# Isotopic ratios for C, N, Si, Al, and Ti in C-rich presolar grains from
massive stars

Jordan Schofield1,9*, Marco Pignatari2,3,4,6,7, Richard J. Stancliffe8, Peter
Hoppe5
1Department of Physics and Mathematics, University of Hull, HU6 7RX, UK
2 Konkoly Observatory, Research Centre for Astronomy and Earth Sciences
(CSFK), Eötvös Loránd Research Network (ELKH),
Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary
3 CSFK, MTA Centre of Excellence, Budapest, Konkoly Thege Miklós út 15-17,
H-1121, Hungary
4E.A.Milne Centre for Astrophysics, University of Hull, HU6 7RX, UK
5Max Planck Institute for Chemistry, Hahn-Meitner-Weg 1, 55128 Mainz, Germany
6NuGrid Collaboration, http://nugridstars.org
7Joint Institute for Nuclear Astrophysics - Center for the Evolution of the
Elements
8H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue,
Bristol BS8 1TL, UK
9NHS North of England Commissioning Support Unit, Appleton House, Lanchester
Road, Durham, DH1 5XZ, UK

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Certain types of silicon carbide (SiC) grains, e.g., SiC-X grains, and low
density (LD) graphites are C-rich presolar grains that are thought to have
condensed in the ejecta of core-collapse supernovae (CCSNe). In this work we
compare C, N, Al, Si, and Ti isotopic abundances measured in presolar grains
with the predictions of 21 CCSN models. The impact of a range of SN explosion
energies is considered, with the high energy models favouring the formation of
a C/Si zone enriched in 12C, 28Si, and 44Ti. Eighteen of the 21 models have H
ingested into the He-shell and different abundances of H remaining from such
H-ingestion. CCSN models with intermediate to low energy (that do not develop
a C/Si zone) cannot reproduce the 28Si and 44Ti isotopic abundances in grains
without assuming mixing with O-rich CCSN ejecta. The most 28Si-rich grains are
reproduced by energetic models when material from the C/Si zone is mixed with
surrounding C-rich material, and the observed trends of the 44Ti/48Ti and
49Ti/48Ti ratios are consistent with the C-rich C/Si zone. For the models with
H-ingestion, high and intermediate explosion energies allow the production of
enough 26Al to reproduce the 26Al/27Al measurements of most SiC-X and LD
graphites. In both cases, the highest 26Al/27Al ratio is obtained with H still
present at $X_{H}\approx 0.0024$ in He-shell material when the SN shock is
passing. The existence of H in the former convective He-shell points to late
H-ingestion events in the last days before massive stars explode as a
supernova.

###### keywords:

nuclear reactions, nucleosynthesis, abundances – stars: abundances – stars:
evolution – stars: massive – supernovae: general

††pubyear: 2021††pagerange: Isotopic ratios for C, N, Si, Al, and Ti in C-rich
presolar grains from massive stars–A

##  1 Introduction

Presolar grains were produced by different types of stars nearby the Sun
before its formation about 5 Gyr ago. These grains were important ingredients
for the first aggregates of solid materials from which the parent bodies of
primitive meteorites formed inside the protoplanetary disk around the young
Sun. These meteorites have been recovered on Earth and can therefore be
analysed in laboratories. The C-rich grains can be isolated from solar
material by dissolving the parent meteorite in acids to leave the resilient
grains behind (e.g. Amari et al., 1994). The isotopic ratios and abundances of
presolar grains can be measured in laboratories providing a powerful
diagnostic for theoretical stellar simulations.

Few isotopic ratios are observable in stellar spectra, and they suffer from
much larger uncertainties compared to data obtained from presolar grains. We
refer to e.g., Carretta et al. (2000); Spite et al. (2006) for C isotopic
ratios, to Hedrosa et al. (2013) for N, to Yong et al. (2003); Carlos et al.
(2018) for Mg and to Chavez & Lambert (2009) for Ti.

Certain types of C-rich grains, e.g., SiC-X grains and low density (LD)
graphites, formed in the ejecta of core collapse supernovae (CCSNe; the
collapse of a massive star with initial mass $\geq$ 9 M⊙, e.g. Woosley et al.,
2002; Nomoto et al., 2013; Sukhbold et al., 2016; Limongi & Chieffi, 2018;
Curtis et al., 2019), identified because their isotopic abundances match the
signatures of these events. Such signatures of CCSNe include 15N-excesses
relative to solar111Unless otherwise stated to be absolute, all excesses and
deficiencies of isotope abundances are discussed relative to solar ratios.,
strong Si isotope anomalies, and evidence for the presence of the radioactive
isotope 44Ti at the time of grain formation. Discovered by Bernatowicz et al.
(1987), SiC grains are a C-rich type of presolar grain that are typically
observed at concentrations of $<50$ppm (but up to $150$ppm) and diameters of
$<0.5\mu$m and up to $30\mu$m (Davis, 2011; Zinner, 2014; Nittler & Ciesla,
2016, and references therein). SiC and graphite grains are believed to only
form in C-rich environments, i.e. where C/O $>1$ (by number fraction). The
strength of the CO molecular bond is such that no other C-rich molecules could
efficiently form (Ebel & Grossman, 2001). There are several sub-types of
presolar SiC grains (Mainstream, AB, C, X, Y, Z, and putative nova; which are
shown in Figure 1 with the exception of mainstream, Y, and Z grains) which are
characterised by specific isotopic ratios. Among other ratios, the most used
to distinguish between different presolar grain types are 12C/13C, 14N/15N,
the 222$\delta$(ratio) = (grain ratio/solar ratio - 1) $\times 1000$delta
ratio $\delta$ 29,30Si and 26Al/27Al (Zinner, 2014).

Figure 1: 12C/13C and 14N/15N isotopic ratios of individual presolar grains.
SiC sub-types of possible SN origin (AB, C, X, and nova) are shown as well as
LD graphites. The solar carbon and nitrogen ratio lines are plotted as solid
lines as well as the terrestrial nitrogen ratio as a dashed line
(14N/15N=272). The solar 14N/15N ratio was taken from Marty et al. (2011). The
SiC and LD graphite grain data were taken from the Washington University
Presolar Grain Database (Stephan et al., 2020; Hynes & Gyngard, 2009).

SiC-X grains (about $1\%$ of all SiC grains, e.g. Zinner, 2014) have a
relative excess of 28Si to 29,30Si compared to solar ratios. Most have a 12C,
15N excess, while some have a 13C, 15N excess compared to solar. The 26Mg and
44Ca excesses are due to the condensation of unstable 26Al and 44Ti
respectively in the grains (e.g. Besmehn & Hoppe, 2003). The majority of SiC-X
grains also show an excess of 49,50Ti relative to 48Ti and 10-20$\%$ show a
large excess of 44Ca (Nittler et al., 1996; Besmehn & Hoppe, 2003; Lin et al.,
2010). SiC-X are known to have originated from CCSNe, primarily due to their
excesses of 28Si and extinct 44Ti (e.g. Nittler et al., 1996). Evidence for
initial 44Ti within at least one of the few SiC grains classified as nova
grains led to the conclusion that they had formed by CCSNe as 44Ti production
is a notable signature of CCSN nucleosynthesis (Nittler & Hoppe, 2005). SiC
type-AB grains ($\sim 4-5\%$ of all SiC grains; Amari et al., 2001b) are
believed to have multiple sources including CCSNe (Liu et al., 2017a; Hoppe et
al., 2019). Putative nova grains, and 15N-rich and possibly also 15N-depleted
AB grains are consistent with the H-ingestion models discussed in this work,
in Pignatari et al. (2015) and in Liu et al. (2016).

Low density graphites (Amari et al., 1995) are another type of C-rich grain,
showing a large 12C/13C ratio range. Excesses and deficits of 28Si relative to
29,30Si are both observed, as are excesses in 26Mg and 44Ca. With few
exceptions, the 14N/15N ratio of LD graphites is mostly consistent at about
300, suggesting heavy contamination from terrestrial nitrogen (e.g. Amari et
al., 1993; Hoppe et al., 1995). Most LD graphites are believed to originate in
CCSNe due to their large range of C isotopic ratios and excesses in signature
isotopes such as 15N, 18O, 26Mg, 28Si, 44Ca, and 49,50Ti (Travaglio et al.,
1999).

Isotopic signatures such as those found in presolar grains are formed in very
specific regions of CCSNe. Classically, the main C-rich region is the He/C
zone (the He-shell of the ejecta) above the O-rich O/C zone (Meyer et al.,
1995). However, Pignatari et al. (2013a) introduced a new set of models
showing a new C-rich zone which was able to explain most observed abundances
of C-rich grains. As the shockwave of the CCSN reaches the bottom of the He/C
zone, its density and temperature increase dramatically. These conditions
efficiently activate explosive He-burning. However, at T > $3.5\times 10^{8}$
K the 12C($\alpha$,$\gamma$)16O reaction is up to orders of magnitudes weaker
relative to the subsequent reactions in the $\alpha$-capture chain, starting
from the reaction 16O($\alpha$,$\gamma$)20Ne. This leads to a 12C- and 28Si-
rich, 16O-deficient region in the deepest He/C shell material, defined by
Pignatari et al. (2013a) as the C/Si zone. Additionally, non-homogeneous
H-ingestion into the He/C zone prior to the explosions results in the variable
production of 13C, 15N, and 26Al by explosive H-burning deep in the C-rich He-
shell, nearby the C/Si zone. H-ingestion combined with the extreme conditions
of the SN shockwave triggers the production of 15N via the hot CNO cycle. This
allows the isotopic ratios of CCSN grains such as low 12C/13C and 15N-excesses
to be reproduced by local mixing of material (Pignatari et al., 2015; Liu et
al., 2016, 2018b; Hoppe et al., 2018).

