# Novae: An Important Source of Lithium in the Galaxy 111Released on March,
1st, 2023

Jun Gao School of Physical Science and Technology, Xinjiang University,
Urumqi, 830046, China  Xinjiang Observatory, the Chinese Academy of Sciences,
Urumqi, 830011, China  Chunhua Zhu  School of Physical Science and Technology,
Xinjiang University, Urumqi, 830046, China  Guoliang Lü  Xinjiang Observatory,
the Chinese Academy of Sciences, Urumqi, 830011, China  School of Physical
Science and Technology, Xinjiang University, Urumqi, 830046, China  Jinlong Yu
College of Mechanical and Electronic Engineering, Tarim University, Alar
843300, PR China  Lin Li  School of Physical Science and Technology, Xinjiang
University, Urumqi, 830046, China  Helei Liu  School of Physical Science and
Technology, Xinjiang University, Urumqi, 830046, China  Sufen Guo  School of
Physical Science and Technology, Xinjiang University, Urumqi, 830046, China
Chunhua Zhu, Guoliang Lü<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

The source of the Galactic Lithium (Li) has long been a puzzle. With the
discovery of Li in novae, extensive research has been conducted. However,
there still exists a significant disparity between the observed abundance of
lithium in novae and the existing theoretical predictions. Using the Modules
for Experiments in Stellar Astrophysics (MESA), we simulate the evolution of
nova with element diffusion and appropriately increased the amount of 3He in
the mixtures. Element diffusion enhances the transport efficiency between the
nuclear reaction zone and the convective region on the surface of the white
dwarf during nova eruptions, which results in more 7Be to be transmitted to
the white dwarf surface and ultimately ejected. Compared to the previous
predictions, the abundance of 7Be in novae simulated in our model
significantly increases. And the result is able to explain almost all observed
novae. Using the method of population synthesis, we calculate Li yield in the
Galaxy. We find that the Galactic occurrence rate of nova is about 130 yr-1,
and about 110 M⊙ Li produced by nova eruption is ejected into the interstellar
medium (ISM). About 73% of Li in the Galactic ISM originates from novae, and
approximately 15%-20% of the entire Galaxy. It means that novae are the
important source of Li in the Galactic.

Chemical abundances (224) — Novae (1127) — Recurrent novae (1366) — Galactic
abundances (2002) — Nucleosynthesis (1131) — Binary stars (154)

##  1 Introduction

Lithium (Li) is an extremely fragile element that is destroyed in the hydrogen
(H)-capture reaction at temperatures as low as 2 $\times$ $10^{6}$K. Its
dominant isotope, 7Li, is the decay product of 7Be with a half-life of 53.3
days. In the process of H burning, 7Be rapidly decays to 7Li through electron
capture (pp II) after being formed via the proton-proton (pp) chain. 7Li
itself is also destroyed through proton capture, resulting in very little
lithium surviving in the H burning process. This makes it almost impossible to
accurately calculate the abundance of Li in most stars during their formation.
The production of primordial 7Li is a sensitive function of the baryon-to-
photon ratio and can be estimated within the framework of standard primordial
nucleosynthesis as long as the baryon density is obtained from the initial
deuterium abundance or fluctuations of the cosmic microwave background (CMB)
(Spergel et al., 2003; Bennett et al., 2013; Planck Collaboration et al.,
2020). The expected primordial value is A(Li)$\approx$2.72 dex (Życzkowski et
al., 1998; Coc et al., 2014), which is 3 - 4 times higher than the measured
values in halo dwarf stars (Spite & Spite, 1982; Planck Collaboration et al.,
2020). This difference is often referred to as the Cosmological lithium
problem (Fields et al., 2014).

Since the measured Li abundance in meteorites that preserves the protosolar in
the interstellar medium (ISM) is A(Li)$\approx$3.3 dex (Asplund et al., 2009;
Lodders et al., 2009), there is need for a galactic source to explain the
increase from the initial value of 2.72 dex. This identification of the source
is commonly known as the Galactic lithium problem. The ISM is the material
that fills the space between the stars within a galaxy. It consists primarily
of gas (atomic, molecular, and ionized) and dust. Planetary nebulae, supernova
explosions, and novae explosions all inject a large amount of chemical
elements into ISM. The ISM is crucial for the formation and evolution of
stars, and it plays a key role in the chemical enrichment and energy balance
of galaxies (Draine, 2011). Various nucleosynthesis processes and sources have
been proposed so far. One confirmed source of Li is spallation and fusion
processes of galactic cosmic rays (GCRs) in the ISM. The integrated spallation
process is estimated to contribute about 10%$\sim$20% to the measured 7Li in
the entire Galactic lifetime (Prantzos et al., 1993; Romano et al., 2001;
Prantzos, 2012). Other proposed sources include spallation processes in the
flares of low-mass active stars, red giants (RGs), asymptotic giant branch
(AGB) stars and neutrino-induced nucleosynthesis during a type II supernova
(Starrfield et al., 1978; Spite & Spite, 1982; Smith & Lambert, 1989; Smith,
Verne V. and Lambert, David L., 1990; Hernanz et al., 1996; Romano et al.,
1999; Travaglio et al., 2001; Alibés et al., 2002; Prantzos, 2012; Tajitsu et
al., 2016; Banerjee, Projjwal et al., 2016; Pignatari et al., 2016; Rukeya et
al., 2017). Although Li abundance is indeed enhanced in some studies, but
their contribution to the entire Galaxy is too small. Therefore, other sources
are still needed for the Galaxy to reach its current value. Subsequently,
Romano et al. (2001) and Prantzos, N. et al. (2017) found that low-mass giants
are the best candidates for reproducing the late rise of the Li metallicity
plateau. However, high A(Li) cannot be sustained for a long period due to
convective activity in these stars, and the low percentage of Li-rich giants
also indicates this (Casey et al., 2016; Yan et al., 2018; Gao et al., 2022).
Therefore, their contribution to the enrichment of Li in the Galactic ISM
remains quite uncertain.

