# A new study on a type Iax stellar remnant and its probable association with
SN 1181

Foteini Lykou Konkoly Observatory, Research Centre for Astronomy and Earth
Sciences, Konkoly-Thege Miklós út 15-17, 1121 Budapest, Hungary  Laboratory
for Space Research, University of Hong Kong, 405B Cyberport 4, 100 Cyberport
Road, Cyberport, Hong Kong  Quentin A. Parker Quentin A. Parker
<EMAIL_ADDRESS>Laboratory for Space Research, University of Hong Kong, 405B
Cyberport 4, 100 Cyberport Road, Cyberport, Hong Kong  Department of Physics,
The University of Hong Kong, Chong Yuet Ming Physics Building, Pokfulam Road,
Hong Kong  Andreas Ritter Laboratory for Space Research, University of Hong
Kong, 405B Cyberport 4, 100 Cyberport Road, Cyberport, Hong Kong  Department
of Physics, The University of Hong Kong, Chong Yuet Ming Physics Building,
Pokfulam Road, Hong Kong  Albert A. Zijlstra Jodrell Bank Centre for
Astrophysics, The University of Manchester, Alan Turing Building, Oxford Road,
M13 9PL, Manchester, U.K.  Laboratory for Space Research, University of Hong
Kong, 405B Cyberport 4, 100 Cyberport Road, Cyberport, Hong Kong  D. John
Hillier Department of Physics and Astronomy & Pittsburgh Particle Physics,
Astrophysics, and Cosmology Center (PITT PACC), University of Pittsburgh, 3941
O’Hara Street, Pittsburgh, PA 15260, USA  Martín A. Guerrero Instituto de
Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía S/N, 18008
Granada, Spain  Pascal Le Dû Kermerrien Observatory, F-29840 Porspoder, France

###### Abstract

We report observations and modeling of the stellar remnant and presumed
double-degenerate merger of Type Iax supernova Pa30, which is the probable
remnant of SN 1181 AD. It is the only known bound stellar SN remnant and the
only star with Wolf-Rayet features that is neither a planetary nebula central
star nor a massive Pop I progenitor. We model the unique emission-line
spectrum with broad, strong O vi and O viii lines as a fast stellar wind and
shocked, hot gas. Non-LTE wind modeling indicates a mass-loss rate of $\sim
10^{-6}\,\rm M_{\odot}\,yr^{-1}$ and a terminal velocity of $\sim$15,000 km
s-1, consistent with earlier results. O viii lines indicate shocked gas
temperatures of $T\simeq 4\,$MK. We derive a magnetic field upper limit of
$B<2.5\,$MG, below earlier suggestions. The luminosity indicates a remnant
mass of 1.0–1.65 M⊙ with ejecta mass $0.15\pm 0.05\,\rm M_{\odot}$. Archival
photometry suggests the stellar remnant has dimmed by $\sim$0.5 magnitudes
over 100 years. A low Ne/O$\,<0.15$ argues against a O-Ne white dwarf in the
merger. A cold dust shell is only the second detection of dust in a SN Iax and
the first of cold dust. Our ejecta mass and kinetic energy estimates of the
remnant are consistent with Type Iax extragalactic sources.

Supernovae (1668), Circumstellar matter (241), Spectroscopy (1558), Photometry
(1234), Plasma astrophysics (1261)

††facilities: GTC (OSIRIS), WIYN (SparsePak), XMM, Swift (XRT), WISE, AKARI,
TESS, IRSA, Planck, IRAS, ROSAT, VOSA, HST (STIS), ATLAS, Gaia††software:
astropy (Astropy Collaboration et al., 2013, 2018), cmfgen (Hillier & Miller,
1998; Hillier, 2012; Hillier & Dessart, 2012)
(http://kookaburra.phyast.pitt.edu/hillier/web/CMFGEN.htm) cloudy (Ferland et
al., 2013), pyphot (https://github.com/mfouesneau/pyphot ), GaiaXPy
(https://gaia-dpci.github.io/GaiaXPy-website/)

,

##  1 Introduction

A new class of thermonuclear supernovae (SNe), produced in low-mass (i.e.,
$M_{*}\leq 8$ M⊙) binary systems, has been identified in the last twenty
years: the Type Iax (e.g., Foley et al., 2013), also known as SN 2002cx-like.
These are the least-understood supernovae. Two scenarios are proposed for
their formation. In the single-degenerate scenario (e.g., Jordan et al., 2012;
Kromer et al., 2015), a carbon-oxygen (CO) white dwarf (WD) that accreted
material from a helium donor fails to detonate. In the double-degenerate
scenario (e.g., Kashyap et al., 2018), the SN is caused by deflagration of the
accretion disk that forms after the merger of a CO WD with an oxygen-neon
(ONe) WD companion. Type Iax SNe are sub-luminous (as faint as $M=-13$ to
$-14$ mag) with expansion velocities from $2000$ to $9000$ km s-1, and may
leave a stellar remnant behind. The currently known Type Iax SNe
population111See also https://www.wiserep.org/, where 44 objects are currently
listed. is only a few tens (Foley et al., 2013; Jha, 2017), so the full range
of observed properties is weakly constrained. All are extra-galactic save two
in our own Galaxy. One is SN Sgr A East near the Galactic Center as suggested
by Zhou et al. (2021). The other222Originally assigned as Type Iax by Oskinova
et al. (2020).  is associated with the nebula Pa 30, identified as the most
probable remnant of the historical SN 1181 AD (Ritter et al., 2021, hereafter
Paper I).

Earlier studies show that the nebula – Pa 30 in Kronberger et al. (2014) and
IRAS 00500+6713 in Gvaramadze et al. (2019) – emits strongly in X-rays
(Oskinova et al., 2020). The nebula appears circular, approximately 3′ - 4′
across depending on the wavelength of the imagery. Faint, diffuse [O iii]
nebular emission is seen via deep narrow-band imaging (Kronberger et al.,
2014; Oskinova et al., 2020; Ritter et al., 2021). An [S ii] shell is
expanding at $1000\pm 100$ km s-1 (Paper I). The stellar remnant, reported by
Gvaramadze et al. (2019) as J005311, is associated with the infrared source
2MASS J00531123+6730023. It is located at the center of Pa 30 and has been
argued to be the result of a double-degenerate CO + ONe WD merger (Gvaramadze
et al., 2019; Oskinova et al., 2020).

In this paper we analyze the stellar wind and nebula in order to constrain the
progenitor system. In the following Section, we describe our own observations
as well as the archival data used in this work. Stellar parameters are derived
through a comparison of the stellar spectra against NLTE and photoionization
models (Sect. 3). In Section 4 we explore the remnant’s potential variability,
followed by a new analysis on the nebular properties in Sect. 5. In the
penultimate Section we discuss the implication of our results on the
progenitor and its relation to other Type Iax sources, while our conclusions
can be found in the last section.

Figure 1: Stellar spectra from SparsePak/WIYN, OSIRIS/GTC, and a small amateur
telescope (P. Le Dû) smoothed and scaled to the same flux level. The
dereddened spectra are also shown for comparison (using interstellar
extinction from Paper I, ). The major discontinuity bluewards of 4000 Å is
seen in the OSIRIS and amateur spectra but the SparsePak spectrum did not go
below 4200 Å. The OSIRIS spectrum had the slit slightly off-center to avoid a
nearby bright star. To correct for the resulting slight flux underestimation
after flux calibration the spectrum was scaled to match the reliable
SparsePak/WIYN flux level.

##  2 Observations and Data Reduction

The stellar remnant 2MASS J00531123+6730023 has a Gaia J2000 position RA: 00h
53m 11.205s, DEC: +67o 30’ 02.381’. The Gaia DR3 parallax is $0.4065\pm
0.0259$ mas and the distance derived from the inverse parallax is $2460\pm
157$ pc. However this transformation is nonlinear and the measured parallax
may have large uncertainties for distant and faint objects. In this case, the
fractional parallax error is approximately 6.4%. Therefore in this work, as in
Paper I, we adopt the distance measurement of Bailer-Jones et al. (2021) at
$2297^{+122}_{-114}$ pc, which was derived from a probabilistic approach on
Gaia data. The Galactic coordinates ($l$,$b$) = (123.1, 4.6) place the stellar
remnant at 180 pc from the plane, so likely part of the old stellar disk.

###  2.1 OSIRIS/GTC spectroscopy

High signal-to-noise spectroscopic data of both star and nebula were obtained
with the OSIRIS instrument on the 10-m Gran Telescopio Canarias (GTC)
telescope in late 2016 as part of our planetary nebula (PN) follow-up program.
The faint nebula spectra from SN 1181 was presented in Paper I with only the
[S ii] 6716 and 6731 Å doublet and [Ar iii] 7136 Å emission lines detectable.
Here, we focus on the spectra we obtained for the stellar core.

OSIRIS covered the wavelength region from 3700 to 7000 Å. The slit width was
0.8″ (Paper I). The most prominent stellar feature is the O vi 3811/34
emission line of remarkable strength below 4000 Å (Figure 1), with additional
broad spectral features beyond 4200 Å. The narrow absorption lines are known
diffuse interstellar bands (DIBs) at 4428, 4502, 4727, 4762, 5418, 5456, 5779,
5796, 6204, 6281, and 6613 Å, identified using the NASA
catalogue333https://leonid.arc.nasa.gov/DIBcatalog.html (Jenniskens & Desert,
1994).

###  2.2 SparsePak/WIYN fibre spectroscopy

We analyzed previously un-extracted spectra of the stellar core from the
SparsePak fibre-based (fiber diameter 4.7″), pseudo-integral field unit on the
3.5-m WIYN telescope taken in late 2014. The spectral observations of the
surrounding nebula Pa 30 are presented in Paper I.

