# Nucleosynthesis of binary-stripped stars.

R. Farmer<EMAIL_ADDRESS>Max-Planck-Institut für Astrophysik,
Karl-Schwarzschild-Straße 1, 85741 Garching, Germany  E. Laplace Heidelberger
Institut für Theoretische Studien, Schloss-Wolfsbrunnenweg 35, 69118
Heidelberg, Germany  Anton Pannekoek Institute for Astronomy and GRAPPA,
University of Amsterdam, NL-1090 GE Amsterdam, The Netherlands  Jing-ze Ma
Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Straße 1, 85741
Garching, Germany  S. E. de Mink Max-Planck-Institut für Astrophysik, Karl-
Schwarzschild-Straße 1, 85741 Garching, Germany  Anton Pannekoek Institute for
Astronomy and GRAPPA, University of Amsterdam, NL-1090 GE Amsterdam, The
Netherlands  S. Justham School of Astronomy & Space Science, University of the
Chinese Academy of Sciences, Beijing 100012, China  National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100012, China  Anton
Pannekoek Institute for Astronomy and GRAPPA, University of Amsterdam, NL-1090
GE Amsterdam, The Netherlands  Max-Planck-Institut für Astrophysik, Karl-
Schwarzschild-Straße 1, 85741 Garching, Germany

###### Abstract

The cosmic origin of the elements, the fundamental chemical building blocks of
the Universe, is still uncertain. Binary interactions play a key role in the
evolution of many massive stars, yet their impact on chemical yields is poorly
understood. Using the MESA stellar evolution code we predict the chemical
yields ejected in wind mass loss and the supernovae of single and binary-
stripped stars. We do this with a large 162 isotope nuclear network at solar-
metallicity. We find that binary-stripped stars are more effective producers
of the elements than single stars, due to their increased mass loss and an
increased chance to eject their envelopes during a supernova. This increased
production by binaries varies across the periodic table, with $\mathrm{F}$ and
$\mathrm{K}$ being more significantly produced by binary-stripped stars than
single stars. We find that the $\mathrm{{}^{12}C}$/$\mathrm{{}^{13}C}$ could
be used as an indicator of the conservativeness of mass transfer, as
$\mathrm{{}^{13}C}$ is preferentially ejected during mass transfer while
$\mathrm{{}^{12}C}$ is preferentially ejected during wind mass loss. We
identify a number of gamma-ray emitting radioactive isotopes that may be used
to help constrain progenitor and explosion models of core-collapse supernovae
with next-generation gamma-ray detectors. For single stars we find
$\mathrm{{}^{44}V}$ and $\mathrm{{}^{52}Mn}$ are strong probes of the
explosion model, while for binary-stripped stars it is $\mathrm{{}^{48}Cr}$.
Our findings highlight that binary-stripped stars are not equivalent to two
single stars and that detailed stellar modelling is needed to predict their
final nucleosynthetic yields.

††software:  mesaPlot (Farmer, 2018), mesaSDK (Townsend, 2019),
ipython/jupyter (Pérez & Granger, 2007; Kluyver et al., 2016), matplotlib
(Hunter, 2007), NumPy (van der Walt et al., 2011), Parallel (Tange, 2021),
VICE (Johnson & Weinberg, 2020; Johnson et al., 2021; Griffith et al., 2021),
MESA(Paxton et al., 2011, 2013, 2015, 2018, 2019; Jermyn et al., 2022), pyMesa
(Farmer & Bauer, 2018), and Webplotdigitizer (Rohatgi, 2022).

##  1 Introduction

The origin of the elements is an unsolved problem (Arnould & Takahashi, 1999;
José & Iliadis, 2011; Diehl et al., 2022). Massive stars play a role in the
formation of the elements through their ejection of processed material in
their winds (Kudritzki & Puls, 2000; Vink et al., 2001; Crowther, 2007; Smith,
2014) and the ejecta from core-collapse (CC) supernovae (Maeder, 1992;
Rauscher et al., 2002; Heger et al., 2003).

Most massive stars have been found to be born with at least one companion
(Abt, 1983; Mason et al., 2009), and the majority are expected to undergo at
least one phase of mass transfer (Sana et al., 2012; Moe & Di Stefano, 2017).
During mass transfer the majority of the hydrogen-rich envelope of the star
(Kippenhahn & Weigert, 1967; Yoon et al., 2010; Götberg et al., 2017) may be
removed and some fraction of it accreted onto its companion. This mass
transfer alters both stars’ subsequent evolution (Podsiadlowski et al., 1992;
Brown et al., 1996; Wellstein & Langer, 1999; Eldridge et al., 2008; Langer,
2012; de Mink et al., 2013) and final chemical element production (Braun &
Langer, 1995a; Laplace et al., 2021; Farmer et al., 2021). Binarity has also
been used to explain the composition of carbon and s-element enhanced metal-
poor (CEMP-s) stars, by requiring efficient wind mass transfer in the system
(Abate et al., 2015).

Explosive nucleosynthesis, during core-collapse (CC) supernova (SN), in
massive stars has been well studied for single star objects (Woosley et al.,
1993; Heger et al., 2001; Heger & Woosley, 2002; Heger et al., 2002; Chieffi &
Limongi, 2004; Woosley & Heger, 2007; Pignatari et al., 2016; Limongi &
Chieffi, 2018) but has been less well studied for binary progenitors (Braun &
Langer 1995b; Brinkman et al. 2019, 2021; see, however, Izzard 2004; Izzard et
al. 2006) The primary uncertainty in the nucleosynethic yields of CC
supernovae is whether the star explodes and forms a neutron star (NS),
ejecting its envelope, or collapses into a black hole (BH), where the envelope
accretes onto the BH. The boundary between these fates is uncertain (Heger et
al., 2003; Ertl et al., 2016; Boccioli et al., 2022), with binary interactions
adding additional complexity (Timmes et al., 1996; Brown et al., 2001;
Podsiadlowski et al., 2004).

Chemical enrichment of galaxies provides a direct test of both the formation
of stars and their evolution (Tinsley, 1980; Pagel & Tautvaisiene, 1997),
though these have also still mostly relied upon single-star models (Nomoto et
al. 2013; Kobayashi et al. 2020; see however De Donder & Vanbeveren 2004).
Wide-field Spectroscopic surveys (such as APOGEE Majewski et al. 2017),
combined with Gaia (Gaia Collaboration et al., 2021, 2022) are revealing the
chemical composition and evolution of the Milky Way (Perryman et al., 2001;
Lian et al., 2022).

Massive stars are not the only source of chemical enrichment in the Universe
(Burbidge et al., 1957). Other sources include the Big Bang (Peebles, 1966;
Wagoner et al., 1967), asymptotic giant branch (AGB) stars (van den Hoek &
Groenewegen, 1997; Herwig, 2005; Karakas, 2010), type Ia SNe (Woosley &
Weaver, 1994; Nomoto et al., 1997; Iwamoto et al., 1999; Eitner et al., 2022),
and double neutron star mergers (Freiburghaus et al., 1999; Arnould et al.,
2007; Kasen et al., 2017; Pian et al., 2017; Tanvir et al., 2017). Each source
leaves a different chemical fingerprint on the composition of the Universe.
Each source also contributes different elements and at different times (Carigi
et al., 2005; Cescutti et al., 2009). For instance, massive stars evolve
rapidly and can enrich the Universe in a few million years after star
formation occurs (Franchini et al., 2020). While AGB (Nissen et al., 2014), SN
Ia (Leung & Nomoto, 2020), and double neutron star mergers (Dominik et al.,
2012, 2013) take much longer to enrich the Universe, due to the slower
evolution of their progenitor stars and/or long gravitational-wave inspiral
times before merger.

In Section 2 we discuss our evolution of single and binary stars, and the
properties of our explosion models. In Section 3 we discuss the total chemical
yields from different mass-loss processes, while Section 4 breaks down the
pre-supernovae yields and section 5 discuss the post-supernovae yields.
Section 6 discusses several caveats with our results. Finally we discuss and
conclude our results in Sections 7 and 8.

##  2 Method

This work builds upon the work in Farmer et al. (2021), which explored the
chemical yields of $\mathrm{{}^{12}C}$, to extend the discussion to a larger
set of isotopes (162) up to $\mathrm{{}^{64}Zn}$. We evolve a grid of single
stars and binary-stripped stars using the MESA stellar evolution code (version
12115, Paxton et al., 2011, 2013, 2015, 2018, 2019; Jermyn et al., 2022).
These stars are evolved from the zero-age main sequence to core collapse and
then through their supernovae until shock breakout. Our single stars and the
primary (initially most massive star) in the binary have initial masses
between $\rm{M_{init}}=11$ – $45\,\rm{M}_{\odot}{}$. For binary stars we set
the initial period to be between 38–300 days and we use a mass ratio of
$\rm{M_{2}/M_{1}}=0.8$ to set each secondary star’s mass. The orbital period
chosen for each system ensures that all the binary stars undergo case B mass
transfer (Paczyński, 1967; van den Heuvel, 1969). We follow the mass transfer
from the primary star in the binary onto the companion assuming fully
conservative mass transfer during Roche-lobe overflow (RLOF).

All models are computed with an initial solar metallicity of Z=0.0142 and are
non-rotating. The single stars and binary stars are evolved with an initial
Y=0.2684 ($\rm{Y=2Z+0.24,}$ Pols et al., 1995a; Tout et al., 1996). All stars
are set to have the same initial composition profile, and is based on the
solar composition of Grevesse & Sauval (1998). Additional physics options are
specified in Appendix A. Four models did not reach core collapse and are
excluded from this analysis, these are the binary-stripped star models with
initial masses of 24, 25, 28, and 29$\,\rm{M}_{\odot}$.

Inlists with all input parameters, data tables, and auxiliary data are made
available online at https://doi.org/10.5281/zenodo.5929870. A sample of the
data available is shown in Appendix B. While we have selected theoretically
and observationally motivated assumptions for our input physics, we have not
performed a systematic calibration of our models as we are interested in the
relative differences between the chemical yields of binary-stripped and single
stars.

To simplify our models we evolve the primary star in a binary system with a
point-mass companion until the end of core helium burning. At this point we
remove the companion and continue the evolution of the binary until core
collapse, assuming these systems will not interact again (Laplace et al.,
2020). Assuming that the Roche-lobe radius does not decrease after core helium
burning and comparing that with the maximum radial extent of our binary stars
post core helium burning, we find that this is a good approximation except for
the $\rm{M_{init}}=22$ and $27\,\rm{M}_{\odot}$ models which would exceed
their Roche-lobe radii (measured at core helium depletion), and the
$\rm{M_{init}}=23\,\rm{M}_{\odot}$ which reaches 80% of its Roche-lobe radius
(measured at core helium depletion). For all other binary-stripped stars the
maximum radius is $<10\%$ of their Roche-lobe radii (measured at core helium
depletion). Whether these stars would interact again, depends on detailed
modelling of the accretor, as any mass it loses via winds would widen the
orbit preventing further mass transfer phases.

Our choice of physics and and modelling assumptions were described in Farmer
et al. (2021) and builds upon the work presented in Laplace et al. (2020,
2021). We update our choice of convective overshoot in “metal” burning regions
(regions burning elements heavier than helium) to an exponential profile
(instead of a step overshoot profile). For that overshooting we assume a value
of $f=0.03$ and $f_{0}=0.001$ above the metal burning regions and $f=0.003$
and $f_{0}=0.0001$ below the metal burning regions (Jones et al., 2017), where
$f$ is the extent of the overshoot region in pressure scale heights and
$f_{0}$ is the point inside the convection zone where the strength of
convective overshoot begins exponentially decaying (in pressure scale
heights). For the other overshoot regions we assume a step overshoot profile
with $f=0.385$ and $f_{0}=0.05$ (Brott et al., 2011). We use the wind
prescriptions of de Jager et al. (1988); Nugis & Lamers (2000); Vink et al.
(2001) (“Dutch”), with a wind efficiency of 1.0. We include semiconvective
mixing with a $\alpha_{\rm{semi}}=1.0$ and do not include thermohaline mixing
(Farmer et al., 2016). We also include MLT++ to improve the numerical
stability of the hydrogen envelopes (Paxton et al., 2013).