For many years, classical novae have been proposed as feasible sites for Li
production (Arnould & Norgaard, 1975; Starrfield et al., 1978). The novae
eruption is the result of unstable hydrogen-burning on the CO or ONeMg white
dwarfs (WDs) surfaces, which accrete hydrogen-rich material from their main
sequence (MS) or red giant (RG) phase companions in low-mass, close binary
systems (Starrfield et al., 2009; Jose, 2016; Starrfield et al., 2016; Rukeya
et al., 2017). When the companion star fills its Roche Lobe, the hydrogen-rich
material flows through the inner Lagrange point to the WD and accretes onto
its surface. This material accumulates and is compressed until thermonuclear
runaways (TNR) is triggered, resulting in mass ejection that ultimately
pollutes the interstellar environment. Both theoretical and observational
evidence confirms that novae contribute many nucleosynthetic isotopes to the
Galactic ISM (José & Hernanz, 1998; Starrfield et al., 1998). For example, the
elements 7Li and 7Be.

7Be is generated through the 3He($\alpha$,$\gamma$)7Be reaction at a
temperature of 150 million K (Hernanz et al., 1996). To avoid destruction, 7Be
needs to be transported to cooler regions quickly through convection, as
described in the Cameron–Fowler (CF) mechanism (Cameron & Fowler, 1971). When
these cooler regions are subsequently ejected, the absorption lines of 7Be
during nova outbursts can be observed (José & Hernanz, 1998), eventually
decaying into 7Li. This view was later confirmed by observations by Izzo et
al. (2015) who detected a potentially detectable 7Li I $\lambda$6708 Å
absorption line in the spectrum of the Nova Centauri 2013 (V1369 Cen),
providing observational evidence for the presence of Li in nova explosions
that had been predicted since the mid-1970s but only recently discovered.
Subsequently, the observation studies continuously detected the progenitor
nucleus 7Be or 7Li in the prominent post-outburst spectra of classical novae
(Tajitsu et al., 2015, 2016; Molaro et al., 2016; Izzo et al., 2018; Selvelli
et al., 2018; Molaro et al., 2020, 2022, 2023).

For a long time, people have continuously used theoretical models to calculate
the accurate Li yield from nova explosions. Hernanz et al. (1996) and José &
Hernanz (1998) calculated the theoretical values for different WD masses and
mixing ratios of ejected material in their nova models. Then Rukeya et al.
(2017) expanded on the nova grid model and computed more detailed mass and Li
yields of the ejecta. They concluded that the Li produced in novae accounts
for 10% of the total Galactic ISM ($\sim$ 150 M⊙) production. However,
Starrfield et al. (2024) predicted that the abundance of Li ejected from CO
novae explosions is A(Li) $\approx$ 6, but most observed novae showed A(Li)
$\textgreater$ 7 (i.e. A(Li)=Log(N(7Li)/N(H)+12)). The actual abundance of
ejected Li is one order of magnitude higher than the theoretical predictions
(Izzo et al., 2015; Molaro et al., 2016; Izzo et al., 2018; Arai et al., 2021;
Molaro et al., 2022).

This suggests that traditional nova models may have deficiencies in their
physical mechanisms, and the Galactic lithium problem unresolved.
Subsequently, researchers have attempted different calculation methods by
adjusting the mass distribution of binary systems, eruption time intervals,
criteria for eruptive episodes, metallicity, and accretion material mixing
ratios to compute Li yields under different scenarios (José & Hernanz, 1998;
Starrfield et al., 2009; Cescutti & Molaro, 2019; José et al., 2020;
Starrfield et al., 2020). Kemp et al. (2022a) demonstrated that using the
yield values given in Molaro et al. (2023), then novae can definitely be the
main factories of lithium in the Galaxy while using the theoretical values,
they could not. Therefore, finding a reasonable nova model and Li production
mechanism that aligns with the observations and theoretical values is of great
significance in addressing the Galactic lithium problem and even the
Cosmological lithium problem. It is well known that the chemical composition
of the ejecta in nova explosions depends on the surface chemical element
composition of the WDs at the moment of the eruption. Several factors can
influence the chemical composition of the WD’s surface, such as metallicity,
accretion efficiency, and element diffusion (Kippenhahn et al., 1980; Dupuis
et al., 1992; Zhu et al., 2021). The effects of nuclear reaction rate,
accretion efficiency and metallicity on the surface material of WDs have been
explored by Starrfield et al. (2016, 2020) and Kemp et al. (2022a, b).
However, element diffusion has been rarely considered. Element diffusion is a
dynamic process that alters the distribution of chemical elements within a
star. It primarily results from the combined effects of pressure, temperature,
and material concentration. Kovetz & Prialnik (1985) investigated that
effective diffusion between the accreted layer and the inner regions for
accreting WD, and they found that the diffusion can lead to enrichment of CNO
(and other metals) in the ejected envelop. However, CNO enhancements are
possible in CO novae only in the absence of the He buffer (Iben et al., 1991).
The presence of helium layer would prevent the diffusion of CNO and metals
(such as 3He), although the average abundance of helium is almost the same as
that of solar (Gehrz et al., 1998; Yaron et al., 2005). Therefore, the 3He
inside the WD cannot be effectively brought to the envelope where TNR occurs
by element diffusion, and there are other sources of 3He in the envelope (Iben
et al., 1991). In our model, 3He comes from the accreted material from the
donor star but not the from the interior of WD. The role of element diffusion
in our model is that 7Be produced by 3He($\alpha$,$\gamma$)7Be among TNR can
be taken more efficiently to WD surface, and then can ejected more easily.
Therefore, a large amount of 7Be can be detected in the ejecta of the nova,
ultimately decaying into 7Li.

In this paper, we assume the novae as main sources of Li. In particular,
Section 2 describes the details of the nova model. Section 3 presents the 7Li
yields predicted by our models and the comparative analysis of the observation
and theoretical results. The summary is given in Section 4.

