11institutetext: Institute for Astronomy (IvS), KU Leuven, Celestijnenlaan
200D, 3001, Leuven, Belgium 22institutetext: School of Physics & Astronomy,
Monash University, Clayton 3800, Victoria, Australia 33institutetext: Centre
of Excellence for Astrophysics in Three Dimensions (ASTRO-3D), Melbourne,
Victoria, Australia 44institutetext: Center for Computational Astrophysics,
Flatiron Institute, New York City, New York, USA 55institutetext: Department
of Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada
66institutetext: Konkoly Observatory, Research Centre for Astronomy and Earth
Sciences, Eötvös Loránd Research Network (ELKH), Konkoly Thege Miklós út
15-17, H-1121 Budapest, Hungary 77institutetext: Astrophysics Research Group,
University of Surrey, Guildford, Surrey GU2 7XH, UK

# Nova contributions to the chemical evolution of the Milky Way

Alex J. Kemp, 1122<EMAIL_ADDRESS>Amanda I. Karakas, 2233 Andrew R.
Casey 2244 Benoit Côté, 5566 Robert G. Izzard 77 Zara Osborn, 2233

(Received May 20, 2024; accepted May 21, 2024 )

###### Abstract

Context. The explosive burning that drives nova eruptions results in unique
nucleosynthesis that heavily over-produces certain isotopes relative to the
solar abundance. However, novae are often ignored when considering the
chemical evolution of our Galaxy due to their low ejecta masses. Galactic
chemical evolution studies including novae are rare and have previously relied
upon simplified treatments for the behaviour of nova populations.

Aims. In this work, we use previously computed synthetic nova populations and
the galactic chemical evolution code OMEGA+ to assess the impact that novae
have on the evolution of stable elemental and isotopic abundances.

Methods. We combine populations of novae computed using the binary population
synthesis code binary_c with the galactic chemical evolution code OMEGA+ and
detailed, white dwarf mass-dependent nova yields to model the nucleosynthetic
contributions of novae to the evolution of the Milky Way. We consider three
different nova yield profiles, each corresponding to a different set of nova
yield calculations.

Results. We examine which nova sites contribute most to which isotopes.
Despite novae from low-mass white dwarfs (WDs) dominating nova ejecta
contributions, we find that novae occurring on massive WDs are still able to
contribute significantly to many isotopes, particularly those with high mass
numbers. We find that novae can produce up to 35% of the Galactic ${}^{13}{\rm
C}$ and ${}^{15}{\rm N}$ mass by the time the model Galaxy reaches [Fe/H] = 0,
and earlier in the evolution of the Galaxy (between [Fe/H] = -2 and -1) novae
may have been the dominant source of ${}^{15}{\rm N}$. Predictions for
[${}^{13}{\rm C}$/Fe], [${}^{15}{\rm N}$/Fe], ${}^{12}{\rm C}$/${}^{13}{\rm
C}$, and ${}^{14}{\rm N}$/${}^{15}{\rm N}$ abundances ratios vary by up to 0.2
dex at [Fe/H] = 0 and by up to 0.7 dex in [${}^{15}{\rm N}$/Fe] and
${}^{14}{\rm N}$/${}^{15}{\rm N}$ between [Fe/H] = -2 and -1 (corresponding
approximately to Galactic ages of 170 Myr and 1 Gyr in our model). The
Galactic evolution of other stable isotopes (excluding Li) is not noticeably
affected by including novae. For most isotopes, agreement is generally good
between the three different yield profiles we consider. Isotopes where
agreement is relatively poor include: ${}^{3}{\rm H}$e (especially at high
$M_{\rm WD}$), ${}^{7}{\rm L}$i, ${}^{18}{\rm O}$, ${}^{19}{\rm F}$, and the
¿1.3 M⊙ regime of ${}^{29}{\rm S}$i, ${}^{33}{\rm S}$, ${}^{34}{\rm S}$,
${}^{35}{\rm C}$l, and ${}^{36}{\rm A}$r.

###### Key Words.:

Stars: Novae, cataclysmic variables; binaries; white dwarfs; ISM: abundances;
Galaxy: abundances, evolution

##  1 Introduction

The origin of the elements is one of the most fundamental and complex
questions in astrophysics (Arcones & Thielemann, 2023). Our theoretical
knowledge of nuclear physics, stellar evolution, galactic evolution, and
primordial cosmology all feed into predictions of how much of each isotope in
different parts of the Milky Way – where the vast majority of our observations
of stellar abundances take place – should have as a function of time. Each of
these fields requires the support of a vast body of observational work (e.g.,
Wilson et al., 2019; Buder et al., 2021) mapping out abundance patterns in
diverse environments in order to constrain, validate, and highlight issues
with our theoretical models.

The role of novae in galactic chemical evolution (GCE) has traditionally been
sidelined due to their low lifetime-integrated ejecta mass when compared to
stellar sources such as supernovae and asymptotic giant branch (AGB) stars
(Gehrz et al., 1998; José & Hernanz, 1998). However, the ability of novae to
significantly over-produce certain rare isotopes relative to their solar
abundance ratios, such as ${}^{13}{\rm C}$, ${}^{15}{\rm N}$, and ${}^{17}{\rm
O}$, raises the prospect of novae playing a non-negligible role in the
Galactic evolution of certain abundance ratios (Gehrz et al., 1998; Romano &
Matteucci, 2003). Due primarily to their characteristic overproduction of
${}^{13}{\rm C}$ and ${}^{15}{\rm N}$, novae have also been proposed as the
origin of a rare (¡1%) subset of SiC pre-solar grains, the ‘nova grains’
(Amari et al., 2001; Amari, 2002; Lodders & Amari, 2005). The true origin of
at least some of these nova grains remains contentious, primarily due to the
difficulty of reproducing abundances of Si and Ti isotopes in nova models
(Nittler & Hoppe, 2005; Jose & Hernanz, 2007).

Previous efforts to estimate the importance of novae in the context of
galactic chemical evolution (e.g., Romano & Matteucci, 2003; Cescutti &
Molaro, 2019; Grisoni et al., 2019) have relied on simplified models for the
behaviour of novae and typically focus on a low number of isotopes in detail.
In this work, we explore the role that novae play in galactic chemical
evolution by combining a metallicity-dependent grid of pre-computed, synthetic
nova populations (Kemp et al., 2022b) with the galactic chemical evolution
code OMEGA+ (Côté et al., 2018). Using theoretical, $M_{\rm WD}$-dependent
nova yields from José & Hernanz (1998), Starrfield et al. (2009), Starrfield
et al. (2020), and José et al. (2020), we examine the contribution of novae to
the evolution of 32 different isotopes: ${}^{3}{\rm H}$e, ${}^{4}{\rm H}$e,
${}^{12}{\rm C}$, ${}^{13}{\rm C}$, ${}^{14}{\rm N}$, ${}^{15}{\rm N}$,
${}^{16}{\rm O}$, ${}^{17}{\rm O}$, ${}^{18}{\rm O}$, ${}^{19}{\rm F}$,
${}^{20}{\rm N}$e, ${}^{21}{\rm N}$e, ${}^{22}{\rm N}$e, ${}^{23}{\rm N}$a,
${}^{24}{\rm M}$g, ${}^{25}{\rm M}$g, ${}^{26}{\rm A}$l, ${}^{26}{\rm M}$g,
${}^{27}{\rm A}$l, ${}^{28}{\rm S}$i, ${}^{29}{\rm S}$i, ${}^{30}{\rm S}$i,
${}^{31}{\rm P}$, ${}^{32}{\rm S}$, ${}^{33}{\rm S}$, ${}^{34}{\rm S}$,
${}^{35}{\rm C}$l, ${}^{36}{\rm A}$r, ${}^{37}{\rm C}$l, ${}^{38}{\rm A}$r,
${}^{39}{\rm K}$, and ${}^{40}{\rm C}$a.