Classically, the explosive $\alpha$-capture at the bottom of the former
convective He-shell activates a neutron burst peaking up to $10^{18-20}$
neutrons cm-3, produced by the 22Ne$(\alpha,n)^{25}$Mg reaction. This
nucleosynthesis process was called the n-process (Blake & Schramm, 1976;
Thielemann et al., 1979). Much later, its signature was identified in heavy
elemental abundances measured in presolar SiC-X grains such as large excesses
of 58Fe, 88Sr, 96Zr, 95,97Mo, and 138Ba (e.g. Meyer et al., 2000; Pellin et
al., 2006; Pignatari et al., 2018) and in the production of the radioactive
isotope 32Si (Pignatari et al., 2015). However, this scenario has been
discounted as a way to explain the r-process because it could not reproduce
the r-process abundance pattern in the Solar System (Blake et al., 1981). The
presence of H in the He-shell during the SN explosion may lead to a
suppression of the n process, where it becomes more probable to destroy 22Ne
by proton capture than by the 22Ne$(\alpha,n)^{25}$Mg reaction (Pignatari et
al., 2015). The production of 44Ti and 40Ca in the C/Si zone along with the
possible strong depletion of 40Ca by neutron capture predicts abundances
consistent with the observation of large 44Ca/40Ca in the C-rich grains
discussed (Pignatari et al., 2013a). It is still matter of debate if in
presolar grains the abundance signatures of H-ingestion coexist with the
neutron-capture signature of the n-process. Indeed, the n-process activation
would be compatible with the 30Si- and 32S-enhancements measured in in some
putative nova grains (Liu et al., 2016; Hoppe et al., 2018), and with the
32Si- and 50Ti-enhancements found in a sample of SiC-AB grains (Liu et al.,
2017a). On the other hand, measurements of the Sr, Mo and Ba isotopic
abundances in SiC-AB grains seem to be compatible with the pre-explosive
s-process abundances in the He shell, and not with the n-process (Liu et al.,
2018b). In the first case, major asymmetries triggered by the H ingestion in
the pre-explosive He shell structure would be required in order to explain for
the same single grain the signatures of both the n-process and of a late
H-ingestion event leaving H behind in the former He shell material. While this
may be a natural expectation from multi-dimensional simulations, it cannot be
captured by one-dimensional stellar simulations. Additionally, those abundance
signatures of high neutron-density exposures could also be the effect of a
local activation of the intermediate neutron-capture process (i-process Cowan
& Rose, 1977), following the H ingestion event. The i-process has been
proposed as a nucleosynthesis source active in massive stars at low
metallicities (e.g., Roederer et al., 2016; Clarkson et al., 2018; Banerjee et
al., 2018), but it also has been proposed as a source of anomalous signatures
in presolar grains for Ti isotopes (HD graphites, Jadhav et al., 2013), Ba
isotopes (in some mainstream SiC grains, Liu et al., 2014) and 32Si-
enrichments (in SiC AB grains, Fujiya et al., 2013). In order to verify all of
these different scenarios, new abundance observations are required for more
presolar grains of different types.

An alternative scenario for the formation of SiC-X grains is that 28Si and
44Ti originate from the Si/S zone, which is the region of the ejecta dominated
by explosive O-burning (Meyer et al., 1995). Figure 2 shows a schematic of the
layered ‘shell‘ structure of a CCSN ejecta as described by Meyer et al. (1995)
with the stellar zones. The Si/S zone is mostly made of 28Si and 32S by O
fusion, and 44Ti is efficiently produced by $\alpha$-capture (Woosley &
Weaver, 1995). The high 12C/13C ratios are signatures of He-burning and high
26Al/27Al ratios can be produced in the He/N zone by H-burning. However, these
isotopic ratios are produced in different, non-neighbouring layers undergoing
different phases of burning prior to the SN explosion (e.g. Woosley & Weaver,
1995; Rauscher et al., 2002). This requires deep, inhomogeneous mixing of
these layers in the CCSN ejecta while maintaining C>O. For instance, Si and Ti
signatures may need contributions from the Ni, O/Si, and Si/S zones where
complete or partial Si-burning and O-burning occur (e.g., Travaglio et al.,
1999; Xu et al., 2015). The He/N and He/C zones where H- and incomplete He-
burning occurs are also required. This is where the C>O condition is met for
SiC condensation (Lodders & Fegley, 1997). This C>O condition necessitates
extremely limited addition of material from the intermediate O-rich layers
(Travaglio et al., 1999). Three-dimensional hydrodynamic models predict mixing
in the ejecta carried out by Rayleigh-Taylor instabilities (Hammer et al.,
2010). It remains to be seen if these instabilities allow the inner regions to
penetrate (while minimising the addition of material from) the O-rich regions
and mix with those rich in C. Astronomical observations of supernovae remnants
have shown extensive mixing within the ejected material (Hughes et al., 2000;
Kifonidis et al., 2003).

Figure 2: A schematic of the layered ’onion shell’ structure of a CCSN ejecta
from a massive star progenitor as described by Meyer et al. (1995) with each
layer is labelled with its most abundant elements excepting for the central
zone. In this case, NS represents the central neutron star formed after the
CCSN explosion. The C/Si zone is also indicated at the bottom of the He/C
zone. Relative concentrations of C and O are indicated for each zone, with the
exception of the deepest Si/S and Ni zones, where there are essentially no C
and O left.

CCSNe also show a large range of explosion energies, from very faint CCSNe
with few $10^{50}$erg to hypernovae, up to $5\times 10^{51}$erg (e.g., Nomoto
et al., 2013). Travaglio et al. (1999) demonstrated that it was possible to
reproduce most isotopic abundances with these models but also highlighted
their shortcomings such as the lack of 15N and the need for the C-rich
condition. To overcome this need for mixing between non-neighbouring layers,
Clayton et al. (1999) and following works suggested the possibility of
condensing C-rich grains in O-rich material. However, this remains
controversial as Ebel & Grossman (2001) concluded that only nanometre-sized
grains such as nano-diamonds may form in this turbulent O>C environment and is
therefore unrealistic for SiC formation. It was also shown by Lin et al.
(2010) that the isotopic ratios of SiC grains of SN origin are inconsistent
with the predictions for O-rich material. On the other hand, the advantage of
the formation of the C/Si zone is to have isotopes such as 28Si and 44Ti made
in a C-rich environment, in the vicinity of C-rich He shell layers.

In this work, we compare the abundance predictions of 21 CCSN models with the
observed isotopic ratios of C, N, Al, Si and Ti of different types of C-rich
presolar grains with established or possible CCSN origin. The structure of the
paper is as follows. Section 2 describes the stellar models. In Section 3, the
theoretic predictions are compared with observed grain abundances. Section 4
summarises the results.

##  2 Theoretical Stellar Models

In this study, 4 sets of CCSN models are used: two progenitor masses, of 15
and 25 M⊙, both with and without the ingestion of H into the He/C zone in the
pre-SN phase. All of the models have a metallicity scaled to Z = 0.02 from the
solar abundances by Grevesse & Noels (1993). A summary of their main features
and specifications can be found in Tables 1 and 2. Detailed information for
the models are published in Pignatari et al. (2015) and Pignatari et al.
(2016).

The stellar progenitors were all calculated using the code GENEC (Eggenberger
et al., 2008). Rotation and magnetic fields were not included. Mass-loss rates
during the Main Sequence phase (log Teff $>$ 3.9, where Teff is the effective
temperature) were taken from Vink et al. (2001). For 3.7 $<$ log Teff $<$ 3.9,
De Jager et al. (1988) prescriptions were used, and for more advanced stages
and log Teff $<$ 3.7, a scaling law with the stellar luminosity was adopted
(Pignatari et al., 2016). Consistently with typical GENEC stellar simulations,
the nuclear network to follow energy generation is made of isotopes included
explicitly (1H, 3He, 4He, 12C, 13C, 14N, 15N, 16O, 17O, 18O, 20Ne, 22Ne, 24Mg,
25Mg, 26Mg, 28Si, 32S, 36Ar, 40Ca, 44Ti, 48Cr, 52Fe, 56Ni) and implicitly in
chain reactions to correctly follow the energy generation up to Si burning
(e.g., Hirschi, 2007).

For the CCSN explosion, the mass cut above which the material is ejected
(i.e., the mass of the final compact remnant) is given by the analytical
formula of Fryer et al. (2012), depending on the initial mass and metallicity
of the progenitor. The amount of matter that falls back after the launch of
the explosion is also taken into account. For the stellar layers ejected, the
main information for the CCSN nucleosynthesis are given by a semi-analytic
description for the shock heating and following temperature and density
evolution in the different layers. The shock velocity through the stellar
structure is defined by the Sedov blastwave solution (Sedov, 1946). The peak
post-shock temperature and density calculated for each zone of the CCSN ejecta
are followed by an adiabatic exponential decay for few seconds, when only
$\beta$-decay nuclear reactions remain active from radioactive unstable
isotopes (Pignatari et al., 2016).

The thermodynamic and structural information from the stellar models and from
the CCSN explosions are used as input for the post-processing nucleosynthesis
calculations which generates complete stellar yields. For these models, we
used the parallel multi-zone code mppnp from the NuGrid post-processing
simulation tool framework. The nuclear network is dynamic, increasing up to
more than 5200 isotopes and 74000 reactions depending on the needs from the
nucleosynthesis conditions found. The detailed description of the post-
processing code, the simulation setup and the nuclear reaction network is
given in Pignatari et al. (2016).