##  2 Models

Our nova model has been using version-12778 of the MESA stellar evolution
code, which constructs CO and ONeMg nova models based on its white dwarf and
nova modules (Paxton et al., 2011, 2013, 2015, 2018, 2019). The advantage of
MESA is its ability to calculate nova outbursts by dividing the outer shell
mass of WD into approximately 1000 or more cells, resulting in smaller errors.
At each cell, such as temperature, density and isotopic composition are
calculated. In MESA, when the luminosity of a star ($L$) exceeds the super-
Eddington luminosity ($L_{\rm Edd}$), it will trigger mass loss. The mass loss
rate is

$\dot{M}=-2\eta_{\rm Edd}\frac{(L-L_{\rm Edd})}{v_{\rm esc}^{2}}$ (1)

where $v_{\rm esc}=\sqrt{2GM/R}$, $L_{\rm Edd}=(4\pi GcM)/\kappa$. $M$ and $R$
are the mass and radius, while $\kappa$ is the Rosseland mean opacity at the
WD’s surface. The scaling factor is taken $\eta_{\rm Edd}=1$ (Denissenkov et
al., 2013). The cells will be ejected when $L>L_{\rm Edd}$. In this paper, it
is set that the nova ejection begins when the total WD luminosity ($L$) is
greater than $10^{4}$ times the solar luminosity ($\rm L_{\odot}$), and ends
when less than $10^{3}$ $\rm L_{\odot}$. Therefore, the MESA code can be used
to simulate multi-cycle nova and construct a large-scale nova model grid from
the accretion phase to expansion, explosion and ejection phases (Paxton et
al., 2011, 2013, 2015).

For CO WD models, the nuclear network selects pp_and_cno_extras_net, while the
ONeMg WD models uses h_burn_net. These nuclear networks include the CNO
burning cycle and the proton-proton reaction chains (pp chain), the latter of
which include 3He($\alpha,\gamma$)7Be, 7Be($e^{-},\nu$)7Li, 8B($\gamma,p$)7Be,
7Li($p,\alpha$)4He, and 8B($e^{+},\nu$)8Be∗(2$\alpha$), which are sufficient
nuclear synthesis to treat 7Be and 7Li nucleosynthesis (Starrfield et al.,
1978). It is worth noting that the degree of mixing also affects the mass and
isotopic abundance of the ejected material (Hernanz et al., 1996). José &
Hernanz (1998), Denissenkov et al. (2014) and Rukeya et al. (2017) have used
the NOVA and MESA codes to calculate the nova eruption model, assuming that
the degree of mixing could be 25%-50%. That is, 25% of WD material and 75% of
solar material, or 50% of WD material and 50% of solar material (Lodders et
al., 2009). We adopted the latter, which is more widely used. However, the 7Be
simulated by the previous models did not explain the observed values.
Subsequent studies suggested that there is a corresponding relationship
between the 7Be and 3He (Boffin et al., 1993; Hernanz et al., 1996; Molaro et
al., 2020; Denissenkov et al., 2021).

The importance of 3He for novae was first studied by Schatzman (1951) in the
context of a theory of novae powered by thermonuclear detonations. The initial
3He abundance for the accreted matter, could potentially come from the donor
star (Shara, 1980; Townsley & Bildsten, 2004). As the donor star are ascending
the red giant branch the convection dredges up 3He enriched material to the
surface which is later expelled into the ISM by wind or is accreted by WDs in
nova systems (Shen & Bildsten, 2009; Denissenkov et al., 2021). Dantona &
Mazzitelli (1982) and Iben & Tutukov (1984) found that the mass fraction of
accreted $X_{0}$(3He) can reach values as high as $4\times 10^{-3}$ during the
evolution of systems with low-mass donors. Furthermore, some observational
studies have shown the existence of relatively high levels of 3He/H in certain
planetary nebulae (Rood et al., 1992; Balser & Bania, 2018). If 3He abundance
of the donor’s envelope is much higher than that in the Sun, this would almost
align the model predictions of 7Be production with observations (Molaro et
al., 2020). However, observations of the ISM indicate that the abundance of
3He in the Galaxy cannot be too high (Dearborn et al., 1996; Romano &
Matteucci, 2003). Denissenkov et al. (2021) demonstrated that an excess of 3He
in accreted material would actually reduce the production of 7Be. Their work
showed that when $X_{0}$(3He) exceeds $3\times 10^{4}$, it could lead to the
early onset of the TNR, result in a reduction in peak temperature and accreted
mass, and thereby suppress the production of 7Be. While this level of 3He-
induced 7Be abundance increase would be slightly elevated, most of it would
still be consumed at high temperatures and not transported to the WD surface
to generate sufficient 7Li, thus not closing the gap with observations.
Therefore, an effective transport mechanism is required to safely transport
7Be to the WD surface and allow it to survive. Element diffusion provides an
effective pathway for this.

Elemental diffusion in stellar interior is mainly driven by a combination of
pressure gradients (or gravity), temperature gradients, compositional
gradients, and radiation pressures. By solving the Burgers equation (Burgers,
1969), Thoul et al. (1994) proposed a general method of arranging the entire
system of equations into a single matrix equation, so that the relative
concentrations of various species have no approximate values and the number of
elements considered is not limited. Therefore, this method is applicable to
various astrophysical problems. In MESA, the method of Thoul et al. (1994) is
used to calculate the diffusion of chemical elements within stars (Paxton et
al., 2015, 2018). This diffusion effect can bring internal elements to the
surface. We speculate that when WD accretes enough hydrogen-rich material from
companion star to reach the critical point, TNR occurs. The thermal
instability caused by the thermonuclear runaway leads to the appearance of a
convective zone, which extends from approximately the middle of the combustion
shell to the surrounding non combustion helium layer (Cameron & Fowler, 1971).
The convective zone can bring 7Be from the stellar interior to the surface,
which is the CF mechanism. Element diffusion improves the mixing efficiency of
the entire convection zone, bringing more 7Be to the surface. When a nova
explosion occurs, a large amount of 7Be on the surface is ejected and decays
into 7Li in the ISM through a short half-life. This work utilize MESA to
construct a large-scale nova grid by setting different basic parameters and
calculated the 7Li production of the nova.