We compare nova contributions of these isotopes to the Milky Way with
asymptotic giant branch (AGB) stars, massive stars (defined as stars that
undergo core-collapse supernova explosions), and type Ia supernovae. We also
examine which WD masses are the most important to the production of each
isotope. Previously this has been discussed in the context of the
nucleosynthetic pathways (Gehrz et al., 1998; José & Hernanz, 1998; Iliadis,
2015; Starrfield et al., 2009, 2020; José et al., 2020; Starrfield et al.,
2024), but different nova systems produce different amounts of ejecta due to
birth and binary stellar evolution considerations. By folding initial mass
function (IMF), binary stellar evolution, and nucleosynthesis considerations
into our modelling, for the first time we can holistically assess the
contributions of different parts of the nova parameter-space. This isotope-
specific discussion is prefaced by a discussion of the metallicity-dependent
distributions of nova ejecta mass, and how – and why – they differ from
distributions of nova events.

In Section 2 we describe our methodology. In Section 3 we present the ejecta-
mass distributions of our nova populations, with comparisons to the event-
weighted distributions. In Section 4 we present our analysis of nova
contributions to the chemical evolution of the Milky Way, with discussion of
which nova white dwarf masses contribute most to which isotopes. Finally, in
Section 5 we present our conclusions.

Machine-readable outputs from the underlying nova populations and machine-
readable yield profiles, both suitable for use in galactic chemical evolution
calculations, are available online on Zenodo
111https://zenodo.org/records/6898161.

##  2 Methodology

Relevant details for the underlying nova and binary stellar physics can be
found in Kemp et al. (2021), and details about the specific binary populations
used in this work can be found in Kemp et al. (2022b). A description of our
Galactic modelling is included in Kemp et al. (2022a). The methodology used in
this paper is nearly identical to that described in Kemp et al. (2022a), which
focused only on Li production in novae. We recommend a review of Section 2 of
that work, which summarises the binary population models, nova yield sets, and
GCE modelling methodology. In this section, we restrict ourselves to a brief
description of details not previously discussed in Kemp et al. (2022a) and
details specific to this work.

Kemp et al. (2022a) describe and employ five different theoretical yield
profiles. Two of these yield profiles, R2017 and R2017simple, only have
${}^{7}{\rm L}$i yields associated with them, as Rukeya et al. (2017) did not
report yields for other isotopes. For this reason, these yield sets are
excluded from our analysis in this work. We instead only consider the
remaining three theoretical yield sets: J1998 (José & Hernanz, 1998),
S2009/2020 (Starrfield et al., 2009, 2020), and J2020 (José et al., 2020);
their composition is unchanged. Since the completion of the original analysis
relevant to both Kemp et al. (2022a) and this work, an additional relevant
yield set has been released in Starrfield et al. (2024), providing updated
O/Ne WD nova yields relative to the previously available Starrfield et al.
(2009) yields. The formal inclusion of a new yield-set integrating these
yields is beyond the scope of the current work. However, a comparison between
the O/Ne WD yields from Starrfield et al. (2009) and Starrfield et al. (2024)
does not lead us to believe that such an inclusion would affect the
conclusions of this work. In particular, we note that while Li production is
increased in these new models, it is still far short of observations of nova
ejecta (Tajitsu et al., 2015; Molaro et al., 2016; Tajitsu et al., 2016;
Selvelli et al., 2018; Molaro et al., 2020; Arai et al., 2021; Izzo et al.,
2022).

When reporting the abundances and masses of the stable isotopes ${}^{18}{\rm
O}$, ${}^{22}{\rm N}$e, and ${}^{26}{\rm M}$g, we account for the decays of
their radioactive parent isotopes ${}^{18}{\rm F}$, ${}^{22}{\rm N}$a, and
${}^{26}{\rm A}$l. We do not account for the evolution of these radioactive
isotopes in detail, and instead assume instantaneous decay into their stable
daughter nuclei. This assumption is easily justifiable for ${}^{18}{\rm F}$
($t_{1/2}\approx 110$ minutes) and ${}^{22}{\rm N}$a ($t_{1/2}\approx 2.5$
years), but not ideal for the longer half-life of ${}^{26}{\rm A}$l
($t_{1/2}\approx$ $7\times 10^{5}$ years). Correctly accounting for the half-
life of ${}^{26}{\rm A}$l would result in a slight reduction of our
${}^{26}{\rm M}$g abundances; however, as we find that novae do not contribute
to ${}^{26}{\rm M}$g at anywhere near the level of AGB or massive stars (see
Section 4, we do not consider this source of error to be concerning when
considering ${}^{26}{\rm M}$g yields.

Our Galactic chemical evolution models are run using the OMEGA+ chemical
evolution code (Côté et al., 2018). Fig. 1 shows, as a function of Galactic
age, the evolution of the star formation rate (SFR), Galactic inflow rate, gas
mass, supernova (SN) rate, [Fe/H] abundance ratios, and metallicity ($Z$) of
our baseline model of the Milky Way without novae. The current Galactic age is
taken to be 13 Gyr, and the current solar age is taken to be 4.5 Gyr. Fig. 2
shows the evolution of the ratios of several important elements relative to
iron plotted against [Fe/H] of this baseline model. The observational
abundance data (grey points) are plotted alongside are from NuPyCEE’s
STELLAB222https://github.com/NuGrid/NuPyCEE/blob/master/stellab_data/abundance_data_library.txt,
Côté et al. (2017) module where available. The bulk galactic properties and
elemental abundances for most key elements are satisfactorily reproduced;
notable exceptions such as K and Sc have long been established as problematic
elements in contemporary stellar evolution and GCE codes (e.g., Kobayashi et
al., 2020). We therefore assert that our model galaxy is good enough for a
meaningful comparison between novae and other stellar sources.

Figure 1: Bulk galactic properties of our baseline model of the Milky Way. The
bounds of the shaded vertical bands are drawn from Flynn et al. (2006);
Robitaille & Whitney (2010); Chomiuk & Povich (2011); Marasco et al. (2012);
Lehner & Howk (2011); Prantzos et al. (2011); Kubryk et al. (2015), which the
model matches very well. Figure 2: Galactic abundances of key elements used to
validate our baseline model of the Milky Way, plotted with observational
abundance data from NuPyCEE’s STELLAB module, where available (all but [P/Fe];
[P/Fe] abundance data are taken from Roederer et al. 2014; Maas et al. 2019,
2022; Nandakumar et al. 2022). The bulk galactic properties and elemental
abundances for most key elements are satisfactorily reproduced. Notable
exceptions such as K and Sc have been long established as problematic elements
for contemporary stellar evolution and GCE codes (see, for example, Kobayashi
et al., 2020).

##  3 Results: Ejecta-weighted nova distributions

In Kemp et al. (2021) and Kemp et al. (2022b), nova evolution was assessed
almost exclusively with the goal of studying distributions of nova events.
These works considered when the nova eruptions occurred and the binary
conditions surrounding them at that time. Although eruptions from different
binary systems were weighted differently (according to the birth probability
of the progenitor system), novae were otherwise treated equally regardless of,
for example, how much ejecta the eruption released into the interstellar
medium (ISM).

In this work, we consider nova contributions to the origin of the elements. To
assume that each nova eruption carries with it equal amounts of ejecta mass is
a gross simplification. The mass ejected from different nova eruptions varies
significantly depending on the binary properties, as shown in Figs. 3 and 4.
These figures present the distributions of ejecta mass for nova populations
computed at $Z$ = $10^{-3}$ and $Z$ = 0.02, respectively. The amount of mass
ejected in a nova explosion varies by over 3 orders of magnitude. The left
panels of Figs. 3 and 4, coloured by the WD composition (C/O or O/Ne), show
that higher ejecta mass eruptions occur on the lower mass C/O WDs. The higher
mass O/Ne WDs are largely restricted to far lower ejecta masses per eruption.

The lower panels of Figs. 3 and 4 highlight which eruptions contribute the
most ejecta to the ISM by tracking the ejecta mass in each bin, rather than
counting the nova eruptions. The vast majority of nova ejecta is produced from
C/O WDs, which typically eject more material per eruption. The underlying
physics behind this behaviour – chiefly the far higher critical ignition
masses required for novae in low-mass WD systems – is described in Appendix A
of Kemp et al. (2022a).

Figure 3: Distribution of mass ejected per H nova eruption, $Z$ = $10^{-3}$.
Top panels count the number of events in each bin while the bottom panels
track the ejecta mass in each bin. Coloured according to the WD’s composition
(left) and the donor stellar type (Hurley et al., 2000, 2002). The donor
stellar types are, in descending order: low-mass main sequence stars, main
sequence stars, Hertzsprung Gap stars, first-ascent giant branch stars, core
He burning stars, early asymptotic giant branch stars, and thermally pulsing
asymptotic giant branch stars. Figure 4: Distribution of mass ejected per H
nova eruption, $Z$ = 0.02.