The larger nuclear network we adopt, compared to Farmer et al. (2021), is not
only necessary for our yield predictions but is also important to capture
important physics associated with the evolution up to core collapse (Farmer et
al., 2016). We use a 162 isotope nuclear network which contains MESA’s
mesa_161.net111This network misses several stable isotopes, namely
$\mathrm{{}^{65}Cu}$, $\mathrm{{}^{66-68}Zn}$, and $\mathrm{{}^{70}Zn}$.
network plus $\mathrm{{}^{47}Ca}$, for all evolutionary stages including the
supernova phase. This network was chosen as a balance between larger networks
(to capture more physics) and being computationally feasible. The addition of
$\mathrm{{}^{47}Ca}$ was so that we could cover all isotopes that were found
to be of interest for next generation gamma-ray observatories (Timmes et al.,
2019; Andrews et al., 2020).

We define the helium core mass of the star as where the helium mass fraction,
$\rm{X_{He}}>0.1$ and the hydrogen mass fraction (at the same mass coordinate)
is $\rm{X_{H}}<0.01$. Finally, we define core collapse to occur when the inner
regions of the star infall at $300{\mathrm{km\ s^{-1}}}$.

We define the yield of an isotope as (Karakas & Lugaro, 2016):

$\rm{Yield}=\sum_{T}\Delta M_{T}\times\left(X_{j}-X_{j,init}\right)$ (1)

where $\Delta M_{T}$ is the mass loss in $\rm{M}_{\odot}\,\rm{yr}^{-1}$over
the time $T$ in years, $\rm{X_{j}}$ is the mass fraction of species $j$, and
$\rm{X_{j,init}}$ is the initial mass fraction of that species.

At the point of core collapse we define the core compactness parameter as
(O’Connor & Ott, 2011):

$\xi_{M}=\frac{M/\,\rm{M}_{\odot}}{R(M=2.5\,\rm{M}_{\odot})/1000\rm{km}}$ (2)

where $M$ is the enclosed mass (taken as 2.5$\,\rm{M}_{\odot}$) and $R$ is the
radius at this mass coordinate in km. As there are multiple criteria possible
for determining the explodability of a model, we also use the criteria of Ertl
et al. (2016) following the w18.0 fit, defining models to explode as those
with:

$\mu_{4}<0.283M_{4}\mu_{4}+0.0430$ (3)

where $M_{4}$ is the mass coordinate (in solar masses) where the entropy per
nucleon S = 4, and $\mu_{4}$ is the mass gradient at this mass coordinate,
defined as:

$\mu_{4}=\left.\frac{\Delta m/\,\rm{M}_{\odot}}{\Delta
r/1000\rm{km}}\right|_{S=4}$ (4)

where we adopt a $\Delta M=0.3\,\rm{M}_{\odot}$ and $\Delta r$ is the change
in radius at S=4 over $\Delta M$.

###  2.1 Core-collapse supernovae

Our explosion models follow those of Farmer et al. (2021). We first excise the
the inner region of each star’s core, by placing the inner boundary of our
model at the point where the entropy per baryon $\rm{S}=4$ (Brown & Woosley,
2013). We then use a thermal bomb, placed at the inner boundary of the model
to inject energy into the star (Aufderheide et al., 1991; Sawada & Maeda,
2019). We do not allow the model to collapse further inwards after the
excising the core, which can alter the final nucleosynthetic signal (Imasheva
et al., 2023). In our default model, energy is then injected over the inner
$0.01\,\rm{M}_{\odot}$ and over 0.0045 seconds. We inject sufficient energy to
bring the total energy of the star (the sum of the kinetic plus thermal energy
minus the gravitational binding energy) to $10^{51}\rm{erg/s}$. While there is
some evidence for choosing different explosion parameters between stripped
envelope supernovae and non-stripped supernovae (Saito et al., 2022), we chose
to use a constant set of parameters to minimise the parameter space explored.
In Section 5.4 we show the uncertainty introduced into the final yields due to
differences in the explosion parameters.

The energy we inject into the star is sufficient to drive a hydrodynamic shock
that travels outwards from the center of our model to the surface. We stop our
models once the shock reaches $0.1\,\rm{M}_{\odot}$ below the surface. In
Farmer et al. (2021) we found that the final total energy of a star would be
5–20% higher than what was injected into the star during the explosion. This
was due to the change in the nuclear networks (between the end of the stellar
evolution and the start of the supernovae) introducing new isotopes that were
not in nuclear statistical equilibrium (NSE)222MESA does not assume NSE,
instead it uses the same nuclear network integration that is used at lower
temperatures (Paxton et al., 2015). In this work, as we have used the same
nuclear network for the entire stars evolution, the core maintains NSE between
the stellar evolution and core collapse phases. The difference in final total
energy of the star compared to the total energy after the energy injection
phase is now $<1\%$.

###  2.2 Stable isotopes

Many of the isotopes in our 162 isotope nuclear network are short-lived
radioactive isotopes and thus would not be expected to contribute to the
Galactic yields. Therefore, we also compute the set of stable isotopes
converting each radioactive isotope into its single most probable decay
product (Timmes, F., priv. com.). This is effectively assuming that we observe
the isotopes on a timescale much longer than their half-lives, and that each
isotope has only one decay channel333This assumption is reasonable for most
isotopes in our network except for $\mathrm{{}^{36}Cl}$, $\mathrm{{}^{46}Sc}$,
$\mathrm{{}^{54}Mn}$, $\mathrm{{}^{58}Co}$, $\mathrm{{}^{64}Cu}$ where
additional decay channels can play a role..

##  3 Total Ejecta

(a) All isotopes

(b) Stable isotopes

Figure 1:  Fraction of the IMF-weighted ejecta (not yields) per element as a
function of the different formation channels. Pre-SN denotes all pre-supernova
mass loss (wind mass loss and RLOF), while SN denotes the ejecta from
successful SN (using the Ertl et al. (2016) criterion). Panel (a) shows the
contribution from all isotopes, while panel (b) shows only the stable isotopes
after decaying all radioactive isotopes to their most likely decay product.
Vertical (horizontal) hatching shows the single (binary) star pre-supernovae
mass loss while reverse (forward) diagonal hatching shows the single (binary)
supernovae mass loss.

We define the fraction of each isotope $F_{i}$ which is ejected by either
single or binary stars in different mass-loss processes as:

$F_{i}=\frac{\int_{11}^{45}\left(E_{pre,i}+f_{SN}E_{post,i}\right)m^{\alpha}dm}{\sum_{b,s}\int_{11}^{45}\left(E_{pre,i}+f_{SN}E_{post,i}\right)m^{\alpha}dm}$
(5)

where $E_{pre,i}$ ($E_{post,i}$) is the ejected mass of isotope $i$, from the
pre-SN mass loss (post-SN mass loss) from either the binary-stripped ($b$) or
single stars ($s$). This is then integrated over the mass range $m$ (in solar
masses) and weighted by the initial mass function (IMF), with an assumed power
law $\alpha=-2.3$ (Salpeter, 1954; Schneider et al., 2018). The factor
$f_{SN}$ is a term that is set to control whether or not we include the
contribution from a star’s post-SN mass loss, depending on whether the
envelope is ejected ($f_{SN}=1$) or not ($f_{SN}=0$). This is then normalized
by summing over the IMF-weighted contributions from all mass loss processes
for both single and binary stars. For the binary-stripped models which did not
evolve to CC, we interpolate their wind yields over the failed models, and
assume that they would not successfully eject their envelopes during core
collapse.

Figure 1 shows the results of Equation 5, which breaks down whether each
element was ejected during wind mass loss or RLOF assuming the secondary star
was able to later eject the material unprocessed (pre-SN), or in the supernova
ejecta (SN). For the supernovae ejecta we assume the explosion model given by
equation 3 of Ertl et al. (2016) (See section 5.1) to set the filter term
$f_{SN}$. Panel (a) shows all elements while panel (b) shows the result of
decaying all unstable isotopes to their most probable stable product. This
assumes that the ratio of single stars to binary-stripped stars is
approximately equal (Sana et al., 2012).

We draw several broad conclusions from Figure 1. Firstly, massive binaries in
general produce larger fractions of most elements compared to massive single
stars (50–60% of the total yield). Most light elements ($Z<8$), lighter than
oxygen, are ejected during wind mass loss (or RLOF), while newly-synthesized
heavier elements unsurprisingly require a supernova to be ejected. Binary-
stripped stars are also able to eject a significant fraction of unstable
isotopes with $20<Z<27$ (calcium to cobalt) in their pre-SN mass loss (See
section 4.1). Stable elements in the $20<Z<27$ (calcium to cobalt) range, in
pre-SN mass loss, are produced in their helium cores via neutron captures.
Thus stripped binaries are able to eject more of those isotopes than single
stars, as they expose their helium cores earlier, allowing for a greater total
amount of mass to be ejected from their helium cores. The same effect is
responsible for the increased $\mathrm{{}^{12}C}$ production in binary-
stripped stellar winds (Farmer et al., 2021).

The large spike at Z=9 (fluorine) for the binary SN ejecta in Figure 1(a) is
due to the production of the short lived isotope $\mathrm{{}^{18}F}$ which
decays to $\mathrm{{}^{18}O}$. The source of stable fluorine is still
uncertain (Renda et al., 2004; Lugaro et al., 2008; Franco et al., 2021), but
Figure 1(b) indicates that massive binaries can make more overall than massive
single stars. Though the final yield will depend on neutrino spallation of
$\mathrm{{}^{20}Ne}$ in the supernovae shock, which we do not follow (Woosley
& Haxton, 1988; Woosley et al., 2002). This increased production of fluorine
is due to two factors, firstly the wind yields are higher in binary-stripped
stars, due to positive yields only occurring in stars that expose their C/O
cores during core helium burning (Meynet & Arnould, 2000). Secondly the
supernovae yields peak for the lowest-mass binary-stripped models, which are
then favoured by the IMF.

At core collapse $\mathrm{{}^{19}F}$ is produced via the chain
$\mathrm{{}^{14}N}\left(\alpha,\gamma\right)\mathrm{{}^{18}F}\left(\beta^{+}\right)\mathrm{{}^{18}O}\left(p,\alpha\right)\mathrm{{}^{15}N}\left(\alpha,\gamma\right)\mathrm{{}^{19}F}$
(Goriely et al., 1990; Limongi & Chieffi, 2018), at the base of the helium
shell. In the binary-stripped models this shell is slightly cooler
($\log(T/K)\approx 8.3$) than in single stars ($\log(T/K)\approx 8.5$) at core
collapse. This leads to an increased destruction of $\mathrm{{}^{18}O}$ in the
single star models, which limits the production of $\mathrm{{}^{19}F}$.

Figure 1 shows that potassium is the element most affected by binary physics,
with most of its contribution coming from the SN ejecta of binary-stripped
stars. Potassium abundances have been challenging to fit in previous models of
chemical enrichment (Kobayashi et al., 2020), which suggests the binary-
stripped stars may be the key to its production. This peak is predominantly
from $\mathrm{{}^{39}K}$ produced by our low mass binary-stripped stars during
their pre-supernovae evolution. The potassium is produced just outside what
will become the compact object, inside the silicon rich-layers. The amount of
$\mathrm{{}^{39}K}$ produced is correlated with the size of this layer and
thus may depend sensitively on the uncertain properties of convection during
Si/Fe burning.

Around $Z\approx 25$ (manganese), single stars produce more odd-Z nuclei in
their supernovae while even-Z nuclei are produced equally by single and binary
stars. This is due to vanadium being produced in the single stars that are
still red super giants (RSG) at core collapse (these have a low initial masses
and are thus highly weighted by the IMF). This vanadium then forms a seed for
alpha captures that then produce manganese and cobalt. Stars that have lost
their H-envelopes (either stars stripped in binaries or high-mass single
stars) produce much less vanadium during core collapse, thus there are less
seed nuclei present for this odd-even pattern. This pattern disappears however
when considering only the stable decay products, therefore a detectable signal
will depend heavily on the timing of the observations relative to the
explosion.

In the online Zenodo material we provide the yields for all isotopes from all
mass-loss processes, as well as diagnostic information about the stellar
models. See Appendix B for an example of the data provided.

##  4 Pre-supernova evolution

During the pre-supernova evolution of our models the chemical yield is
affected by both the wind mass loss and the mass lost during RLOF (for
binaries). This difference in mass-loss processes has two effects on the
yields, firstly it changes the total mass loss and the timing when that mass
is lost, secondly the mass loss has an effect on the core structure of the
star leading to changes in its composition and core mass (Kippenhahn &
Weigert, 1967; Habets, 1986; Laplace et al., 2021). In general the greater the
fraction of the star’s mass that is lost, and the earlier that it is lost in
the star’s life, the lower the final core mass becomes.