MESA is one-dimensional code, and only simulate spherically symmetric nova
outburst. However, based on the images of NOVA V5668 SAG combining the optical
and radio observations from the Hubble Space Telescope and the Very Large
Array telescope, Mukai & Sokoloski (2019) suggested that the geometry
distribution of nova ejecta is not spherical symmetry but is the shape of an
equatorial torus. It indicates that ejecta from novae has very complicated
structure. It is unclear which physical process led to such an unsymmetric
structure. Up until now, there have been few instances of 2D or 3D simulations
depicting nova outbursts. Therefore, it should be noted that the MESA nova
model also has its limitations.

##  3 result

According to Yaron et al. (2005), the WD mass ($M_{\rm WD}$), accretion rate
($\dot{M}$), WD core temperature ($T_{\rm c}$), and composition of the
accreted material constitute the four basic input parameters that determine
the nova eruption (Starrfield et al., 2016; Jose, 2016). Yaron et al. (2005)
constrained the parameters of the nova eruption and set a three-dimensional
restricted space for the nova eruption conditions. Our model set the $T_{\rm
c}$ at 3$\times$107K and selected CO WD model mass: 0.5 $\rm M_{\odot}$, 0.6
$\rm M_{\odot}$, 0.7 $\rm M_{\odot}$, 0.8 $\rm M_{\odot}$, 0.9 $\rm
M_{\odot}$, 1.0 $\rm M_{\odot}$, 1.1 $\rm M_{\odot}$, 1.2 $\rm M_{\odot}$; and
ONeMg WD model mass: 1.0 $\rm M_{\odot}$, 1.1 $\rm M_{\odot}$, 1.2 $\rm
M_{\odot}$, 1.3 $\rm M_{\odot}$; with accretion rates ($\dot{M}$) of 1
$\times$ $10^{-11}$ $\rm M_{\odot}$ yr-1, 1 $\times$ $10^{-10}$ $\rm
M_{\odot}$ yr-1, 1 $\times$ $10^{-9}$ $\rm M_{\odot}$ yr-1, 1 $\times$
$10^{-8}$ $\rm M_{\odot}$ yr-1, 1 $\times$ $10^{-7}$ $\rm M_{\odot}$ yr-1. In
addition to the above four parameters, it is expected that material
transferred from the companion (solar-like) will mix with the outer layers of
the WD. This model adopts the widely accepted composition of 50% WD material
and 50% solar material. Solar component data is taken from Lodders et al.
(2009). Molaro et al. (2020) argued that the variety of high 7Be/H abundances
in nova could be originated in a higher than solar content of 3He in the donor
star. Observations show relatively high levels of 3He/H in some planetary
nebulae, but observations of ISM indicate that the abundance of 3He in the
Galaxy cannot be too high (Rood et al., 1992; Dearborn et al., 1996; Romano &
Matteucci, 2003; Balser & Bania, 2018). According to the $X_{0}$(3He) range:
2.96$\times$10-5$\thicksim$2.96$\times$10-3 used by Denissenkov et al. (2021),
we set $X_{0}$(3He) to be 4$\times$104.

###  3.1 Novae models as stellar sources of Lithium

Figure 1: Nova explosion process with $M_{\rm WD}$ = 1$\rm M_{\odot}$ and
$\dot{M}$ = 1 $\times$ $10^{-10}$ $\rm M_{\odot}$ yr-1. Profiles of 7Be during
the nova explosion show in panels. The y axis represents the boundary radius
of WD during explosion and the x axis represents the lifetime of the nova
explosion. Green shadow shows the convective zone of different models.

It is well known that during the occurrence of TNR, there are intense nuclear
reactions, primarily dominated by hydrogen burning due to the WD accreting
hydrogen-rich material from the companion. During hydrogen burning, a large
amount of 7Be is produced through 3He($\alpha$,$\gamma$)7Be, with some being
convectively transported to the WD’s surface while the rest is depleted at
high temperatures. In our models with element diffusion, the transport
efficiency within the WD is enhanced. Figure 1 shows the evolution of elements
during nova explosion. The left two panels clearly display the effect of
element diffusion. There are some blank discontinuous area on the surface
convection zone (green shadow) of the model without element diffusion,
indicating weak or even no mixing activity in these areas, as shown in the
left-upper panel. In Figure 1, the mixing area within the convection zone of
the WD model with element diffusion becomes more continuous and dense, and the
mixing activity becomes stronger, as shown in the left-lower panel. In the
nova model with element diffusion, a large amount of 7Be generated by nuclear
reactions is effectively transported by this strong mixing effect to the low-
temperature region of the surface, thereby avoiding depletion at high
temperatures. On the contrary, the model without element diffusion cannot send
out more 7Be, which is consumed by high temperature.

Meanwhile, the improvement of 3He can generate more 7Be to contribute to the
transport to the surface as shown by the right-top panel in Figure 1. The 3He
increase greatly enhances the yield of 7Be in envelope, which is shown by pink
color area. However, the increase of 3He causes the convective region to move
inward, resulting in the failure to bring 7Be to a sufficiently low
temperature surface. This result is consistent with Denissenkov et al. (2021),
who stated that excessively high 3He actually reduces the 7Be of nova
ejection. However, combining the element diffusion and the increase of 3He,
the large amount of 7Be produced via enhancing 3He can be efficiently
transfered to WD surface, which are clearly shown by the right-lower panel.

Figure 2: Comparison with observed Li abundances and the numerical simulations
along with WD masses. Solid lines of different colors represent CO nova models
with different accretion rates, while dashed lines represent ONeMg nova
models. Red bordered circles denote the observed abundances of CO WD novae,
and the squares denote the ONeMg WD novae. Since evaluating the quality of
each WD is difficult, we simply plotted the error bars for each observed nova.
The black, yellow, and red dotted lines correspond to theoretical predictions;
highest values for each WD mass in José & Hernanz (1998), the “123-321 models”
of José et al. (2020), and 25%–50% mixing model of Starrfield et al. (2024),
respectively. The blue pentagram represents the prediction of nova M31N
1926-07c and the blue triangle represents the nova T CrB.