The overall influence of metallicity on nova productivity is presented in Fig.
5, analogous to Fig. 5 from Kemp et al. (2022b) but including the ejecta mass
and mean ejecta mass per system. Table 3 is a similarly updated version of
Table 3 from Kemp et al. (2022b).

The ejecta mass tracks the event productivity fairly well, implying that the
influences governing the metallicity dependence of nova productivity are not
dominated by influences specific to ejecta mass considerations. The main
discrepancy between the scaling of ejecta mass and nova event counts with
metallicity is that the nova event counts exhibit far more scatter. As
described in Kemp et al. (2022b), the origin of much of the scatter in the
number of events is due to a single, well-defined channel that is sensitive to
the initial primary mass, and can be considered numerical. This source of
scatter is largely absent in the ejecta mass plot because high-mass WDs
contribute far less ejecta, making this channel relatively unimportant.

Comparing the two metallicity cases presented in Figs. 3 and 4, increasing the
metallicity reduces the ejecta contributions of the C/O WDs, following the
reduced relative importance of low-mass WDs at higher metallicities when
considering event counts (see Kemp et al. 2022b). Figures 3 and 4 highlight
the increased importance of giant donor stars at high metallicity,
particularly for low ejecta-mass novae occurring on the massive O/Ne WDs.

It was noted in Appendix A of Kemp et al. (2022a) that the WD mass
distribution showed the greatest variation when comparing nova events to
ejecta masses. Figs. 6 and 7 demonstrate this variation graphically. Although
high-mass WDs contribute significantly to overall nova counts, they contribute
very little to overall nova ejecta mass contributions. This is mostly due to
the lower critical ignition masses associated with high-mass WDs (responsible
for their high nova counts in the first place) now acting against them when
considering ejecta-mass weighted distributions. The result is that the initial
mass function’s (Kroupa, 2001) preference for low-mass WD systems causes low-
mass WDs to dominate the ejecta mass distribution.

Kemp et al. (2022b) discuss the emergence of a bimodal feature in the WD mass
distribution of nova events at low metallicities. In short, as metallicity
reduced, contributions from low-mass WDs increased in importance, particularly
in a broad peak from 0.8-1.0 M⊙ and in a narrow peak from 0.6-0.7 M⊙.
Examining the lower panels of Figs. 6 and 7, we see similar behaviour in the
ejecta-mass distributions, although low WD-mass features become more
pronounced. Even in the $Z$ = 0.02 population, where contributions to total
nova counts from lower mass WDs are low compared to lower metallicity
populations, most of the nova ejecta is produced from WDs between 0.5 and 0.8
M⊙. Coupled with the introduction of the sharp peak in nova event
contributions around 0.6-0.7 M⊙at low metallicities, this produces a prominent
spike in the $Z$ = $10^{-3}$ distribution of ejecta mass. The influence of the
emergence of the second, broader peak in nova counts present at low
metallicity (around 0.8-1.0 M⊙) is less pronounced, but still discernable in
Fig. 6. The right-hand panels of Figs. 6 and 7 confirm the common evolutionary
origin of these peaks: increased nova productivity driven by giant (FGB and
TPAGB) donor stars (see also discussion in Kemp et al. 2022b).

Figs. 8 and 9 and Tables 2 and 4 provide a more comprehensive view of how
different mass WDs contribute to ejecta and event counts at different
metallicities. The WD mass brackets are tailored to the WD masses with
detailed simulations of nova abundances (José & Hernanz, 1998; Starrfield et
al., 2009; José et al., 2020; Starrfield et al., 2020, 2024). Large
contributions from high-mass WDs are ubiquitous across all metallicities when
considering event counts. In contrast, relative contributions from
intermediate mass WDs increase at lower metallicities, reflecting the
emergence of the low-intermediate mass bimodal feature. When considering
ejecta mass contributions shown in Figure 7, low-mass WD contributions
dominate across all metallicities, while high-mass WD contributions remain
very small. The emergence of the bimodal feature is visible in the rise in
contributions from intermediate mass WDs at lower metallicities.

Figure 5: Fractional changes N($Z$) = $X(Z)/\mathrm{max}(X(Z))$ of the
aggregate number (summed over 15 Gyr) of nova events, nova systems, and the
number of nova events per system as a function of the metallicity. There is a
significant anti-correlation between all three of these quantities, with the
total nova productivity from the highest metallicity systems roughly half that
of the lowest. The ejecta mass tracks the event productivity well,
particularly for metallicities above $Z=0.01$. This figure is an updated
version of Figure 5 in (Kemp et al., 2022b), including the mass of ejected
material. Table 1: Updated version of Table 3 from (Kemp et al., 2022b),
presenting the aggregate number (summed over 15 Gyr) of nova events, nova
systems, and the number of nova events per system for each metallicity.

$Z$ | Events / M⊙SFM | Ejecta / M⊙SFM | Systems / M⊙SFM | Events / System | Ejecta / System
---|---|---|---|---|---
0.0001 | 11.00393 | 0.000338 | 0.013471 | 816.8 | 0.025
0.00025 | 9.715102 | 0.000366 | 0.013556 | 716.6 | 0.027
0.0005 | 9.721356 | 0.000391 | 0.013428 | 723.9 | 0.029
0.001 | 8.002775 | 0.000365 | 0.0127 | 630.1 | 0.028
0.002 | 7.710307 | 0.000351 | 0.011822 | 652.1 | 0.029
0.0025 | 8.324096 | 0.000339 | 0.011417 | 729 | 0.029
0.003 | 9.060606 | 0.000332 | 0.011191 | 809.6 | 0.029
0.005 | 5.372794 | 0.000273 | 0.010169 | 528.3 | 0.026
0.007 | 5.742047 | 0.000257 | 0.009954 | 576.8 | 0.025
0.01 | 6.843398 | 0.000245 | 0.009589 | 713.6 | 0.025
0.0125 | 4.346741 | 0.000193 | 0.009043 | 480.6 | 0.021
0.015 | 5.053725 | 0.000188 | 0.00882 | 572.9 | 0.021
0.0175 | 4.972212 | 0.000182 | 0.008595 | 578.4 | 0.021
0.02 | 5.300315 | 0.000177 | 0.008352 | 634.5 | 0.021
0.025 | 4.016605 | 0.000145 | 0.007923 | 506.9 | 0.018
0.03 | 4.606218 | 0.000148 | 0.007669 | 600.5 | 0.019

333 The events, ejecta, and systems columns are normalised per unit mass of
star forming material (M⊙SFM).

(a)

(b)

(c)

(d)

Figure 6: Nova WD mass distributions for $Z$ = $10^{-3}$, weighting by number
of novae (top) and ejecta mass (bottom) and colouring by WD composition (left)
and donor stellar type (right).

(a)

(b)

(c)

(d)