###  4.1 Composition of stellar winds

Figure 1 shows that the pre-supernovae mass loss contributes almost the
entirety of the chemical yields for low-mass elements. For higher-mass
elements, massive binary-stripped stars are able to eject $\approx 20\%$ of
their total ejecta in iron-group elements, while for massive single stars this
is closer to $\approx 10\%$. This occurs due to the increased mass loss in the
binary-stripped stars exposing the He-core during core helium burning. This
material is enriched in neutron capture isotopes (see also the much larger
contribution of the binary pre-SN mass loss in Figure 1a). These neutrons come
primarily from $\mathrm{{}^{22}Ne}\left(\alpha,n\right)\mathrm{{}^{25}Mg}$
(Prantzos et al., 1987). See Appendix C for a discussion of the sensitivity of
the isotopic yields due to the wind-scaling factor, and hence total wind mass
loss.

We can divide the yields into 3 broad categories: 1) those that change
approximately linearly with mass lost (e.g. $\mathrm{{}^{1}H}$,
$\mathrm{{}^{4}He}$) either positively or negatively; 2) those that are small
or negative until the star exposes its helium core (e.g. $\mathrm{{}^{12}C}$
or $\mathrm{{}^{19}F}$) before increasing; 3) those that fall into neither of
those categories, which we discuss below.

####  4.1.1 $\mathrm{{}^{17}O}$

For massive single stars $\mathrm{{}^{17}O}$ has positive yields only for
stars with $\rm{M_{init}}<31\,\rm{M}_{\odot}$, with the yield increasing as
the initial mass decreases. The peak formation is at
$\rm{M_{init}}=18\,\rm{M}_{\odot}$ before the yield then decreases at even
lower masses. For massive binary stars the yields are positive for masses
below $\rm{M_{init}}\lessapprox 25\,\rm{M}_{\odot}$, with no turnover in the
yields. The stripped binaries have larger yields than single stars below
$\rm{M_{init}}<16\,\rm{M}_{\odot}$.

####  4.1.2 $\mathrm{{}^{24}Mg}$

Both our stripped binaries and single stars show positive yields for
$\mathrm{{}^{24}Mg}$. However, for single stars the yields peak at
$\rm{M_{init}}=36\,\rm{M}_{\odot}$ (when the star exposes its helium core),
before decreasing at higher masses. In contrast, for the binaries the yield
always increases as the initial mass increases.

####  4.1.3 $\mathrm{{}^{51}V}$

We find that $\mathrm{{}^{51}V}$ is the only isotope in our nuclear network
that has a positive wind yield from binary-stripped massive stars while having
a negative wind yield from single stars. While this would make wind mass loss
from stripped-binaries an candidate source of $\mathrm{{}^{51}V}$ we find that
the total yield of $\mathrm{{}^{51}V}$ is dominated by the core-collapse
yields from single stars. Electron captures onto vanadium can play a key role
in setting the final electron fraction of the core before collapse
(Aufderheide et al., 1994; Heger et al., 2001).

###  4.2 Composition of mass lost during RLOF

Farmer et al. (2021) showed that the mass transferred during Case B RLOF
stripping is not enriched in $\mathrm{{}^{12}C}$ compared to the initial
abundances, however the structural changes caused by the extra mass loss would
affect the star’s evolution, and thus the final $\mathrm{{}^{12}C}$ yield.
This was due to the fact that $\mathrm{{}^{12}C}$ was primarily produced
during core helium burning which occurred after mass transfer finished.

However, there are also a number of isotopes that are produced in hydrogen
envelopes and thus can be ejected during the mass transfer process. These are
generally light elements that are either produced in the low temperature
environment of the hydrogen envelope or are able to be mixed out of the
hydrogen core/shell into the envelope and then ejected.

Figure 1(b) shows similar total ejecta from single and binary-stripped massive
stars. However, the net contribution to the Universe will be reduced in the
binary-stripped stars as compared to single stars, as their contribution to
the composition of the Universe will depend sensitively on how conservative
mass transfer is and how the secondary reprocesses and re-ejects any accreted
material. We assume for the calculation of the RLOF phase that all the
material we eject from the donor accretes onto the accretor (fully
conservative). However, we track these isotopes separately and can infer what
the composition might be if some fraction of this accreted material is ejected
during RLOF or is re-ejected later by the accretor without further nuclear
processing as a wind. We will note when we include the contribution from RLOF
(or not). Overall, for elements Phosphorus (Z=15) and heavier, the absolute
yields from RLOF are $<1\%$ of the absolute wind yields. While for lighter
elements the absolute RLOF yields can be comparable to the absolute wind
yields.

Figure 2:  The IMF weighted relative yield fraction of ejected isotopes from
RLOF compared to wind mass loss in binary systems. The x-axis is the proton
number, Z, while the y axis is the number of neutrons (N) minus the number of
protons (Z). Hatched squares indicate that one or both ejection processes
(RLOF or winds) have negative yields or the yields from either RLOF or wind
mass loss are below $10^{-15}\,\rm{M}_{\odot}$.

Figure 2 shows the relative contribution to the IMF-weighted yield from pre-SN
mass loss, due to RLOF and stellar winds. Red regions signify that the isotope
is predominately ejected in stellar winds, while blue signifies that the
isotope is predominately ejected during RLOF. The blue regions show that
$\mathrm{{}^{13}C}$, $\mathrm{{}^{14}N}$, and $\mathrm{{}^{21}Ne}$ are
primarily ejected during RLOF (we ignore $\mathrm{{}^{7}Be}$ from this
discussion, see section 6.2).

As the hydrogen-burning core recedes it will leave behind CNO processed
material, allowing the envelope to be enriched in $\mathrm{{}^{14}N}$ which is
then ejected during RLOF. The NeNa-cycle is able to convert hydrogen to helium
(similar to the CNO cycle) via neon, sodium, and magnesium. Above temperatures
of $T>3.5\times 10^{7}$K $\mathrm{{}^{21}Ne}$ is destroyed via
$\mathrm{{}^{21}Ne}\left(p,\gamma\right)\mathrm{{}^{22}Na}\left(\beta^{+}\right)\mathrm{{}^{22}Ne}$,
while below this temperature $\mathrm{{}^{21}Ne}$ is produced via
$\mathrm{{}^{20}Ne}\left(p,\gamma\right)\mathrm{{}^{21}Na}\left(\beta^{+}\right)\mathrm{{}^{21}Ne}$
(Wiescher & Langanke, 1986; José et al., 1999). The amount of
$\mathrm{{}^{21}Ne}$ is maximised when there is H burning in the temperature
range $3\leq T/10^{7}\rm{K}\leq 3.5$ (Arnould et al., 1999). Thus significant
amounts of $\mathrm{{}^{21}Ne}$ can only be ejected if the material is burnt
in the H-shell and mixed outwards before the H-shell can further process the
material.

$\mathrm{{}^{13}C}$ can provide a significant fraction of the neutron flux at
stellar densities and temperatures, via the reaction
$\mathrm{{}^{13}C}\left(\alpha,n\right)\mathrm{{}^{16}O}$ (Busso et al.,
1999), thus its production (and destruction) plays a key role in the s-process
(Gallino et al., 1998). The ratio of $\mathrm{{}^{12}C}$/$\mathrm{{}^{13}C}$
has also been used as a a probe of galactic chemical evolution (Milam et al.,
2005).

Table 1: The ratio of the IMF integrated $\mathrm{{}^{12}C}$/$\mathrm{{}^{13}C}$ ejected during different mass loss processes. | Single | Binary
---|---|---
Winds | 50 | 802
RLOF | - | 17
pre-SN total | 50 | 123
post-SN total | 360 | 321
Total including RLOF | 154 | 193
Total not including RLOF | 154 | 446

Table 1 shows the IMF weighted $\mathrm{{}^{12}C}$/$\mathrm{{}^{13}C}$ ratio
from the different mass loss processes. The totals show the
$\mathrm{{}^{12}C}$/$\mathrm{{}^{13}C}$ ratio depending on whether the mass
donated by the primary is ejected from the system (with RLOF) or is assumed to
be accreted onto the accretor and mixed inwards (without RLOF), thus not being
ejected into the Universe. This assumes the accretor does not re-eject the
material at a later time. Table 1 therefore indicates that the contribution to
the Galactic $\mathrm{{}^{12}C}$/$\mathrm{{}^{13}C}$ from massive stars will
depend sensitivity on how conservative mass transfer is, thus how much mass is
accreted, and whether the accretor re-ejects the material or it is mixed into
the core. Thus the $\mathrm{{}^{12}C}$/$\mathrm{{}^{13}C}$ ratio in regions
where the dominant enrichment is from massive stars could potentially be used
as a tracer of how conservative mass transfer is, as the ejection of
$\mathrm{{}^{13}C}$ occurs primarily during the mass transfer process, while
$\mathrm{{}^{12}C}$ is primarily ejected from WR wind mass loss.

The Solar system has $\mathrm{{}^{12}C}$/$\mathrm{{}^{13}C}$$\approx 90$
(Romano et al., 2019; Botelho et al., 2020), which is lower than the values in
Table 1, thus the primary producer of $\mathrm{{}^{13}C}$ is likely lower-mass
stars, for instance AGB and TP-AGB stars which can have
$\mathrm{{}^{12}C}$/$\mathrm{{}^{13}C}$ values between $\sim 10$–$180$
depending on the initial mass (Karakas & Lugaro, 2016).

###  4.3 Core composition

Figure 3: Comparison of $\mathrm{{}^{12}C}$ mass fractions at the end of core
helium burning. Black solid line: Single stars, Black dashed line: Binary-
stripped stars, Blue: Sukhbold et al. (2016), Orange: Chieffi & Limongi
(2020), Green solid line: Single star models from Schneider et al. (2021),
Green dashed line: Case B binary models from Schneider et al. (2021).

The final fate of a star depends on many quantities, however the core mass and
the central $\mathrm{{}^{12}C}$ fraction at the end of core helium burning are
two of the most important (Chieffi & Limongi, 2020; Patton & Sukhbold, 2020).
Figure 3 shows a comparison of the core $\mathrm{C}$ fraction at the end of
core helium depletion for various solar metallicity models. In general we can
see that as the initial mass increases, the core $\mathrm{{}^{12}C}$ fraction
decreases. It is set by the combination of the $3\alpha$ rate and the
${}^{12}\rm{C}\left(\alpha,\gamma\right)^{16}\\!\rm{O}$ reaction (Sukhbold &
Adams, 2020). For our single star models, the $\mathrm{{}^{12}C}$ fraction
agrees well with Schneider et al. (2021), which is unsurprising as Schneider
et al. (2021) also used MESA with similar physics choices, although there is a
divergence at high initial mass, which may be due to our different choices of
chemical mixing. Schneider et al. (2021) also uses a similar wind prescription
as this work, but with a different dependence on the metallicity.

Our binary-stripped models also closely match the values of Schneider et al.
(2021) case-B binaries, with differences likely due to the different method of
removing the envelope, as Schneider et al. (2021) takes the material off with
an ad-hoc prescription, while we follow the binary mass transfer. Our models
show a variability in the $\mathrm{{}^{12}C}$ trend, not seen in Schneider et
al. (2021), in the 20–30$\,\rm{M}_{\odot}$ mass range. This is where both the
MLT++ approximation is important and the envelope is not significantly removed
by winds before mass transfer begins. Thus the envelopes properties depend
sensitively on the ad-hoc MLT++ prescription, which propagates as an
uncertainty in how wind mass loss occurs, and how efficient RLOF is at
removing the envelope. How mass is lost from a star has been shown to
significantly impact the internal structure of massive stars (Renzo et al.,
2017).

Our binary-stripped models also agree well with the Chieffi & Limongi (2020)
single star models, for $\rm{M_{init}}<20\,\rm{M}_{\odot}$. Both Chieffi &
Limongi (2020) and this work use NACRE (Angulo et al., 1999) for the 3$\alpha$
rate. For the ${}^{12}\rm{C}\left(\alpha,\gamma\right)^{16}\\!\rm{O}$ rate
Chieffi & Limongi (2020) uses Kunz et al. (2002) while we use Angulo et al.
(1999) rate. Therefore differences likely stem from different choices in the
nuclear physics. Thus binary stripping has a similar effect on the core
abundance as variations in the
${}^{12}\rm{C}\left(\alpha,\gamma\right)^{16}\\!\rm{O}$ reaction rate.

As shown extensively in Laplace et al. (2021) the effect of the extra mass
loss due to RLOF causes structural changes to the cores of massive stars.
These changes cause the cores to become smaller (in mass) and to have extended
chemical gradients. This leads to differences in the intensity and timing of
nuclear shell burning episodes, which compounds the differences between single
and binary-stripped stars. While Farmer et al. (2021) has shown how the binary
interactions affect the final $\mathrm{{}^{12}C}$ yield.