We find that the abundance of 7Be in the model combining the element diffusion
and the increase of 3He can be increased by about 4 - 10 times. It means that
7Be abundance calculated in this work is consistent with the observational
values (Izzo et al., 2015; Tajitsu et al., 2015; Molaro et al., 2020, 2023).

In order to compare our results with the observations, we selected 13
published observational samples of CO and ONeMg novae with relatively accurate
measurements of parameters such as mass and Be abundance (9 CO novae and 4
ONeMg novae) (e.g. Tajitsu et al. (2015, 2016); Molaro et al. (2016); Izzo et
al. (2018); Selvelli et al. (2018); Molaro et al. (2020); Arai et al. (2021);
Molaro et al. (2022, 2023)). We calculated the 7Be abundance ejected in a
single nova eruption using the criteria that the eruption begins when the
total WD luminosity ($L$) is greater than $10^{4}$ $\rm L_{\odot}$ and ends
when it is below $10^{3}$ $\rm L_{\odot}$.

Figure 2 presents a comparison of the Be abundance produced by our simulated
nova models with other models and matching to observations. The solid lines in
different colors represent the CO nova models in the mass range of $0.7\rm
M_{\odot}-1.0\rm M_{\odot}$, with accretion rates from 1 $\times$ $10^{-7}$
$\rm M_{\odot}$ yr-1 to 1 $\times$ $10^{-11}$ $\rm M_{\odot}$ yr-1. The bold
dashed lines depict the results of the ONeMg nova models in the mass range of
$1.1\rm M_{\odot}-1.3\rm M_{\odot}$, with accretion rates from 1 $\times$
$10^{-7}$ $\rm M_{\odot}$ yr-1 to 1 $\times$ $10^{-9}$ $\rm M_{\odot}$ yr-1.
The results simulated by other literatures also are given, such as the black
and red dotted lines, representing models constructed by José & Hernanz
(1998); José et al. (2020) with 50% mixing and different WD masses, and the
yellow dotted line representing models constructed by Starrfield et al. (2024)
with 25% and 50% mixing and different WD masses. It is worth mentioning that
our model provide 7Be yields for a range of accretion rates for each $M_{\rm
WD}$, rather than sampling only at a fixed accretion rate of 2 $\times$
$10^{-10}$ $\rm M_{\odot}$ yr-1 as in the other models mentioned above. It is
evident that the 7Be abundance produced by our model is significantly higher
compared to other models and covers almost all CO and ONeMg nova observational
samples. In addition, we have made predictions for the two upcoming nova T CrB
and M31N 1926-07c eruptions in 2024 and marked the expected abundance of
ejected 7Be in Figure 2. This result indicates that element diffusion enhances
the transport efficiency between the interior and surface convective region of
the WD, transporting sufficient 7Be to the surface region. Our results are
consistent with observations and successfully explain the high 7Be abundance
observed in the spectra after nova eruptions.

Figure 3: 7Li yields vs. WD mass for all CO WDs in the grid.

Due to the intense shock produced by nova eruption, the ash of TNR is
partially ejected into the ISM (Tajitsu et al., 2015; Izzo et al., 2015;
Molaro et al., 2022, 2023; Starrfield et al., 2024). The ejected 7Be during
nova eruption decays into7Li. This contributes to the total Li elements in the
Galactic ISM. Therefore, we consider the abundance of ejected 7Be to be 7Li.
In our simulations, Li mass produced by a nova outbursts is calculated by
$M_{\rm Li}=\int\dot{M}X({\rm{}^{7}Li}){\rm d}t$, where $\dot{M}$ is the mass-
loss rate of WD during nova outburst (See Eq.1), $X(^{7}{\rm Li})$ is the mass
fraction of 7Li in the nova ejecta. Figure 2 shows $X(^{7}{\rm Li})$. Compared
to the previous theoretical results in José & Hernanz (1998), José et al.
(2020) and Starrfield et al. (2024), the Li abundances in our simulations are
higher and are closer to the observed values. Figure 3 gives the Li yields for
a nova outbursts. Our results are consistent with those of Starrfield et al.
(2024). Based on Figures 2 and 3, our model may underestimate the mass-loss
rate $\dot{M}$, which is described by Eq.1. Observations indicate that the
range of ejection masses falls between 10-6 to 10-4 M⊙, and José & Hernanz
(1998) proposed an average ejection mass of $2\times 10^{-5}$ M⊙ for novae. In
our models, we calculate the range of ejection masses falls between
$9.17\times 10^{-7}$ to $5.93\times 10^{-5}$ M⊙. This result is slightly
smaller than the observed value. As mentioned by Denissenkov et al. (2021),
the increase of 3He in the accretion layer of our WD model can lead to an
earlier TNR, a decrease in peak temperature and accreted mass, and ultimately
result in a smaller ejection mass. By utilizing the Li and Be abundances and
the ejected mass of WDs output by MESA, we can obtain the Li mass for each
burst ejection.

The known novae are mainly concentrated in the range of WD mass $M_{\rm
WD}$=0.8 M⊙ \- 1.0M ⊙ and accretion rates around $1\times 10^{-10}$ $\rm
M_{\odot}$ yr-1. In this range, our estimating Li yield reaches to about
$2\times 10^{-10}$ M⊙. This yield is slightly lower than the observations of
the latest recurrent novae RS Oph (Izzo et al., 2015; Molaro et al., 2023),
but it has already reached the same order of magnitude. It can be demonstrated
that the nova model constructed in this paper can explain a large part of the
observations in the Galaxy.