Figure 7: Nova WD mass distributions for $Z$ = 0.02. Figure 8: Aggregate number (summed over 15 Gyr) of nova events per unit star forming material as a function of metallicity, broken down by WD mass bracket. The data is tabulated in Table 2. Contributions from high-mass WDs are ubiquitous across metallicity, while intermediate mass WD contributions are higher at low metallicity. $Z$ |  $M_{\rm WD}$<0.7 | 0.7<$M_{\rm WD}$<0.9 | 0.9<$M_{\rm WD}$<1.075 | 1.075<$M_{\rm WD}$<1.2 | 1.2<$M_{\rm WD}$<1.3 | 1.3<$M_{\rm WD}$ | All
---|---|---|---|---|---|---|---
0.0001 | 2.072137 | 1.680010 | 1.068057 | 0.220397 | 1.301370 | 4.650666 | 10.99264
0.00025 | 2.111505 | 1.937149 | 1.401279 | 0.017795 | 0.744554 | 3.506661 | 9.718943
0.0005 | 2.136337 | 1.931354 | 1.548759 | 0.044335 | 0.652409 | 3.406756 | 9.719950
0.001 | 1.981952 | 1.559799 | 1.345211 | 0.100697 | 0.636987 | 2.379447 | 8.004093
0.002 | 1.883467 | 1.219091 | 1.232788 | 0.346584 | 0.731531 | 2.293006 | 7.706468
0.0025 | 1.800458 | 1.116510 | 1.048383 | 0.407171 | 0.936668 | 2.984717 | 8.293906
0.003 | 1.797227 | 0.974580 | 0.997121 | 0.306053 | 0.874978 | 4.109652 | 9.059610
0.005 | 1.579250 | 0.672812 | 0.572286 | 0.115527 | 0.376039 | 2.072693 | 5.388607
0.007 | 1.398327 | 0.721754 | 0.500943 | 0.141881 | 0.722456 | 2.259692 | 5.745053
0.01 | 1.270525 | 0.669482 | 0.469553 | 0.373532 | 0.753295 | 3.301617 | 6.838003
0.0125 | 1.131020 | 0.448098 | 0.295811 | 0.157540 | 0.375305 | 1.935096 | 4.342870
0.015 | 1.108896 | 0.390628 | 0.290160 | 0.171892 | 0.534657 | 2.556340 | 5.052573
0.0175 | 1.041641 | 0.378872 | 0.276474 | 0.193417 | 0.716184 | 2.342184 | 4.948772
0.02 | 0.982697 | 0.367568 | 0.295257 | 0.227497 | 0.705073 | 2.737965 | 5.316057
0.025 | 0.839674 | 0.267833 | 0.190316 | 0.122393 | 0.636342 | 1.964759 | 4.021317
0.03 | 0.795438 | 0.288432 | 0.221746 | 0.205154 | 0.731924 | 2.358992 | 4.601686
Table 2: Total number of events per unit star forming material produced by
each WD mass bracket at each metallicity. Fig. 8 presents this information
graphically. Figure 9: Aggregate number (summed over 15 Gyr) of nova ejecta
per unit star forming material as a function of metallicity, broken down by WD
mass bracket. The data is tabulated in Table 4. In contrast with Fig. 8, which
shows the event distribution, low-mass WD contributions dominate the ejecta
mass profiles at all metallicities, although an increase in intermediate-mass
WD contributions also be seen at low metallicities. Table 3: Total mass
ejected per unit star forming material produced by each WD mass bracket at
each metallicity.

$Z$ |  $M_{\rm WD}$<0.7 | 0.7<$M_{\rm WD}$<0.9 | 0.9<$M_{\rm WD}$<1.075 | 1.075<$M_{\rm WD}$<1.2 | 1.2<$M_{\rm WD}$<1.3 | 1.3<$M_{\rm WD}$ | All
---|---|---|---|---|---|---|---
0.0001 | 2.241E-04 | 7.060E-05 | 3.148E-05 | 2.497E-06 | 5.163E-06 | 4.062E-06 | 3.379E-04
0.00025 | 2.371E-04 | 8.680E-05 | 3.640E-05 | 1.951E-07 | 3.277E-06 | 2.367E-06 | 3.662E-04
0.0005 | 2.489E-04 | 9.629E-05 | 4.053E-05 | 5.127E-07 | 3.096E-06 | 2.589E-06 | 3.919E-04
0.001 | 2.418E-04 | 8.120E-05 | 3.596E-05 | 8.463E-07 | 3.148E-06 | 2.732E-06 | 3.656E-04
0.002 | 2.444E-04 | 6.674E-05 | 3.187E-05 | 2.768E-06 | 3.101E-06 | 2.543E-06 | 3.514E-04
0.0025 | 2.378E-04 | 6.169E-05 | 2.882E-05 | 3.769E-06 | 3.472E-06 | 2.762E-06 | 3.383E-04
0.003 | 2.410E-04 | 5.349E-05 | 2.766E-05 | 3.206E-06 | 3.646E-06 | 3.303E-06 | 3.323E-04
0.005 | 2.166E-04 | 3.785E-05 | 1.520E-05 | 1.181E-06 | 1.736E-06 | 2.142E-06 | 2.747E-04
0.007 | 1.953E-04 | 4.184E-05 | 1.398E-05 | 1.819E-06 | 3.053E-06 | 2.098E-06 | 2.581E-04
0.01 | 1.817E-04 | 3.954E-05 | 1.343E-05 | 4.038E-06 | 3.184E-06 | 3.154E-06 | 2.450E-04
0.0125 | 1.581E-04 | 2.391E-05 | 7.222E-06 | 1.354E-06 | 1.371E-06 | 1.661E-06 | 1.936E-04
0.015 | 1.539E-04 | 2.135E-05 | 7.357E-06 | 1.767E-06 | 2.062E-06 | 1.990E-06 | 1.884E-04
0.0175 | 1.458E-04 | 2.180E-05 | 7.321E-06 | 2.293E-06 | 2.675E-06 | 2.100E-06 | 1.820E-04
0.02 | 1.401E-04 | 2.151E-05 | 8.104E-06 | 2.700E-06 | 2.893E-06 | 2.563E-06 | 1.779E-04
0.025 | 1.214E-04 | 1.439E-05 | 4.373E-06 | 1.449E-06 | 2.282E-06 | 1.543E-06 | 1.454E-04
0.03 | 1.177E-04 | 1.665E-05 | 6.026E-06 | 2.607E-06 | 2.959E-06 | 2.192E-06 | 1.482E-04

444Fig. 9 presents this information graphically.

Distributions of the accretion rate at the time of nova eruption are shown in
Figs. 10 and 11. Shifts in the $\dot{M}$ parameter-space are less significant
than in $M_{\rm WD}$-space when comparing the event-weighted and ejecta-
weighted distributions. The main differences are a reduction in the importance
of systems with $\dot{M}$ $\gtrsim$ $10^{-8}$ M${}_{\odot}\,\textrm{yr}^{-1}$,
and an enhancement of very slowly accreting systems ($\dot{M}$ $\lesssim$
$10^{-10}$ M${}_{\odot}\,\textrm{yr}^{-1}$).

Particularly evident in Figs. 10 and 11 – although also visible in Figs. 3, 4,
6 and 7 – is the shifting relevance of main sequence (LMMS and MS) vs giant
(FGB and TPAGB) donor stellar types. This is especially clear in at $Z$ = 0.02
(Figs. 4, 7 and 11), where main sequence donors make up a larger portion of
the low-mass WD nova population. Disentangling the root cause of this shifting
is somewhat problematic. Systems involving main sequence donor stars tend to
have lower accretion rates, driving up the critical ignition (and ejecta)
mass. Therefore, we expect MS donor stars to be more significant when
considering the origin of nova ejecta. However, it is clear from Figs. 6 and 7
that the productivity is highly correlated with $M_{\rm WD}$, a property with
which the critical ignition mass is far more sensitive. Therefore, most of the
shifting between donor types is likely just what the shift in $M_{\rm WD}$
looks like in donor space. Many of the novae produced by giant donor stars
occurred on massive O/Ne WDs (Fig. 7), and those systems produce very little
ejecta mass, reducing the apparent importance of giant donor stars overall.
The influence of accretion rates on critical ignition masses undoubtedly also
plays a role, but it is likely a secondary one, and difficult to isolate.

(a)

(b)

(c)

(d)

Figure 10: Nova accretion rate ($\dot{M}$) distributions for $Z$ = $10^{-3}$,
weighting by number of novae (top) and ejecta mass (bottom) and colouring by
WD composition (left) and donor stellar type (right).

(a)

(b)

(c)

(d)

Figure 11: Nova accretion rate ($\dot{M}$) distributions for $Z$ = 0.02.

Figs. 12-15 present another way of looking at the parameter space surrounding
nova ejecta contributions. These figures show the number of novae produced
(Figs. 12 and 14) and mass ejected (Figs. 13 and 15) over each nova system’s
lifetime against that system’s properties (primary mass, secondary mass, and
orbital separation) at birth (left panels) and at the time of the first nova
eruption (right panels). Figs. 12-15 provide a lot of information about the
relevance of different nova systems and their progenitors in these figures. We
shall begin with an examination of the $Z$ = $10^{-3}$ simulation (Figs.
12-13), with attention to which features can be linked to specific
evolutionary channels, before discussing the changes to these distributions
that occur when increasing the metallicity.