###  2.3 Kermerrien Observatory spectroscopy

Low resolution ($R\sim 540$) optical spectroscopy of Pa 30’s central star by
our amateur collaborators with a 20-cm $F/D\sim 5$ telescope at Kermerrien
observatory in Porspoder, France, brought its remarkable spectrum and its
strong O vi 3811/34 emission line to our attention in October 2018. The low
signal-to-noise spectra were not properly flux-calibrated and were scaled and
smoothed to be compared against our OSIRIS/GTC spectrum in Figure 1.

###  2.4 Archival data

####  2.4.1 X-ray observations

Faint X-ray emission was first recorded by the _ROSAT_ All-Sky Survey (Voges
et al., 2000) within 12″ of the central star at a PSPC count rate in the
0.1–2.4 keV band of $17\pm 7$ cnts ks-1. Most counts ($>$70%) have energies
greater than 0.5 keV. A _Swift_ XRT (Evans et al., 2014) 1.94 ks observation
(ID 00358336000, 26th July 2009) serendipitously registered this source.
Analysis of these observations confirms a point source detection at the star’s
position with a _Swift_ XRT count rate in the 0.2–5 keV band of $3.6\pm 1.4$
cnts ks-1, together with possible diffuse emission.

Recently Oskinova et al. (2020) presented deep, sensitive _XMM-Newton_ EPIC
X-ray observations that detect a central point source while confirming diffuse
nebula emission. Their spectral analysis of the diffuse emission describes an
optically-thin, thermal plasma composed of carbon, oxygen, neon, and magnesium
(see their Table 1). These abundances are attributed to carbon-burning ashes,
suggesting Pa 30 is a supernova remnant. The total mass of the X-ray-emitting
nebula, estimated as $\simeq$0.1 $M_{\odot}$, strengthens this conclusion.

The point source _XMM-Newton_ EPIC spectra are described by a hot plasma at
temperatures 1–100 MK. A non-thermal component, that would reduce the plasma
temperature to $\sim$1–20 MK, cannot be excluded. The EPIC spectra are
consistent with the _Swift_ and _ROSAT_ data, but their much higher quality
allow a detailed spectral fit (Oskinova et al., 2020). The un-absorbed X-ray
luminosity in the 0.2–12 keV band implied by Oskinova et al. (2020) is reduced
to $6.6\times 10^{32}$ erg s-1 at our adopted distance of $2.3\pm 0.1$ kpc.

To contribute SED high energy points presented in Section 5.2 we re-processed
the _XMM-Newton_ EPIC MOS1, MOS2, and pn data corresponding to Obs.ID.
0841640101 and 0841640201 using _SAS_ and relevant calibration files. MOS1,
MOS2, and pn background-subtracted spectra of the central star of Pa 30 were
extracted using a circular aperture (radius=20″) with suitable background
regions and calibration matrices computed using the corresponding _SAS_ tasks.
The 0.2–7.0 keV extended emission image reveals a shell with a diameter of
$\approx$4′ with a filled morphology.

####  2.4.2 Infrared imaging

We mined the IRSA/IPAC archive444https://irsa.ipac.caltech.edu/ for available
infrared imaging 3′ around Pa 30. Apart from the WISE data presented
previously (Gvaramadze et al., 2019; Oskinova et al., 2020) and Paper I,
usable mid- and far-infrared images exist from AKARI (Doi et al., 2015) and
IRAS (Neugebauer et al., 1984). Only the central star is visible in the near-
infrared, while the nebula is prominent beyond 10µm. The far-infrared maps
(i.e., AKARI and IRAS) do not have sufficient resolution to resolve the
central star from the nebula, but they resolve Pa 30 which retains its
apparent circular shape. The 12µm WISE image shows a round nebula with a
radius of 83″$\pm$4″, corresponding to a physical radius of $0.93\pm 0.04$ pc,
identical to the size of the [O iii] shell, Paper I. The extended X-ray shell
seen by XMM-Newton is roughly 120″ in radius. No nebular emission has been
detected in submillimeter Planck maps.

The infrared photometry from these datasets assume unresolved sources although
the nebular component can exceed the size of the apertures. We re-evaluate the
photometric measurements taking into account the observed nebular size. In
Section 5.2, we present estimates of the nebula’s surface brightness.

####  2.4.3 Photometry

The central star of Pa 30 is relatively bright, at $G\approx 15.4$ mag. It has
been covered in many sky surveys from which we retrieved all available
temporal optical and photometric data together, in order to investigate
temporal variability (cf. Sect. 4).

####  2.4.4 Spectroscopy

In the following sections, we directly compare our OSIRIS/GTC and
SparsePak/WIYN stellar spectra with Gvaramadze et al. (2019) and Garnavich et
al. (2020). These archival long-slit spectra were very kindly provided by
these authors.

We also used reduced archival ultraviolet spectra from the Space Telescope
Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST) under program
GO15864 (P.I. G. Graefener; epoch: 4 November 2020). The spectral coverage was
from 1150 to 3150 Å, with a slit width of 0.2″. These spectra provided a
comparison against the cmfgen models in Sect. 3.2.

Finally, we complemented our observations with very recent Gaia DR3 BP/RP low
resolution spectra of $R=30-100$ (Montegriffo et al., 2022) that extends
beyond OSIRIS/GTC, i.e., from 3200Å to 1$\mu$m and covers the O vi 3811/34
emission line. The Gaia telescope is outside the atmosphere so telluric lines
are not present. The spectra were obtained from the UK Gaia Data Mining
Platform555https://www.gaia.ac.uk/data/uk-gaia-data-mining-platform and are
encoded as Hermite functions. The spectra show instrumental distortions around
the O vi 3811/34 line. Between 4000 and 4500Å, the feature wavelengths differ
by 30 Å from our ground-based spectra, possibly due to the response of the
Hermite functions to the sharp edge of the O vi 3811/34 line. The wavelength
calibration appears correct for $\lambda>5000$Å.

###  2.5 Extinction

Figure 2: $A_{0}$ (550 nm) extinction values for field stars taken from the
Gaia DR3 catalogue. Black points are for stars within a radius of 5 arcmin of
Pa 30, and red points for stars within 2 arcmin. The blue line shows the
extinction curve for this direction from Vergely et al. (2022), and the black
dashed line marks the parallax of Pa 30.

Paper I adopted $A_{V}=2.4\,\pm\,0.1$ mag but field stars now imply this may
be an underestimate. Figure 2 shows parallax and $A_{0}$ from Gaia DR3 field
stars within a 5 arcmin radius (black points) from the central star of Pa 30.
Red points are stars within 2 arcmin. The curve is the model extinction plot
from Vergely et al. (2022) from the explore platform666https://explore-
platform.eu/sdas at a spatial resolution of 25 pc (30 arcmin at the distance
of Pa 30).

At the parallax of the central star (dashed line), the nominal extinction is
$A_{0}=2.9$ mag, albeit with a large scatter between individual stars. The
extinction is primarily due to clouds at around 400 pc and at 800 pc. The
Vergely et al. (2022) curve ends at a distance of 3 kpc. Gaia DR3 finds some
higher extinctions beyond 2.5 kpc but this is not included in the curve.

The data indicates an extinction $A_{0}=2.8\pm 0.4$ mag. The central value is
the same as listed for our star in Gaia DR3, but that is fortuitous in view of
the complexity of the spectrum. In this paper we will argue that the
extinction for the central star is at the higher end of the range.

##  3 The stellar remnant

###  3.1 The stellar spectrum

The central star of Pa 30 has a unique spectrum (Figure 1) with very broad,
very high excitation emission lines and a striking discontinuity bluewards of
4000 Å. There is a complete absence of hydrogen, helium and nitrogen lines.
The broad lines are mostly identified with very high ionization stages of
oxygen (Figure 3). The sharp and significant emission line that cuts-on around
4000 Å is identified as O vi 3811/34 Å. This feature turns over near the
atmospheric cut-off as confirmed in the recent spectrum of Garnavich et al.
(2020). This doublet is the defining criteria for the WO spectral type in both
Pop I stars (e.g., Crowther et al., 1998; Gvaramadze et al., 2019), as well as
old low-mass central stars of planetary nebulae (designated as [WO]) before
they enter the white dwarf phase (e.g., Smith & Aller, 1969; Sanduleak, 1971).
The broadened emission at 5270/91 Å is identified as O vi. The central star of
Pa 30 seems unique in arising from neither pathway if the double degenerate
merger and accretion fed Type Iax SN are correct (Gvaramadze et al., 2019;
Oskinova et al., 2020).

In addition to these strong, broad features, a number of weaker, individual
lines are seen. Their profiles can be accurately fitted with Gaussians with
FWHM of $0.015c$. The wings extend to velocities as high as 15,000 km s-1
($\approx 0.05c$). Several lines coincide with O viii and are tentatively
identified as such. They are well centered on the systemic velocity.

Figure 3: (a) An example of an oxygen- and neon-rich model by cmfgen
(He/C/O/Ne mass fractions : 0.017/0.129/0.414/0.436) where contributions by
individual C, O and Ne lines are clearly indicated. The O v and O vi lines
broaden certain spectral features in the model spectrum. Luminosity and
temperature was 36,000 L⊙ and 237,000 K, respectively. The strongest optical
lines are: O VI $\lambda\lambda 3811-3833$ (3p 2Po \- 3s 2S), Ne VII
$\lambda\lambda 3859-3910$ (3s 3d 3 D - 2s 3p 3P${}^{\scriptstyle o})$, Ne
VIII $\sim\lambda 4341$ (9 - 8), O VI $\sim\lambda 5291$ (7 - 6), O V
$\lambda\lambda 5572-5604$ (3s 3d 3D - 2s 3p 3P${}^{\scriptstyle o})$, and O
VI $\sim\lambda 7737$ (8 - 7). (b) The cmfgen model (red) extended to the
ultraviolet and compared to archival STIS/HST spectra (blue), the OSIRIS/GTC
spectrum (purple), and the Garnavich et al. (2020) spectrum (scaled, pink).