Explosive He burning conditions are particularly relevant for our study. The
triple-$\alpha$ and 12C($\alpha$,$\gamma$)16O reaction rates are from Fynbo et
al. (2005) and Kunz et al. (2002), respectively. The 22Ne($\alpha$,n)25Mg
reaction rate is from Jaeger et al. (2001). More recent rates are becoming
available for this reaction (e.g., Talwar et al., 2016; Ota et al., 2021;
Adsley et al., 2021), which is the dominant source of neutrons in explosive He
burning (Thielemann et al., 1979; Meyer et al., 2000; Pignatari et al., 2018).
However, nuclear uncertainties should have a limited impact at the relevant
temperatures for this study, of the order of $10^{9}$ Kelvin or higher.
Neutron capture rates are from the KADoNIS 0.3 compilation where available
(Dillmann et al., 2006), otherwise for unstable isotopes the theoretical rates
adopted were from the JINA REACLIB version 1.1 (e.g., Cyburt et al., 2010).
Available stellar $\beta$-decay rates are from Fuller et al. (1985) and Oda et
al. (1994) for light isotopes, and for the iron group isotopes and beyond we
used Langanke & Martínez-Pinedo (2000) and Goriely (1999).

For this work, we use three 15M⊙ models by Pignatari et al. (2013a) and
Pignatari et al. (2016). The explosion simulations include the fallback
prescription by Fryer et al. (2012) and use the recommended initial shock
velocity for one case, while two further cases with the shock velocity divided
by two and four have also been calculated (models 15d, 15r2 and 15r4,
respectively). For model 15d, the shock velocity of material that does not
fall back is $2\times 10^{9}$cm s-1, corresponding to an explosion energy of
3-$5\times 10^{51}$erg. Models 15r2 and 15r4 correspond to SN explosion
energies of 1-$2\times 10^{51}$erg and less than $10^{51}$erg, respectively
(Pignatari et al., 2013a, 2016). Note that with the semi-analytic approach
used for our models, the SN shock is driven off the proto-neutron star based
on the mass cut derived from Fryer et al. (2012). With this approach, the
initial shock velocity becomes a crucial parameter, directly related to the
temperature and density peaks in different stellar layers during the CCSN
explosion (e.g., Pignatari et al., 2016; Ritter et al., 2018). However, shock
velocities cannot be mapped directly to CCSN explosion energies. Therefore,
for each model we provide an indicative range of CCSN energies corresponding
to the given initial shock velocities, instead of a single explosion energy.

Our approach for the CCSN models is different from other studies in the
literature, where several methods were adopted to produce large scale one-
dimensional nucleosynthesis and abundance yield calculations. Different
engines have been used to artificially drive the explosion, among others a
piston (Woosley & Weaver, 1995; Rauscher et al., 2002; Sieverding et al.,
2018), a thermal bomb (e.g., Thielemann et al., 1996; Nomoto et al., 2013),
the injection of thermal energy (e.g., Limongi & Chieffi, 2003), or more
recently effective neutrino-driven models (Perego et al., 2015; Sukhbold et
al., 2016; Curtis et al., 2019). While the greatest impact of the methods used
to simulate the CCSN explosion are expected to be seen in the most internal
layers of the CCSN ejecta where the iron group elements are made, the more
external regions of the CCSN ejecta relevant for this work (the former C-rich
He shell) are not much affected by the adopted approach to simulate the
explosion. A much greater impact is instead due to the evolution of the
stellar progenitor and to the uncertainties in the progenitor structure (e.g.,
Pignatari et al., 2015).

In the present simulation framework, for the most energetic CCSN models
described above (15d and 15r2), the temperature rises from $3.1\times 10^{8}$K
in the pre-SN stage to a peak of up to about $2.0\times 10^{9}$K in the
forming C/Si zone (Pignatari et al., 2013a). Note that for these models in the
former O/C zone and at the bottom of the C/Si zone there is still a small
region where O is destroyed but there is not enough 4He to make 28Si. Here the
temperature rises up to about $2.2\times 10^{9}$K (see Table 1). In the region
of the former He shell relevant for explosive nucleosynthesis, the SN peak
temperature in model 15r4 is about 30-40% lower than in 15d, while 15r2 and
15d are the same.

The 25d model is calculated for a 25M⊙ progenitor star. Since no substantial
56Ni is ejected by the explosion, we may classify 25d as a faint SN model
(Pignatari et al., 2016). After core C-burning ends in the progenitor star,
the convective He-shell becomes unstable and ingests H into it from above the
He-rich region. The beginning of core O-burning deactivates the convective
zone completely until the SN explosion, leaving the He-rich shell with a H
abundance of about $1.2\%$. With 25d, Pignatari et al. (2015) introduced
25d-H5, 25d-H10, 25d-H20, 25d-H50, and 25d-H500 (25d model set). These models
are the same as 25d in all respects except the H abundance in the He-shell is
reduced by a factor of 5, 10, 20, 50, and 500 respectively.

Pignatari et al. (2015) also introduced the 25T model set where the
temperature and density of 25d are artificially increased to reproduce the
explosive conditions of a 15M⊙ star in the He shell layers (15d model,
included in this study). The bottom of the C/Si zone in the 15d model reaches
a peak temperature 3.3 times higher than in the 25d model ($2.3\times 10^{9}$K
rather than $0.7\times 10^{9}$K), with the 25T model reaching $2.2\times
10^{9}$K. The peak density is also 100 times higher. The same range of pre-
explosion He-shell concentrations of H are examined here; 25T-H, 25T-H5,
25T-H10, 25T-H20, 25T-H50, and 25T-H500. As an example, the abundance profiles
in the He-shell ejecta of 25T-H and 25T-H20 are shown in Figure 3. Relevant
differences are the stronger 12C depletion in 25T-H compared to 25T-H20,
partially compensated by the production of 13C. The pre-SN 14N and 15N
abundances are both increased by the SN explosion in model 25T-H, by up to an
order of magnitude and two orders of magnitudes respectively in some of the He
shell zones shown in the figure. On the other hand, in the 25T-H20 model the N
ejecta will be more representative of the pre-SN abundances, defined by the
specific H ingestion event (Pignatari et al., 2015). In Figure 3, for both the
two models we can see the formation of the so-called O/Nova zone in the
ejected CCSN abundances just above the bottom of the He shell (Pignatari et
al., 2015), where oxygen is more abundant than carbon. Indeed, the combined
12C depletion and 16O production allows an O-rich region to form from the
C-rich pre-explosive He shell. In these conditions, the explosive “Nova-like”
H-burning nucleosynthesis on the previous H-ingestion products provides a
nucleosynthesis characterized by high enrichments of e.g., 15N, 25Mg and 26Al.
Such anomalous signatures have been studied by several presolar grains studies
recently, supporting the existence of the conditions discussed here based on
isotopic measurements of both presolar SiC grains (Liu et al., 2017a, 2018a;
Hoppe et al., 2019) and presolar silicates (Hoppe et al., 2021). For each
model, the mass coordinates of the O/Nova zones formed during the CCSN
explosions are given in Table 2.

Figure 3: Isotopic abundances (mass fractions) in the lower He-shell ejecta of
the 25T-H and 25T-H20 models (upper and lower panels respectively) immediately
after the CCSN explosion. The abundance profiles for H, 4He, 12,13C, 14,15N
and 16O are shown, taking into account their radiogenic contributions. The
secondary x-axis on the top is showing the scale of the CCSN shock peak
temperatures in GK (109 K units) at different mass coordinates.

In this work we also present a new set of six CCSN models, aiming at refining
the study of the impact of different explosion energies in models with
H-ingestion. The 25av model set was designed to be an intermediate to the 25d
and 25T sets by having its shock peak temperature and peak density at the
midpoint of the two. Again, the 25av set has a range of H concentrations as
described above. These are labelled as: 25av-H, 25av-H5, 25av-H10, 25av-H20,
25av-H50, and 25av-H500. Note that the temperature at the bottom of the C-rich
region of models 25av is similar to the temperatures found in model 15r4 (see
Table 2).

Models without H-ingestion
---
Model set 15d | 15d | 15r2 | 15r4
Shock Peak Temperature [K] | $2.2\times 10^{9}$ | $2.2\times 10^{9}$ | $1.6\times 10^{9}$
C/Si zone [M⊙] | $2.945-2.975$ | $2.945-2.975$ | $2.945-2.975$
He-shell [M⊙] | $2.945-3.3$ | $2.945-3.3$ | $2.945-3.2$
Explosion Energy [erg] | $3-5\times 10^{51}$ | $1-2\times 10^{51}$ | $<10^{51}$
Table 1: The three 15M⊙ CCSN models used for the work and introduced by
Pignatari et al. (2013a) are summarised. They are without H-ingestion. For
these models, the table shows the mass coordinates of the He-shell and C/Si
zone, the shock peak temperature at the bottom of the deepest C-rich ejecta
(i.e., the C/Si zone in the 15d and 15r2 models) as well as the explosion
energy range of each model. Models with H-ingestion
---
XH in He-shell | $1.2\%$ | $0.24\%$ | $0.12\%$ | $0.06\%$ | $0.024\%$ | $0.0024\%$
before SN shock |  |  |  |  |  |
Model set 25T | 25T-H | 25T-H5 | 25T-H10 | 25T-H20 | 25T-H50 | 25T-H500
Shock Peak Temperature [K] | $2.3\times 10^{9}$
C/Si zone [M⊙] | $6.815-6.820$
O/nova zone [M⊙] | $6.83-7.04$ | $6.84-7.02$ | $6.86-7.00$ | $6.87-6.96$ | … | …
He-shell [M⊙] | $6.81-9.23$
Model set 25av | 25av-H | 25av-H5 | 25av-H10 | 25av-H20 | 25av-H50 | 25av-H500
Shock Peak Temperature [K] | $1.5\times 10^{9}$
C/Si zone [M⊙] | …
O/nova zone [M⊙] | $6.82-6.87$ | $6.82-6.85$ | $6.82-6.85$ | $6.82-6.84$ | … | …
He-shell [M⊙] | $6.82-9.23$
Model set 25d | 25d-H | 25d-H5 | 25d-H10 | 25d-H20 | 25d-H50 | 25d-H500
Shock Peak Temperature [K] | $0.7\times 10^{9}$
C/Si zone [M⊙] | …
O/nova zone [M⊙] | …
He-shell [M⊙] | $6.82-9.23$
Table 2: The 18 CCSN models used for the work and with H-ingestion are
summarised as follows. The 25M⊙ models have H-ingestion into the He/C in the
pre-SN phase. Model 25d was fully published by Pignatari et al. (2016). The
rest of the 25d set and the 25T set were introduced by Pignatari et al.
(2015). The 25av set is introduced in this work. For each H-ingestion model,
the table shows the shock peak temperature at the bottom of the deepest C-rich
ejecta (i.e., the C/Si zone in the 15d and 25T models, a C-rich region with
mild O depletion triggered by explosive He-burning for the 25av models and the
He/C zone for the 25d models), mass coordinate of the He-shell and O-rich
O/nova zone, and the abundance of H remaining in the He-shell from ingestion
before the SN shock.