Details of key stellar properties can be found in Appendix D and in Tables 3
and 4. These include the final total and core mass, total mass lost to
different mass loss processes, and final masses of H, He, and C.

##  5 Supernovae

The nucleosynthetic yields from core-collapse supernovae are the result of (i)
whether or not the star can successfully explode and produce ejecta and (ii)
the pre-collapse structure and composition.

Figure 4: The compactness parameter as a function of the initial stellar mass
for massive single stars (blue) and binary stars (red). The grey lines mark
$\xi_{M=2.5}=0.16$ and $\xi_{M=2.5}=0.36$ (with $dm$ averaged over
0.3$\,\rm{M}_{\odot}$) as the approximate boundaries between all models
undergoing a successful explosion ($\xi_{M=2.5}\leq 0.16$), no model
undergoing a successful explosion ($\xi_{M=2.5}\geq 0.36$), and an
intermediate mixed state. Star symbols mark models that would successfully
explode under the two-component fit of Ertl et al. (2016) calibrated against
the model w18.0, while black circles denote models that would not be expected
to produce successful explosions (and thus ejecta).

###  5.1 Explodability

We first determine whether a star will successfully explode and eject its
envelope, or not. Figure 4 shows two measures of a star’s explodability: its
compactness (O’Connor & Ott, 2011) (y-axis) and the two component fit of Ertl
et al. (2016) (symbols), as a function of the initial mass. As shown in many
other works (e.g. Sukhbold et al., 2016; Farmer et al., 2016; Renzo et al.,
2017; Sukhbold & Adams, 2020; Patton & Sukhbold, 2020), the evolution to core
collapse and the star’s final structure is sensitive to the choice of physics,
treatment of chemical mixing boundaries (Chieffi & Limongi, 2020), and
numerical choices (Farmer et al., 2016) made by the software instrument used.
In Figure 4 we define three regions based on the two component fit of Ertl et
al. (2016)444See also Boccioli et al. (2022) for a potential new criterion for
determining explodability. One region contains models that only make NSs
($\xi_{M=2.5}\leq 0.16$), another contains those that only make BHs
($\xi_{M=2.5}\geq 0.36$), and there is an intermediate region in which we
consider the outcomes to be less certain. The boundaries of these regions are
almost the same as the boundaries found by Ugliano et al. (2012)
($\xi_{M=2.5}\leq 0.15$ for NS and $\xi_{M=2.5}\geq 0.35$ for BH). But the
presence of the mixed region shows why the compactness, on its own, is not a
good measure for determining the explosion outcome.

In Figure 4 we can find several regions that are expected to undergo
successful explosions, with only slight movement of the boundaries between
single and binary stars. Between $11<\rm{M_{init}}/\,\rm{M}_{\odot}<21$ and
$31<\rm{M_{init}}/\,\rm{M}_{\odot}<36$ stars end their lives with similar
compactness parameters (and with similar explosion success metrics). In
contrast, between $21<\rm{M_{init}}/\,\rm{M}_{\odot}<31$ (though there are a
number of missing models here) and $\rm{M_{init}}>38\,\rm{M}_{\odot}$ the
final states of the stars are very different between single and binary-
stripped stars, leading to differences both in the explodability and their
final nucleosynthetic yields.

The structure seen in Figure 4 is related to the transition in how different
fuels ignite in the core (Sukhbold & Woosley, 2014; Laplace et al., 2021). The
peak at $\rm{M_{init}}\approx 25\,\rm{M}_{\odot}$ is when carbon changes from
central to off-center burning while the peak at $\rm{M_{init}}\approx
34\,\rm{M}_{\odot}$ is coincident with neon going from central to off-center
burning (Schneider et al., 2021). The shift in the location of the peaks
between binary-stripped and single stars is due to the binary-stripped stars
having smaller core masses, due to the core receding when RLOF removed the
envelope (Farmer et al., 2021).

We include the fallback prescription of Goldberg et al. (2019). Here zones
near the inner boundary are removed that have a total energy, when integrated
from the core to the zone, that is negative. This is done by moving the inner
boundary of the model to the point where the material has a positive total
energy, and thus is unbound from the core. This is repeated at each time step.
See Appendix A of Goldberg et al. (2019) and Paxton et al. (2015) for the full
details of this fallback treatment. For the models presented here and with our
default explosion parameters, the amount of fallback is negligible
($\Delta\rm{M}\lessapprox 10^{-3}\,\rm{M}_{\odot}$) even in cases that do not
formally explode via the Ertl et al. (2016) criterion. As the amount of
fallback is negligible in these models, for the choices of explosion physics
used here, we simplify our modelling by using an explodability criterion. This
lack of fallback is driven by our choice of a fixed $10^{51}\rm{erg/s}$
explosion, lower energy explosions can have larger fallback masses with the
prescription as implemented in MESA (Goldberg et al., 2019).

Schneider et al. (2021) found that for case B binaries (where they
artificially remove the envelope), NS production occurs for $\rm{M_{init}}\leq
31.5\,\rm{M}_{\odot}$ and $\rm{M_{init}}>34.0\,\rm{M}_{\odot}$, while for
single stars the range is between $\rm{M_{init}}\leq 21.5\,\rm{M}_{\odot}$ and
$23.5\leq\rm{M_{init}}/\,\rm{M}_{\odot}\leq 34.0$. These boundaries can shift
if fallback accretion is taken into account (Timmes et al., 1996). We find a
somewhat more complex boundary between NS and BH formation for
$\rm{M_{init}}\leq 22\,\rm{M}_{\odot}$ and $\rm{M_{init}}>36\,\rm{M}_{\odot}$.
Differences between the boundaries found by Schneider et al. (2021) and those
in this work are likely due to differences in the physical assumptions, such
as the choice of convective boundary mixing, timing of mass loss, and the
choice of nuclear network. These have been shown to lead to large changes in
the final structure (Farmer et al., 2016; Renzo et al., 2017; Farmer et al.,
2021).

###  5.2 SN yields

(a) Supernovae yield

(b) Ratio of yields compared to our single star model

Figure 5: Panel (a): The stable isotopic yields from core collapse for a
13$\,\rm{M}_{\odot}$ star from the literature; LC18 (Limongi & Chieffi, 2018):
light blue, S16/W18 (Sukhbold et al., 2016; Woosley, 2018): orange) as
compared to our $\rm{M_{init}}=13\,\rm{M}_{\odot}{}$ single (dark blue) and
$\rm{M_{init}}=13\,\rm{M}_{\odot}{}$ binary-stripped star (red). Panel (b):
The ratio of the core collapse stable yields from the literature and our
$\rm{M_{init}}=13\,\rm{M}_{\odot}{}$ binary-stripped star compared to our
$\rm{M_{init}}=13\,\rm{M}_{\odot}{}$ single star.

Figure 5 shows a comparison between our 13$\,\rm{M}_{\odot}$ single555Formally
our 13$\,\rm{M}_{\odot}$ single star does not explode by any of the fits
provided in Ertl et al. (2016), however given the limited range of initial
masses in Limongi & Chieffi (2018) that overlap with our models, we chose this
initial mass as the binary-stripped model comfortably forms a NS, while both
the 15$\,\rm{M}_{\odot}$ models are on the edge between NS and BH, the
20$\,\rm{M}_{\odot}$ models both make BHs, and we have no model for a
25$\,\rm{M}_{\odot}$ stripped-binary.  and binary-stripped stars with yields
available in the literature666We made use of the VICE (Johnson & Weinberg,
2020; Johnson et al., 2021; Griffith et al., 2021) software package to provide
this information.. Panel (a) shows the total elemental yields (as a sum of the
stable isotopes), while Panel (b) shows the ratio of the elemental yield for
our single star model as compared to the literature values. Our supernova
models were exploded with our default explosion physics.

Overall, we over predict (as compared to the literature) elements in the
Z=10–21 range by a factor of 5. For higher mass elements we have a good
agreement with the Kepler based results (Sukhbold et al., 2016; Woosley, 2018)
while diverging to a factor 10 over prediction compared to the results of
(Limongi & Chieffi, 2018) which are based on the FRANEC code. Our large
disagreement for Zinc is due to the fact that our nuclear network stops at
Zinc, thus isotopes will pile up at the edge unable to produce heavier
isotopes. Other differences are likely due to differences in the stellar
micro-physics and physical assumptions. For instance, we showed in Farmer et
al. (2021) that the, currently unconstrained, choice for the amount of
overshoot during carbon burning can have a significant impact on the carbon
yields, that would then propagate as an uncertainty on the product of carbon
burning namely $\mathrm{{}^{20}Ne}$, $\mathrm{{}^{23}Na}$, and
$\mathrm{{}^{24}Mg}$. This is due to a $\mathrm{{}^{12}C}$ yield being
sensitive to the size of the pocket of $\mathrm{C}$ that survives, between the
top of the final carbon-burning shell and the helium shell (Farmer et al.,
2021). This pocket, however, can be eroded by convective overshoot from the
final convective carbon-burning shells.

Figure 5b also shows the comparison between a binary-stripped model and a
single star model, for the same initial mass. Here we can see that the binary-
stripped model produces more of the intermediate-mass elements ($15<Z<24$) by
up to a factor $\approx 4$, while producing slightly less of the higher mass
elements ($Z>24$), as well as producing less magnesium and aluminum (Z=12 and
Z=13).

###  5.3 Explosive nucleosynthesis

(a) Single stars

(b) Binary-stripped stars

Figure 6: The logarithmic ratio of the IMF weighted pre-SN composition,
outside of the mass cut, to the IMF weighted composition of the models near
shock breakout. Blue indicates isotopes produced in the SN, while red indicate
isotopes destroyed in the SN. We did not decay any isotopes to their stable
versions. The colors are truncated to be between -1 and 1.

Figure 6 shows the relative change in the IMF-weighted material ejected in a
SN between its pre-SN composition and its post-SN composition. Blue regions
indicate isotopes that are produced in the SN while red regions indicate
isotopes that are destroyed in the SN. The color bar has been truncated, to
better show the details, however the (blue) material produced can peak at
$\approx 10^{15}$ times more (for isotopes in the bottom right corner), and
the (red) material destroyed peaks at only $\approx 10^{4}$ times less.

We can see in Figure 6 that most of the region of change occurs for $Z>20$ and
$N-Z<4$. These are generally the proton-rich isotopes, that have very low
abundances outside of the mass cut pre-SN. Thus even a small production during
the SN causes a large relative increase in the composition. There is also an
increase in the more neutron rich isotopes, typically expected for r-process,
in the top right of each panel in Figure 6. This includes the isotope
$\mathrm{{}^{60}Fe}$ which is of interest for gamma-ray observations (Mahoney
et al., 1982; Leising & Share, 1994).

Comparing Figures 6(a) to 6(b), we can see that both show this enhancement in
proton-rich isotopes, though the single stars show a greater fraction of
material coming from the pre-SN evolution for the most proton-rich isotopes of
Ti, Cr, and Fe. For the more neutron-rich isotopes ($N-Z\approx 8$), the
single stars show material coming more from the explosive nucleosynthesis
during the SN than before. For neutron-rich isotopes of Al–Sc, binary-stripped
stars are generally producing this material pre-SN (and outside what will
becomes the compact object), while in single stars this occurs during the
explosive nucleosynthesis in the SN.

We reconfirm our finding the $\mathrm{{}^{12}C}$ is not affected by the
supernova shock (Farmer et al., 2021). We find, with our larger number of
isotopes, that $\mathrm{{}^{12}C}$ is in fact the isotope least affected by
the supernova explosion. This is due both to its location near the He-shell,
thus little $\mathrm{{}^{12}C}$ is lost to the formation of the compact
object, and when the shock finally reaches the He-shell it has cooled
sufficiently to be unable to drive additional $\mathrm{{}^{12}C}$ burning.

###  5.4 SN uncertainties

Following the method of Farmer et al. (2021) we explore the sensitivity of our
SN yields to the uncertain explosion physics. We took a
17$\,\rm{M}_{\odot}$777Our 17$\,\rm{M}_{\odot}$ single star model does not
formally explode given the fits in Ertl et al. (2016), though it does have a
similar compactness to the 17$\,\rm{M}_{\odot}$ binary-stripped model. single
and binary-stripped star models and exploded each of them $\approx 100$ times.
For each sample we would randomly vary the following four parameters: the
injection energy, mass cut, injection mass, and injection time. As an
improvement over Farmer et al. (2021) we sample all four explosion parameters
simultaneously as opposed to doing two grids, which sampled only two
parameters at a time. We vary the injection energy between $0.5$–$5.0\times
10^{51}\rm{erg/s}$, the mass cut between $1.0$–$2.0\,\rm{M}_{\odot}$, the
injection mass $10^{-2}$–$5\times 10^{-1}\,\rm{M}_{\odot}$, and the injection
time $10^{-3}$–1.0s. We assume a thermal bomb for our explosions, however a
piston driven explosion may produce different yields for the same input energy
(Young & Fryer, 2007).