###  3.2 Contribution of 7Li produced by novae to the Galactic

Theoretically, Rukeya et al. (2017) and Starrfield et al. (2024) estimated the
specific contribution of 7Li produced by novae to the Galactic, and they found
that this contribution is approximately 10%. However novae have been proposed
as the main factories of lithium in the Galaxy is something that was proposed
in the 1970s by Arnould & Norgaard (1975) and Starrfield et al. (1978), and
then demonstrated in Izzo et al. (2015), Tajitsu et al. (2015) and Molaro et
al. (2016, 2023), based on the detection of lithium and beryllium in a few
novae. As shown by Figure 3, compared with the observations, the theoretical
predictions underestimate Li yields produced by nova eruption.

In order to estimated the contribution of 7Li produced in our nova models to
the Galactic ISM, we use the method of binary population synthesis (BPS),
which has been applied by our group (Lü et al., 2006, 2009, 2013; Rukeya et
al., 2017; Yu et al., 2019; Lü et al., 2020; Yu et al., 2021; Gao et al.,
2022). BPS is a robust approach to evolve a large number of stars (including
binaries) so that we can explain and predict the properties of a population of
a type of stars (Han et al., 2020). In the population synthesis method for
binary systems, input parameters include the star formation rate (SFR), the
initial mass function (IMF) of the primaries, the initial mass ratio
distribution, the initial orbital distribution, the eccentricity distribution,
and the metallicity Z of binary systems. Here, with help of the rapid binary
evolution (BSE) code, originating from Hurley et al. (2002), we can rapidly
evolve a large-sample binaries into nova binaries, in which $M_{\rm WD}$ and
the $\dot{M}$ are given.

Figure 4: Li mass contributions from different sources as a function of
Galactic age. The orange line represents our work, while the green and gray
dashed lines represent the model results for Rukeya et al. (2017) and Kemp et
al. (2022a). The shaded area is the error range of the latter. The results of
AGB are represented by purple dotted lines.

Using MESA, we construct a grid for each nova eruption with $M_{\rm WD}$,
$\dot{M}$ and 7Li yields. For every nova simulated using the BSE code, by a
bilinear interpolation of the above two physical quantities ($M_{\rm WD}$ and
$\dot{M}$) in MESA, one can then calculate the 7Li yields of every nova.

Following Lü et al. (2006), in the method of population synthesis, we use the
initial mass function of Miller & Scalo (1979) for the mass of the primary
components and a flat distribution of mass ratios (Kraicheva et al., 1989;
Goldberg & Mazeh, 1994). A logarithmic flat distribution of initial
separations between 10 and 106 R⊙ is used.

In the binary evolution, the common envelope (CE) evolution is critical
important for the formation of nova systems. In BSE code, a combined parameter
$\alpha_{\rm CE}\times\beta_{\rm CE}$ is used to calculate common envelope
evolution, where $\alpha_{\rm CE}$ is the fraction of binary binding energy
which is spent to expel the CE, and $\beta_{\rm CE}$ is a parameter for the
envelope structure of the donor. As discussed in Rukeya et al. (2017),
$\alpha_{\rm CE}\times\beta_{\rm CE}$ has a weak effect on 7Li yields produced
by novae. In this work, we take $\alpha_{\rm CE}\times\beta_{\rm CE}=1.0$.
Simultaneously, circle orbits and solar metallicity for all binary systems are
taken. To calculate the production rate of 7Li, we assume a constant star
formation rate of 5 M⊙ yr-1 over the past 13 Gyr. In the case of a constant
star formation rate, one simulates that $10^{6}$ binary systems, in which the
primaries are more massive than 0.8 $\rm M_{\odot}$, which causes a
statistical error for Monte Carlo simulations lower than 1% in classical
novae.

Figure 4 shows the evolutionary trajectory of 7Li produced by novae in the
Galaxy at a constant star formation rate. According to the results of
population synthesis, we obtained an average 7Li yield of about 6.4 $\times$
$10^{-11}$ $\rm M_{\odot}$ for each nova eruption, with approximately 8,000
eruptions per nova binary, which is consistent with the previous results
(Shara et al., 1986; Molaro et al., 2020). We then select nova systems from
binary systems, the primary is a white dwarf (including CO white dwarf and
ONeMg white dwarf) and is accreting material from its secondary (a main
sequence or red giant star) via Roche lobe or stellar wind. The result is that
among the $10^{6}$ binary systems, 17368 of them evolve into nova systems,
accounting for approximately 1.7%. This is consistent with Rukeya et al.
(2017) ($\sim$1.5%) and Hurley et al. (2002) ($\sim$1.9%). Based on this, we
can conclude that the nova rate is 130 per year, which is within the predicted
range (Sharov, 1972; della Valle & Livio, 1994; Shafter, 1997, 2002, 2017).
Among the $10^{6}$ binary systems, 1.7% of them evolve into nova systems,
resulting in an annual 7Li production of approximately 8.4 $\times$ $10^{-9}$
$\rm M_{\odot}$. Considering the age of the Galaxy to be $1.3\times 10^{10}$
years, the contribution of novae to 7Li is estimated to be around 110 $\rm
M_{\odot}$, compared to the total Li content of approximately 150 $\rm
M_{\odot}$ in the interstellar medium of the Galaxy (Hernanz et al., 1996;
Molaro et al., 2016). Therefore, novae contribute approximately 73% of the 7Li
in the Galactic ISM.

In Figure 4, the solid red line represents the 7Li production at the age scale
of the Galaxy, which is significantly higher than the results obtained by
Rukeya et al. (2017). Kemp et al. (2022a) used the binary population synthesis
code binary_c, to simulate the novae in the Galactic and, by using observed Li
production, effectively explained the Li abundance in the early Sun. The 7Li
production calculated in our model falls within the predicted error range for
nova 7Li production, as demonstrated by Kemp et al. (2022a), proving that
novae are indeed the most significant contributors to Li in the Galaxy. In
addition, we also calculate the contribution of asymptotic giant branch (AGB)
stars using the same method. The hot bottom burning mechanism of AGB stars can
bring Li elements to the surface, which will evolve into the planetary nebulae
stage and ultimately be ejected into the ISM (Smith, Verne V. and Lambert,
David L., 1990; Romano et al., 2001). After calculation, each AGB star
produces approximately $10^{-9}$ $\rm M_{\odot}$ of 7Li, resulting in a final
contribution to 7Li of around 1 $\rm M_{\odot}$, which is only 1%. This result
has been consistent with previous research (Romano et al., 2001; Doherty et
al., 2014; Rukeya et al., 2017).