##  3 Comparison with presolar grains

In this section, we compare the stellar models to the grain data. We will only
consider the abundance profiles in C-rich regions of the SN ejecta for the
comparison, i.e., the He/C zone and the C/Si zone (if the SN conditions allow
its formation). For the models affected by H ingestion, we will also consider
the O/nova zone as discussed by Pignatari et al. (2015). Indeed, although it
is O-rich, its position between the C/Si and the He/C zones makes it
reasonable to expect that local mixing of stellar material would still result
in C-rich mixtures.

In Figure 4, the C and N isotopic ratios of individual SiC grains and LD
graphites are compared to the CCSN abundances predicted from across the He/C
zone of the models. The 15d, 15r2, and 15r4 models in the top left Panel have
the same stellar progenitor but have different explosion energies and no
H-ingestion. The 25T models in the top right Panel have the same explosion
energy (extremely similar to that of 15d, see § 2) but have different initial
conditions. They allow us to explore the impact of different amounts of H
remaining from ingestion, ranging from 25T-H (about 1.2% of H left at the SN
shock passage from the previous H-ingestion event) down to 25T-H500 (about
0.0024%). In the 25T-H500 case, there is no significant explosive H-burning
nucleosynthesis taking place, but still has the signatures of H-ingestion such
as the production of 13C and 14,15N via the CNO-cycle.

The 25av and 25d model sets are shown in the bottom left and right Panels
respectively, covering the same parameter space for H as the 25T set. However,
these model sets have different explosion energies (see § 2). Note that the
-H10 and -H50 models are not shown in these figures, since they appear to
follow a linear behaviour with the initial H concentration in between models
-H5 and -H500. As discussed in Pignatari et al. (2013a), in the 15d model a
C/Si zone is developed by CCSN nucleosynthesis with large 12C/13C ratios
($10^{5}$-$10^{9}$, off the right of the plot). The outer region of the He/C
zones and the He/N zone in the 15M⊙ models are affected by H-burning, with a
subsolar C ratio of about 4. Assuming different combinations of local mixing
between the C/Si zone, the He/C zone and other external CCSN layers, these
models would be potentially suited to explain the C and N ratios for the SiC-X
grains and LD graphites with C ratios larger than solar (Pignatari et al.,
2013a). For the 25M⊙, H-ingestion models, most of the He/C zone contains CCSN
abundances that skirt along the edge of the presolar SiC-AB grains at a
12C/13C ratio of around 20, covering 14N/15N values in the range $10^{2}$ \-
$10^{4}$. In these regions of the ejecta, the 12C/13C ratio is defined by the
main properties of the H-ingestion event and it is not affected by the CCSN
explosion. Since these models share the same stellar progenitor, they all show
the same ratio. On the other hand, we should expect that different H
ingestions in different real progenitors could naturally produce a large
variation of sub-solar 12C/13C ratios in He-shell layers, possibly even within
the same star. Indeed, depending on the timescale and strength of the
ingestion the C ratio may change significantly. In order to explore the
realistic range of C ratios to be expected from H ingestion in massive stars,
multi-dimensional hydrodynamics simulations are needed (e.g. Herwig et al.,
2014a; Woodward et al., 2015a; Clarkson & Herwig, 2021). In general, from our
models we find that the C-rich He shell in models with H-ingestion carries a
much lower C ratio compared to the models without H-ingestion, reaching values
much lower than solar. Therefore, these models appeared to be more suited to
explain presolar C-rich grains from CCSNe with low C ratios (Pignatari et al.,
2015).

The deepest layers of the He/C zone are strongly affected by explosive H
burning, and produce low 12C/13C and 14N/15N ratios that are consistent even
with the most extreme abundance signatures measured in putative SiC nova
grains (Pignatari et al., 2015; Liu et al., 2016; Hoppe et al., 2018), and
with some degree of local mixing with SiC-AB grains (Liu et al., 2017a; Hoppe
et al., 2019). The differences in the models compared to the upper He/C zone
is due to the partial activation of the hot CNO cycle (e.g., Wiescher et al.,
2010). Models with more remaining H in the deep He/C zone achieve lower
12C/13C and 14N/15N ratios in the CCSN ejecta due to radiogenic contributions
to 13C and 15N. For example, 25T-H has the most H remaining from ingestion and
develops the lowest 12C/13C and 14N/15N ratios of all the models, while
25T-H500 has no H deep in the He/C zone, so develops high 12C/13C and 14N/15N
ratios. The CCSN abundances in the C/Si zone develop 12C/13C and 14N/15N
ratios of about $10^{7}$ \- $10^{9}$ and 0.01 - $400$ respectively, so with
local mixing between the C/Si zone and the deep He/C zone, the 25T-H, 25T-H5,
and 25T-H20 models could potentially reproduce all SiC-X grains, including
those with 12C/13C ratios higher than solar (e.g. Hoppe et al., 2018).

In the bottom left Panel, despite the much lower SN energy, the 25av models
show a similar evolution of the C and N ratios in the CCSN ejecta compared to
the 25T set. The high 12C/13C region to the right of the plot represents the
C-rich region at the top of the O/C zone extending from 6.73 to 6.82M⊙. Mixing
this region with material in the He/C zone and the intermediate O-rich O/nova
zone may explain the large scatter of anomalous ratios measured in presolar
grains, still satisfying the constraint of a C-rich mixture. Since the 25av
explosions are less energetic than 25T, both less 14N and 15N are made at the
bottom of the He/C zone, but still showing similar N isotopic ratios overall.

In the bottom right Panel, at the bottom of the He/C zone (6.82M⊙), the models
25d-H5 and 25d-H20 show trends similar to their analogous models at higher
energies. However, the lowest C ratio reached by model 25d-H is 0.5, which is
not as extreme as the 25T-H and 25av-H models. The SN explosive conditions
combined with the lower H concentration allow 25d-H500 and 25d-H20 to provide
12C/13C and 14N/15N ratios consistent with 14N-rich SiC-AB grains in the deep
He/C zone around 6.82M⊙. Alternatively, Hoppe et al. (2019) suggested
adjustments of C and Al isotopic ratios in the 25T models in order to
simultaneously match C, N, and Al isotopic ratios of AB grains (both 15N-rich
and 15N-poor).

Figure 4: 14N/15N and 12C/13C isotopic ratios as predicted across the He/C
zone of four sets of models, compared with the measured data for individual
SiC grains (sub-types AB, nova, X, and C) and LD graphites. The top left Panel
shows the CCSN abundances for the 15d, 15r2, and 15r4 models, exploring
different SN energies. The top left Panel shows the 25T set that has a single
energy (energetically similar to 15d but has different initial conditions) and
explores the H left from ingestion. The bottom left and right Panels show the
25av and 25d sets respectively, which have same parameter space for H but have
different energies. The continuous vertical and horizontal black lines
indicate the solar ratios.

In Figure 5, the Si isotopic ratios for SiC grains (sub-types AB, nova, X, and
C) and LD graphites are shown with the CCSN abundances predicted from the four
model sets. In the top left Panel, the 15d and 15r2 models show a large 28Si-
excess in the C/Si zone as shown by low delta values for 29Si/28Si and
30Si/28Si. By assuming some mixing with more external stellar material
carrying a 28Si-deficit or a close-to-solar Si isotopic composition, these
models can qualitatively reproduce grains which show 28Si-excess such as
SiC-X, a relevant number of LD graphites, and a few nova grains (Pignatari et
al., 2013a). On the other hand, in the same region of the ejecta 15r4 does not
develop a C/Si zone and the 28Si-rich signature obtained in 15d and 15r2. In
the intermediate He/C zone of 15d, 15r2, and 15r4, there are strong 28Si-
deficits due to the production of both 29Si and 30Si by neutron capture (this
is the neutron-burst signature due to the strong activation of the n-process,
see e.g. Meyer et al., 2000; Pignatari et al., 2013b; Pignatari et al., 2018),
resulting in higher Si $\delta$-values (up to 18000 and 25000 for 30/28Si and
29/28Si respectively) than in the deeper He/C zone. In particular, the more
energetic models show a more efficient production of 30Si compared to 29Si.
This material may be consistent with the 28Si-deficit seen in SiC-C grains
that continue off the right of the plotted area, since mixing with material
with ratios close-to-solar will result in much less extreme ratios. In the
CCSN ejecta, Si isotopic ratios become less extreme in the outer He/C zone,
with solar ratios or mild 28Si-deficit due to the pre-explosive s-process
production in the He shell (e.g., Rauscher et al., 2002; Pignatari et al.,
2016; Sukhbold et al., 2016).