The behaviour at initial orbital separations (¿$10^{3}$ R⊙) is relatively
simple due to these systems being limited to relatively simple binary
evolution channels. Fig. 16 shows the common-envelope (CE) ‘scatter-pie’ plot
for $Z$ = $10^{-3}$, showing that systems above approximately $10^{3}$ R⊙ do
not undergo CE interactions. The majority of these nova systems, and all of
those at the longest separations, are powered by wind or wind-RLOF (Abate et
al., 2013) accreting WDs that have not experienced dramatic orbital shrinkage
due to CE evolution or stable pre-nova-phase mass transfer via RLOF. This is
reflected in the similarity in this regime between panels a and b in both the
nova event and nova ejecta distributions (Figs. 12 and 13). As the orbital
separation increases, the number of novae and the amount of ejecta both
decline as the mass transfer becomes less conservative, resulting in a less
efficient build-up to the critical ignition mass.

The orbital separation-space becomes far more complex at shorter separations,
where CE physics plays a significant role in the evolution of many nova
systems, resulting in diverse evolutionary channels. In terms of the number of
nova events, the most extreme systems (producing over $5\times 10^{4}$ novae
each) are readily identifiable in panels a and b of Fig. 12. These systems
exhibit significant orbital shrinkage by the time of the first nova, from just
under $10^{3}$ R⊙ to between 1 and 10 R⊙. These extreme systems are rare,
involving a high-mass WD (panel d) accreting from a relatively low-mass donor
star (¡3 M⊙, panels e-f) at a low accretion rate, resulting in low accretion
efficiencies that allow the WD to undergo many nova eruptions without reaching
$M_{\rm Ch}$.

When considering the mass of ejecta produced (Fig. 13), rather than the number
of novae, the most extreme nova systems look quite different, although once
again CE evolution is important. The main block of the extremely high
($\gtrsim$ 0.1 M⊙) ejecta-mass systems exists between initial separations of
$10^{2}$ and $10^{3}$ R⊙, with a smaller, distinct block existing below
$10^{2}$ R⊙. By the time of the first H nova, these two blocks have merged to
form a single block with orbital separations less than $10^{2}$ R⊙, with the
majority less than $10^{1}$ R⊙. The initial primary masses and WD masses for
these systems are remarkably diverse; almost the entire initial mass and
$M_{\rm WD}$ parameter space is represented, reflecting the ability of even
massive WDs to process significant amounts of material under the right
conditions (specifically, when accretion efficiencies are very close to or
below zero). The secondary masses are more constrained, restricted to ¡4 M⊙
stars both in initial mass and when considering the mass at the time of the
first H nova.

Panels e-f of Fig. 12 and 13 highlight the existence of a population of Algol
nova systems, defined here as systems with donor stars of mass greater than 10
M⊙ at the time of the first nova. We resolve approximately 1300 examples of
these systems in our $Z$ = $10^{-3}$ simulation, with donor stars as massive
as 18 M⊙. The bulk of these systems occur at orbital separations between
$10^{2}$ and $10^{3}$ R⊙ at the time of the first nova, with two small (¡10
systems resolved) satellite populations around $2\times 10^{3}$ and between
20-30 R⊙. Significant pre-nova widening is evident in most of these systems,
with almost all beginning with orbital separations between 10 and $\lesssim$
$10^{2}$ R⊙. The initial primary masses for these systems range between 6 and
10 M⊙, and the WD in these systems is always greater than 0.9 M⊙ at the time
of the first nova. The number of novae these systems produce can be as high as
$10^{3}$ and as low as 1, but the range in ejecta masses is far smaller, with
these systems producing between $10^{-4}$ and $10^{-3}$ M⊙ each.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 12: Total number of novae produced in each nova system plotted against
the initial system properties (left) and the system properties at the time of
the first H nova (right). Distributions shown are from the $Z$ = $10^{-3}$
population, and coloured by the number of systems per mass of star forming
material.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 13: Total mass of nova ejecta produced in each nova system plotted
against the initial system properties (left) and the system properties at the
time of the first H nova (right). Distributions shown are from the $Z$ =
$10^{-3}$ population, and coloured by the number of systems per mass of star
forming material.

Figs. 14 and 15 present the $Z$ = 0.02 distributions for the event counts and
ejecta masses per system respectively, with the ‘scatter-pie’ shown in Fig. 17
summarising the CE space. The morphological differences between Figs. 16 and
17 are discussed in terms of the initial primary mass and orbital separation
with metallicity in Kemp et al. (2022b), and a complete analysis of the
variations in CE properties with metallicity in the context of novae is beyond
the scope of this work. However, it was found in Kemp et al. (2022b) that
variation in CE behaviour is unlikely to be the primary driver of metallicity-
dependent variation in nova rates. Inspection of Figs. 16 and 17 supports this
finding, as it appears that there are few significant variations in the
distributions of CEs, at least in terms of the number that occur prior to the
onset of the nova phase. Most importantly, the initial orbital separation
above which no CEs occur is almost identical.

In agreement with this similarity around separations $\gtrsim$ $10^{3}$ R⊙, we
find that the morphology in Figs. 14 and 15 in the long initial orbital
separation regime is similar in location to that at $Z$ = $10^{-3}$ (Figs. 12
and 13). The primary difference is that there is more scatter in this regime
at solar metallicity, with more novae able to be produced in systems with
initial orbital separations between $10^{-4}$ and $10^{-5}$ R⊙ in particular.

The extreme nova and nova ejecta producing systems for the two metallicity
cases behave similarly. The same basic structures can be found in the same
parts of the parameter space, although at $Z$ = 0.02 the space is better
‘filled out’ (Figs. 14 and 15). This is probably due to larger radii
permitting a wider range of systems to enter the nova phase, promoting more
diverse evolutionary channels.

The previously described Algol nova systems are still present at solar
metallicity (approximately 800 examples resolved at $Z$ = 0.02), although
these systems now typically produce an order of magnitude fewer novae and nova
ejecta. This is in spite of the fact that the parameter-space these systems
occupy is very similar to that at $Z$ = $10^{-3}$.

This conundrum is resolved by examination of the evolution of these systems
during the nova phase itself. The nova phase of the Algol nova systems
typically occurs immediately before or during the start of core He burning in
the donor and ends with a CE event as the donor star grows to increasingly
larger radii. The productivity of an Algol nova system therefore primarily
depends on how much mass is transferred prior to this CE event, meaning that
it is a balance of how quickly mass can be lost from the donor and how quickly
that star expands. For example, the longer orbital-separation systems (with
separations close to $10^{3}$ R⊙) tend to have a longer nova phase, resulting
in more novae per system and more ejecta. At higher metallicity, the donor
stars expand more rapidly during core helium burning due to their higher
opacity while also losing less mass due to their lower core masses and
luminosities. The result is less mass transferred prior to the CE terminating
the nova phase and, therefore, fewer novae and less ejecta, despite the
initial parameter-space being similar.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 14: Total number of novae produced in each nova system plotted against
the initial system properties (left) and the system properties at the time of
the first H nova (right). Distributions shown are from the $Z$ =0.02
population, and coloured by the number of systems per mass of star forming
material.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 15: Total mass of nova ejecta produced in each nova system plotted
against the initial system properties (left) and the system properties at the
time of the first H nova (right). Distributions shown are from the $Z$ = 0.02
population, and coloured by the number of systems per mass of star forming
material. Figure 16: ‘Scatter-pie’ plot for $Z$ = $10^{-3}$ illustrating the
distribution of number of CE events which occur throughout the lifetime of
each nova system. Each point is a pie chart looking ‘into the page’ to
summarise the variation due to $M_{2\rm\ initial}\ (\rm M_{\odot})$. Figure
17: ‘Scatter-pie’ plot for $Z$ = 0.02., equivalent to Fig. 16.

##  4 Results: Elemental and isotopic abundances

In this section, we will address the contributions of novae to the
nucleosynthesis of elements other than Li555Li is dealt with in Kemp et al.
(2022a). in the MW, as well as which nova sites – distinguished in terms of
the WD mass – contribute significantly to which isotopes. Novae occurring on
different WD masses produce different nucleosynthesis and have different
delay-time distributions and overall importance, all important factors that
are folded into our simulations.

