 244.166 | 0.54 | 0.036 | -0.349 | 0.145 | 0.269 | 0.137 | False
2094417 | 77.37589 | -67.52166 | 6607.698 | 94.121 | 1.489 | 0.014 | -0.872 | 0.129 | 0.037 | 0.054 | False
2360222 | 77.3794 | -67.52045 | 6650.82 | 54.514 | 1.381 | 0.012 | -0.424 | 0.136 | 0.027 | 0.03 | True
4275360 | 77.38571 | -67.52132 | 5655.744 | 225.258 | 0.617 | 0.031 | -0.348 | 0.152 | 0.313 | 0.136 | False
4304067 | 77.3827 | -67.52268 | 5203.318 | 193.617 | 0.716 | 0.035 | -0.352 | 0.146 | 0.311 | 0.138 | False
4705369 | 77.37783 | -67.52192 | 5789.892 | 210.41 | 0.646 | 0.027 | -0.363 | 0.142 | 0.28 | 0.134 | True
4728380 | 77.3771 | -67.51996 | 4997.528 | 8.752 | 3.896 | 0.013 | -0.96 | 0.057 | 0.003 | 0.004 | False
4769912 | 77.37471 | -67.52032 | 5758.987 | 189.441 | 0.761 | 0.025 | -0.364 | 0.141 | 0.263 | 0.13 | False
5394004 | 77.37623 | -67.51961 | 5161.428 | 16.844 | 2.683 | 0.015 | -0.721 | 0.114 | 0.007 | 0.01 | False
Table 4: An abbreviated example of 10 stars with their extracted parameters.
The full table including the magnitudes used for fitting is available as a
supplemental online data product.

###  4.4 Results of Stars Identified in A22

We additionally modeled the three stars identified in A22 that reside very
near the dynamical center of SNR 0509$-$67.5, within 1.4 arcsec corresponding
to a velocity $V\approx 1000$ km s-1 at the distance of the remnant. They are
fainter than the detection limits of the HSC, so they are unsurprisingly the
smallest and coolest stars in Figure 5. All three stars appear to be a natural
extension of the temperature-radius main sequence of the general LMC stellar
population where M-dwarfs are expected to reside, and also lie within the
contours estimated by the surrounding population, despite initial differences
in aperture photometry. However, one of the three stars, which we refer to as
HHE 5 in line with Hovey (2016), is poorly fit by our models and we discuss it
further in Appendix C. Like the other two stars, we support an ordinary
M-dwarf classification for HHE 5.

##  5 Discussion

We have conducted a deep, systematic search of the Ia remnant SNR 0509$-$67.5
to identify a surviving companion, using a sample of existing archival HST
wide band photometry. We investigated a large enough search region to allow
for the fastest moving surviving companions, i.e. hypervelocity white dwarfs
tracing back to double detonation progenitor systems (e.g. Shen et al., 2018).
All models, regardless of the explosion mechanism of the primary, predict that
a nearby secondary that is impacted by expanding supernova ejecta will show
some combination of high effective temperature or inflated radius for at least
thousands of years. In Table 2, we show a compilation of expected lower
temperatures and radii predicted from various models approximately 1000 years
after being impacted by SN Ia ejecta. In contrast, none of the stars inside
the SNR 0509$-$67.5 close enough to the center to be surviving companion
candidates in the remnant show astrophysical parameters that suggest exotic
identities. For any of the models considered here, this finding rules out the
existence of such a surviving companion as such a star would be clearly
identifiable as separate from the main sequence stellar population. We note
that we cannot rule out the existence of a He WD companion in line with Shen &
Schwab (2017) in SNR 0509$-$67.5. However, this model solely considered
luminosity generated due to the delayed decay of 56Ni on the surface of the
donor WD, which may not remain the dominant source of over-luminosity at
timescales associated with the remnant (see e.g Pan et al., 2014; Liu et al.,
2021).

We rule out the existence of a surviving companion in the remnant down to a
limiting optical AB magnitude of 25.5, with the one exception being that the
surviving companion is indistinguishable from the local stellar population in
combined temperature-radius space. The list of considered surviving companion
models we show is not exhaustive, and new models not yet explored or published
are still in development. We encourage models not considered here to be
compared to the astrophysical properties of this stellar population.