In the top right Panel of Figure 5, the 25T models also develop a 28Si-rich
C/Si zone. However, with the exception of 25T-H500, the 25T models predict
less extreme Si ratios in the He/C zone. Indeed, during the SN explosion
proton capture on 22Ne is in competition with $\alpha$-capture, reducing the
activity of the 22Ne($\alpha$,n)25Mg reaction and the strength of the
n-process (Pignatari et al., 2015; Liu et al., 2018b). Therefore, a lower
remaining abundance of H from ingestion (e.g. 25T-H500) allows the production
of larger 28Si-deficit. By comparing with the models in the top left Panel, a
novel CCSN nucleosynthesis signature in 25T-H and 25T-H5 is observed at the
bottom of the He/C zone. Combined mild positive $\delta$(30Si/28Si) and
negative $\delta$(29Si/28Si) are obtained, to a degree that is directly
compatible with measurements in putative nova grains. This is simply due to
the explosive H-burning active in that region, favouring the production of
30Si with respect to 29Si. The same feature is obtained in simulations for ONe
novae (e.g., Amari et al., 2001a; José et al., 2001; José & Hernanz, 2007a;
Denissenkov et al., 2014). In model 25T-H, just at the boundary between the
He/C zone and the O/Nova zone, a positive $\delta$(30Si/28Si) starts also to
be developed. The same signature in nova models can be reached for the most
massive ONe novae (see e.g., Amari et al., 2001a; José & Hernanz, 2007b).
However, due to the higher temperatures involved in the O/Nova zone together
with the high concentration of H, a much larger 28Si-deficit is achieved. We
defer a discussion of the details of O/nova zone nucleosynthesis to a future
work. Here we are instead interested in the specific differences obtained in
models 25T-H and 25T-H5. These models have the same explosion energy, but
different H concentration in the stellar progenitor. In Figure 6, we show a
more zoomed version of the top right Panel from Figure 5, showing also the
evolution of the ejected CCSN abundances in the O/Nova zone. In this region,
25T-H is evolving toward high positive $\delta$(29Si/28Si) and
$\delta$(30Si/28Si) up to 35000 and 60000 per mil respectively (outside the
plot boundary), while in the C/Si zone the ratios are returning to be
consistent with 15d, shown in the top left Panel of Figure 5. Model 25T-H5
shows instead a completely different trend. The negative $\delta$(29Si/28Si)
is maintained, while with the higher energies the negative $\delta$(30Si/28Si)
is eventually obtained, consistent with the SiC-X observed slope. The SN
explosion is clearly not the cause of the difference, since the two models
share the same SN prescription. The different trends between 25T-H and 25T-H5
is only due to the different combination of explosive H-burning and explosive
He-burning nucleosynthesis in the O/Nova zone, due to the different H
concentration. This result is interesting and deserves further study, since it
might provide future constraints for stellar models with H ingestion.

In the bottom left Panel of Figure 5, no C/Si zone is formed by explosive
nucleosynthesis due to their lower explosion energy. On the other hand, the
nucleosynthesis of Si isotopes in the He/C zone shows several similarities
compared to the 25T models with analogous H fuel. Also at these explosion
energies the different Si production triggered in 25av-H with respect to
25av-H5 is visible, confirming that the result mostly depend on the H
concentration.

In the bottom right Panel, the 25d models predict similar high Si
$\delta$-values in the He/C zone, with close to solar ratios in the
intermediate and upper mass region. Only 25d-H shows a negative
$\delta$(29Si/28Si) combined with the positive $\delta$(30Si/28Si) in the
deepest part of the He/C zone, as discussed in models 25T and 25av.

Figure 5: Si isotopic ratios in $\delta$-notation for SiC grains (sub-types
AB, nova, X, and C) and LD graphites are compared with the C-rich regions of
the models, where $\delta$(ratio) = (grain ratio/solar ratio - 1) $\times
1000$. Abundance ratios measured in grains and CCSN abundance profiles from
stellar models are shown in the four panels with the same symbols used in
Figure 4. Figure 6: Zoomed version of the top right Panel in Figure 5, Only
for models 25T-H (red line with circles) and 25T-H5 (blue line with
triangles), but showing the isotopic abundances for both C-rich CCSN ejecta
(continuous line) and the O-rich O/Nova zone (dashed line). Abundance ratios
measured in grains are shown with the same symbols used in Figure 4.

Figure 7 presents the 12C/13C and 26Al/27Al isotopic ratios for CCSN abundance
simulations and grains. Compared to Figure 4, the full range of 12C/13C ratio
obtained in the CCSN ejecta is shown. In the top left Panel, models with
different explosion energies but no H ingestion do not reach the 26Al
enrichment needed to reproduce the full range of grains observations, as
already discussed in Pignatari et al. (2013a) and Pignatari et al. (2015). The
comparison shown in the top right Panel has been already discussed by
Pignatari et al. (2015) and we report them here for completeness. In
particular, 12C/13C shows a variation up to 11 orders of magnitude, with the
highest ratios obtained in the C/Si zone on the right of the plot, to the
lowest sub-solar ratios obtained at the intersection between the O/Nova zone
and the He/C zone. The C-rich regions are plotted as solid lines whereas the
O/nova zone is plotted as dashed lines. Based on preliminary calculations, we
can anticipate that it is possible to reproduce the grains with highest
26Al/27Al ratios through mixing of the He/C, O/nova, and C/Si zones of models
25T-H and 25T-H5. This is obtained even with the model 25T-H10 (not shown in
the figure), considering mixtures of matter predominantly from the O/Nova zone
with small contributions of matter from the C-rich zones below and above
(Hoppe et al., 2022, submitted).

The bottom left Panel shows that the same high 26Al production during the CCSN
explosion noted in the top right Panel can also be obtained in models at lower
energy (25av), keeping the same H-ingestion parameterisation. In this case,
the H left at the CCSN shock passage is controlling the 26Al production. As
with 25T-H5 compared to the other 25T models, 25av-H5 is the model showing the
largest 26Al/27Al ratio in the O/Nova zone, over the full range of measured C
ratios. This is an interesting result. First, we would naively expect the 26Al
enrichment due to explosive H-burning to increase with the amount of H left in
the He shell. This is not the case for the 25T and the 25av stellar sets. Both
26Al and 27Al are made during the explosion in the O/Nova zone. Above a
certain H abundance, 27Al is produced more efficiently than 26Al and the
relative ratio decreases. In Pignatari et al. (2015), we have seen that model
25T-H10 (see Table 2) shows similar 26Al/27Al ratios in the O/Nova zone
compared to 25T-H. A maximum value of 26Al/27Al is reached with H left between
about 1% and 1 per mill. More models would be needed to identify what is the
amount of H yielding the largest 26Al/27Al ratio, that could be higher than
the abundances of 25T-H5. With the present models, the same conclusions can be
derived for the 25av set at lower SN energies. By taking into account the
measured scatter for C, N, Al and Si abundances in presolar grains (see also
Figures 4, 5 and 6), models 25T-H5 and 25av-H5 seem to provide the required
conditions to match the typical H-burning signatures identified, and higher H
concentrations do not help or make even worse the comparison with
observations.

Finally, in the bottom right Panel the CCSN abundances ejected from model 25d
cannot explain the highest 26Al/27Al ratios observed. The temperatures reached
in the He shell in these models during the SN shock passage are not high
enough to efficiently make 26Al. The pre-SN 26Al abundance made during the H
ingestion in our models is more than an order of magnitude too low compared to
the presolar grains measurements of 26Al-rich SiC-X and graphites. Beyond the
scope of this paper, it would be useful to produce in the future one or two
additional sets of CCSN simulations where the impact of the SN explosion
energy is explored between 25d and 25av settings (see § 2).

Figure 7: 26Al/27Al and 12C/13C isotopic ratios predicted by the CCSN models
and compared with SiC grains (sub-types AB, nova, X, and C) and LD graphites
are shown. For abundance ratios measured in grains and abundance profiles from
stellar simulations, symbols are used as in Figure 4 in the four panels.
Continuous lines represent the He/C and C/Si zones, while the dashed lines
indicate the O/nova zone between them.

Figure 8 shows the 44Ti/48Ti and $\delta$(30Si/28Si) isotopic ratios for
presolar grains and the four model sets. It is worth taking into consideration
here that 48Ti and 48Ca are indistinguishable when measuring isotopic
abundances in grains. However, 48Ca condenses much less efficiently into SiC
than 48Ti (Lodders & Fegley, 1995). The fractionation used for 48Ca/48Ti is
0.0001, i.e. only 1 Ca atom condenses for every 10000 Ti atoms. In the Figure,
therefore, the abundance of 48Ti also takes into account the contribution of
48Ca after fractionation. The same fractionation is applied for 44Ca and the
radioactive isotope 44Ti. As shown for 15d, 15r2, and 25T models in the top
Panels, 28Si-rich material coincides with high 44Ti in the C/Si zone as they
are both products of the explosive $\alpha$-capture chain (Pignatari et al.,
2013a). In the central layers of the C/Si zone these models achieve high
values of 44Ti/48Ti, above the plotted area: the maximum ratios obtained are
3.78 and 2.97 for 15d and 15r2 respectively, and 29.9, 26.2, 26.1, and 26.1
for 25T-H, 25T-H5, 25T-H20, and 25T-H500 respectively (beyond the plot range).
In particular for the 25T models, a large range of 44Ti/48Ti is obtained in
the C/Si zone, from no 44Ti to the high values mentioned above. As discussed
in Pignatari et al. (2013a), this variation of 44Ti production is a natural
outcome of the $\alpha$-capture chain of reactions triggered by the explosive
He-burning, where 44Ti is at the end of the production chain and requires high
temperatures and $\alpha$-capture efficiency to be made. The milder 44Ti/48Ti
ratios observed in some 28Si-deficient graphites grains and SiC-C grains can
be also reproduced in the top left Panel, but not in the top right. Instead,
15r4 (top left Panel), 25av (bottom left Panel), and 25d models (bottom right
Panel) are not energetic enough to form the C/Si zone with 28Si and 44Ti
during the CCSN explosion. All of the models shown develop extremely high
$\delta$(30Si/28Si) in the He/C as the curve continues far past the right edge
of the plot.