Fig. 18 summarises the contributions from novae, AGBs, type Ia supernovae, and
massive stellar sources for a range of isotopes, highlighting which nova model
produced the most of each isotope at [Fe/H]=0. Also shown in each panel is the
fraction of each isotope (at [Fe/H] = 0) produced by novae. For example,
according to our models 8.3-36.7% of Galactic ${}^{13}{\rm C}$ is produced by
novae, where the range reflects the variation between different nova yield
profiles. Note that not all isotopes have reported contributions from every
yield profile: ${}^{36}{\rm S}$ is only reported in the S2009/2020 profile,
${}^{37}{\rm C}$l, ${}^{38}{\rm A}$r, and ${}^{39}{\rm K}$ are not reported in
the S2009/2020 profile, and ${}^{40}{\rm C}$a is not reported in the J1998
yield profile.

Figure 18: Contributions to each isotope from stellar sources. The background
color of each panel highlights which nova yield profile produces the most of
the relevant isotope by [Fe/H] = 0 (yellow for J1998, blue for S2009/2020, and
green for J2020). Besides ${}^{13}{\rm C}$, ${}^{15}{\rm N}$, and ${}^{17}{\rm
O}$, nova contributions for most isotopes are small (¡2%) compared to other
stellar sources.

Nova contributions are small (¡2%) for most isotopes relative to contributions
from other stellar sources. Besides ${}^{7}{\rm L}$i (Kemp et al., 2022a),
notable exceptions include ${}^{13}{\rm C}$, ${}^{15}{\rm N}$, and
${}^{17}{\rm O}$, although even for these isotopes nova contributions are (at
most) around 35%. Fig. 19 shows the evolution of [${}^{13}{\rm C}$/Fe],
[${}^{15}{\rm N}$/Fe], and [${}^{17}{\rm O}$/Fe] as a function of [Fe/H],
while Fig. 20 shows the evolution of ${}^{12}{\rm C}$/${}^{13}{\rm C}$,
${}^{14}{\rm N}$/${}^{15}{\rm N}$, ${}^{16}{\rm O}$/${}^{17}{\rm O}$, and
${}^{18}{\rm O}$/${}^{17}{\rm O}$ ratios.

Figures 19 and 20 demonstrate that nova contributions to ${}^{13}{\rm C}$ and
${}^{15}{\rm N}$ produce non-negligible variations in both the logarithmic
abundance ratios relative to iron and their ratios relative to their dominant
elemental isotopes. At [Fe/H] = 0, the predicted Galactic [${}^{13}{\rm
C}$/Fe] and [${}^{15}{\rm N}$/Fe] ratios show minor discrepancies (at most 0.2
dex). Nova contributions to ${}^{17}{\rm O}$ cause only barely discernable
variation in these figures.

Of these isotopes, ${}^{15}{\rm N}$ shows the most interesting behaviour, with
[${}^{15}{\rm N}$/Fe] showing significant deviations between [Fe/H] = -2 and
-1, up to 0.7 dex. From a close examination of the ${}^{15}{\rm N}$ panel in
Fig. 18, it can be seen that beyond a few hundred Myr nova contributions to
${}^{15}{\rm N}$ overtake AGB contributions and are comparable to massive
stellar contributions by 1 Gyr. Beyond [Fe/H] = -0.8 (a galaxy age of almost 2
Gyr), production of ${}^{15}{\rm N}$ from massive stars resurges, causing the
large spike in Fig. 19. The effects can be seen equally clearly in the ratios
of ${}^{14}{\rm N}$/${}^{15}{\rm N}$. It is worth mentioning that the
evolution of our isotopic ratios is similar in shape to those presented in
Figure 31 of Kobayashi et al. (2020), although their ${}^{14}{\rm
N}$/${}^{15}{\rm N}$ ratio peaks somewhat earlier. Unfortunately, there are no
observational data on ${}^{14}{\rm N}$/${}^{15}{\rm N}$ abundances relevant to
this metallicity regime.

Figure 19: [X/Fe] abundances for the isotopes where the inclusion of novae in
the model makes a difference to the overall Milky Way abundance. The inclusion
of novae has negligible influence on other isotopes (excluding Li, see Kemp et
al. 2022a) Figure 20: Isotopic ratios where the inclusion of novae in the
model makes a non-negligible difference to the overall Milky Way abundance.

Previously, we asserted that for different isotopes, different parts of the
nova $M_{\rm WD}$ parameter space would be important, primarily depending on
the interplay between $M_{\rm WD}$-dependent reaction rates and the $M_{\rm
WD}$-dependent ejecta masses, which govern the ejecta delay-time distributions
for each of the mass brackets. Figs. 22, 23, and 24 show the isotopic
contributions from novae from different parts of the $M_{\rm WD}$ parameter
space – using the J1998, S2009/2020, and J2020 yield profiles respectively –
as a function of Galaxy age. Fig. 21 presents a slice from each of these
figures at [Fe/H] = 0 in side-by-side bar charts, allowing easier comparison
between the three nova yield profiles.

There is a wealth of information in these figures, showing which parts of the
nova parameter-space are most important for each isotope at different times
during the Galaxy’s evolution. Before proceeding, the reader should be
reminded that the following discussion is strictly concerned with comparing
different parts of the nova $M_{\rm WD}$ parameter space. Galactic production
of most of the isotopes discussed here is dominated by non-nova stellar
sources at all times during the evolution of the Milky Way (Fig. 18).

We will begin by examining some of the main trends and underlying physics
surrounding the J1998 case (Fig. 22), and will proceed with our discussion
from there. The first thing to note is that there is a systematic difference
in the delay-times for different WD masses. Contributions from more massive
progenitors kick in earlier, as these WDs form first. For this reason, in some
cases the relative importance of different $M_{\rm WD}$-regimes shifts as a
function of Galaxy age. For example, if we consider ${}^{15}{\rm N}$, the
lowest mass WDs (¡0.7 M⊙) contribute significantly by 10 Gyr, but lag behind
the contributions of more massive WDs at times earlier than 1 Gyr.

Nova productivity of the low mass-number isotopes from ${}^{3}{\rm H}$e to
${}^{19}{\rm F}$ is eventually dominated by these ¡0.7 M⊙ WDs, with their high
ejecta masses but slower delay-time distributions. At earlier times, these
isotopes are generally dominated by nova contributions from WDs with masses
between 0.7 and 1.075 M⊙, with more massive WDs also being significant to the
early production of ${}^{15}{\rm N}$ and ${}^{19}{\rm F}$. From ${}^{20}{\rm
N}$e onwards, the eventual dominance of low-mass WDs is no longer assured.
${}^{20}{\rm N}$e and ${}^{21}{\rm N}$e contributions are dominated by the
¿1.075 O/Ne WD regime, before ¡1.075 M⊙ WDs return to prominence in the
production of ${}^{22}{\rm N}$e, formed as a decay product of ${}^{22}{\rm
N}$a. ${}^{23}{\rm N}$a production is dominated by the most massive WDs (¿1.3
M⊙), but the second most productive regime by 10 Gyr is the ¡0.7 M⊙ mass WDs.
${}^{24}{\rm M}$g, ${}^{25}{\rm M}$g, and ${}^{26}{\rm M}$g are all eventually
dominated by ¡0.7 M⊙ WD contributions, while from ${}^{27}{\rm A}$l to
${}^{36}{\rm A}$r (excepting ${}^{36}{\rm S}$), WDs more massive than 1 M⊙
dominate. ${}^{36}{\rm S}$ shows entirely different behaviour, with lower mass
WDs being the most important contributors and massive WDs being the least.

Most isotopes do not exhibit a nice monotonic progression, with either the
low-mass or high-mass WDs being dominant, but contributions from WD masses
between these extremes being far less prominent. Each of these panels reflects
the balance of several highly non-linear influences, and the somewhat chaotic
behaviour in most of the isotopes reflects that. In general, the massive WDs
benefit from faster delay-times and higher reaction rates (manifesting as
higher mass fractions in our yield profiles), but are disadvantaged by the
lower mass of nova ejecta that they produce (e.g., Fig. 6). Massive white
dwarfs contribute at significantly higher levels than other nova sites for
${}^{30}{\rm S}$i, ${}^{31}{\rm P}$, ${}^{33}{\rm S}$, ${}^{34}{\rm S}$,
${}^{35}{\rm C}$l, and ${}^{37}{\rm C}$l.