###  5.1 Spin-up/spin-down models

This work probes the interior stellar population of SNR 0509$-$67.5 for
signatures of interaction both before and during the explosion of the primary
WD. The models we show in Table 2 generally assume that the surviving
companion is close enough to the primary when it explodes for the secondary to
experience Roche lobe overflow. However, some models have been proposed in
which the secondary donates mass to the primary C/O WD before the process
halts and the secondary evolves in isolation. The mass transfer process
imparts additional angular momentum onto the primary C/O WD which prevents it
from experiencing thermonuclear runaway until it can dissipate the accrued
angular momentum or spin down (Di Stefano et al., 2011; Justham, 2011; Hachisu
et al., 2012). The spin-down timescale is poorly constrained to be between
$10^{5}$ and $10^{9}$ years (but see Kerzendorf et al. 2018 and enclosed
references for further constraints), and the secondary may have time to
exhaust hydrogen evolve in to a WD. If so, the secondary can retain a large
enough orbital separation from the primary to remain largely unaffected by the
explosion. The secondary will then remain near the center of the remnant as an
isolated WD that has cooled for up to the spin-down time. No isolated WD is
detected in the archival photometry used in this work near the center of SNR
0509$-$67.5 , which can be translated to a constraint on spin-down timescale
of the system that is dependent on the mass of the companion (see Di Stefano &
Kilic 2012, but also Meng & Podsiadlowski 2013 for further discussion).

##  6 Conclusions

We present a full stellar classification of the interior stellar population to
SNR 0509$-$67.5 to probe the parameter space sensitive to ejecta interaction
and search for a surviving companion to the exploded star that created the
remnant. We considered a generous search region corresponding to an ejection
velocity of 2500 km s-1 and a remnant expansion age of 400 years. Within this
region, we do not detect an anomalously hot or radially extended star as
predicted by the interaction of supernova ejecta with a nearby companion in
both the degenerate and non-degenerate companion cases in which the companion
survives.

This result holds consistent with other recent non-detections of surviving
companions in Ia remnants that may point to SN Ia progenitor channels that do
not leave bound stellar remnants behind (see Ruiz-Lapuente 2019). However, the
sporadic nature of previous surviving companion searches with inconsistent
limits and parameter space exploration makes conclusive statements about the
viability of specific progenitor channels difficult to support.

The constraints of the LMC as well as the new developments to the HSC that
made the stellar characterization central to this work possible remain
consistent across other known SN Ia remnants in the LMC. Similar studies of
those remnants would enable statistical statements about the viability of
specific progenitor channels.

##  7 Acknowledgments

This work was based on observations made with the NASA/ESA Hubble Space
Telescope, and obtained from the Hubble Legacy Archive, which is a
collaboration between the Space Telescope Science Institute (STScI/NASA), the
Space Telescope European Coordinating Facility (ST-ECF/ESAC/ESA) and the
Canadian Astronomy Data Centre (CADC/NRC/CSA). PA and JPH acknowledge support
from HST GO Program 16161 (PI: Arunachalam). JPH, the George A. and Margaret
M. Downsbrough Professor of Astrophysics, acknowledges the Downsbrough heirs
and the estate of George Atha Downsbrough for their support.

The data presented in this paper were obtained from the Mikulski Archive for
Space Telescopes (MAST) at STScI. The specific observations analyzed can be
accessed via https://doi.org/10.17909/T97P46 (catalog DOI: 10.17909/T97P46)
through the HSC CasJobs database.

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##  8 Contributor Roles

  * •

Conceptualization: Joshua V. Shields, John P. Hughes, Prasiddha Arunachalam

  * •

Data curation: Joshua V. Shields, Sofia Biriouk

  * •

Formal Analysis: Joshua V. Shields

  * •

Funding acquisition: Wolfgang Kerzendorf, John P. Hughes

  * •

Investigation: Joshua V. Shields, Prasiddha Arunachalam

  * •

Methodology: Joshua V. Shields

  * •

Project administration: Wolfgang Kerzendorf

  * •

Software: Johannes Buchner, Wolfgang Kerzendorf, Joshua V. Shields

  * •

Supervision: Wolfgang Kerzendorf, John P. Hughes, Joshua V. Shields

  * •

Validation: Joshua V. Shields, Prasiddha Arunachalam, Sofia Biriouk

  * •

Visualization: Joshua V. Shields, Prasiddha Arunachalam, Hayden Monk, John P.
Hughes

  * •

Writing - original draft: Joshua V. Shields

  * •

Writing - review & editing: Joshua V. Shields, Wolfgang Kerzendorf, Prasiddha
Arunachalam, John P. Hughes, Johannes Buchner