Figure 8: 44Ti/48Ti and 30Si/28Si isotopic ratios of SiC grains (sub-types AB,
nova, X, and C) and LD graphites are compared with CCSN model predictions
across the C-rich zones. For abundance ratios measured in grains and abundance
profiles from stellar models symbols are used as in Figure 4 in the four
panels. The $\delta$-notation is used for the Si ratio.

Figure 9 shows the 49Ti/48Ti and 46Ti/48Ti ratios for our models compared to
presolar grains. The isotope 49V is a radioactive parent of 49Ti, with a half-
life of 330 days. This means that some 49V remains when the grains are
condensing. Vanadium (in the form of VC0.88) and Ti (as TiC) are incorporated
in ideal solid solution into SiC at the same 50% condensation temperature
(Lodders & Fegley, 1995). Therefore, 49V can be expected to condense at a
similar rate to 49Ti in SiC grains and graphites, and we do not apply any
fractionation between V and Ti in Figure 9. Instead, the contributions from
the stable isobars 46Ca and 48Ca to 46Ti and 48Ti respectively, are taken into
account as in Figure 8. All of the CCSN stellar sets presented in Figure 9
show the capability to produce high 49Ti/48Ti ratios in the C-rich ejecta. In
the top left Panel, for the C/Si zone 15d and 15r2 make 49Ti mostly as 49V. An
additional 49Ti component is made in the He/C zone by neutron captures,
directly as 49Ti or as radiogenic contribution from the neutron-rich
radioactives 49Ca and 49Sc. Models in the top right Panel still have the
49V-rich component in the C/Si zone, but neutron captures in the He/C zone are
suppressed in the models with most H left. However, in 25T-H and 25T-H5 the
abundant pristine 48Ti is partially converted by direct proton captures to 49V
in the O/Nova zone and at the bottom of the He/C zone during the CCSN
explosion, generating also in these conditions a super-solar 49Ti/48Ti ratio
(48Ti and 49Ti are respectively 73.72% and 5.41% of the solar Ti). The 25av
models (bottom left Panel) and 25d models (bottom right Panel) also reproduce
the observed scatter measured in presolar grains. Therefore, depending on the
SN explosion energy and on the occurrence of H-ingestion, we can identify
three components yielding super-solar 49Ti/48Ti ratio: a 49V-rich one in the
C/Si zone due to explosive He burning, a (possibly) 49V-rich one in the O/Nova
zone (and in the deepest He/C zone layers) due to proton-captures and, if no
significant amount of H is present at the onset of the SN explosion, the 49Ti-
rich neutron-capture component in the He/C zone. The neutron-burst in the He/C
zone is suppressed in one-dimensional CCSNe models developing the O/Nova zone
(Pignatari et al., 2015). Therefore, if we do not consider the mild pre-SN
s-process signature in the He shell, the proton-capture and the neutron-
capture components discussed above could be alternative results of local
explosive nucleosynthesis. However, the multi-dimensional dynamic nature of H
ingestion could easily lead to asymmetries and local differences in the He
shell which could make the two components complementary products of the same
CCSN explosion. While there are several studies of H ingestion with multi-
dimensional hydrodynamics simulations for low-mass stars (Stancliffe et al.,
2011; Herwig et al., 2014b; Woodward et al., 2015b), at present the same
extensive studies are not available for massive stars to better constrain the
stellar progenitors (see e.g., Clarkson & Herwig, 2021). The present
limitations of one-dimensional models used in this work need to be taken into
account, and therefore we cannot derive strong constraints about the relative
relevance of these difference components at the moment. Based on the same
generation of models, Liu et al. (2018a) used the 49Ti signature to
distinguish between the contribution of the C/Si and the Si/S zones to
condense SiC-X grains. They argued that by invoking the Si/C zone as the main
source of 28Si, the 49Ti from the He/C zone would be the dominant contributor
to the 49Ti measured in grains, at odds with the data. Their analysis was
based on considering the Ti/Si ratio of the Si/C zone, which is orders of
magnitude lower than that of the He/C zone in CCSN models. Given what we have
said above and taking into account the uncertainties involved, we do not think
these conclusions can be driven yet just based on the Ti/Si ratio. In
particular, while the abundance of C in the Si/S region is negligible, the
abundances of both C and Si are higher by at least an order of magnitude in
the C/Si zone compared to the He/C zone. In the stellar progenitor the He/C
zone is only a partial He-burning region (the former convective He shell), and
at the onset of the collapse still a lot of He fuel is left: 4He is the most
abundant isotope in the He/C zone. The C/Si zone is located instead at the
bottom of the former He shell, where hydrostatic He-burning was almost
complete. This is the reason why C can be even an order of magnitude higher
than in the He/C zone. Additionally, in this region explosive He-burning is
destroying the pre-SN O to make Si and other elements, while C is not depleted
because the 12C($\alpha$,$\gamma$)16O rate is orders of magnitudes weaker than
the 16O($\alpha$,$\gamma$)20Ne reaction rate (Pignatari et al., 2013a).
Therefore, independently from the Ti/Si ratio, the high enrichment in both C
and Si is generating a qualitative expectation that ejecta from the C/Si zone
will have a much higher formation efficiency of SiC grains compared to the
He/C zone. Ti should then condense in these grains from consistent mixtures of
C-rich and Si-rich stellar material. More detailed predictions for Ti
chemistry in environments with different degrees of C and Si enrichment would
require complete network calculations with chemical reactions, that are beyond
the scope of this paper.

Figure 9: 49Ti/48Ti and 46Ti/48Ti isotopic ratios in $\delta$-notation of
individual SiC grains (sub-types AB, nova, X, and C) and LD grains compared
with abundance predictions of CCSN models. For abundance ratios measured in
grains and abundance profiles from stellar models symbols are used as in
Figure 4 in the four panels.

For the sake of completeness, in the Appendix Figures 12 and 13 provide the
isotopic ratios 47Ti/48Ti with respect to 46Ti/48Ti, and 50Ti/48Ti with
respect to 46Ti/48Ti for our models in comparison to presolar grains. No
additional constraints can be derived from these figures compared to what we
have already discussed. Nevertheless, as for Si isotopes and other Ti isotopes
discussed so far, a novel nucleosynthesis in the O/Nova zone compared to
massive star models without H ingestion can be also identified. We defer to a
future paper for the detailed analysis of the nucleosynthesis in the O/Nova
zone.

##  4 The abundance signatures of radioactive isotopes 26Al and 44Ti in
presolar grains

In this section we look further at the implications of the models predictions,
and for each grain type we consider the distributions of isotopic abundance
ratios for the radioactive isotopes 26Al and 44Ti.

Figure 10, top Panel, shows the 26Al/27Al and 12C/13C isotopic ratios
predicted by a selection of our CCSN models 15d, 25T-H5 and 25av-H5 and
compared with presolar grains. The distribution of isotopic ratios for each
grain type is shown and the respective median values are reported. Based on
the considerations made in the previous section, we used here for the analysis
25T-H5 and 25av-H5, and not the analogous CCSN models with the highest initial
H concentration. Note however that the results that we derive from the
discussion would not be much different. As we have seen in Figure 7, the
ejected abundance products from 25T-H5 and 25av-H5 have a sub-solar 12C/13C
ratio in the He/C zone above the O/Nova zone. In both of the two models, the
ratio is becoming super-solar moving inward within the O/Nova zone, and with a
depletion of both C isotopes by proton captures. At the bottom of the O/Nova
zone, both the C/Si zone in 25T-H5 and residual C-rich layers in 25av-H5 are
12C-rich. In the 15d model, both the C/Si zone and the He/C zone have a
12C/13C ratio higher than solar, while the upper part of the He/C zone and the
He/N zone are sub-solar (Pignatari et al., 2013a).

If now we check more carefully the abundance distributions in single presolar
grains, SiC-X grains appear to show two 26Al enrichment peaks, one distinct at
around 26Al/27Al $\approx$ 0.2 and potentially a second peak (less clear with
fewer data points) at 26Al/27Al $\approx$ 0.05. More data points would be
required to clarify whether these are indeed two distinct peaks or simply a
single distribution with a long tail toward low 26Al abundances. Based on
Pignatari et al. (2015) and results presented in § 3, the first peak may be
the signature of late H-ingestion and SN explosions at higher energy (25T or
25av). The potential second peak could be explained from mixing of the He/C
and He/N zones (15d reaches these values), or H-ingestion in low-energy CCSNe
(e.g. 25d, see Figure 7). This should be confirmed by future works, where
mixing models are applied to reproduce the composition of single presolar
grains. The first peak is much stronger, which would be consistent with the
scenario where most of SiC-X are forming in high-energy explosions (Pignatari
et al., 2013a). We cannot derive a direct constraint on the frequency of
H-ingestion in CCSNe. This is because most of the observed CCSN dust could
have originated from a single CCSN immediately before the formation of the
Solar System, with late H-ingestion and asymmetric ejecta. The distribution of
26Al/27Al measured in LD graphites is quite different to that of SiC-X grains,
despite the overall similar range of ratios found. This may appear to be quite
surprising, considering that the two types of grains are formed in the same
parts of the CCSN ejecta. There is a higher peak at 26Al/27Al $\approx$ 0.06
and a shallow broad peak at $\approx$ 0.01. Like for SiC-X grains, it is still
unclear if this second peak really exists. However, the distribution of
26Al/27Al ratios appear to be shifted toward higher values for SiC-X compared
to LD graphites. This could be explained assuming that LD graphites condensed
efficiently in CCSN ejecta exposed to a broader range of nucleosynthesis
conditions compared to SiC-X grains, including less extreme temperature and
density peaks during the SN explosion (e.g., Pignatari et al., 2018). On the
other hand, as Travaglio et al. (1999) pointed out we cannot exclude that the
26Al/27Al measured today in graphites was affected by loss of radiogenic 26Mg,
which would also explain these lower ratios. SiC-AB grains show a broad
distribution with a peak at 0.003. Since different types of stellar sources
are contributing to these grains (Amari et al., 2001b; Liu et al., 2017a, b;
Hoppe et al., 2019), we cannot derive clear constraints applying specifically
to CCSNe from the overall distribution shown. Possibly because of the low
number of data, the 26Al/27Al in putative Nova grains is scattered over two
orders of magnitudes, partially overlapping with the SiC AB grains, and with a
median value of 0.062 that is consistent with the LD graphites higher peak.