(a) Single stars

(b) Binary-stripped stars

Figure 7:  The logarithmic ratio of the variation in the isotopic ejecta when
considering the uncertainties in explosion physics ($\Delta\rm{Explosion}$)
and the uncertainties in the progenitors ($\Delta\rm{Progenitor}$).
$\Delta\rm{Explosion}$ is defined as the spread in the final ejecta
composition for a 17 $\,\rm{M}_{\odot}$ model when the explosion physics is
varied. $\Delta\rm{Progenitor}$ is the spread in the final ejecta composition
for all models that explode with fixed explosion physics, varying the initial
mass of the progenitor. The colors are truncated to be between -1 and 1.

Figure 7 shows for which isotopes it is more important to understand the
progenitor
($\log\left(\Delta\rm{Explosion}/\Delta\rm{Progenitor}\right)=-1.0$) and for
which isotopes it is more important to understand the explosion mechanism
($\log\left(\Delta\rm{Explosion}/\Delta\rm{Progenitor}\right)>-1.0$ ). Where
$\Delta\rm{Explosion}$ is the spread in the final ejecta composition for a
17$\,\rm{M}_{\odot}$ model where we vary the explosion physics, and
$\Delta\rm{Progenitor}$ is the spread in the final ejecta composition for
fixed explosion physics but considering our entire range of initial masses.
Both $\Delta\rm{Explosion}$ and $\Delta\rm{Progenitor}$ are defined separately
for our single and binary-stripped stars.

Figure 7 also shows that there is a difference between single stars and
binary-stripped stars in which isotopes are uncertain, and thus which types of
supernovae could be used to constrain different isotopes if detectable either
through spectroscopy or radioactive decay signatures. These differences occur
due to the differences in the time needed for the shock to break out of the
photosphere, in the less massive single stars (which still have a RSG
envelope) shock breakout is approximately a day after the core collapses,
while in our binary-stripped stars (and high-mass single stars that lose their
H-envelopes) shock breakout occurs much less than a day after the core
collapses. Thus stripped-envelope supernovae explode faster and have less time
for short lived radioactive nuclei to decay before the shock breakout phase.
This hints that stripped-envelope supernovae from binaries could be
interesting locations to study radioactive decay products from explosive
nucleosynthesis, with sufficiently early time observations and sufficient
chemical mixing to bring them to the photosphere.

###  5.5 Gamma ray emitters

In Andrews et al. (2020) a number of isotopes ($\mathrm{{}^{43}K}$,
$\mathrm{{}^{47}Ca}$, $\mathrm{{}^{44}Sc}$, $\mathrm{{}^{47}Sc}$,
$\mathrm{{}^{48}V}$, $\mathrm{{}^{48}Cr}$, $\mathrm{{}^{51}Cr}$,
$\mathrm{{}^{52}Mn}$, $\mathrm{{}^{59}Fe}$, $\mathrm{{}^{56}Co}$,
$\mathrm{{}^{57}Co}$, and $\mathrm{{}^{57}Ni}$) were determined to be
interesting candidates for next-generation gamma-ray detectors. This was due
to their accessible gamma-ray energies as well as their sensitivity to the
structure of the progenitor ($\mathrm{{}^{48}V}$ and $\mathrm{{}^{57}Co}$) or
the explosion energy ($\mathrm{{}^{43}K}$, $\mathrm{{}^{47}Ca}$,
$\mathrm{{}^{44}Sc}$, $\mathrm{{}^{47}Sc}$, $\mathrm{{}^{59}Fe}$).

If we assume the (arbitrary) point of
$\log\left(\Delta\rm{Explosion}/\Delta\rm{Progenitor}\right)>0.1$ as the point
where isotopes are probing for the explosion mechanism (instead of them
profiling the stellar structure) we can then use the isotope list of Andrews
et al. (2020) to determine whether these isotopes are interesting for our
binary-stripped stars. We find that the following are interesting isotopes, by
that definition, for probing the explosion properties in single stars:
$\mathrm{{}^{48}V}$, $\mathrm{{}^{48}Cr}$, $\mathrm{{}^{51}Cr}$,
$\mathrm{{}^{52}Mn}$, $\mathrm{{}^{56}Co}$, $\mathrm{{}^{57}Co}$, and
$\mathrm{{}^{57}Ni}$, while for binaries it is: $\mathrm{{}^{44}Sc}$,
$\mathrm{{}^{48}Cr}$, $\mathrm{{}^{59}Fe}$, $\mathrm{{}^{57}Co}$, and
$\mathrm{{}^{57}Ni}$. Note that the two lists do not overlap, nor does each
isotope have the same level of sensitivity to the explosion between single and
binary-stripped stars. We find $\mathrm{{}^{48}V}$ and $\mathrm{{}^{52}Mn}$
are much stronger probes of the explosion physics in single stars than in
binaries, while $\mathrm{{}^{48}Cr}$ is more sensitive to the explosion
mechanism in binaries than in singles.

##  6 Caveats

###  6.1 Al26

$\mathrm{{}^{26}Al}$ is a short-lived isotope that decays to an excited state
of $\mathrm{{}^{26}Mg}$. This excited $\mathrm{{}^{26}Mg}$ then rapidly emits
a 1.81 MeV $\gamma$-ray. Given the the short half life of
$\mathrm{{}^{26}Al}$, its detection in the Galaxy requires a continuous
production source (Diehl et al., 2010). $\mathrm{{}^{26}Al}$ has multiple
formation sites inside stars, mainly via proton captures onto
$\mathrm{{}^{25}Mg}$ (Limongi & Chieffi, 2006). However, $\mathrm{{}^{26}Al}$
has several isomers which complicate the decay chain. The ground state of
$\mathrm{{}^{26}Al}$ decays to $\mathrm{{}^{26}Mg}$ with a half life of $\sim
700$ kyr, however the excited state of $\mathrm{{}^{26}Al}$ decays to
$\mathrm{{}^{26}Mg}$ in $\sim 6$ seconds (Misch et al., 2021). At the
temperatures found in stellar envelopes, excited $\mathrm{{}^{26}Al}$ decays
to $\mathrm{{}^{26}Mg}$ before it can de-excite back to its ground state, this
rapidly converts most of the $\mathrm{{}^{26}Al}$ into $\mathrm{{}^{26}Mg}$.
Our nuclear network does not contain the $\mathrm{{}^{26}Al}$ isomers, with
the decay rate of $\mathrm{{}^{26}Al}$ only considering the ground state
transitions. Thus we significantly over produce the amount of
$\mathrm{{}^{26}Al}$ in our wind yields and RLOF ejecta (see for instance the
models of Brinkman et al. (2019, 2021) for $\mathrm{{}^{26}Al}$ yields from
binary stars). This over production ranges from a factor 10 to 10,000
depending on the initial mass, with low mass stars having larger
overproduction factors. Thus we can make no statement on the production of
$\mathrm{{}^{26}Al}$ in stellar winds, without further post-processing of the
chemical yields. Tests with a nuclear network that contains the
$\mathrm{{}^{26}Al}$ isomers give wind and RLOF results that are consistent
with those of Brinkman et al. (2021). In our models we have
$\mathrm{{}^{26}Mg}$ wind yields of $M\approx 10^{-3}\,\rm{M}_{\odot}$, while
$\mathrm{{}^{26}Al}$ wind yields of $M\approx 10^{-4}\,\rm{M}_{\odot}$ (at
$\rm{M_{init}}\approx 20\,\rm{M}_{\odot}$). Thus the lack of
$\mathrm{{}^{26}Al}$ excited-state decays to $\mathrm{{}^{26}Mg}$ leads to a
systematic change of order 10% (depending on the initial stellar mass) in the
$\mathrm{{}^{26}Mg}$ wind yields.

###  6.2 Neutral ion electron captures

MESA’s default reaction rate for
$\mathrm{{}^{7}Be}(e^{-},\nu_{e})\mathrm{{}^{7}Li}$ (for version r12115) came
from REACLIB (Cyburt et al., 2010). However, REACLIB is only defined for
temperatures above $T>10^{7}$K, thus it assumes that all atoms are ionised.
While this is a reasonable assumption for most rates, which occur deep in the
stellar interior, significant lithium production occurs in stellar envelopes
with temperatures below $T<10^{7}$K where the reaction rate can then depend on
the level of ionisation (Schwab, 2020). This has been corrected in MESA
version 2c2ad6c by switching to the rate of Simonucci et al. (2013) which
includes this effect, but this was not available in MESA for this work. We
caution against making any inferences for either $\mathrm{{}^{7}Be}$ or
$\mathrm{{}^{7}Li}$ from this work. Other isotopes that are sensitive to the
level of ionisation may also be affected, if their rates are provided by
REACLIB.

##  7 Discussion

We have used in this work the default MESA set of reaction rates, which is a
mix of rates from NACRE and JINA’s REACLIB (Angulo et al., 1999; Cyburt et
al., 2010). These rates in turn are based on experimental data and thus have
experimental errors associated with them (Sallaska et al., 2013). Changes in
the nuclear reaction rates can have two different effects on the resulting
nucleosynthesis, directly changing the amount of a species produced (Bliss et
al., 2020; Subedi et al., 2020; Sieverding et al., 2022), and secondly
indirectly by changing stellar properties like the core mass (Brown et al.,
1999, 2001; West et al., 2013; Fields et al., 2018; Sukhbold & Adams, 2020;
Farmer et al., 2020). Of critical importance is the
${}^{12}\rm{C}\left(\alpha,\gamma\right)^{16}\\!\rm{O}$ reaction (deBoer et
al., 2017; Farmer et al., 2020) during core helium burning. Variations within
its known uncertainties can lead to core masses changing by $\pm
2\,\rm{M}_{\odot}$ (Sukhbold & Adams, 2020) and central carbon fractions by
$\pm 80\%$ (Fields et al., 2016, 2018). This can alter models such that they
change from exploding to non-exploding, significantly changing the final
yields. Observations of WO stars suggest that the
${}^{12}\rm{C}\left(\alpha,\gamma\right)^{16}\\!\rm{O}$ reaction needs a
reduction by up to 50% to match the observed C/O ratio (Aadland et al., 2022).
Further work is need to integrate reaction rate uncertainties, for all
reaction rates, into stellar models.

Significant uncertainties remain in the treatment of mass transfer between
binaries (e.g. Klencki et al., 2020, 2022; Sen et al., 2022), whether the
stars lose their entire hydrogen envelopes (Götberg et al., 2017; Yoon et al.,
2017; Laplace et al., 2020), and how much of the material lost by the donor is
accreted by the companion (de Mink et al., 2009; Janssens et al., 2021). In
this work we have assumed fully conservative mass transfer (all material lost
is accreted by the companion), if mass transfer was not fully conservative
(some mass is lost during RLOF) then the Universe can be enriched with those
products lost from the hydrogen envelope (see Section 4.2).

Related to whether a star fully strips during RLOF is the wind mass loss, and
its scaling with the metallicity. Lower wind mass loss rates, either
intrinsically or due to lower metallicities (Sander et al., 2020; Sander &
Vink, 2020), may allow stars to keep part of their hydrogen envelopes (Götberg
et al., 2017; Yoon et al., 2017; Laplace et al., 2020). If a star keeps its
hydrogen envelope then the yields for the higher-mass elements seen in Figure
1(a) will decrease as the star will not expose its helium core. At low
metallicities, binary stars may not become fully stripped (Götberg et al.,
2017; Yoon et al., 2017; Laplace et al., 2020; Klencki et al., 2022), this
would lead to the binary stars having yields closer to those of single stars.

We modelled our binaries as Case B systems, where stable RLOF occurs during
the Hertzsprung gap. Depending on the initial period, binaries can also
interact earlier during the main sequence (Case A) or later during core helium
burning (Case C). Interaction during Case A RLOF is likely to lead to a
smaller core mass (Schneider et al., 2021), which would then be more likely to
explode successfully in a SN. While interaction during Case C may occur too
late in the star‘s life to significantly affect the core evolution. Though, if
the star was likely to form a BH, then Case C mass loss will liberate some of
the envelope that would have otherwised collapsed into the BH.