Fig. 23 is analogous to Fig. 22, presenting our Milky Way model relying on the
S2009/2020 yield profile. For now, we shall forgo a detailed description of
the differences in the quantities of each isotope produced, and instead focus
on changes to the qualitative behaviour of each isotope. Using this yield
profile, ¡0.7 M⊙ WDs remain significantly weaker producers of ${}^{15}{\rm N}$
than the other mass brackets throughout the simulation, with the 0.9-1.075
$M_{\rm WD}$ mass bracket dominant. Other than massive WDs now dominating the
production of ${}^{18}{\rm O}$ and ${}^{19}{\rm F}$, the other low mass-number
isotopes behave similarly to the J1998 case. ${}^{20}{\rm N}$e-${}^{34}{\rm
S}$ also show similar behaviour, although there is far more spread between
different $M_{\rm WD}$ contributions for ${}^{23}{\rm N}$a, and ${}^{34}{\rm
S}$ shows less prominent ¿1.3 M⊙ contributions in the S2009/2020 model. Yields
of isotopes from ${}^{36}{\rm S}$-${}^{39}{\rm K}$ were not reported by
Starrfield et al. (2009, 2020), while ${}^{40}{\rm C}$a was reported by
Starrfield et al. (2009, 2020) but not by José & Hernanz (1998). ${}^{40}{\rm
C}$a becomes dominated by low-mass contributions beyond 1 Gyr, with high-mass
WD contributions remaining low throughout.

Finally, the third of our nova yield profiles is presented in Fig. 24. The
J2020 profile is unique in that the yields do not rely on any premixing
assumptions, instead combining 3D and 1D modelling to treat the evolution of
the eruption (José et al., 2020). However, this profile also includes distinct
nova yields for only two different WDs: a 1.0 M⊙ C/O WD and a 1.25 M⊙ O/Ne WD.
The evolution of low mass-number isotopes (${}^{3}{\rm H}$e-${}^{19}{\rm F}$)
is, qualitatively, mostly similar to the J1998 case, with low-mass WDs
dominating. The main difference is that novae from massive WDs do not
contribute to ${}^{3}{\rm H}$e at all. ${}^{20}{\rm N}$e-${}^{23}{\rm N}$a
behave similarly to the J1998 and S2009/2020 yield profiles, although ¡0.7M⊙
contributions to ${}^{20}{\rm N}$e are higher in J2020. Nova contributions
from massive WDs dominate ${}^{24}{\rm M}$g production, differing from the
J1998 and S2009/2020 profiles. ${}^{25}{\rm M}$g and ${}^{26}{\rm M}$g remain
dominated by low-mass WD contributions. From ${}^{27}{\rm A}$l-${}^{36}{\rm
A}$r the behaviour diverges significantly from the J1998 and S2009/2020
models; where previously massive WDs were dominant in most of this regime, the
J2020 profile finds that low-mass WDs are dominant. This may be due to the
poor $M_{\rm WD}$ resolution of this profile; the high reaction rates
obtainable on the most massive WDs are essential to their ability to overcome
their low ejecta masses compared to low-mass WDs. For this profile, we are
applying the yields computed by José et al. (2020) for a 1.25 M⊙ WD to all our
massive WDs, while in the J1998 and S2009/2020 profiles we had the benefit of
nova yields computed at 1.15, 1.25, and 1.35 M⊙. However, despite this
limitation, the behaviour of ${}^{38}{\rm A}$r, ${}^{39}{\rm K}$, and
${}^{40}{\rm C}$a appears similar to the J1998 and S2009/2020 cases.

Finally, we compare the quantitative variations at [Fe/H] = 0, considering the
different yield profiles and the different aspects of the $M_{\rm WD}$
parameter space. Aspects of our previous discussion on the $M_{\rm WD}$
parameter space can be seen more easily in Fig. 21, which allows for easier
inspection of the relative productivities of the different yield profiles.
Recall that the actual amount of raw mass ejected by the binary models from
each of these simulations is the same; what changes between the models are the
mass fractions in that nova ejecta.

Many of the previously discussed trends can be seen more easily in Fig. 21,
such as the preference among the low mass-number elements – excepting
${}^{15}{\rm N}$ and ${}^{19}{\rm F}$ – for lower mass WDs, while new features
become apparent. Three orders of magnitude more ${}^{18}{\rm O}$ is produced
in the J1998 model from WDs less than 1.2 M⊙ than either of the other models,
with only S2009/2020’s ¿1.3 M⊙ WD contributions comparable to J1998’s
production for this isotope. Similar behaviour (although not as extreme) is
exhibited by ${}^{19}{\rm F}$, with the J1998 model again predicting far more
material than the other models, excepting the most massive WD regime. Other
isotopes where there is particular variation between the different models are
${}^{3}{\rm H}$e (especially at high $M_{\rm WD}$), ${}^{7}{\rm L}$i
(specifically the low values in the J2020 model, which were discussed briefly
in Kemp et al. 2022a), and the ¿1.3 M⊙ regime of ${}^{29}{\rm S}$i,
${}^{33}{\rm S}$, ${}^{34}{\rm S}$, ${}^{35}{\rm C}$l, and ${}^{36}{\rm A}$r.

Also illustrated in Fig. 21 is that variation in productivity can often be
non-monotonic with increasing WD mass regime. The low mass-number isotopes
(${}^{3}{\rm H}$e-${}^{19}{\rm F}$) are the most consistent, with all – once
again excepting ${}^{15}{\rm N}$ and ${}^{19}{\rm F}$ – models showing an
unambiguous decline in productivity with increasing mass regime. We find no
examples of isotopes where productivity increases monotonically and
unambiguously with increasing WD mass, but there are many examples where
increasing the WD mass first reduces and then increases the productivity. The
resulting ‘U’ curve is not unexpected; from Figs. 6 and 7, we can see that, in
a simple stellar population, a huge part of the ejecta mass of our population
originates from the ¡0.7 M⊙ regime. The sharp fall-off in nova ejecta with
increasing $M_{\rm WD}$ mass results in this initial decline before the ejecta
mass-$M_{\rm WD}$ distribution flattens – to a very low value – beyond 1 M⊙,
allowing the increased nuclear efficiency of novae on the massive WDs to
compensate for their low ejecta masses. This ‘U’ behaviour is almost
ubiquitous among the high mass-number isotopes, usually with the high-mass WDs
having the highest contributions overall.

Figure 21: Bar plot summarising the contributions to each isotope by [Fe/H] =
0 for each nova yield profile, distinguishing between nova progenitor WD
masses. Figs. 22, 23, and 24 present the full evolution history for each
isotope, also distinguishing progenitor masses.

##  5 Discussion and conclusions

In this work, we explore the nucleosynthesis of stable isotopes by novae in
the context of galactic chemical evolution, with attention to which parts of
the $M_{\rm WD}$-parameter space contribute to which elements.

We discussed the influences that determine which parts of the nova parameter
space produce the most nova ejecta, focusing on how this differs from which
nova systems produce the most nova events. Lower mass WDs have higher ejecta
masses per eruption due to their higher critical ignition masses, a fact that
disadvantages them when considering the number of novae that such a system
produces but does not when considering the ejecta mass. While some nova
systems with massive WDs can produce amounts of nova ejecta comparable to the
most productive low-mass nova systems, they are far fewer in number, as they
are heavily selected against by the initial mass function.

When comparing with AGB stars, massive stars, and type Ia supernovae, we find
that novae do not dominate the elemental abundances other than Li (see Kemp et
al. 2022a). However, we find that novae do contribute sufficient ${}^{13}{\rm
C}$ and ${}^{15}{\rm N}$ (up to 35% by [Fe/H] = 0) to noticeably affect the
abundances of these isotopes at certain times during the evolution of the
Galaxy. The evolution of [${}^{15}{\rm N}$/Fe] and ${}^{14}{\rm
N}$/${}^{15}{\rm N}$ from [Fe/H] = -2 to -1 in particular shows significant
variation (up to 0.7 dex) dependent on the inclusion of novae and the nova
yield profile adopted. Unfortunately, there are no observations constraining
${}^{15}{\rm N}$ abundances at this metallicity, nor are there likely to be in
the future. The variation due to novae in the predicted abundance ratios of
${}^{13}{\rm C}$ and ${}^{15}{\rm N}$ at solar metallicity, where we do have
observations courtesy of isotopic analyses of meteorites (e.g., Lodders et
al., 2009), is far smaller, at most around 0.2 dex.