In the top Panel, we also report the abundance distribution with the position
of the median line for the measured 12C/13C ratios. Interestingly, as we have
seen for Al isotopes, we find again that the C distribution for SiC-X and LD
graphites is different, with the median at 172 (higher than solar) and 79
(lower than solar) respectively. This is an intrinsic difference of the two
populations of grains, and it is clearly not due to a different solar
contamination or loss of radiogenic material as it could be for 26Mg. In the
figure, we report 106 SiC-X grains with 22% of 12C/13C ratios less than solar
and 78% 12C/13C greater than solar, and 173 LD graphites with 52% of 12C/13C
ratios less than solar and 48% 12C/13C greater than solar. In the classic
scenario where 28Si is formed in the Si/S zone, there is no explanation of
these differences, since the Si/S zone is C-poor (and Al-poor) and would not
affect the C-ratio. Additionally, if we assume that both 13C and 26Al found in
grains are a product of explosive H-burning or of the He/N zone, because the
12C/13C median of LD graphites is lower than in SiC-X data we would also
expect the 26Al/27Al median to be higher. This is not the case. On the other
hand, this appears to be further confirmation of the C/Si zone as the origin
of 28Si in these grains. Compared to LD graphites, a larger fraction of SiC-X
are 28Si-rich and 12C-rich like the C/Si zone. This could qualitatively
explain why a larger fraction of SiC-X grains have 12C/13C larger than solar,
independently from the nucleosynthesis source of 13C and 26Al. The SiC-X
grains preferentially form in high-energy CCSNe or in high energy components
of asymmetric CCSNe ejecta where the C/Si zone is created during the
explosion. On the other hand, LD graphites are formed in a larger range of
conditions, in ejecta with and without the 28Si-rich and 12C-rich C/Si zone.
Finally, SiC nova grains and SiC-AB grains show consistent 12C/13C
distributions, with medians equal to 5.1 and 4.4, respectively.

Figure 10: Top Panel: 26Al/27Al and 12C/13C isotopic ratios predicted from
15d, 25T-H5 and 25av-H5 are compared with SiC grains (178 sub-types AB, 15
nova, and 106 X) and 173 LD graphites. The presolar grains data are available
from (Hynes & Gyngard, 2009; Stephan et al., 2020). As a reference, we also
show the data for 185 SiC mainstream grains (labelled as M), which are the
most abundant type of SiC presolar grains and they are made in Asymptotic
Giant Branch stars (Zinner, 2014, and references therein). The median
26Al/27Al ratios are 0.1740, 0.0028, 0.0620 and 0.0006 for SiC-X, AB, Nova and
Mainstream, respectively. The median value for LD graphites is 0.0184.
Continuous lines on the main plot represent the He/C and C/Si zones, while the
dashed lines indicate the O/nova zone between them. The histograms on the axes
show the distribution of each grain type in their respective isotopic ratio,
with a solid opaque line indicating the median ratio. Bottom Panel: the same
as in the top panel, but for 26Al/27Al and 14N/15N isotopic ratios. Both solar
and terrestrial N ratios are shown, as in Figure 4.

In figure 10, bottom Panel, we show the 26Al/27Al and 14N/15N isotopic ratios
from the CCSN abundances predicted in 15d, 25T-H5 and 25av-H5 and we compare
them with SiC grains. Models 25T-H5 and 25av-H5 show the same abundances in
the external part of the He/C zone, with an 26Al/27Al of the order of 0.05,
generated from the H-ingestion event, and a 14N/15N ratio higher than solar,
but quickly decreasing with moving deeper in the He/C zone. At the bottom of
the He/C zone a sudden rise of the 26Al/27Al up to about a value of 0.3 is
also seen for both the two models. We can clearly see that in these regions
nucleosynthesis patterns are shaped by nuclear reactions, which are the same
in the two models. The 26Al/27Al ratio rises up to 2-3 in the O/Nova zones of
both 25T-H5 and 25av-H5. However, the N isotopic ratio decreases in 25T-H5 and
increases in 25av-H5. For the presolar grains analysis of the N abundances the
bottom of the O/Nova zone and the C/Si zones are not relevant, since they are
both N-poor. The model 15d shows higher ratios in the external He/C zone
compared to the two models with H-ingestion, reaching a maximum 26Al/27Al
value of 0.2 but with much lower N abundances (Pignatari et al., 2015). In the
He/C zone and in the C/Si zone 26Al is not made efficiently by explosive
nucleosynthesis. The explosive production of 15N allows the reduction of the N
isotopic ratio, but its production is too weak compared to observations
(Bojazi & Meyer, 2014), and the whole N abundances in the deepest C-rich
ejecta shown in the figure would not be relevant once some small degree of
mixing is allowed for ejected stellar material.

We have already discussed in the top Panel the 26Al/27Al distribution in
presolar grains. The 14N/15N for LD graphites is not indicative of the
original composition because of terrestrial contamination. Where contamination
from terrestrial material did not completely erase the N signature, the LD
graphites carry a low N ratio, particularly for high 26Al/27Al ratios. The
original 15N-rich signature was likely very high in these grains. Concerning
the different types of SiC grains shown in the figure, there is a general
trend (due to nuclear astrophysical reasons) of correlated 15N and 26Al
abundances across the whole grain population, but within a large grain-to-
grain scatter. Putative nova grains again behave like a 15N-rich tail of the
SiC-AB grain spread (14N/15N medians of SiC Nova and SiC-AB grains are 31 and
252, respectively). The population of SiC-X grains carry a higher 26Al
compared to other grains with the same N ratio. The sub-solar 14N/15N ratios
show a scatter of a factor of 20, with a median of 66 that is in between SiC
Nova and SiC-AB grains.

Figure 11 shows the 26Al/27Al and 44Ti/48Ti isotopic ratios from the final
CCSN abundances in 15d, 25T-H5 and 25av-H5 and compared with SiC-X and LD
graphites. Only a limited number of grains have been measured for both 26Mg
(26Al) and 44Ca (44Ti): 15 SiC-X and 11 LD graphites. A particular problem for
Ca isotope measurements is contamination of the grains with terrestrial Ca,
such that existing 44Ca excesses may remain hidden (Besmehn & Hoppe, 2003).
This may explain that from the 138 X grains measured for Ca, only 38 showed
resolvable excesses in 44Ca, although it should be noted that Ca contamination
has no effect on inferred 44Ti/48Ti ratios. Because of the low statistics
available, we cannot derive any significant conclusions from the abundance
distribution in the histogram aspect of this figure. It is interesting to note
that for SiC-X grains the 26Al/27Al medians between this sample and the
extended sample from Figure 10 are consistent within 12%. For LD graphites,
the 11 grains here have a median that is a factor of 3.7 higher compared to
the extended sample in Figure 10. However, we cannot yet conclude that 44Ti-
rich LD graphites tend to be also 26Al-rich based on 11 grains only. More
grains with both 44Ti and 26Al measurements would be needed.

Concerning the abundance curves from CCSN models shown in Figure 11, the C/Si
zone in 15d and 25T-H5 provides the 44Ti, with 44Ti/48Ti ratios larger than
0.001 (see e.g., Pignatari et al., 2013a). The C/Si zone does not make 26Al.
Instead, in the figure this radioactive isotope is provided by the O/nova zone
(in 25T-H5 and 25av-H5) and at the bottom of the He/C zone (the region around
44Ti/48Ti $\lesssim$ 0.0001). We may anticipate here that a local mixing of
these regions would result in a large degree of 26Al and 44Ti enrichment. In
the future, extensive comparisons between mixing models from CCSN models with
H ingestion and single presolar grains carrying both 44Ti- and 26Al-enrichment
are needed. Previously, Xu et al. (2015) used the models 15r (really similar
to the model 15d presented here) and 15r4 (presented in this work) to
reproduce a sample of single SiC X grains including both 26Al and 44Ti.
However, both these models are without H ingestion. In Hoppe et al. (2018),
for the first time 44Ti was explored for two SiC-X grains and a SiC-C grain in
the context of the 25T H-ingestion SN models presented here. From that study,
it was shown that predictions for 44Ti are too high when C-, N-, and Si-
isotopic compositions and 26Al/27Al ratios are well fitted. The possible
sources of such a discrepancy were considered, among others the extension and
detailed abundance profiles of the C/Si zone. Interestingly, in the high
energy CCSN model 25T-H5 we also see a 44Ti production in the O/nova region,
with 44Ti/48Ti increasing up to about 0.2 with decreasing mass coordinate. The
absolute abundance of 44Ti in this region is about three orders of magnitudes
lower than in the C/Si zone, reaching a maximum abundance in the order of 10-6
in mass fraction. The nucleosynthesis in the deepest layers of the O/Nova zone
is given by the combination of proton captures and $\alpha$-captures, that
start to become relevant at these conditions. Some 44Ti is made and at the
same time the initial 48Ti is depleted by a factor of 2-3, which explains the
rise of the 44Ti/48Ti ratio.