##  Appendix A Methodology verification - The Sun

To validate our stellar astrophysical parameter extraction, we obtained AB
magnitudes and magnitude uncertainties of the Sun from Willmer (2018). We
applied the same methodology that we used in our study to these observations,
excluding our treatment of dust, to recover derived solar astrophysical
parameters. Specifically, we obtained the same five HST band AB magnitudes
from our work, F475W, F555W, F875W, F110W, and F160W, and performed Bayesian
inference to extract stellar parameters which we could then compare to known
intrinsic values. The results of the parameter extraction are shown in Figure
6. We used the same uninformative uniform temperature and radius priors as in
the rest of our work but changed the metallicity prior to a normal
distribution centered on solar metallicity (Mean = 0.00, $\sigma=0.15$). As
shown, our methodology powerfully constrains the temperature and radius of the
star, producing strong agreement with true values, but once again recovering
the prior on metallicity. See Appendix B for further discussion on our
metallicity constraints.

Figure 6: An example fit corner plot of extracted astrophysical parameters of
the Sun for methodological validation. We obtained and fit magnitudes from
Willmer (2018). The true values are shown with blue lines. Our parameter
extraction shows strong agreement with the true solar values of temperature
and radius, within $1\sigma$.

##  Appendix B Measuring Metallicity With Photometry

We report metallicity measurements for each of the stars in this work but do
not attempt to quantitatively probe this space for surviving companions. We
made this choice because both the general ability of pure photometry and the
combination of filters required to detect metallicity enhancement in a star
has a complex relationship with effective temperature. In Figure 7 we show the
relative differences in flux between metal-poor ($[\frac{M}{H}]=-1$) and
metal-rich ($[\frac{M}{H}]=1$) stars at 6000 K and 10000 K. For the filters
used in this work, [F475W, F555W, F814W, F110W, and F160W] these stars would
show differences of [-0.04, 0.07, 0.17, 0.13, 0.04] mags and [0.15, 0.15,
0.14, 0.11, 0.11] mags at 6000 K and 10000 K respectively. The difference in
metallicity for both temperature stars is possibly constrained by photometry,
but this enrichment in a 6000 K star creates a more obvious signature,
distinguishable from a change in temperature or radius.

In either case, the level of metallic enrichment expected for a surviving
companion could potentially be constrained from the photometry of this work,
as the differences in HST magnitudes from comparing the spectra in Figure 7
are significantly higher than the uncertainties of many observations,
especially in the brighter stars in our sample. However, none of the stars in
our sample showed an obvious signature tracing back to a departure from
typical LMC metallicities, so the metallicities of stars in our sample are
usually not constrained beyond our prior.

Figure 7: An example showing the effects of metallicity at different
temperatures. The top panel shows the spectra of a metal-poor
($[\frac{M}{H}]=-1$) 6000 K star and a metal-rich ($[\frac{M}{H}]=1$) 6000 K
star. The bottom shows the same, but comparing 10000 K stars. The purple
dashed lines show the transmission curves of the same filters used in the rest
of this work, and the gray line shows the difference between the two spectra.
At some temperatures, sufficiently sensitive photometry is capable of
constraining metallicity, detecting relative enhancements and diminishments in
the redder and bluer optical portions of the spectrum.

##  Appendix C Investigating HHE 5

In Figure 8, we show our fit of the SED belonging to HHE5 and originating from
photometry in Hovey (2016). The F814W measurement lies multiple standard
deviations away from the constrained spectrum, and in general cannot lie on a
standard stellar spectrum anchored by the infrared observations. Investigating
further, we note that the F814W measurement of HHE 5 is the faintest F814W
measurement present in the reported catalog of Hovey (2016). While not
conclusive, this could point to the measurement being unphysical.

The location of HHE 5, very near the dynamical center of SNR 0509$-$67.5, is
the strongest argument in favor of a surviving companion identification, and
we acknowledge that the unusual photometry here could be seen as further
support towards an exotic identification. However, no current surviving
companion models predict the narrow F814W suppression seen in the SED. We
support the explanation that the F814W measurement is unphysical, rather than
invoking an exotic scenario capable of explaining this feature.

Figure 8: Our fit for HHE 5, similar to that shown in Figure 3. The model does
a poor job fitting the observations, primarily because of the single F814W
observation that is impossible to explain with a stellar spectrum capable of
fitting the other four observations. The other points can be suitably
explained by a typical stellar spectrum, in accordance with the possibility of
an unphysical F814W measurement.