###  3.2 The stellar wind cmfgen models

The broad, prominent spectral features are indicative of a strong stellar
wind. We modeled it using the non-LTE line-blanketed radiative transfer code
cmfgen777http://kookaburra.phyast.pitt.edu/hillier/web/CMFGEN.htm adapted to
WC and WO stars (Hillier & Miller, 1998; Hillier, 2012; Hillier & Dessart,
2012). Input parameters were our OSIRIS/GTC spectrum that includes the O vi
doublet at 3811/44 Å with the interstellar extinction derived in Paper I, and
a wind velocity of 15,000 km s-1. A classic velocity law is used,

$v(r)=v_{\infty}\left(1-{r\over R_{*}}\right),$ (1)

where $v_{\infty}$ is the wind terminal velocity measured from the spectra and
$R_{*}$ is the stellar radius. There is a consensus that stellar winds are
clumped. This is taken into account in cmfgen modeling via a volume filling
factor, adopted here as $f=0.1$. For the spectral modeling the ratio
$\dot{M}/\sqrt{f}$, where $\dot{M}$ is the mass-loss rate, can be considered
an invariant.

We explored a range of stellar luminosity and temperature, mass-loss rate,
stellar radius, velocity law and chemical abundances, summarized in Table 1.
Given the limited spectral coverage of our OSIRIS/GTC spectrum (and indeed of
all available optical spectra- except that from Gaia, see above), we could not
find a unique model that completely reproduces the observations (unlike
Gvaramadze et al., 2019, although they also stated large uncertainties, e.g.,
Table 1). Nevertheless, many models could reproduce most spectral features.
The results shown are best approximations and/or upper limits to the
individual parameters. Most models tested could reproduce the visual and near-
infrared photometry. Determining errors on the fits is tricky and we refrain
from giving error bars as the errors are not easily transformed into a
standard deviation and strong coupling exists between some parameters.
Potentially four species can have mass fractions $>$0.1, so changing the mass
fraction of one species necessitates a corresponding change of at least one
other species. Therefore, below, we provide viable ranges for the stellar
parameters and indicate the properties used to constrain them.

The three primary modeling constraints come from matching the mean flux level,
the strength of the O vi 3811/34 Å doublet, and the O v 5572–5604 Å line
strength. Only models with luminosities between 25,000 and 60,000 L⊙ provide
reasonable fits. Below the low luminosity limit either the O vi doublet is too
weak and/or O v too strong, while at the upper limit either O vi is too strong
and/or O v is too weak. At very high luminosities the O vi doublet strength is
suppressed (but other O vi lines remain strong) since the upper levels
preferentially decay directly to the ground state. We hence set an upper limit
at $\leq$260,000 K888This is the classical effective temperature defined at a
Rosseland optical depth of 2/3. Due to the dense wind this is somewhat lower
(around 10%) than would be defined using the radius of the star at the sonic
point..

The peak near 5300 Å is due to O vi offset to the red from observations,
perhaps due to the overlapping O v line being too strong in the model (Figure
3). The model matches bumps seen at $\sim$4500 Å and $\sim$4659 Å, but fails
to predict the feature near 4250 Å which is assigned to O viii. An alternative
suggestion for this emission is Ne viii, which has approximately the same
wavelength as the O viii line. In a model with a slightly lower mass loss, the
Ne viii is clearly visible in predicted spectra though the overall fit to the
spectrum is worse. As apparent from Figure 3, the broad emission lines blend
together making it impossible to see the true continuum.

We provide some upper limits for mass fractions of key elements (He, C, O and
Ne) assuming Solar abundance ratios for other elements, that is Na, Mg, Al,
Si, S, Ar, Cl, Ca, Fe, and Ni999f For the following transitions: Na iv \- Na
x, Mg iv \- Mg xi, Al iv \- Al xii, Si iv \- Si xi, S v \- S xi, Ar vi \- Ar
x, Cl vi \- Cl viii, Ca vi \- Ca xii, Fe vi \- Fe xvii, and Ni vi \- Ni xvii.
In these hot models helium has little influence on the spectra. From the
apparent absence of the He ii 4686 Å line we place an upper limit of 0.4 on
$X_{\rm He}$. The O vi features at 3811/34 Å and 5270/91 Å are clear
indicators that the stellar atmosphere is oxygen-rich. Therefore we used an
oxygen-rich model atmosphere with an oxygen mass fraction $<0.647$. This
reproduces the O vi doublets, as well as O v lines. All the strongest features
can be reproduced but not some weaker individual ones. The lines at 4500 and
4658 Å are sitting on a broader O vi feature whose strength depends on
continuum choice, uncertain due to the density.

Carbon-free and carbon-enhanced models were tested. The C iv line can
contribute to the 4568Å line but otherwise there is no easily distinguishable
carbon line contribution. We set an upper limit for $X_{\rm C}\leq 0.261$. We
explored a range of neon abundances (Table 1) and find an enhanced neon
abundance could contribute to the spectral features at the 3600–4000 Å plateau
(Ne vii), at 4341Å and at 6070Å (Ne viii). Inclusion of neon does not affect
our ability to get a good fit to the oxygen lines. On the other hand, the 4341
Å line can also be identified with O viii (see below).

The fit shown in Figure 3 provides a ‘maximum’ model where as many features as
possible are reproduced. Oxygen is well fitted, but carbon may be less certain
and neon is likely significantly over predicted. The plotted model has $X_{\rm
Ne}=0.436$ and may be considered as the upper limit. A more carbon-rich
composition cannot reproduce the spectrum. The ranges of chemical abundance of
carbon, oxygen and neon in Table 1 agree with those derived by Oskinova et al.
(2020) from the central star’s X-ray spectrum.

Table 1: Range of stellar parameters for cmfgen models. The last two columns show the values from Gvaramadze et al. (2019) and from the hot gas model in the Sect. 3.3.  Parameter | Explored range | Best fit range | Illustrated model | Gvaramadze et al. (2019) | Hot gas model
---|---|---|---|---|---
$L_{*}$ ($\rm L_{\odot}$) | 10,000 – 200,000 | 30,000 – 60,000 | 36,000 | $39,810^{+20,144}_{-10,970}$ |
$T_{*}$ (K) | 145,000 – 580,000 | 200,000 – 280,000 | 237,000 | 211,000${}^{+40,000}_{-23,000}$ |
$\dot{M}$ ($\rm M_{\odot}$/yr) | 7.5$\times$ 10-7 – 2.5$\times$ 10-6 |  $\leq$ 4$\times$ 10-6 | 2.6 $\times$ 10-6 | $3.5(\pm 0.6)\times 10^{-6}$ |
$R_{*}$ ($\rm R_{\odot}$) | 0.04 – 0.22 | $\leq 0.2$ | 0.155 | 0.15$\pm$0.04 |
v∞ (kms) | – |  $\sim$15,000 | 15,000 | 16,000$\pm$1,000 |
Mass fractions |  |  |  |  |
$X_{\rm H}$ | – | – | – | – | –
$X_{\rm He}$ | 0.017 – 0.135 | $<0.4$ | 0.017 | $<0.1$ | $\leq 0.44$
$X_{\rm C}$ | 0.0 – 0.261 | $\leq 0.26$ | 0.13 | $0.2\pm 0.1$ | 0.13
$X_{\rm O}$ | 0.414 – 0.697 | $\leq 0.7$ | 0.41 | $0.8\pm 0.1$ | 0.39
$X_{\rm Ne}$ | 0.011 – 0.501 | $\leq 0.5$ | 0.44 | 0.01 | 0.04

The broad wind profile ($\approx$15,000 km s-1) provides a slightly better fit
to the broad spectral profiles for both the O vi doublets and O v feature at
5900 Å (Figure 3). This value is close to the measured value of Gvaramadze et
al. (2019, 16,000 km s-1). Since O v is present, this emerges from the outer
regions, and so a higher terminal velocity is needed to fit both oxygen
features simultaneously. As found by Gvaramadze et al. (2019) radiation
pressure appears insufficient to drive the wind. Though the OSIRIS/GTC spectra
do not extend below 3600 Å, the cmfgen models predict an O vi line at 3435 Å
similar to Gvaramadze et al. (2019) and has been observed in the spectra of
Garnavich et al. (2020).

After finalizing the model, we compared it to HST ultraviolet (UV) spectra of
the stellar remnant (Sect. 2.4.4). To fit the UV data we needed to adjust the
reddening to E(B-V)$=1.05$. Although we eventually updated our reddening, our
initial models started off assuming the reddening from Paper I. With the new
reddening the fluxes no longer matched, so we recomputed the model with scaled
parameters that would yield the same spectral shape, and this model is shown
in Figure 3.101010To a good approximation an accurate distance is not needed
for the spectral fitting. For stars with dense stellar winds, models with the
same abundances, effective temperature, and value of $\dot{M}/R_{*}^{3/2}$
produce similar spectra – only differing in flux (Schmutz et al., 1989). The
parameters for one distance can be scaled to a new distance using the
following scaling relations: $L\propto d^{2}$, $R_{*}\propto d$ and
$\dot{M}\propto d^{3/2}$. Given the O vi 3811/34 emission line’s strength, the
estimated reddening should be more accurate than that obtained using optical
fluxes over a limited wavelength range.