The consequences of stellar mergers for the final structure also depend on the
timing of the merger. Mergers which occur when both stars are on the main
sequence (MS) are expected to increase the core mass of the resulting star, as
compared to that of the primary star in the pre-merger binary, and the later
evolution would likely be approximately described by that of an initially more
massive single star (although see, e.g., Renzo et al. 2022 for details of the
structure which may also differ for post-merger stars). For post-MS mergers,
any erosion of the hydrogen-depleted core — either during the merger (e.g.
Ivanova & Podsiadlowski, 2003) or by dredge-out during post-merger relaxation
(Justham et al., 2014) — would not be reversed by growth of a convective MS
core. The consequences of this decrease in core mass may make many such merger
products more explodable than the primary star would have become if single,
despite the increase in stellar mass (Justham et al., 2014).

We have ignored the evolution of the accretor in this work. Their most
significant contribution would likely be due to the mass gain, moving stars
that are initially too light to explode ($\rm{M_{init}}\approx
6-8$$\,\rm{M}_{\odot}$) to gain enough mass that they now explode
(Podsiadlowski et al., 2004; Zapartas et al., 2017, 2019). Secondly, their
contribution will depend on how much of the mass that they accreted, remains
bound to the accretor and is further processed inside the accretor. For
instance, SN 2016bkv shows nucleosynthetic signals that it may have accreted
material, but with no significant reprocessing of the accreted material
(Deckers et al., 2021). Detailed modelling of the nucleosynthetic signature of
accretors is deferred to later work.

We modelled our stars as non-rotating objects, however rotation can play a key
role in the evolution of massive stars (Meynet & Maeder, 2000). This is due to
both changes in the core structure (Ekström et al., 2012; Murphy et al.,
2021), chemical mixing of elements to the surface (Meynet et al., 2006; Groh
et al., 2019), and changes to the observed chemical composition (Hunter et
al., 2007, 2008, 2009). Indeed, rotation may be needed to explain s-process
enrichment in the Solar system (Rizzuti et al., 2019, 2021; Prantzos et al.,
2020). Rotation will also play a role during the explosion, and whether the
compact object forms a jet which may alter the final nucleosyntheic signal
(Winteler et al., 2012; Reichert et al., 2023).

##  8 Conclusion

Motivated by the differences we found in the $\mathrm{{}^{12}C}$ yields in
Farmer et al. (2021) we have extended our study of the nucleosynthesis of
massive binary-stripped and single stars with a larger nuclear network. With
the high fraction of massive stars being inferred to be in binaries, accurate
modelling of binary evolution is needed to be able to predict the
nucleosynthetic yields of massive stars.

To achieve this we have modelled the evolution of binary-stripped and single
stars from the onset of hydrogen burning to core collapse, at solar
metallicity. We have then modelled the nucleosynthetic yields due to the
supernovae shock. This was done using a large 162-isotope nuclear network for
all phases of the star’s evolution.

Our results can be summarised as follows:

  * •

We find that, in general, stars stripped in binaries synthesize and then eject
more mass of all elements than single stars. The increase in the yields
depends strongly on the isotope. This is due to the increased mass loss in
binary-stripped stars ejecting more material during the star’s evolution and
binary-stripped stars being more explodable and thus ejecting more material
during the supernovae.

  * •

$\mathrm{{}^{13}C}$/$\mathrm{{}^{12}C}$ from massive stars may provide
information on the efficiency of mass transfer. This is because
$\mathrm{{}^{13}C}$ is primarily only ejected during RLOF, while
$\mathrm{{}^{12}C}$ is ejected primarily during WR wind mass loss.

  * •

In qualitative agreement with previous work, we find that stars stripped in
binaries are somewhat more likely to successful explode in a core-collapse
supernova, especially at higher masses. This is due the changes in the core
mass due to the mass loss in RLOF.

  * •

Depending on the element, the difference between single and binary-stripped
stars can be as large as the difference between different software
instruments. However, we stress we have not attempted to calibrate our results
to observations.

  * •

We have identified a number of radioactive isotopes that may prove useful in
constraining the explosion mechanism or progenitor structure with next
generation gamma-ray detectors.

  * •

In the online Zenodo material we provide tables of chemical yields for all
isotopes for all types of mass loss.

We conclude that the yields from massive binary-stripped stars are different
from those of massive single stars, and that this difference depends on the
isotope. Thus there is no single scale factor for taking into the account of
binary interactions on the chemical yields. Therefore the effects of binarity
require explicit modelling of all isotopes that are of interest.

##  Appendix A Other physics choices

MESA depends on a number of sources for its micro-physics; with its EOS being
a blend of several sources; OPAL (Rogers & Nayfonov, 2002), SCVH (Saumon et
al., 1995), PTEH (Pols et al., 1995b), HELM (Timmes & Swesty, 2000), and PC
(Potekhin & Chabrier, 2010). While opacities are primarily from OPAL (Iglesias
& Rogers, 1993, 1996) with additional data from Buchler & Yueh (1976);
Ferguson et al. (2005); Cassisi et al. (2007)

The nuclear reaction rates are a combination of NACRE and JINA’s REACLIB
(Angulo et al., 1999; Cyburt et al., 2010) compilations. Additional weak
reaction rates are from Fuller et al. (1985); Oda et al. (1994); Langanke &
Martínez-Pinedo (2000). Screening of the nuclear reaction rates is computed
with the prescription of Chugunov et al. (2007). Thermal neutrino loss rates
are provided from the fits of Itoh et al. (1996). The Roche lobe radii in
binary systems is computed from the fit of Eggleton (1983). In our Roche lobe
overflowing binary systems we compute the mass loss rate using the the
prescription of Kolb & Ritter (1990).

##  Appendix B Data tables

Table 2 shows the $\mathrm{{}^{19}F}$ yields from our models. This includes
both the wind mass loss, RLOF, and supernovae yields. We provide supernova
yields for all models, as there are multiple different criteria that can be
used to determine whether a star successfully ejects its envelope in a
supernovae. The online Zenodo material contains yield tables for all
162-isotopes from our nuclear network.

Table 2: A representative sample of the data available. Data is available online for all 162 isotopes. The amount of $\mathrm{{}^{19}F}$ ejected in solar masses broken down by mass-loss type for both single stars and the primary star in the binary. “Init” marks the amount that is from the initial composition of the star. All ejecta masses are in units of $10^{-5}$ solar masses. Blank values indicate models that did not evolve successfully to core collapse. We have included the supernova yields from all models, assuming all models successfully explode.  Initial mass [$\,\rm{M}_{\odot}$] | Single [$10^{-5}$$\,\rm{M}_{\odot}$] | Binary [$10^{-5}$$\,\rm{M}_{\odot}$] |
---|---|---|---
| $\rm{M_{Winds}}$ | $\rm{M_{Winds,init}}$ | $\rm{M_{CC}}$ | $\rm{M_{CC,init}}$ | $\rm{M_{Winds}}$ | $\rm{M_{Winds,init}}$ | $\rm{M_{RLOF}}$ | $\rm{M_{RLOF,init}}$ | $\rm{M_{CC}}$ | $\rm{M_{CC,init}}$
11 | 0.051 | 0.058 | 1.262 | 0.276 | 0.009 | 0.025 | 0.209 | 0.251 | 0.265 | 0.064
12 | 0.070 | 0.079 | 0.206 | 0.287 | 0.011 | 0.031 | 0.222 | 0.266 | 1.459 | 0.076
13 | 0.092 | 0.104 | 1.045 | 0.299 | 0.013 | 0.037 | 0.234 | 0.280 | 1.248 | 0.089
14 | 0.118 | 0.135 | 0.888 | 0.298 | 0.015 | 0.045 | 0.245 | 0.293 | 0.120 | 0.097
15 | 0.149 | 0.170 | 0.256 | 0.293 | 0.017 | 0.054 | 0.255 | 0.306 | 0.622 | 0.111
16 | 0.183 | 0.211 | 0.232 | 0.291 | 0.021 | 0.063 | 0.263 | 0.320 | 0.849 | 0.122
17 | 0.210 | 0.245 | 0.266 | 0.300 | 0.024 | 0.075 | 0.271 | 0.330 | 0.238 | 0.135
18 | 0.235 | 0.279 | 0.345 | 0.298 | 0.028 | 0.086 | 0.277 | 0.345 | 0.384 | 0.143
19 | 0.244 | 0.298 | 0.475 | 0.318 | 0.033 | 0.096 | 0.282 | 0.363 | 0.794 | 0.152
20 | 0.235 | 0.297 | 0.621 | 0.347 | 0.040 | 0.074 | 0.286 | 0.382 | 0.375 | 0.192
21 | 0.243 | 0.315 | 0.642 | 0.363 | 0.047 | 0.090 | 0.284 | 0.391 | 0.432 | 0.199
22 | 0.273 | 0.356 | 0.585 | 0.360 | 0.061 | 0.086 | 0.267 | 0.363 | 0.271 | 0.262
23 | 0.323 | 0.421 | 1.268 | 0.310 | 0.068 | 0.095 | 0.275 | 0.381 | 0.240 | 0.264
24 | 0.337 | 0.447 | 10.390 | 0.328 |  |  |  |  |  |
25 | 0.331 | 0.434 | 1.472 | 0.378 |  |  |  |  |  |
26 | 0.367 | 0.496 | 1.539 | 0.348 | 0.086 | 0.189 | 0.283 | 0.399 | 2.250 | 0.259
27 | 0.374 | 0.514 | 1.001 | 0.365 | 0.110 | 0.170 | 0.248 | 0.355 | 1.323 | 0.357
28 | 0.371 | 0.532 | 0.706 | 0.382 |  |  |  |  |  |
29 | 0.382 | 0.550 | 0.732 | 0.402 |  |  |  |  |  |
30 | 0.379 | 0.555 | 0.780 | 0.433 | 0.134 | 0.264 | 0.240 | 0.366 | 6.873 | 0.367
31 | 0.395 | 0.575 | 0.853 | 0.445 | 0.147 | 0.238 | 0.248 | 0.373 | 0.972 | 0.413
32 | 0.397 | 0.593 | 1.352 | 0.460 | 0.149 | 0.329 | 0.252 | 0.385 | 28.069 | 0.339
33 | 0.408 | 0.650 | 1.943 | 0.435 | 0.264 | 0.355 | 0.257 | 0.386 | 1.573 | 0.346
34 | 0.412 | 0.661 | 2.232 | 0.464 | 0.207 | 0.380 | 0.245 | 0.370 | 1.518 | 0.375
35 | 0.419 | 0.695 | 32.298 | 0.468 | 0.678 | 0.409 | 0.240 | 0.385 | 1.527 | 0.366
36 | 0.422 | 0.737 | 0.913 | 0.453 | 0.635 | 0.431 | 0.224 | 0.389 | 1.293 | 0.376
37 | 0.461 | 0.749 | 1.396 | 0.476 | 1.343 | 0.477 | 0.228 | 0.366 | 1.398 | 0.391
38 | 0.529 | 0.770 | 1.416 | 0.489 | 1.420 | 0.501 | 0.219 | 0.362 | 1.516 | 0.409
39 | 0.624 | 0.793 | 1.415 | 0.500 | 1.519 | 0.529 | 0.208 | 0.357 | 1.499 | 0.423
40 | 0.696 | 0.815 | 1.319 | 0.516 | 1.566 | 0.554 | 0.198 | 0.352 | 1.541 | 0.435
41 | 0.792 | 0.838 | 1.250 | 0.544 | 1.628 | 0.581 | 0.188 | 0.347 | 1.432 | 0.446
42 | 0.905 | 0.863 | 1.328 | 0.549 | 1.703 | 0.610 | 0.176 | 0.340 | 1.496 | 0.471
43 | 0.994 | 0.886 | 1.243 | 0.561 | 1.743 | 0.638 | 0.163 | 0.333 | 1.217 | 0.467
44 | 1.096 | 0.911 | 2.062 | 0.582 | 1.967 | 0.687 | 0.150 | 0.318 | 1.375 | 0.485
45 | 1.175 | 0.934 | 1.293 | 0.591 | 1.998 | 0.715 | 0.137 | 0.310 | 1.211 | 0.504

##  Appendix C Wind sensitivity

Figure 8: The top panel shows the $\mathrm{{}^{12}C}$ yield in solar masses
for $\rm{M_{init}}$=45$\,\rm{M}_{\odot}$, single (blue) and binary (red),
stars as a function of the wind scaling factor $\rm{\eta_{Dutch}}$. The grey
line in this panel shows a value of zero. The bottom panels shows the absolute
values of the ratio of the two yields. Two models are shown that have
anomalous behaviour and are excluded from the curves. The grey line in this
panel shows where the ratio equals one.