Figure 11: 26Al/27Al and 44Ti/48Ti isotopic ratios predicted from the CCSN
models 15d, 25T-H5 and 25av-H5 are compared with 15 SiC-X grains and 11 LD
graphites. The median 26Al/27Al ratios are 0.16 and 0.07, respectively.
Continuous lines on the main plot represent the He/C zone (squeezed at
44Ti/48Ti $\lesssim$ 10-4) and the C/Si zone, while the dashed lines indicate
the O/nova zone between them. The histogram on the 26Al/27Al axis shows the
distribution of each grain type, with a solid opaque line indicating the mean
ratio. Also a histogram of 44Ti/48Ti ratios is shown.

##  5 Conclusions

This work has compared the isotopic abundances of presolar SiC grains and
graphites from CCSNe with the predictions of four sets of one-dimensional CCSN
models with a range of energies, both with and without H-ingestion: 15d, 25T,
25av and 25d. Compared to previous works, we are including in our analysis six
additional CCSN models with H ingestion (set 25av), and intermediate explosion
energies between the 25T and 25d stellar sets (Pignatari et al., 2015). The
primary aim of this work is to study the impact of differing energies and
remaining H ($0.0024\%\leq X_{H}\leq 1.2\%$) in H-ingestion models as well as
comparing the predictions of models with and without H-ingestion but with the
same range of explosion energies. The isotopic ratios focused on were C, N,
Al, Si, and Ti of LD graphites and SiC grains of Type X, AB, C and nova, which
have potentially condensed from CCSN ejecta. In particular, we discuss the
production of the radioactive isotopes 26Al and 44Ti.

The 15d, 15r2, and 25T models develop a C/Si zone, ranging in explosion energy
between 1-$5\times 10^{51}$erg and with a temperature at the bottom of the
C-rich region between $2.2\times 10^{9}$K (15r2) and $2.3\times 10^{9}$K (25T;
Pignatari et al., 2015). These models are able to reproduce the 28Si- and
44Ti-excesses of SiC-X grains and LD graphites, consistently with the
nucleosynthesis signatures of Si and Ti isotopes measured. The most H-rich
25av models still develop an O/Nova zone, but the C-rich layers ejected at the
bottom of the region are not forming a fully built C/Si zone: the peak
temperature of $1.5\times 10^{9}$K was not high enough to efficiently convert
16O into 28Si. However, we do see the destruction of 16O here as well as a
small signatures for 20Ne and 24Mg production. The nucleosynthesis signatures
calculated in the O/Nova zone shows remarkable similarities in the 25T and
25av sets, showing that in principle it is possible to disentangle the impact
of the amount of H present in the He shell at the CCSN onset from the impact
of the CCSN explosion energy. The main reason is that by increasing the
explosion energy the O/Nova zone is extending more outward in the former
convective He shell, mitigating the effect of the higher temperatures
generated. For both the two CCSN sets 25T and 25av, we find that the models
with initial $X_{H}\approx 0.0024$ (25T-H5 and 25av-H5) are producing the
highest 26Al/27Al ratios, reproducing the most extreme 26Al enrichment
measured in grains. In particular, the 26Al/27Al ratio is not increasing
linearly with the increasing of the initial H, independently from the
explosion energy. We show that both the two sets of models develop Si isotopic
ratios at the bottom of the He/C zone that are consistent with SiC-Nova
grains, together with the C and N ratios (models 25T-H, 25T-H5 and 25T-H10,
25av-H, 25av-H5 and 25av-H10). On the other hand, the nucleosynthesis of Si
isotopes in the O/Nova zone is quite different between 25T-H (25av-H) and
25T-H5 (25av-H5), with the highest H abundances driving an efficient
production of both 29Si and 30Si. We discuss some of the relevant similarities
between the nucleosynthesis obtained in the O/Nova environment compared to ONe
Novae (e.g., Amari et al., 2001a).

Finally, we discussed the abundance distribution in presolar grains, looking
in particular at C and N isotopic ratios, 26Al and 44Ti. Two distinct
populations can be possibly identified for both SiC-X grains and LD graphites,
an 26Al-rich one and an 26Al-poor. However, the 26Al-poor component is less
clearly defined, and more statistics is needed. in order to draw meaningful
conclusions. The C abundance distribution instead show relevant differences
between SiC-X grains and LD graphites. Combined with the Al signature, we
discuss and found these distributions consistent with the scenario where the
28Si-rich contribution would come from the 12C-rich C/Si zone. On the other
hand, the same explanation would not apply if the 28Si-rich contribution would
come from the 12C-poor Si/S zone. Unfortunately, there is only a limited
number of grains with both 26Al and 44Ti measured. More data would be required
to derive trends between 26Al and 44Ti enrichments.

In future works, we plan to study in detail the nucleosynthesis in the O/Nova
zone for the models discussed here. We identify significant differences in the
production of Si and Ti isotopes by reducing from initial H concentrations in
the order of 1% (models 25T-H and 25av-H) to few per mill (models 25T-H5 and
25av-H5). While the production path of the radioactive isotope 26Al is
similar, the resulting 26Al/27Al ratio does not behave linearly with the
initial abundance of H explored. Additionally, these models need to be further
tested by comparing their predictions with elements and isotopic ratios on a
grain by grain basis, where the qualitative consistency of the abundance
signatures described in this work need to be quantitatively compared within
mixtures of CCSN layers to match the measured data (e.g., Travaglio et al.,
1999; Xu et al., 2015; Liu et al., 2016, 2017a, 2018b; Hoppe et al., 2018,
2019, 2021). This would act as further diagnosis of these models and allow the
continued improvement upon them where grain signatures are not reproduced. The
network of nuclear reactions used for our stellar calculations is becoming
more reliable at the temperatures range relevant for explosive He-burning (see
however, e.g., Bojazi & Meyer, 2014; Pignatari et al., 2013c). The CCSN
explosion energy as a single parameter to explore from the different
nucleosynthesis patterns is relatively easy to handle by specific nuclear
astrophysics studies. However, as we stressed in Pignatari et al. (2015) and
other more recent works the outcome of H ingestion events in one-dimensional
models should be taken only as a qualitative guidance in specific comparisons
with single presolar grains. While proton-capture rates are typically well
known at temperatures in the order of 2-3$\times$108 K, multi-dimensional
hydrodynamics models are needed to define the evolution of the structure of
He-burning layers, the local nucleosynthesis driven during the H ingestion and
eventually the amount of H left in the He-burning ashes. To this end, presolar
grains represent the most powerful observational diagnostic available to study
these events in massive star progenitors of past CCSNe.

##  6 Acknowledgements

We acknowledge significant support to NuGrid from STFC (through the University
of Hull’s Consolidated Grant ST/R000840/1), and access to viper, the
University of Hull High Performance Computing Facility. Thanks from JS go to
the support provided by the University of Hull Internal Internship Programme.
MP thanks the following for their support: the National Science Foundation
(NSF, USA) under grant No. PHY-1430152 (JINA Center for the Evolution of the
Elements), the "Lendulet-2014" Program of the Hungarian Academy of Sciences
(Hungary), the ERC Consolidator Grant (Hungary) funding scheme (Project
RADIOSTAR, G.A. n. 724560), the ChETEC COST Action (CA16117), supported by the
European Cooperation in Science and Technology, the US IReNA Accelnet network
(Grant No. OISE-1927130), and the European Union’s Horizon 2020 research and
innovation programme (ChETEC-INFRA – Project no. 101008324).

##  7 Data Availability

The stellar data used for this article will be shared on reasonable request to
the corresponding author. Stellar data files are in hdf5 format, and tools to
load and use the data are available on the public NuGrid github repository
(https://github.com/NuGrid/NuGridPy). Presolar grains data are publicly
available at the open source Presolar Grain Database
(https://presolar.physics.wustl.edu/presolar-grain-database/).

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##  Appendix A Additional Figures: $\delta$(47Ti/48Ti) and $\delta$(50Ti/48Ti)

Figure 12: 47Ti/48Ti and 46Ti/48Ti isotopic ratios in $\delta$-notation of
individual SiC grains (sub-types AB, nova, X, and C) and LD grains compared
with predictions of models across the He/C zone. The C/Si zone of the 15d and
25T sets continue off the plots to the upper right of the region shown. For
abundance ratios measured in grains and abundance profiles from stellar models
symbols are used as in Figure 4 in the four panels. Strong abundance
variations are seen in the C/Si zone and the He/C zone, ejecting material with
depletion of 47Ti with respect to 48Ti in some regions of the C/Si zone, or
with strong production of 47Ti in the He/C zone. Figure 13: 50Ti/48Ti and
46Ti/48Ti isotopic ratios in $\delta$-notation shown for individual SiC grains
(sub-types AB, nova, X, and C) and LD grains compared with predictions of
models. For abundance ratios measured in grains and abundance profiles from
stellar models symbols are used as in Figure 4 in the four panels. As we have
seen for 49Ti in Figure 9, high 50Ti/48Ti is made by three main channels: in
the C/Si zone, 50Ti stable isobars 50V and 50Cr are mostly made (but they
cannot be distinguished from 50Ti in presolar grain measurements); in the
O/Nova zone, as 50V from proton capture on 49Ti or as 50Cr from the proton-
capture chain 48Ti(p,$\gamma$)49V(p,$\gamma$)50Cr; by neutron captures in the
He/C zone, and 50Ti is mostly ejected as itself. In the figure no
fractionation is applied when adding the 50Ti, 50V and 50Cr signatures. The
highly abundant initial 50Cr is boosting the $\delta$(50Ti/48Ti) to almost
4000 per mil even in the more external layers of the He/C zone, shown in the
figure with normal 46Ti/48Ti ratios.