No further model modifications were made and there is excellent agreement
between the STIS/HST fluxes and the OSIRIS/GTC spectrum. Figure 3 shows the
cmfgen model correctly predicts the O v and Ne viii blend at $\sim$2800 Å and
the strong O v emission at $\sim$1370 Å. The model also predicts strong O vi
resonance emission (1032, 1038 Å). Absorption shortward of 1500 Å is from the
C vi resonance transition (1548, 1551 Å) being too strong, possibly indicating
a lower carbon abundance than in the model. The strong 2200 Å band and its
Galactic variation make it difficult to judge agreement between model and
observation for features in the band.

We computed additional models to better constrain the parameters and
potentially improve the fit, but this did not lead to a change in the adopted
parameters. One possible exception is the neon abundance – a model with the
abundance reduced by a factor of 2 might give a better fit to the UV spectrum.
However, a better understanding of the interstellar 2200 Å band is required to
draw firm conclusions.

In a recent study of two WO stars in the Large Magellanic Cloud by Aadland et
al. (2022) it was found that X(C)/X(O) was greater than 5 despite the presence
of strong O vi features at 3811/34Å. However this star is descended from a
massive O star and has a very different evolutionary history than the central
star of Pa30. Further on, the spectra are quite distinct - in the WO stars,
for example, the C iv spectrum is still very prevalent and neon lines are
relatively weak and can be matched by a neon abundance similar to that
expected from the processing of CNO into 14N in the CNO cycle, and the
subsequent processing into 22Ne. The high temperatures used in our models will
weaken the C iv lines, but this alone cannot explain the weakness of the
carbon spectrum and the strength of the oxygen spectrum.

###  3.3 Shocked gas: cloudy models

The X-ray spectrum indicates an additional high temperature gas component
(Oskinova et al., 2020) that is strong compared to what is typical for OB
stars. The unabsorbed X-ray to bolometric luminosity ratio, $\log(L_{\rm
X}/L_{\rm bol})$, is in the range of $-4.8$ to $-6.1$, one to two orders of
magnitude larger than OB stars, i.e., $\log(L_{\rm X}/L_{\rm
bol})=-6.912\,\pm\,0.153$ (Sana et al., 2006). Oskinova et al. (2020)
attribute the bulk of the remnant’s thermal X-ray emission to the wind’s outer
regions.

The wind model describes well the shape and many features of the optical
spectrum. However, some weaker lines are not fitted and the 4340 Å feature
requires Ne viii at a high neon abundance. This line coincides with a high-
excitation O viii line. We therefore explore a spectral contribution from the
high-temperature gas component which is not included in the wind model.

As a hydrogenic ion, O viii has a restricted number of lines. The 4340 Å line
coincides with the O viii 8–9 transition and the 6069 Å line with the O viii
9–10 transition. These transitions have a wavelength ratio of 5/7 and the two
line profiles overplot accurately when wavelengths are scaled by this ratio.
The observed intensity ratio of the two lines (after subtraction of an
estimated continuum) is reproduced by these O viii lines for an extinction in
agreement with the foreground extinction. This strengthens identification as O
viii, although other lines may contribute to these features. The temperature
required for O viii is $>$1 MK, far above the photospheric or wind
temperature.

We ran exploratory photo-ionisation models using the cloudy code (ver. 17.03
Ferland et al., 2017). In the ‘coronal mode’ gas temperature is pre-defined
and all lines are assumed collisionally excited. There is no input radiation
field. A single shell model was used, with a constant density and temperature
and without considering optical depth effects. Models were run for a range of
temperatures and abundances. The hydrogen density was set to $\log n=7.5$. All
lines were assumed to have a Gaussian profile with sigma of
$v/c=\Delta\lambda/\lambda=0.0092$ as found from line fitting. The cloudy line
output list was convolved with this Gaussian profile to obtain model spectra.
The model spectra were multiplied by the extinction curve of Cardelli et al.
(1988) and scaled to the peak intensity of the 4340 Å line. The ratio of the
integrated line strength of the 4337 Å and 6064 Å lines was used to derive the
extinction $A_{V}$, where all contributions to these features were taken into
account.

The broad wind features at 3800 Å and 5200 Å are not reproduced in this model:
the temperatures are too high for significant O vi emission. However, the
weaker lines absent from the wind model could be reproduced with this hot gas.

The model fit is shown in Figure 4 along with the observed spectra for a gas
temperature of $T=4$ MK. The best fit gave abundances (number ratios) of
He/C/N/O/Ne = 0.73/0.07/0.02/0.16/0.01, where helium must be considered as an
upper limit. These abundances are within the wind model range. The brightest
predicted lines between 3000 Å and 7000 Å are listed in Table 2.

An estimated constant-value continuum was subtracted from the observed
spectrum across the full wavelength range with no attempt to correct for any
continuum slope. The line strengths depend on the continuum choice. This
introduces an uncertainty, as the dominant broad wind features obliterate most
of the continuum. The subtraction of a constant level from the WIYN spectrum
brought both the blue and red ends to zero. For the GTC spectrum, a constant
subtraction left an offset between the ends. We used the WIYN spectrum for the
fit. The procedure indicated an extinction of $A_{V}=2.9\pm 0.2$ mag from the
WIYN data, in excellent agreement with that found in Sect. 2.5 and with the UV
extinction indicated by the wind model. We adopted $A_{V}=3.0$ mag for the
final model. The model is shown with the continuum-subtracted WIYN spectrum in
Figure 4.

Table 2: Predicted, brightest ultra-high excitation (UHE) lines from the cloudy models. The line intensity, $I_{0}$, is relative to the 4337 Å O viii 8-9 transition, and are not corrected for extinction.  $\lambda$ (Å) | Ion | $I_{0}$
---|---|---
4337 | O viii 8-9 | 1.00
4498 | O viii 11-14 | 0.12
4655 | O viii 10-12 | 0.24
4681 | O viii 12-16 | 0.06
4686 | He ii 3-4 | 0.07
4795 | Ne ix | 0.29
4940 | Ne x 12-14 | 0.05
5243 | Ne x 10-11 | 0.16
5288 | C vi 7-8 | 0.05
5670 | O vii | 0.16
5690 | O viii 12-15 | 0.08
6060 | O viii 11-13 | 0.15
6064 | O viii 9-10 | 0.54
6481 | Ne ix | 0.13
6894 | Ne x 10-11 | 0.09
7080 | O viii 13-16 | 0.05
7728 | O viii 12-18 | 0.09
8203 | O viii 10-11 | 0.30
8521 | Ne ix | 0.04
8672 | O viii 14-17 | 0.03
8857 | Ne x | 0.04
9668 | O viii 13-15 | 0.06
Figure 4: A cloudy model for the hot gas emission at a gas temperature of 4 MK
(red line) and $A_{V}=3.0$ mag compared to the central star’s SparsePak/WIYN
spectrum (black) . The spectrum has an estimated constant continuum level
subtracted of 1.45 on the scale of the plot. For further description see Sect.
3.3.

The cloudy model fits the 4337, 4655, and 6064 Å with the O viii 8-9, 10-12,
and 9-10 transitions, respectively, though the observed 4655 Å line is
stronger than predicted. Another O viii line at 5790 Å coincides with a peak
inside the broad wind band. This identification is not as secure because of
the unknown optical depth in this wind band. The 4800 Å feature is reproduced
with Ne ix. The He ii line at 4686 Å contributes to the observed line at this
wavelength together with the O viii line. A good fit requires a helium
abundance ratio of He/O = 4 (by number). However, there is also a C vi and an
Ne x line at this wavelength which could contribute. Hence, this helium
abundance is considered as an upper limit. The 4940 Å feature is not
reproduced. A weaker model line predicted at 5290 Å is due to C vi but it is
likely obscured by the broad wind feature.

Our cloudy hot-gas model is able to reproduce most lines not present in the
wind model, using abundances equivalent to that of the wind model, for a gas
temperature of $T=3.5$–$4$ MK. Importantly, all lines which are predicted to
be detectable are seen in the spectrum, with a sole exception the Ne x line at
6900 Å, which is affected by a telluric feature.

The carbon abundance is poorly constrained because of a lack of bright lines
though several fainter carbon lines do coincide with features in the spectra.
Figure 5 shows a model with the carbon abundance (by number) increased to C/O
= 4.5, and with a lower helium abundance. This produces a good fit to many of
the lines but adds a strong component to the 5290 Å line which is already well
fitted in the wind model without this component. There is no other evidence
for such a high carbon abundance and the wind model needs oxygen-rich gas. We
therefore do not adopt these abundances.

Figure 5: As in Figure 4, but with a much higher carbon abundance and a lower
helium abundance.

Figure 6 shows the same fit, but now the observed spectra are shown with the
wind model subtracted. Only wavelength regions free of the broad wind features
are shown. The wind model accounts for almost all of the continuum present at
these wavelengths. A small excess was subtracted shortward of 5000 Å. This
shows that the combination of the wind and hot gas models can explain much of
the observed spectra.

Figure 6: Hot-gas cloudy model (red) against the residual SparsePak/WIYN
(black) and OSIRIS/GTC (blue) spectra after subtraction of the wind model. A
residual continuum of 0.1 for the WIYN spectrum and 0.2 for the GTC spectrum
was subtracted shortward of 5000 Å. Vertical bars indicate wavelengths of
diffuse interstellar bands which are visible in the spectra. The cloudy model
was scaled to the 4363 Å line with an extinction $A_{V}=3.0$.