In our simulation, the lithium mass produced by novae is $\sim$ 110 M⊙. It
indicates that the novae can provide about 70% of the contribution to the
Galactic ISM. However, compared to the total Li mass in the entire Galaxy
($\sim$ 1000 M⊙) (Molaro et al., 2023), Li produced by the novae is limited
(about 15%-20%), and most of Li may originate from the Big Bang.

##  4 summary

We used the MESA code to construct nova models with element diffusion to
calculate the abundance of 7Be on the surface of the WD during the occurrence
of a TNR, as well as the production of 7Li after the eruption. Element
diffusion enhances the efficiency of transport between the nuclear reaction
zone and the convective region on the surface of the WD, allowing more
material to be transported to the surface. Based on theoretical and
observational evidence, we appropriately increased the amount of 3He produced
during the mixing of material from the donor star and the accretor star,
leading to more 7Be being produced. A transport channel within the WD is
formed due to the increased transmission efficiency caused by element
diffusion. This channel effectively transports the 7Be from the hydrogen-
burning region of the WD to the convective envelope, where it decays into 7Li.
Therefore, a large amount of 7Be produced by the nuclear reaction process in
the WD can be transferred to the surface and ultimately ejected. The abundance
of 7Be on the surface of the WD during the occurrence of a TNR in our model is
consistent with the values obtained from the observed nova samples.

When the 7Be ejected by the nova eruption decays into 7Li in a short period of
time, we use population synthesis methods to calculate the production of 7Li
from the nova eruption. We find that about 1.7% binary systems in the Galaxy
can evolve into nova binaries. Every nova binary evenly can occur about 8,000
eruptions, and the occurrence of nova eruption is about 130 yr-1. Each
eruption can produce about 6.4 $\times$ $10^{-11}$ M⊙ of 7Li. There are about
110 M⊙ Li produced by novae, which is about 73% of total Li mass in the
interstellar medium of the Galaxy, and approximately 15%-20% of the entire
Galaxy. It means that novae are the primary source of Li in the Galactic ISM,
and also one of the important sources of lithium in the entire Galaxy.

## Acknowledgements

This work received the generous support of the National Natural Science
Foundation of China under grants 12163005, U2031204, 12373038 and 12288102,
the science research grants from the China Manned Space Project with No.
CMSCSST-2021-A10 and the Natural Science Foundation of Xinjiang Nos.
2021D01C075, No.2022D01D85, and 2022TSYCLJ0006.