Figure 8 shows the ratio of the $\mathrm{{}^{12}C}$ yields between a
45$\,\rm{M}_{\odot}$ binary-stripped and single star as a function of the wind
scale factor $\rm{\eta_{Dutch}}$. As $\eta_{Dutch}$ increases the total wind
mass loss increases. This increases the amount of the C/O rich helium core
removed once the star is stripped of its hydrogen and helium layers. For all
$\rm{\eta_{Dutch}}>0.5$ binary-stripped stars produce more $\mathrm{{}^{12}C}$
than single stars, with a peak in the fraction coming from binaries at
$\rm{\eta_{Dutch}}\approx 0.8$. This is due to the single star not removing
its helium layers and thus not exposing its C/O rich helium core, while the
binary star does (Farmer et al., 2021). The online Zenodo material contains
the wind yields for all isotopes, for a $\rm{M_{init}}=45\,\rm{M}_{\odot}$
single and binary-stripped stars.

##  Appendix D Evolution properties

Tables 3 and 4 detail the main properties of our stellar models during their
evolution.

Table 3: Properties of our single star models during their evolution. $\rm{M_{init}}$ is the initial mass, $\rm{M_{Final}}$ is the final mass of the star, Age is the total lifetime of the star, $\rm{He_{core}}$ is the helium core mass at collapse, $\rm{C_{core}}$ is the carbon core mass at collapse, $\rm{\Delta M_{wind}}$ is the mass list due to winds, $\rm{\Delta M_{RLOF}}$ is the mass loss due to RLOF, $\rm{\mathrm{{}^{12}C}_{cntr}}$ is the central $\mathrm{{}^{12}C}$ fraction at core helium depletion, $\rm{H_{fin}}$, $\rm{He_{fin}}$, $\rm{C_{fin}}$ are the final mass of $\mathrm{{}^{1}H}$, $\mathrm{{}^{4}He}$, and $\mathrm{{}^{12}C}$ at collapse.  $\rm{M_{init}}$ | $\rm{M_{Final}}$ | Age | $\rm{He_{core}}$ | $\rm{C_{core}}$ | $\rm{\Delta M_{wind}}$ | $\rm{\Delta M_{RLOF}}$ | $\rm{\mathrm{{}^{12}C}_{cntr}}$ | $\rm{H_{fin}}$ | $\rm{He_{fin}}$ | $\rm{C_{fin}}$
---|---|---|---|---|---|---|---|---|---|---
$\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ | Myr | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ |  | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$
11 | 9.36 | 23.59 | 3.78 | 2.34 | 1.64 | 0.00 | 0.33 | 3.82 | 2.98 | 0.13
12 | 9.77 | 20.38 | 4.27 | 2.75 | 2.23 | 0.00 | 0.32 | 3.75 | 3.04 | 0.12
13 | 10.04 | 17.95 | 4.78 | 3.16 | 2.96 | 0.00 | 0.31 | 3.58 | 3.07 | 0.18
14 | 10.18 | 16.06 | 5.29 | 3.61 | 3.82 | 0.00 | 0.30 | 3.30 | 3.05 | 0.18
15 | 10.18 | 14.55 | 5.82 | 4.07 | 4.82 | 0.00 | 0.30 | 2.91 | 2.98 | 0.17
16 | 10.03 | 13.32 | 6.36 | 4.54 | 5.97 | 0.00 | 0.29 | 2.41 | 2.86 | 0.18
17 | 10.05 | 12.30 | 6.85 | 4.99 | 6.95 | 0.00 | 0.28 | 2.07 | 2.78 | 0.19
18 | 10.08 | 11.45 | 7.34 | 5.44 | 7.92 | 0.00 | 0.28 | 1.74 | 2.70 | 0.31
19 | 10.55 | 10.73 | 7.76 | 5.82 | 8.45 | 0.00 | 0.27 | 1.75 | 2.76 | 0.27
20 | 11.57 | 10.11 | 8.04 | 6.08 | 8.43 | 0.00 | 0.27 | 2.22 | 3.05 | 0.32
21 | 12.05 | 9.58 | 8.42 | 6.39 | 8.95 | 0.00 | 0.27 | 2.26 | 3.17 | 0.32
22 | 11.90 | 9.12 | 8.78 | 6.74 | 10.10 | 0.00 | 0.26 | 1.81 | 3.13 | 0.34
23 | 11.05 | 8.72 | 9.41 | 7.32 | 11.95 | 0.00 | 0.24 | 0.73 | 2.80 | 0.20
24 | 11.31 | 8.35 | 9.15 | 7.81 | 12.69 | 0.00 | 0.23 | 0.57 | 2.75 | 0.30
25 | 12.68 | 8.02 | 10.35 | 8.20 | 12.32 | 0.00 | 0.23 | 1.05 | 3.23 | 0.30
26 | 11.94 | 7.72 | 11.70 | 9.47 | 14.06 | 0.00 | 0.21 | 0.05 | 2.20 | 0.37
27 | 12.42 | 7.46 | 11.98 | 9.73 | 14.58 | 0.00 | 0.21 | 0.11 | 2.39 | 0.41
28 | 12.89 | 7.23 | 12.15 | 9.87 | 15.11 | 0.00 | 0.21 | 0.23 | 2.60 | 0.39
29 | 13.38 | 7.01 | 12.62 | 10.31 | 15.62 | 0.00 | 0.20 | 0.24 | 2.64 | 0.43
30 | 14.26 | 6.80 | 13.09 | 10.73 | 15.74 | 0.00 | 0.20 | 0.40 | 2.92 | 0.31
31 | 14.68 | 6.61 | 12.80 | 11.70 | 16.32 | 0.00 | 0.20 | 0.16 | 2.60 | 0.30
32 | 15.16 | 6.44 | 14.41 | 11.98 | 16.84 | 0.00 | 0.20 | 0.23 | 2.72 | 0.24
33 | 14.57 | 6.29 | 14.57 | 12.66 | 18.43 | 0.00 | 0.20 | 0.00 | 1.56 | 0.57
34 | 15.24 | 6.14 | 15.24 | 13.60 | 18.76 | 0.00 | 0.20 | 0.00 | 1.59 | 0.64
35 | 15.27 | 6.01 | 15.27 | aaThe C core mass is ill-defined due to convective mixing bluring the chemical gradient at the edge of the C core in these models.  | 19.73 | 0.00 | 0.20 | 0.00 | 1.18 | 0.91
36 | 15.11 | 5.88 | 15.11 | aaThe C core mass is ill-defined due to convective mixing bluring the chemical gradient at the edge of the C core in these models.  | 20.89 | 0.00 | 0.20 | 0.00 | 0.82 | 0.66
37 | 15.75 | 5.74 | 15.75 | 13.74 | 21.25 | 0.00 | 0.20 | 0.00 | 0.14 | 1.11
38 | 16.16 | 5.63 | 16.16 | 12.44 | 21.84 | 0.00 | 0.20 | 0.00 | 0.13 | 1.20
39 | 16.51 | 5.53 | 16.51 | 10.74 | 22.49 | 0.00 | 0.20 | 0.00 | 0.15 | 1.20
40 | 16.89 | 5.44 | 16.89 | 14.23 | 23.11 | 0.00 | 0.20 | 0.00 | 0.28 | 1.19
41 | 17.23 | 5.35 | 17.23 | 14.82 | 23.77 | 0.00 | 0.20 | 0.00 | 0.19 | 1.21
42 | 17.53 | 5.26 | 17.53 | 14.31 | 24.47 | 0.00 | 0.19 | 0.00 | 0.21 | 1.28
43 | 17.86 | 5.18 | 17.86 | 9.57 | 25.14 | 0.00 | 0.19 | 0.00 | 0.19 | 1.24
44 | 18.16 | 5.10 | 18.16 | 7.30 | 25.84 | 0.00 | 0.19 | 0.00 | 0.22 | 2.00
45 | 18.50 | 5.03 | 18.50 | 15.84 | 26.50 | 0.00 | 0.19 | 0.00 | 0.14 | 1.35
Table 4: Properties of our binary-stripped stars during their evolution. Columns have the same meaning as in Table 3.  $\rm{M_{init}}$ | $\rm{M_{Final}}$ | Age | $\rm{He_{core}}$ | $\rm{C_{core}}$ | $\rm{\Delta M_{wind}}$ | $\rm{\Delta M_{RLOF}}$ | $\rm{\mathrm{{}^{12}C}_{cntr}}$ | $\rm{H_{fin}}$ | $\rm{He_{fin}}$ | $\rm{C_{fin}}$
---|---|---|---|---|---|---|---|---|---|---
$\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ | Myr | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ |  | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$
11 | 3.17 | 23.69 | 3.17 | 1.93 | 0.70 | 7.12 | 0.38 | 0.00 | 1.16 | 0.06
12 | 3.58 | 20.44 | 3.58 | 2.22 | 0.87 | 7.55 | 0.37 | 0.00 | 1.24 | 0.08
13 | 3.98 | 17.99 | 3.98 | 2.55 | 1.06 | 7.95 | 0.36 | 0.00 | 1.28 | 0.16
14 | 4.39 | 16.08 | 4.39 | 2.88 | 1.29 | 8.32 | 0.35 | 0.00 | 1.35 | 0.11
15 | 4.79 | 14.56 | 4.79 | 3.23 | 1.54 | 8.67 | 0.34 | 0.00 | 1.33 | 0.19
16 | 5.15 | 13.33 | 5.15 | 3.56 | 1.78 | 9.07 | 0.33 | 0.00 | 1.34 | 0.22
17 | 5.52 | 12.31 | 5.52 | 3.91 | 2.13 | 9.35 | 0.32 | 0.00 | 1.31 | 0.22
18 | 5.77 | 11.46 | 5.77 | 4.14 | 2.43 | 9.80 | 0.32 | 0.00 | 1.31 | 0.25
19 | 6.00 | 10.75 | 6.00 | 4.36 | 2.71 | 10.29 | 0.31 | 0.00 | 1.19 | 0.35
20 | 7.07 | 10.12 | 7.07 | 5.27 | 2.09 | 10.83 | 0.29 | 0.00 | 1.39 | 0.36
21 | 7.36 | 9.58 | 7.36 | 5.55 | 2.56 | 11.08 | 0.29 | 0.00 | 1.36 | 0.35
22 | 9.27 | 9.15 | 8.48 | 6.49 | 2.43 | 10.30 | 0.25 | 0.32 | 2.31 | 0.35
23 | 9.50 | 8.71 | 7.44 | 7.09 | 2.70 | 10.80 | 0.26 | 0.14 | 2.12 | 0.40
24 |  |  |  |  |  |  |  |  |  |
25 |  |  |  |  |  |  |  |  |  |
26 | 9.31 | 7.70 | 9.31 | 7.46 | 5.37 | 11.32 | 0.27 | 0.00 | 0.86 | 0.84
27 | 12.12 | 7.47 | 11.15 | 8.97 | 4.81 | 10.07 | 0.23 | 0.36 | 2.58 | 0.33
28 |  |  |  |  |  |  |  |  |  |
29 |  |  |  |  |  |  |  |  |  |
30 | 12.12 | 6.79 | 12.12 | 0.00 | 7.50 | 10.38 | 0.23 | 0.00 | 1.33 | 0.72
31 | 13.66 | 6.61 | 12.43 | 11.15 | 6.75 | 10.58 | 0.21 | 0.03 | 2.26 | 0.21
32 | 11.75 | 6.43 | 11.75 | 9.72 | 9.32 | 10.93 | 0.24 | 0.00 | 0.38 | 1.04
33 | 11.98 | 6.28 | 11.98 | 9.91 | 10.08 | 10.94 | 0.23 | 0.00 | 0.29 | 1.14
34 | 12.71 | 6.14 | 12.71 | 10.53 | 10.78 | 10.51 | 0.23 | 0.00 | 0.27 | 1.22
35 | 12.47 | 6.00 | 12.47 | 10.32 | 11.60 | 10.93 | 0.23 | 0.00 | 0.30 | 1.22
36 | 12.73 | 5.88 | 12.73 | 10.55 | 12.24 | 11.04 | 0.23 | 0.00 | 0.29 | 1.25
37 | 13.11 | 5.75 | 13.11 | 10.89 | 13.52 | 10.37 | 0.22 | 0.00 | 0.28 | 1.29
38 | 13.50 | 5.64 | 13.50 | 6.22 | 14.22 | 10.28 | 0.22 | 0.00 | 0.17 | 1.12
39 | 13.86 | 5.54 | 13.86 | 6.31 | 15.00 | 10.14 | 0.22 | 0.00 | 0.20 | 1.19
40 | 14.29 | 5.44 | 14.29 | 6.55 | 15.72 | 9.99 | 0.21 | 0.00 | 0.20 | 1.23
41 | 14.69 | 5.35 | 14.69 | 7.22 | 16.48 | 9.83 | 0.21 | 0.00 | 0.19 | 1.21
42 | 15.06 | 5.27 | 15.06 | 6.49 | 17.29 | 9.65 | 0.21 | 0.00 | 0.19 | 1.28
43 | 15.48 | 5.19 | 15.48 | 12.92 | 18.09 | 9.43 | 0.21 | 0.00 | 0.30 | 1.21
44 | 15.49 | 5.11 | 15.49 | 7.01 | 19.49 | 9.01 | 0.21 | 0.00 | 0.18 | 1.22
45 | 15.91 | 5.04 | 15.91 | 9.77 | 20.29 | 8.80 | 0.20 | 0.00 | 0.21 | 1.28

##  Appendix E Explosion properties

Tables 5 and 6 detail the main properties of our stellar models during the
core collapse phase of their evolution.