The abundances in the cloudy model were adopted from the wind model. The
nitrogen abundance is not constrained in this model because of a lack of
bright lines. There are potential C vi lines at 6195 Å and at 4683 Å, which
can fit lines at these locations, however these lines need a C/O ratio well
above unity to fit the corresponding features, while the wind model does not
support C/O $>1$. In addition, the 5290 Å C vi line becomes too strong at
higher carbon abundance. The temperature is mainly constrained by O viii lines
which affect the 6064 Å line at temperatures below 3 MK, and the Ne x line at
6894 Å which becomes too strong for $T>4$ MK. Because of the model’s
simplicity these constraints should be viewed with caution, along with the
assumption of uniform temperature and density, and the fact that other wind
lines may be present.

The line widths and temperature indicate that the hot gas is closely related
to the stellar wind. The line widths are similar or slightly smaller to that
of the wind. The assumption of a gaussian profile is not identical to the wind
profile of Eq (1). The symmetric line profiles favor a physical location
embedded in the outer wind. The gas can be heated by shocks as regions with
different speeds collide. This is a common situation in OB stellar winds. A
smaller line width for the hot gas could argue for a location further inside
the wind but this remains to be investigated.

For Wolf-Rayet winds (hydrogen poor), the shocks can be considered
approximately isothermal (Hillier et al., 1993). We use the relation (Hillier
et al., 1993):

$T_{x}\approx 5.8\times 10^{6}\,{\mu\over 1+\gamma}\left({v_{\rm s}\over
500\,{\rm km\,s^{-1}}}\right)^{2},$ (2)

where $v_{\rm s}$ is the differential velocity between wind and shock front,
$\mu$ is the mean ionic weight, and $\gamma$ the ratio of electrons to ions.
Putting in O viii as the dominant ion, the second term is approximately unity.
For $T_{x}\sim 5\,$MK, $v_{\rm s}\sim 500\,\rm km\,s^{-1}$. This is much less
than the wind velocity but plausible as internal differential velocities.

Figure 7: The Gaia BP/RP spectrum (black). Upper panel: the wind model (red).
Lower panel: wind model (dashed, red), the hot-gas model (red), hot gas model
with three times higher neon abundance (dashed, blue). In the lower panel, for
clarity a level of 1.0 has been subtracted from the Gaia spectrum and wind
model

###  3.4 Neon

Figure 7 shows the Gaia BP/RP spectrum. It covers a much larger wavelength
range to the red. The sensitivity is less than that of our other spectra, and
there are calibration issues as mentioned before. The top panel shows the wind
model overplotted with the Gaia spectra. It shows that the wind feature at
7500–8000Å is well reproduced. We use this ‘above atmosphere’ spectrum to
discuss the neon abundance.

Table 2 lists a number of expected neon lines. The chosen neon abundance was
based on lines in our optical spectra. The predicted Ne x line at 6894 Å is
too strong but this coincides with a strong telluric feature that was removed
from the ground-based spectra.

The bottom panel shows the Gaia spectrum with the wind model (red, dashed;
shifted down for clarity). The lower red line shows the hot-gas model. The
blue-dashed line shows the same model but with three times higher neon
abundance. The neon lines now disagree with the observed spectrum. From this
we deduce an upper limit of Ne/O $<0.15$ by number.

The wind spectrum is seen to overpredict the line at 8200 Å. In the wind model
this is a Ne vii complex, while the hot-gas model has an O viii line at this
location. The model that is shown has a high neon abundance. Again this points
at a lower neon abundance for the remnant.

###  3.5 Magnetic fields

The presence of strong magnetic fields has been proposed by Gvaramadze et al.
(2019). This is based on predictions of WD merger models which yield $B\sim
200$ MG (Ji et al., 2013), and on the expectation that the stellar wind is
magnetically driven from a very rapidly rotating star. For the SN 1181 stellar
remnant, Kashiyama et al. (2019) carried out magneto-hydrodynamic simulations
that argue for a WD remnant with a strong magnetic field (20 – 50 MG) but
still an order of magnitude lower than Gvaramadze et al. (2019).

Magnetic fields have been proposed for hot ($T>60$ kK), hydrogen-poor (DO)
white dwarfs with O viii lines and other ultra-high excitation lines (UHE) in
absorption. Reindl et al. (2019) attributes these coronal lines to gas trapped
in an equatorial, magnetically-confined, shock-heated magnetosphere. The
confinement requires

$\eta={B^{2}R_{\ast}^{2}\over\dot{M}v_{w}}>1,$ (3)

where $B$ is the magnetic field strength, $R_{*}$ the stellar radius, $v_{w}$
the wind speed, and $\dot{M}$ the mass-loss rate. For this star, the mass-loss
rate from the cmfgen models require $B>0.1$ MG for $\eta>1$, a modest magnetic
field for such stars.

The hydrogenic O viii lines can provide strong constraints on magnetic field
strength due to Zeeman splitting of the line into $\pi$ and $\sigma$
components. For moderate fields, the central $\pi$ component remains unchanged
in wavelength, whilst the two $\sigma$ components shift to either side. The
relative strength of the $\pi$ component depends on the magnetic field’s
orientation angle: it is absent when the magnetic field points at the observer
and it is equal in intensity to the sum of the $\sigma$ lines if the magnetic
field is perpendicular to the line of sight. Each of the three Zeeman
components can be considered as a Gaussian of width derived from the
temperature. The observed line is the sum of these three Gaussians. For small
shifts much less than the width of each line, this sum is itself a Gaussian
widened by the shift. For larger shifts the line profile deviates.

The shift $\Delta\lambda$ between the two $\sigma$ lines can be parametrized
as $\Delta\lambda=\alpha B$, where $\alpha$ is a constant for each ion and
transition. The value for $\alpha$ is tabulated by Blom & Jupén (2002, their
Table 1). For transitions considered here, that is O viii 8-9, O viii 9-10,
and C vi 7-8, and for field strengths in Gauss, the $\alpha$ parameter is
$1.8\times 10^{-5}$, $3.4\times 10^{-5}$, and $2.6\times 10^{-5}$,
respectively. The 6064 Å O viii line has a FWHM of 93 Å. Assuming a separation
between the $\sigma$ lines equal to the FWHM would have strongly distorted the
shape, we constrain $B<2.7$ MG. The 4340 Å line with FWHM of 69 Å gives a
conservative upper limit of 3.8 MG.

We ran models adding the Zeeman components assuming all three Zeeman lines
have equal intensity. This ratio corresponds to a magnetic field orientation
to the line of sight of 55 degrees. We then fit the profile of the 6064 Å
line, where the intrinsic width is a fitting parameter. For $B=1.2$ MG an
acceptable fit to the line shape is found. For $B=1.5$ MG the line profile
deviation was clearly visible at 6064 Å, and developed a flat peak. Running
the same test on the 4337 Å line shows it is indeed a bit less sensitive. We
also ran the test with the central $\pi$ line twice as strong as each
accompanying $\sigma$ line corresponding to a magnetic field oriented along
the line of sight. Here the line remains centrally peaked which makes it
easier to fit the profile. A notable deviation from the observed profile of
the 6064 Å line was found for a field of 2.5 MG. At this field strength, half
the line width is due to Zeeman splitting.

The O viii line shapes give an upper magnetic field limit of $B<2.5$ MG,
easily within the requirement of the magnetically-confined toroidal structure
proposed by Reindl et al. (2019). Based on the available data we can not rule
out the alternative of such a structure.

This new field strength limit is far below that proposed by Gvaramadze et al.
(2019, 200 MG) and of typical low-mass, magnetic WDs (10 MG). There is some
caution here. If the hot gas is located in the wind, then the surface magnetic
field may be underestimated because the field strength of a magnetic dipole
will go down as $1/r^{2}$ with distance $r$. Also, the star has a very high
luminosity and temperature, and so a larger radius than a typical WD. If it
evolves as a WD it will contract significantly, and the field would
strengthen. Hence, our limits are not inconsistent with known field strengths
of magnetic WDs, which are of order 10 MG but they do not support values as
high as 200 MG previously proposed.

Figure 8: IPHAS $r$-band image of Pa 30 identifying the faint and bright stars
mentioned in Sect. 4. The green circle (radius 22″) is centered on the stellar
remnant and it indicates the distance to the brightest star in the field. Gaia
DR3 sources within a 25″ radius from the remnant are marked as blue circles.

##  4 Stellar variability

###  4.1 Photometry

The stellar remnant (Gaia DR3 526287189172936320) has been observed by various
terrestrial and space-based all-sky photometric surveys over many decades.
Some offer short cadences to detect transient events (e.g., TESS 2-min and
30-min cadence), while others cover decades of sparse photometric sampling
with long exposures (e.g, DASCH). Many have variable depth and sensitivity and
large effective detector pixel sizes and large photometric apertures. This can
result in blending and nearby source contamination.

A faint, foreground star (Gaia DR3 526287189166341504) is 2.3″ eastwards of
the stellar remnant (Figure 8). Though this star is clearly distinguished in
short-exposure IPHAS (Drew et al., 2005) images, it is $\sim 4.5$ mag fainter
in Gaia filters and well below limits of earlier photographic imagery so
should not affect recorded optical photometry. A very bright star (Gaia DR3
526287257892412928) is $\sim$21″ directly west. Because recent all-sky surveys
use large photometric apertures (e.g., the ASAS-SN PSF is $\sim$15″, or
single-pixel aperture $\sim$17″ in OMC), the bright star ($G\sim 11$ mag) can
affect adjacent pixels and influence photometric results. However, it is well
separated from the stellar remnant in scanned data from all older photographic
plates recorded in DASCH and so it is unlikely any variability for the stellar
remnant is affected by the brighter star in 20th century observations.