Recent work by Bekki & Tsujimoto (2024) has found that novae on O/Ne WDs
contribute significantly to the Galactic [P/Fe] abundance ratio. In this work,
as previously discussed, we find that nova contributions to P – and most other
elements – are negligible compared with other stellar sources. Bekki &
Tsujimoto (2024)’s parametric model for novae borrows many of its parameters
from Kemp et al. (2022b), notably the high contribution of O/Ne WDs to the
total number of novae. They combine this with an estimate for the total number
of novae, an assignment for the ejecta mass per eruption, and a gradient for a
metallicity-dependent nova rate to form their model for nova ejecta, relying
on yields from José & Hernanz (1998)’s massive WD simulations for the mass
fraction of P in each eruption.

There are other details to the model, but these are the most relevant to
explaining their high levels of P from novae compared to this work. Bekki &
Tsujimoto (2024) consider a range of nova ejecta, but the lowest considered is
$10^{-5}$ M⊙ per nova event. As can be seen in Figs. 3 and 4, this is actually
very high for O/Ne WDs; most have at least an order of magnitude less ejecta
per eruption, and this is particularly true for the most massive WDs (where P
production will be the highest, as assumed by Bekki & Tsujimoto 2024). As
discussed previously in this work, the high importance of ONe WDs to nova
counts is inextricably linked to their low critical ignition masses, which
translates to lower ejecta masses. it is almost certainly the decoupling of
these two factors (by taking the high fraction of O/Ne WDs implied by Kemp et
al. (2022b)’s nova rate calculations but also assuming a relatively high
ejecta mass for each eruption) that leads to the high contributions of novae
to Galactic [P/Fe] in Bekki & Tsujimoto (2024).

These kinds of parametric models are typical of how novae have been included
within GCE models in the past. Indeed, many of the assumptions necessary to
the nova model Bekki & Tsujimoto (2024) are very similar to Romano & Matteucci
(2003), where a parametric model was used to test the effect of novae on C/N/O
abundance ratios, finding that novae have potential to account for secondary
production of certain isotopic ratios. Similarly to Bekki & Tsujimoto (2024),
Romano & Matteucci (2003) also assumed $10^{4}$ novae per system and $2\times
10^{-5}$ solar masses of ejecta per nova, implying roughly 0.2 solar masses of
material per nova system on average. Comparing these assumptions with Table 3,
this is roughly 10 times more ejecta per nova system on average than we find
in our models (between 0.02 and 0.03 M⊙ per system, depending on the
metallicity). This is likely the reason we find relatively little impact from
novae on these C/N/O abundance ratios compared to older works.

More recent works have linked novae to explaining details of the [F/Fe]
distribution, finding good agreement when nova contributions are increased by
factors of a few and yields from massive O/Ne WDs are employed (Spitoni et
al., 2018; Grisoni et al., 2020), but negligible impact without this
artificial enhancement. We are in agreement with these works insofar as that
our models, which do not include artificial enhancements, also find negligible
contributions from novae.

Kemp et al. (2022a) highlighted that theoretical nova models severely under-
produce Li relative to observations of nova ejecta. A natural question to ask
is whether they also under-produce other elements. No direct observations of
isotopic abundances have been made in nova ejecta; therefore, we must rely
upon elemental abundances to provide a sanity check. Helton et al. (2010)
provide detailed spectroscopic analysis of the dusty nova V1065 Cen, reporting
a O/Ne white dwarf composition and logarithmic He ($-0.89\pm 0.11$), N ($-2\pm
0.11$), O($-1.54\pm 0.17$), Ne ($-1.57\pm 0.09$), Mg ($-2.75\pm 0.11$), S
($-3.14\pm 0.37$), Ar ($-3.90\pm 0.13$), and Fe ($-0.89\pm 0.13$) abundances.
In comparison, converting the reported yields from the ‘ONe5’ model of a 1.15
M⊙O/Ne WD from José & Hernanz (1998) to abundances results in: He (-0.7); N
(-1.72, including ${}^{14,15}{\rm N}$ contributions); O (-1.6, including
${}^{16,17,18}{\rm O}$ contributions); Ne (-1.5); Mg (-3.4, including
${}^{24,25,26}{\rm M}$g contributions); and S (-4.0). S and – to a lesser
extent – Mg are both under-predicted, but recomputing these abundances using
José & Hernanz (1998)’s 1.25 M⊙ model (‘ONe6’) results in abundances of Mg
(-3.0) and S (-2.2), reducing the discrepancy in Mg and bracketing the S
abundance. This leads us to conclude that, at least where observations are
available, the theoretical yields are not necessarily in tension for most
elements. It is beyond the scope of this discussion to repeat this assessment
for a comprehensive set of novae with elemental yields. However, we note that
José & Hernanz (1998) compare their theoretical mass fractions with the
observational yields of five different novae (V693 CrA 1981, V1370 Aql 1982,
QU Vul 1984, PW Vul 1984, and V1688 Cyg 1978), finding that – allowing for the
possibility of different mixing fractions between novae – their theoretical
yields match relatively well.

In this work, we only considered the evolution of stable isotopes. We
therefore can make no comment on the importance of novae to the production of
radioactive isotopes in the Milky Way. However, of the radio-isotopes expected
to be produced by novae, only ${}^{26}{\rm A}$l has a significantly long half-
life ($t_{1/2}\approx$ $7\times 10^{5}$ years). We note that recent GCE
modelling by Vasini et al. (2022) find that including novae is necessary to
recover the mass of ${}^{26}{\rm A}$l derived from COMPTEL and INTEGRAL
$\gamma$-ray observations (Schönfelder et al., 1984; Diehl et al., 1995;
Prantzos & Diehl, 1996; Winkler, 1996; Diehl et al., 2010).

We examined the relative importance of different nova sites for all considered
isotopes, where different sites are distinguished according to the WD mass. We
found that, by the time the Galaxy has reached [Fe/H] = 0, low-mass WDs
dominate the production of most low mass-number isotopes ($\leq$${}^{19}{\rm
F}$), while massive WDs dominate most of the more massive isotopes. Agreement
between the three nova yield profiles is relatively good for most isotopes.
Isotopes where the agreement is relatively poor – at least in certain $M_{\rm
WD}$ regimes – include ${}^{3}{\rm H}$e (especially at high $M_{\rm WD}$),
${}^{7}{\rm L}$i, ${}^{18}{\rm O}$, ${}^{19}{\rm F}$, and the ¿1.3 M⊙ regime
of ${}^{29}{\rm S}$i, ${}^{33}{\rm S}$, ${}^{34}{\rm S}$, ${}^{35}{\rm C}$l,
and ${}^{36}{\rm A}$r.

Ultimately, we find that novae play a non-negligible role in the origin of the
elements. They appear to dominate Galactic Li production when considering
observed Li yields (Kemp et al., 2022a). Further, we find that novae may
produce up to 35% of Galactic ${}^{13}{\rm C}$ and ${}^{15}{\rm N}$ by [Fe/H]
= 0, and that novae may – briefly – be the dominant sources of ${}^{15}{\rm
N}$ between [Fe/H] $=-2$ and $-1$, producing at a level at least comparable
with massive stars. We have not formally explored the affect that uncertain
binary evolution parameters could have on the evolution of ${}^{13}{\rm C}$
and ${}^{15}{\rm N}$, and we regret that such an analysis must be left to
future work. However, we comment that the impact of novae on these isotopes is
far less than it was for Li, and so it is certainly possible that there are
combinations of uncertain binary parameters that could reduce nova
contributions to ${}^{13}{\rm C}$ and ${}^{15}{\rm N}$ significantly.

###### Acknowledgements.

A. R. C. is supported in part by the Australian Research Council through a
Discovery Early Career Researcher Award (DE190100656). B. C. acknowledges
support from the National Science Foundation (NSF, USA) under grant No.
PHY-1430152 (JINA Center for the Evolution of the Elements). R. G. I. thanks
the STFC for funding, in particular Rutherford fellowship ST/L003910/1 and
consolidated grant ST/R000603/1. Parts of this research were supported by the
Australian Research Council Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D), through project number CE170100013.

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##  Appendix A Additional figures

Figure 22: Contributions to each isotope according to the J1998 yield profile,
distinguishing between nova progenitor WD masses. Figure 23: Contributions to
each isotope according to the S2009/2020 yield profile, distinguishing between
nova progenitor WD masses. Figure 24: Contributions to each isotope according
to the J2020 yield profile, distinguishing between nova progenitor WD masses.