Table 5: Properties of our single star models during the supernovae explosion. $\rm{M_{init}}$ is the initial mass, $\rm{M_{Final}}$ is the final mass of the star, $\rm{M_{Fe}}$ is the mass of the iron core, $\rm{M_{Ni56}}$ is the mass of $\mathrm{{}^{56}Ni}$ at the time of shock breakout, $\rm{E}$ is the total energy of the model at shock breakout, $\rm{M_{rem}}$ is the mass of the compact object at shock breakout (assuming the envelope did not fallback onto the compact object), $\rm{Fate}$ is the final fate as given by Ertl et al. (2016).  $\rm{M_{init}}$ | $\rm{M_{Final}}$ | $\rm{M_{Fe}}$ | $\rm{\xi_{M=2.5}}$ | $\rm{M_{4}}$ | $\rm{\mu_{4}}$ | $\rm{M_{Ni56}}$ | $\rm{E}$ | $\rm{M_{rem}}$ | $\rm{Fate}$
---|---|---|---|---|---|---|---|---|---
$\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ |  | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}/1000\rm{km}$ | $\,\rm{M}_{\odot}$ | $10^{51}\rm{erg/s}$ | $\,\rm{M}_{\odot}$ |
11 | 9.36 | 1.36 | 0.05 | 1.52 | 0.06 | 0.04 | 1.00 | 1.53 | NS
12 | 9.77 | 1.35 | 0.09 | 1.62 | 0.05 | 0.02 | 1.00 | 1.62 | NS
13 | 10.04 | 1.40 | 0.18 | 1.57 | 0.10 | 0.08 | 1.00 | 1.57 | BH
14 | 10.18 | 1.43 | 0.22 | 1.73 | 0.10 | 0.04 | 1.00 | 1.73 | BH
15 | 10.18 | 1.47 | 0.19 | 1.88 | 0.07 | 0.04 | 1.00 | 1.88 | NS
16 | 10.03 | 1.47 | 0.22 | 1.77 | 0.10 | 0.06 | 1.00 | 1.78 | BH
17 | 10.05 | 1.41 | 0.17 | 1.56 | 0.12 | 0.14 | 1.00 | 1.56 | BH
18 | 10.08 | 1.39 | 0.19 | 1.62 | 0.08 | 0.04 | 1.00 | 1.62 | BH
19 | 10.55 | 1.40 | 0.18 | 1.53 | 0.10 | 0.11 | 1.00 | 1.53 | BH
20 | 11.57 | 1.44 | 0.21 | 1.71 | 0.09 | 0.06 | 1.00 | 1.71 | BH
21 | 12.05 | 1.41 | 0.16 | 1.75 | 0.06 | 0.02 | 1.00 | 1.75 | NS
22 | 11.90 | 1.43 | 0.15 | 1.68 | 0.08 | 0.08 | 1.00 | 1.68 | BH
23 | 11.05 | 1.64 | 0.41 | 2.27 | 0.12 | 0.07 | 1.00 | 2.27 | BH
24 | 11.31 | 1.70 | 0.51 | 2.02 | 0.27 | 0.31 | 1.00 | 2.02 | BH
25 | 12.68 | 1.71 | 0.53 | 1.96 | 0.30 | 0.39 | 1.00 | 1.96 | BH
26 | 11.94 | 1.61 | 0.39 | 2.08 | 0.14 | 0.14 | 1.00 | 2.08 | BH
27 | 12.42 | 1.62 | 0.38 | 2.06 | 0.14 | 0.13 | 1.00 | 2.06 | BH
28 | 12.89 | 1.62 | 0.38 | 2.06 | 0.14 | 0.13 | 1.00 | 2.06 | BH
29 | 13.38 | 1.57 | 0.34 | 1.98 | 0.12 | 0.13 | 1.00 | 1.98 | BH
30 | 14.26 | 1.49 | 0.26 | 1.99 | 0.09 | 0.06 | 1.00 | 1.99 | NS
31 | 14.68 | 1.51 | 0.25 | 2.07 | 0.07 | 0.06 | 1.00 | 2.07 | NS
32 | 15.16 | 1.53 | 0.26 | 2.12 | 0.07 | 0.05 | 1.00 | 2.12 | NS
33 | 14.57 | 1.65 | 0.44 | 2.22 | 0.15 | 0.17 | 1.00 | 2.22 | BH
34 | 15.24 | 1.67 | 0.49 | 2.09 | 0.25 | 0.30 | 1.00 | 2.09 | BH
35 | 15.27 | 1.51 | 0.29 | 2.00 | 0.13 | 0.12 | 1.00 | 2.00 | BH
36 | 15.11 | 1.60 | 0.37 | 2.25 | 0.10 | 0.08 | 1.00 | 2.25 | NS
37 | 15.75 | 1.57 | 0.33 | 2.24 | 0.08 | 0.07 | 1.00 | 2.24 | NS
38 | 16.16 | 1.58 | 0.34 | 2.28 | 0.08 | 0.05 | 1.00 | 2.28 | NS
39 | 16.51 | 1.58 | 0.37 | 2.32 | 0.08 | 0.06 | 1.00 | 2.32 | NS
40 | 16.89 | 1.61 | 0.44 | 2.26 | 0.15 | 0.14 | 1.01 | 2.26 | BH
41 | 17.23 | 1.57 | 0.40 | 1.79 | 0.21 | 0.33 | 1.00 | 1.79 | BH
42 | 17.53 | 1.59 | 0.42 | 1.96 | 0.20 | 0.26 | 1.00 | 1.96 | BH
43 | 17.86 | 1.58 | 0.43 | 1.94 | 0.22 | 0.28 | 1.00 | 1.94 | BH
44 | 18.16 | 1.49 | 0.33 | 1.66 | 0.19 | 0.30 | 1.00 | 1.66 | BH
45 | 18.50 | 1.55 | 0.38 | 1.74 | 0.19 | 0.33 | 1.00 | 1.74 | BH
Table 6: Properties of our binary-stripped models during the supernovae explosion. Columns have the same meaning as in Table 5.  $\rm{M_{init}}$ | $\rm{M_{Final}}$ | $\rm{M_{Fe}}$ | $\rm{\xi_{M=2.5}}$ | $\rm{M_{4}}$ | $\rm{\mu_{4}}$ | $\rm{M_{Ni56}}$ | $\rm{E}$ | $\rm{M_{rem}}$ | $\rm{Fate}$
---|---|---|---|---|---|---|---|---|---
$\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ | $\,\rm{M}_{\odot}$ |  | $\,\rm{M}_{\odot}$ |  | $\,\rm{M}_{\odot}$ | $10^{51}erg/s$ | $\,\rm{M}_{\odot}$ |
11 | 3.17 | 1.26 | 0.01 | 1.36 | 0.03 | 0.03 | 1.00 | 1.36 | NS
12 | 3.58 | 1.32 | 0.03 | 1.43 | 0.06 | 0.08 | 1.00 | 1.43 | NS
13 | 3.98 | 1.32 | 0.10 | 1.46 | 0.06 | 0.07 | 1.00 | 1.46 | NS
14 | 4.39 | 1.35 | 0.10 | 1.64 | 0.04 | 0.02 | 1.00 | 1.64 | NS
15 | 4.79 | 1.40 | 0.18 | 1.64 | 0.08 | 0.08 | 1.00 | 1.64 | BH
16 | 5.15 | 1.46 | 0.21 | 1.69 | 0.10 | 0.12 | 1.00 | 1.69 | BH
17 | 5.52 | 1.44 | 0.17 | 1.69 | 0.08 | 0.11 | 1.00 | 1.69 | BH
18 | 5.77 | 1.44 | 0.19 | 1.71 | 0.09 | 0.11 | 1.00 | 1.71 | BH
19 | 6.00 | 1.43 | 0.19 | 1.69 | 0.09 | 0.10 | 1.00 | 1.69 | BH
20 | 7.07 | 1.38 | 0.21 | 1.62 | 0.10 | 0.11 | 1.00 | 1.62 | BH
21 | 7.36 | 1.44 | 0.20 | 1.70 | 0.09 | 0.10 | 1.00 | 1.70 | BH
22 | 9.27 | 1.46 | 0.17 | 1.85 | 0.06 | 0.06 | 1.00 | 1.85 | NS
23 | 9.50 | 1.51 | 0.23 | 2.03 | 0.08 | 0.06 | 1.00 | 2.03 | NS
24 |  |  |  |  |  |  |  |  |
25 |  |  |  |  |  |  |  |  |
26 | 9.31 | 1.58 | 0.34 | 1.96 | 0.15 | 0.16 | 1.00 | 1.96 | BH
27 | 12.12 | 1.69 | 0.50 | 1.99 | 0.26 | 0.34 | 1.00 | 1.99 | BH
28 |  |  |  |  |  |  |  |  |
29 |  |  |  |  |  |  |  |  |
30 | 12.12 | 1.38 | 0.13 | 1.71 | 0.05 | 0.03 | 1.00 | 1.71 | NS
31 | 13.66 | 1.43 | 0.18 | 1.95 | 0.06 | 0.02 | 1.00 | 1.95 | NS
32 | 11.75 | 1.69 | 0.49 | 2.13 | 0.22 | 0.26 | 1.01 | 2.13 | BH
33 | 11.98 | 1.65 | 0.46 | 2.15 | 0.19 | 0.21 | 1.00 | 2.15 | BH
34 | 12.71 | 1.62 | 0.39 | 2.08 | 0.14 | 0.15 | 1.00 | 2.08 | BH
35 | 12.47 | 1.62 | 0.39 | 2.09 | 0.14 | 0.15 | 1.00 | 2.09 | BH
36 | 12.73 | 1.61 | 0.38 | 2.06 | 0.14 | 0.15 | 1.00 | 2.06 | BH
37 | 13.11 | 1.60 | 0.36 | 2.03 | 0.13 | 0.14 | 1.00 | 2.03 | BH
38 | 13.50 | 1.45 | 0.18 | 1.90 | 0.06 | 0.06 | 1.00 | 1.90 | NS
39 | 13.86 | 1.46 | 0.19 | 1.87 | 0.08 | 0.10 | 1.00 | 1.87 | NS
40 | 14.29 | 1.48 | 0.20 | 1.94 | 0.07 | 0.08 | 1.00 | 1.94 | NS
41 | 14.69 | 1.49 | 0.22 | 2.03 | 0.07 | 0.07 | 1.00 | 2.03 | NS
42 | 15.06 | 1.48 | 0.21 | 1.69 | 0.14 | 0.20 | 1.00 | 1.69 | BH
43 | 15.48 | 1.58 | 0.32 | 2.24 | 0.08 | 0.05 | 1.00 | 2.24 | NS
44 | 15.49 | 1.51 | 0.23 | 1.73 | 0.14 | 0.20 | 1.00 | 1.73 | BH
45 | 15.91 | 1.47 | 0.28 | 1.60 | 0.19 | 0.32 | 1.00 | 1.60 | BH

We acknowledge helpful discussions with M. Renzo. SdM and SJ acknowledge
funding by the Netherlands Organization for Scientific Research (NWO) as part
of the Vidi research program BinWaves (project number 639.042.728). This work
was also supported by the Cost Action Program ChETEC CA16117. EL acknowledges
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (Grant agreement No. 945806).
This research has made use of NASA’s Astrophysics Data System.

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