Here, we show $B$ band results from various surveys as this filter has the
best temporal coverage. The data include photographic photometry from DASCH,
the Ukrainian FON astrographic catalogue (Andruk et al., 2016) and the Palomar
Observatory Sky Surveys (POSS-I and POSS-II); CCD data from the AAVSO
Photometric All-Sky Survey (APASS DR10, Henden et al., 2018), the INT Galactic
Plane Survey (IGAPS/UVEX; $g,r$; Monguió et al., 2020), the Panoramic Survey
Telescope and Rapid Response System (Pan-STARRS1, $g,r,i$; Tonry et al.,
2012), the Asteroid Terrestrial-impact Last Alert System survey (ATLAS, $o,c$;
Tonry et al., 2018), the Transiting Exoplanet Survey Satellite (TESS; Ricker
et al., 2015), and the Near-Earth Object Wide-field Infrared Survey Explorer
Reactivation Mission (NEOWISE, $3.6,4.5\rm\mu m$; Mainzer et al., 2014). The
single epoch IGAPS/UVEX $g,r$ photometry from Pan-STARRS1, and the Pan-STARRS1
$g,r,i$ photometry, were converted to $B$ using the transformations of Tonry
et al. (2012). The optical light curves are shown in Figure 9 and the infrared
light curve is shown in Figure 10.

Figure 9: Extended light curve of the stellar remnant from 1920 until today.
Top: DASCH $B_{j}$ GSC calibrated photometry from 1920 to 1950 with the best-
fit linear trend line plotted. Middle: limited photographic (pre-2000) and CCD
(post-2010) optical photometry in the $B$-band. Respective surveys are
indicated in the legend. Bottom: ATLAS binned photometry in the “cyan” (c)
lower band (4200-6500Å) and the “orange” (o) upper band (5600-8200Å). Figure
10: WISE $W1$ (blue; 3.4µm) and $W2$ (red; 4.6µm) light curves binned per
epoch. The errors are the standard deviations of the binned measurements. The
abscissa is given in years and Mean Julian Date.

The stellar remnant is faint and the optical light curve sparsely populated
over much of its recorded history (Figure 9) but evidence of dimming is seen.
The photographic $B_{j}$ magnitude estimates, calibrated via the GSC 2.3.2
(Lasker et al., 2008) provided by DASCH for measurements between 1924.8 and
1950.7, show a mean $B_{j}$ magnitude of $15.6\pm 0.2$ mag, and maximum
magnitude variation of 0.85 from 37 data points with a dimming slope of 0.02
magnitudes/year and an $R^{2}=0.38$ (which indicates a weak though positive
correlation). Exposures where the recorded plate limit was within 0.3 mags of
the star’s value are omitted as unreliable. Seven nearby stars, both fainter
and brighter (including the bright star to the west), have much lower $R^{2}$
values (average of 0.047 with rms of 0.064) and are flat (average slope of
0.0007 mag/yr with rms also of 0.007). See the top panel in Figure 9. Overall,
the temporal coverage is rather sparse apart from the ATLAS data111111Which
has a pixel size of $\sim 2$″ in two bands: the “cyan” (c) band (4200-6500Å)
and the “orange” (o) band (5600-8200Å).. For the ATLAS dataset (before
binning), no significant peaks were found in Lomb-Scargle periodograms so the
source appears stable on short timescales in optical bands.

We extracted archival photometry from the Wide-field Infrared Survey Explorer
(WISE) 3-band Cryo data release (Wright et al., 2010), and the NEOWISE latest
data release. Figure 10 shows the averaged photometry per epoch in bands $W1$
(3.4µm) and $W2$ (4.6µm). Each epoch covers about six months. Frame inspection
showed there may be bright star contamination within the standard photometric
aperture of NEOWISE (radius 8.25″). There is no nebula contamination as this
is not visible at those wavelengths. The $W1$ and $W2$ light curves show a
modest decline of $\sim$0.01 mag/year over 11 years, half the rate seen at
earlier epochs in the optical $B$-band.

The wind model indicates some weak but no strong emission features in the WISE
$W1$ and $W2$ filters: the emission is dominated by continuum. Since the Pa 30
nebula is not visible at these wavelengths, we can exclude nebular lines such
as [Fe ii] and [Ar vi] or the 3.3µm PAH band. Therefore the potential decline
would be likely due to the continuum.

Figure 11: Spectral differences between four epochs: our SparsePak/WIYN (2014)
and OSIRIS/GTC (2016) against the Gvaramadze et al. (2019, epoch: 2017) and
Garnavich et al. (2020, epoch: 2020). In panel (a) all spectra are scaled to
the SparsePak/WIYN (blue) levels to accommodate for slit losses. In all
remaining panels spectra have been scaled to a mean value of 1.0 to achieve
the best overlap and make differences in the shape of individual lines more
obvious. See main text (Sect. 4.2) for more details.

Kashiyama et al. (2019) propose that the central star (WD J005311 in their
paper) is a highly-magnetic WD spinning at an angular frequency of 0.2 to 0.5
s-1. This would suggest very short light-curve variability at a period of 12.6
to 31.4 seconds. The current data does not trace this time scale.

###  4.2 Wind variability

In Section 3.1 we hinted at variability in the stellar wind. The
SparsePak/WIYN data from 2014, our 2016 OSIRIS/GTC spectra, the 2017 spectrum
by Gvaramadze et al. (2019), and the averaged spectra in 2020 by Garnavich et
al. (2020) are examined for long-term spectral variability (Figure 11). The
SparsePak/WIYN fibre is 4.7″ and should include all stellar flux assuming the
fibre is well placed. Comparison of the synthetic photometry from this
spectrum (using the Python package
pyphot121212https://github.com/mfouesneau/pyphot) to the photometric
measurements provided by the individual surveys justifies this assumption.
Hence, all slit spectra are scaled to match the SparsePak/WIYN spectrum. To
improve the signal-to-noise ratio the SparsePak/WIYN and Garnavich et al.
(2020) spectra have been smoothed with a mean filter of length of 7 and 9
pixels respectively.

The most striking differences are intensity changes in the O vi 3811/34
emission line, as seen in panels (a) and (b) of Figure 11. The discontinuity
in the Gvaramadze et al. (2019) spectrum at 3850 Å and the different spectral
shape further to the blue are to be taken with caution, since flux calibration
is less reliable in the far blue. Garnavich et al. (2020) found that the O vi
3811/34 line shows short-term $<2$hour variability, which was attributed to
clumpiness in the stellar wind. Calibration differences among the different
instruments do not allow a direct comparison of wind variability within the O
vi 3811/34 line, but the OSIRIS/GTC spectra overall shape appears consistent
with the averaged spectra of Garnavich et al. (2020). A decrease in the peak
emission of the O vi 5300 Å line between 2014 and 2017 (panel (e) in Figure
11) is also seen, perhaps associated with a change in the stellar wind. Small
changes in continuum slope beyond 5500 Å can be due to instrumental and
calibration effects between epochs, as the photometry appears to have remained
constant throughout (cf. Sect. 4). Future photometric monitoring observations
should be obtained at cadences of 10 seconds or less in the visual and at
angular resolutions sufficient to allow separation of the target from the
adjacent bright star (e.g., $\leq 5$″).

Figure 12: Infrared spectral energy distribution of Pa 30 including the new
photometry in Sect. 5.2 (60 K blackbody; blue) and the OSIRIS/GTC spectrum
(red). There is no IR excess below 10µm. The photometry below 3µm and spectrum
have been dereddened using extinction from Paper I.

##  5 The outer nebula

###  5.1 Hydrogen emission

Although no hydrogen lines were detected in the nebular spectrum from large
aperture telescopes (Paper I), the outer Pa 30 nebula is tentatively detected
in deep, $\approx$1 Rayleigh sensitivity131313Compared to the $\simeq$3
Rayleighs for IPHAS where only the central star is visible. H$\alpha$ imaging
from the low angular resolution (pixel size 1.6′) Virginia Tech “H$\alpha$”
Spectral-line Survey (VTSS; Dennison et al., 1998) that revealed a single
enhanced pixel at Pa 30’s position. The 5-$\sigma$ excursion within a
15′$\times$15′ region indicates a low-surface brightness hydrogen (H$\alpha$)
shell of similar size to the [O iii] shell found in Paper I. The VTSS survey
limit corresponds to $5.661\times 10^{-18}$ erg s-1 cm-2 arcsec-2 at
H$\alpha$. The continuum-corrected surface brightness within a 1 pc radius of
Pa 30 is $\approx 5.6$ Rayleigh $\approx 8.8\times 10^{-13}$ erg s-1 cm-2.
Adopting the extinction law of Howarth (1983) for H$\alpha$,
$c_{H\alpha}=0.99\,E(B-V)$, then the dereddened H$\alpha$ brightness becomes
$7.4\times 10^{-12}$ erg s-1 cm-2 for $A_{V}=2.9$, which translates to $L_{\rm
H\alpha}\leq 1.2\,\rm L_{\odot}$. Deeper narrow-band H$\alpha$ imagery is
needed to confirm this tentative detection.

###  5.2 Infrared emission

Pa 30 is visible at mid- and far-infrared wavelengths though not detected in
the IRAS 12µm maps. In the far-infrared, the shell is round as indicated by
AKARI 65 to 140µm maps, extending from 88″ up to 128″($\pm 5$″) from the
central star, or else a radius of about 0.98 – 1.42 pc at the adopted
distance. Foreground interstellar emission confuses the images beyond 100µm.
We attribute the far-infrared wavelengths to dust emission and the mid-
infrared emission to line emission.

Given the infrared shell sizes and the uncertainties in archival point-source
photometry, we have re-estimated surface brightnesses for all IRAS and AKARI
images. Images were downloaded from IRSA/IPAC with the same angular resolution
(15″/pixel): HIRES maps for IRAS, and Far-Infrared Surveyor maps for AKARI. An
100″ radius aperture was selected for all maps. We use the conversion factor
of Ueta et al. (2019) to derive flux densities. The final photometry beyond
100µm was corrected for interstellar contamination (Table 3). IRAS 12µm and
AKARI 160µm flux densities are upper limits (non detection). The new
measurements are given in Figure 12, along with archival photometry from Pan-
STARRS1, Gaia, IPHAS, 2MASS, and WISE. The IRAS and AKARI fluxes integrated
over the nebula indicate the shell flux peaks at $\lambda\sim$90µm, while the
foreground emission is colder. Using the aperture photometry results for the
nebula and the VOSA tool, we derive a shell blackbody temperature of 60 K (cf.
Figure 12).

Table 3: Pa 30 nebula surface photometry vs. cloudy predictions. Band ($\mu$m) |  $F_{\nu}$ (Jy) |  cloudy model (Jy)
---|---|---
IRAS/12† | $\leq 0.25$ | 0.25
IRAS/25 | $1.41\,(\pm 0.09)$ | 1.4
IRAS/60 | $13.24\,(\pm 0.26)$ | 16.6
AKARI/65 | $11.72\,(\pm 0.25)$ | -
AKARI/90 | $19.99\,(\pm 0.32)$ | -
IRAS/100 | $7.25\,(\pm 0.20)$ | 7.8
AKARI/140 | $\leq 6.39\,(\pm 0.51)$ | -
AKARI/160† | $\leq 5.27\,(\pm 0.66)$ | 2.0

We ran a cloudy model for the shell assuming it is ionized gas with normal ISM
abundances. We assume a blackbody star with $L_{*}=3\times 10^{4}\,\rm
L_{\odot}$, $T_{*}=2.3\times 10^{5}\,\rm K$, surrounded by a shell with inner
and outer radius of 0.8 and 1.2 pc, and density $n=17\,\rm cm^{-3}$. Standard
ISM abundances and dust content were used as defined in cloudy, with a range
of grain size and a dust-to-gas ratio of $3.8\times 10^{-3}$. This gives a
total gas mass of $\sim 2.1\,\rm M_{\odot}$ and a dust mass of $8\times
10^{-3}\,\rm M_{\odot}$. The model predicts broadband fluxes listed in Table
3, in good agreement with the infrared measurements. At shorter wavelengths,
the model flux is dominated by a few strong emission lines: [Ne vi] at 7.6µm,
[Ne v] at 14.7µm and 25µm, and [O iv] at 25.9µm. The longer wavelength
emission cannot be explained by emission lines and is from dust. The predicted
H$\alpha$ flux is $2.2\times 10^{-11}\,\rm erg\,s^{-1}\,cm^{-2}$, which, after
extinction correction, gives 13 Rayleighs, 2.3$\times$ the VTSS H$\alpha$
surface brightness. The model explains the infrared photometry but
overpredicts the apparent H$\alpha$ surface brightness.

Alternatively, it can be assumed that the H$\alpha$ emission comes from the
accelerated gas seen in the [S ii] emission reported in Paper I. The average
density of this component, derived from the [S ii] lines, is $N_{\rm
e}=120\,\rm cm^{-3}$. We assume a temperature $T_{\rm e}=10^{4}$ K and use the
relation (Pottasch, 1984):

$M_{\rm ion}\,[{\rm M_{\odot}}]=11.06\times F({\rm
H}\beta)\,\frac{d^{2}\,(T_{\rm e}/10^{4})^{0.88}}{N_{\rm e}},$ (4)

where $F({\rm H}\beta)$ is in units of $10^{-11}$ erg cm-2 s-1, distance $d$
in kpc, electron temperature $T_{e}$ in K, and electron density $N_{e}$ in
cm-3. The intrinsic H$\beta$ flux, derived from the H$\alpha$ flux assuming
recombination Case B for a theoretical H$\alpha$ to H$\beta$ ratio of 2.85, is
$F(\rm H\beta)\approx 7.2\times 10^{-12}$ erg cm-2 s-1. Hence, an ionized mass
of $\approx 0.3\,\rm M_{\odot}$ is derived.

The mass is therefore dominated by the outer shell, rather the accelerated gas
seen in [S ii]. The overprediction of H$\alpha$ for the outer shell may
indicate that this gas is hydrogen-poor, in which case the mass is less than
the derived 2.1 M⊙.

The presence of dust in the circumstellar shell is strongly supported. The
mass is dependent on composition and grain size. The dust origin remains open:
it can be supernova dust, interstellar dust heated by the star, or dust from
previous mass loss. The circumstellar shell could represent swept-up ISM or
matter ejected in a mass-loss episode before the supernova explosion, such as
a relic planetary nebula.

##  6 Discussion

###  6.1 SN shell mass

Oskinova et al. (2020) estimate the amount of hydrogen-free, X-ray-emitting
nebula gas to be $0.1~{}\rm M_{\odot}$. Our ionized mass estimate from the
tentative H$\alpha$ detection is an additional 0.3 to 2.1 $\rm M_{\odot}$
(Sec. 5.2). However, the relation of this gas to the supernova is unclear (see
next subsection) and its kinematics are not known.

Consider the kinetic energy of the H-poor ejecta, $E_{\rm kin}=(1/2)\,M_{\rm
ej}v^{2}_{\rm exp}$, where $v_{\rm exp}$ is the ejecta expansion velocity. In
Paper I, we find the shocked emission has a radial velocity of 1100 km s-1. If
the extended halo-like feature in the AKARI 90µm data (radius $128\pm 5$
arcsec) is the farthest extent of the nebula, then the ejecta velocity would
be $\sim$1700 km s-1 not much different to the shocked emission. Both values
are consistent with the general decline of ejecta velocities more than 100
days post-eruption in Type Iax SNe (e.g., Kawabata et al., 2018; Srivastav et
al., 2021).

Using the above ejecta mass and velocities, the kinetic energy of the ejecta
$E_{\rm kin}$ ranges from $1\times 10^{48}$ to $3\times 10^{48}$ erg. These
are conservative estimates since this is a lower limit for ejected mass, while
the expansion velocity at the time of eruption could have been higher.

We compare these tentative estimates against known extragalactic Type Iax SNe
in Figure 13. These include theoretical models by Lach et al. (2022, open
diamonds), the proposed range of values for Type Iax by Foley et al. (2013,
black dashed bar), and a few examples of extragalactic sources: 2008ha and
2010ae (gray; Stritzinger et al., 2014), 2007gd (blue; McClelland et al.,
2010), 2014ck (orange; Tomasella et al., 2016), 2019gsc (magenta; Srivastav et
al., 2020), and 2020kg (green; Srivastav et al., 2021). Both the low $E_{\rm
kin}$ and ejecta mass estimate are consistent with observed ranges for Type
Iax sources. However, they do not agree with the model predictions for pure
deflagrations of Chandrasekhar-mass CO WDs of Lach et al. (2022).

Figure 13: Comparison of the ejecta mass against kinetic energy released by
Type Iax SNe. Pa 30/SN 1181 is marked in red. Lach et al. (2022) models are
also shown (open diamonds), while the range of expected values for Iax by
Foley et al. (2013) is shown in black (dashed). A few examples of known
extragalactic Iax are also shown: 2008ha and 2010ae data by Stritzinger et al.
(2014), 2007gd by McClelland et al. (2010), 2014ck by Tomasella et al. (2016),
2019gsc by Srivastav et al. (2020), and 2020kg by Srivastav et al. (2021).

###  6.2 Merger and ejected mass

The stellar luminosity and temperature place the star on a location in the HR
diagram similar to post-AGB stars. In these stars, the stellar luminosity
comes from residual hydrogen burning and follows the core mass–luminosity
relation, originally proposed by Paczyński (1970). Using the star’s luminosity
determined as $L_{*}=(40\pm 10)\times 10^{3}\,\rm L_{\odot}$, this relation
gives a core mass (which is essentially the mass of the remnant star) of
$M_{*}=1.20\pm 0.17\,\rm M_{\odot}$. The relation from Vassiliadis & Wood
(1994) gives 0.1 M⊙ less.

The application of these models to post-merger evolution can be queried. In
the absence of detectable hydrogen, helium burning may be expected. The models
of Vassiliadis & Wood (1994) find a similar luminosity for stable helium
burning, however this helium very quickly runs out in post-AGB stars and the
luminosity subsequently declines.

Merger models published by Schwab et al. (2016) and Schwab (2021) reach a
similar location in the HR diagram as carbon burning stars, but take 10 to 20
kyr to reach this. They reach the post-AGB phases at 30% lower luminosity than
predicted by the Vassiliadis & Wood (1994) for their mass. Lower mass merger
models by Schwab & Bauer (2021) take 170 kyr to reach the post-AGB phase and
similar models from Wu et al. (2022) reach the right luminosity but do so as
cool red giant stars. All these merger models spend a long time as red giants.
The models assume a red giant mass loss recipe. The evolution could
conceivably be much accelerated if an instantaneous mass loss is assumed,
either due to the explosion or akin to common envelope systems, thereby
skipping the red giant phase and the early post-AGB phase. Accretion may also
affect the evolution in the post-AGB region of the HR diagram.

Assuming the change in luminosity by 30%, the mass of the star would become
$1.45\pm 0.2\,\rm M_{\odot}$. The mass range does not require the star to have
super-Chandrasekhar mass as proposed by Gvaramadze et al. (2019), although
this is not ruled out either.

The range of possible masses fits with WD merger products. The CO WD mass
distribution peaks at approximately 0.6 M⊙, while helium WDs are approximately
0.45 M⊙. Two merging CO WDs or a CO+He WD can therefore reach the minimum
remnant mass. O-Ne WDs are more massive and a merger involving one (Gvaramadze
et al., 2019) would lead to a more massive remnant. The moderate neon
abundance may not support involvement of such a WD.

The mass ejected in the merger should be included in the progenitor masses.
The minimum ejecta mass is that derived from the X-ray emission (Oskinova et
al., 2020) of 0.1 M⊙. The outer shell may contain further mass ejected during
the merger. The hydrogen mass in the shell cannot come from the merger as WDs
have very thin hydrogen layers and this should not be be counted in the ejecta
mass. The hydrogen is seen only in the VTSS detection and needs confirmation.
If the outer shell is hydrogen-free, then it may add another 0.1 M⊙. The
merger ejecta are therefore estimated at $M_{\rm ej}=0.15\pm 0.05\,\rm
M_{\odot}$.

This leaves the question of where the outer shell originates. If there is
hydrogen in the outer shell, it can be swept-up ISM or from mass lost by the
WD progenitor. If so the faint, outer shell is a relic planetary nebula, re-
ionized by the luminous, hot post-merger star.

###  6.3 Dust

Pa 30 is only the second detection of dust emission in Type Iax SNe and the
only known case of cold dust. The other example is the recent Type Iax SN
2014dt in M 61. Spitzer observations by Fox et al. (2016) found excess mid-
infrared emission (3.6 and 4.5$\rm\mu m$) one year post-eruption in 2014dt,
that could be a pre-existing dusty circumstellar matter or newly formed dust
($\sim 10^{-5}\,\rm M_{\odot}$ of carbonaceous material). Coincidentally,
2014dt has been suggested as a possibly bound remnant (Kawabata et al., 2018).
We note that cold dust, as in Pa 30, would not be detectable in extragalactic
SNe.

###  6.4 The lack of a kicked stellar remnant

Theoretical models of Type Iax explosions predict a kicked stellar remnant
(e.g., Jordan et al., 2012; Kashyap et al., 2018). However, the radial
velocity of Pa 30’s stellar remnant, as well as the mean radial velocity of
its surrounding nebula, is nearly zero, while the tangential velocity is low
($\sim 30$ km s-1). The Gaia DR3 proper motion indicates the central star
could have moved by at most $\sim 2$″ since 1181 AD. It clearly remains at the
center of Pa 30. So these data are already a challenge to existing models. The
nearby faint star (Figure 8) cannot be a kicked companion as this star is in
the foreground ($1.1^{+0.4}_{-0.3}$ kpc; Bailer-Jones et al., 2021) with a
much higher proper motion (21.285 mas yr-1)

Lach et al. (2022) estimate kick velocities between 6.9 km s-1 and 369.8 km
s-1 for bound remnants in Type Iax explosions. These could be in the ballpark
for Pa 30.

The (only) CO+ONe WD merger model is by Kashyap et al. (2018) with a predicted
kick velocity of $\sim 90$ km s-1. However, an ONe WD may not be required here
because of the remnant mass and the moderate neon abundance.

##  7 Conclusions

The association of Pa 30 with the supernova of 1181 AD (Paper I) makes this
system one of only two Galactic Type Iax supernovae known, the other being Sgr
A East (Zhou et al., 2021). Pa 30 is the only bound SN with a visible stellar
remnant in the Galaxy. Its Wolf-Rayet-type optical spectrum is the only
example known that is neither the central star of a planetary nebula nor the
product of a high-mass Population I progenitor. This system, unique in several
respects, is the nearest and youngest Type Iax remnant known and amenable to
detailed study. It is also the only example where a Type Iax stellar and
nebular remnant can be related to an observed eruption almost a millennium
earlier.

Most features of the optical spectrum can be reproduced with a stellar wind
model, with $v_{\rm w}=15,000\,\rm km\,s^{-1}$ and mass loss rate $\dot{M}\sim
10^{-6}\,\rm M_{\odot}\,yr^{-1}$. The wind appears H-free, is strongly
deficient in helium relative to C, N, O, and Ne, and has C/O$\sim 0.25$ by
number. The wind cannot be driven by radiation pressure alone. Some broad O
viii lines not reproduced by the wind model can be well fitted with hot gas
with $T\simeq 4$ MK, either shocked gas in the outer or inner wind where the
opacity of the wind favours the former. This gas, with the same abundances as
the wind, is seen in lines of O viii and possibly C vi. The hot gas shows a
low neon abundance, Ne/O$\,<0.15$ by number.

The infrared spectrum can be fitted with a circumstellar shell where shorter
wavelengths (10–30µm) show line emission and longer wavelengths show emission
from cold dust, with $M_{\rm dust}\sim 8\,\times\,10^{-3}\,\rm M_{\odot}$. The
shell is also tentatively detected in wide-field H$\alpha$ imaging. This is
only the second detection of dust in a Type Iax SN and the only detection of
cold dust. The origin of this dust is open: possibilities are supernova dust,
heated interstellar dust, or dust from previous mass loss from the system.

On timescales of the order of a century, the visual light curves of the
central star show evidence of $\sim 0.5$ magnitude dimming between 1925 and
1950 around a value of $B_{j}\sim$15.8 mag. Recent mid-infrared data from WISE
may also show a slight fading over 11 years of about 0.1 magnitudes for $W1$
and $W2$.

The abundances, ejecta mass, explosion luminosity and energetics are all
consistent with a type Iax supernova. There are two scenarios for this type of
supernova: a pure deflagration of a Chandrasekhar-mass CO WD, and a double-
degenerate merger. The observed parameters and the presence of a highly
evolved post-eruption star indicate that the stellar remnant is an example of
the second scenario: a merger of two WDs (also proposed by Gvaramadze et al.,
2019; Oskinova et al., 2020). The luminosity , as derived from the stellar
wind modeling $L=(40\pm 10)\times 10^{3}\,\rm L_{\odot}$ for the assumed
distance and reddening, indicates a mass of the remnant star of $1.2\pm 0.2$
M⊙ to $1.45\pm 0.2$ M⊙ dependent on the stellar models used for the post-AGB
region of the HR diagram. This allows for the possiblity of masses below the
Chandrasekhar mass, in which case the object might not go supernova again
(Gvaramadze et al., 2019). The mass is consistent with a merger between two CO
WDs or a high-mass CO+He WD. The low neon abundance may argue for the former.
The ejecta indicate that $0.15\pm 0.05$ M⊙ was lost during the merger. The
outer shell, if indeed H-rich, cannot be purely explained as merger ejecta and
could be swept-up ISM or a fossil planetary nebula from pre-merger mass-loss.

Merger products are expected to be fast rotators. Our observations cannot
establish a short rotational period and this remains to be tested. Merger
products are also assumed to be the progenitors of highly magnetic WDs. The
absence of detectable Zeeman splitting places an upper limit of $B<2.5$ MG,
way below the previously predicted values from Gvaramadze et al. (2019, 200
MG) but may increase during future remnant contraction.

The mass of the merger progenitor stars, the ejecta and circumstellar mass,
the non-detection of a significant magnetic field, the fact that the remnant
has remained at the center of its bound nebula post-eruption, and the
possibility of modest photometric dimming of the stellar remnant, are some of
its key observed properties that that somewhat deviate from the typical
(inferred or assumed) properties of Type Iax SNe, and therefore merit detailed
investigation to improve our understanding of Type Iax evolutionary models.

## Acknowledgements

We especially thank the anonymous referee for their constructive review that
helped improve our manuscript, as well as Dr. G. Gräfener and Dr. P. Garnavich
for providing their spectra. We thank Dr. András Pál for help with qualitative
analysis of the TESS data. We thank Dr. Laurence Sabin for designing the
OSIRIS/GTC observations.

QAP thanks the Hong Kong Research Grants Council for support under GRF grants
17326116 and 17300417. FL and AR thank HKU for postdoctoral fellowships. AAZ
thanks the Hung Hing Ying Foundation for the provision of a visiting
professorship at HKU. MAG was funded under grant number PGC2018-102184-B-I00
of the Ministerio de Educación, Innovación y Universidades co-funded with
FEDER funds. This work was partially funded by Kepler/K2 grant
J1944/80NSSC19K0112 & HST GO-15889, and STFC grants ST/T000414/1,
ST/T000198/1, ST/S006109/1 and by the EU HORIZON2020 program under grant
101004214.

Part of this work is based on data from (i) the OMC Archive at CAB (INTA-CSIC)
pre-processed by ISDC; (ii) data products from the Near-Earth Object Wide-
field Infrared Survey Explorer (NEOWISE) funded by NASA; (iii) the Swift
public data archive; (iv) the NASA/IPAC Infrared Science Archive; ( v) the
AAVSO Photometric All-Sky Survey (APASS); (vi) data from the Asteroid
Terrestrial-impact Last Alert System (ATLAS) project; (v) Extinction data from
the EXPLORE platform funded by the EU under grant 101004214; (vi) Gaia
spectroscopy from the Gaia Data Mining Platform at the Royal Observatory
Edinburgh, funded by STFC.

For the purpose of open access, the authors have applied a Creative Commons
Attribution (CC BY) licence to any Author Accepted Manuscript version arising.
This publication is supported by multiple datasets which are openly available
at locations cited in the References.

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