## References

  * Alibés et al. (2002) Alibés, A., Labay, J., & Canal, R. 2002, ApJ, 571, 326, doi: 10.1086/339937
  * Arai et al. (2021) Arai, A., Tajitsu, A., Kawakita, H., & Shinnaka, Y. 2021, ApJ, 916, 44, doi: 10.3847/1538-4357/ac00bf
  * Arnould & Norgaard (1975) Arnould, M., & Norgaard, H. 1975, A&A, 42, 55
  * Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481, doi: 10.1146/annurev.astro.46.060407.145222
  * Balser & Bania (2018) Balser, D. S., & Bania, T. M. 2018, AJ, 156, 280, doi: 10.3847/1538-3881/aaeb2b
  * Banerjee, Projjwal et al. (2016) Banerjee, Projjwal, Qian, Yong-Zhong, Heger, Alexander, & Haxton, Wick. 2016, EPJ Web of Conferences, 109, 06001, doi: 10.1051/epjconf/201610906001
  * Bennett et al. (2013) Bennett, C. L., Larson, D., Weiland, J. L., et al. 2013, ApJS, 208, 20, doi: 10.1088/0067-0049/208/2/20
  * Boffin et al. (1993) Boffin, H. M. J., Paulus, G., Arnould, M., & Mowlavi, N. 1993, A&A, 279, 173
  * Burgers (1969) Burgers, J. M. 1969, Flow Equations for Composite Gases
  * Cameron & Fowler (1971) Cameron, A. G. W., & Fowler, W. A. 1971, ApJ, 164, 111, doi: 10.1086/150821
  * Casey et al. (2016) Casey, A. R., Ruchti, G., Masseron, T., et al. 2016, MNRAS, 461, 3336, doi: 10.1093/mnras/stw1512
  * Cescutti & Molaro (2019) Cescutti, G., & Molaro, P. 2019, MNRAS, 482, 4372, doi: 10.1093/mnras/sty2967
  * Coc et al. (2014) Coc, A., Uzan, J.-P., & Vangioni, E. 2014, J. Cosmology Astropart. Phys, 2014, 050, doi: 10.1088/1475-7516/2014/10/050
  * Dantona & Mazzitelli (1982) Dantona, F., & Mazzitelli, I. 1982, ApJ, 260, 722, doi: 10.1086/160292
  * Dearborn et al. (1996) Dearborn, D. S. P., Steigman, G., & Tosi, M. 1996, ApJ, 465, 887, doi: 10.1086/177472
  * della Valle & Livio (1994) della Valle, M., & Livio, M. 1994, A&A, 286, 786
  * Denissenkov et al. (2013) Denissenkov, P. A., Herwig, F., Bildsten, L., & Paxton, B. 2013, ApJ, 762, 8, doi: 10.1088/0004-637X/762/1/8
  * Denissenkov et al. (2021) Denissenkov, P. A., Ruiz, C., Upadhyayula, S., & Herwig, F. 2021, MNRAS, 501, L33, doi: 10.1093/mnrasl/slaa190
  * Denissenkov et al. (2014) Denissenkov, P. A., Truran, J. W., Pignatari, M., et al. 2014, MNRAS, 442, 2058, doi: 10.1093/mnras/stu1000
  * Doherty et al. (2014) Doherty, C. L., Gil-Pons, P., Lau, H. H. B., et al. 2014, MNRAS, 441, 582, doi: 10.1093/mnras/stu571
  * Draine (2011) Draine, B. T. 2011, Physics of the Interstellar and Intergalactic Medium
  * Dupuis et al. (1992) Dupuis, J., Fontaine, G., Pelletier, C., & Wesemael, F. 1992, ApJS, 82, 505, doi: 10.1086/191728
  * Fields et al. (2014) Fields, B. D., Molaro, P., & Sarkar, S. 2014, arXiv e-prints, arXiv:1412.1408, doi: 10.48550/arXiv.1412.1408
  * Gao et al. (2022) Gao, J., Zhu, C., Yu, J., et al. 2022, A&A, 668, A126, doi: 10.1051/0004-6361/202243871
  * Gehrz et al. (1998) Gehrz, R. D., Truran, J. W., Williams, R. E., & Starrfield, S. 1998, PASP, 110, 3, doi: 10.1086/316107
  * Goldberg & Mazeh (1994) Goldberg, D., & Mazeh, T. 1994, A&A, 282, 801
  * Han et al. (2020) Han, Z.-W., Ge, H.-W., Chen, X.-F., & Chen, H.-L. 2020, Research in Astronomy and Astrophysics, 20, 161, doi: 10.1088/1674-4527/20/10/161
  * Hernanz et al. (1996) Hernanz, M., Jose, J., Coc, A., & Isern, J. 1996, ApJ, 465, L27, doi: 10.1086/310122
  * Hurley et al. (2002) Hurley, J. R., Tout, C. A., & Pols, O. R. 2002, MNRAS, 329, 897, doi: 10.1046/j.1365-8711.2002.05038.x
  * Iben & Tutukov (1984) Iben, I., J., & Tutukov, A. V. 1984, ApJ, 284, 719, doi: 10.1086/162455
  * Iben et al. (1991) Iben, Icko, J., Fujimoto, M. Y., & MacDonald, J. 1991, ApJ, 375, L27, doi: 10.1086/186080
  * Izzo et al. (2015) Izzo, L., Della Valle, M., Mason, E., et al. 2015, ApJ, 808, L14, doi: 10.1088/2041-8205/808/1/L14
  * Izzo et al. (2018) Izzo, L., Molaro, P., Bonifacio, P., et al. 2018, MNRAS, 478, 1601, doi: 10.1093/mnras/sty435
  * Jose (2016) Jose, J. 2016, Stellar Explosions: Hydrodynamics and Nucleosynthesis, doi: 10.1201/b19165
  * José & Hernanz (1998) José, J., & Hernanz, M. 1998, ApJ, 494, 680, doi: 10.1086/305244
  * José et al. (2020) José, J., Shore, S. N., & Casanova, J. 2020, A&A, 634, A5, doi: 10.1051/0004-6361/201936893
  * Kemp et al. (2022a) Kemp, A. J., Karakas, A. I., Casey, A. R., et al. 2022a, ApJ, 933, L30, doi: 10.3847/2041-8213/ac7c72
  * Kemp et al. (2022b) Kemp, A. J., Karakas, A. I., Casey, A. R., Kobayashi, C., & Izzard, R. G. 2022b, MNRAS, 509, 1175, doi: 10.1093/mnras/stab3103
  * Kippenhahn et al. (1980) Kippenhahn, R., Ruschenplatt, G., & Thomas, H. C. 1980, A&A, 91, 175
  * Kovetz & Prialnik (1985) Kovetz, A., & Prialnik, D. 1985, ApJ, 291, 812, doi: 10.1086/163117
  * Kraicheva et al. (1989) Kraicheva, Z. T., Popova, E. I., Tutukov, A. V., & Yungel’Son, L. R. 1989, Astrophysics, 30, 323, doi: 10.1007/BF01003893
  * Lodders et al. (2009) Lodders, K., Palme, H., & Gail, H. P. 2009, Landolt Börnstein, 4B, 712, doi: 10.1007/978-3-540-88055-4_34
  * Lü et al. (2006) Lü, G., Yungelson, L., & Han, Z. 2006, MNRAS, 372, 1389, doi: 10.1111/j.1365-2966.2006.10947.x
  * Lü et al. (2013) Lü, G., Zhu, C., & Podsiadlowski, P. 2013, ApJ, 768, 193, doi: 10.1088/0004-637X/768/2/193
  * Lü et al. (2020) Lü, G., Zhu, C., Wang, Z., et al. 2020, ApJ, 890, 69, doi: 10.3847/1538-4357/ab6bcc
  * Lü et al. (2009) Lü, G., Zhu, C., Wang, Z., & Wang, N. 2009, MNRAS, 396, 1086, doi: 10.1111/j.1365-2966.2009.14777.x
  * Miller & Scalo (1979) Miller, G. E., & Scalo, J. M. 1979, ApJS, 41, 513, doi: 10.1086/190629
  * Molaro et al. (2020) Molaro, P., Izzo, L., Bonifacio, P., et al. 2020, MNRAS, 492, 4975, doi: 10.1093/mnras/stz3587
  * Molaro et al. (2016) Molaro, P., Izzo, L., Mason, E., Bonifacio, P., & Della Valle, M. 2016, MNRAS, 463, L117, doi: 10.1093/mnrasl/slw169
  * Molaro et al. (2022) Molaro, P., Izzo, L., D’Odorico, V., et al. 2022, MNRAS, 509, 3258, doi: 10.1093/mnras/stab3106
  * Molaro et al. (2023) Molaro, P., Izzo, L., Selvelli, P., et al. 2023, MNRAS, 518, 2614, doi: 10.1093/mnras/stac2708
  * Mukai & Sokoloski (2019) Mukai, K., & Sokoloski, J. L. 2019, Physics Today, 72, 38, doi: 10.1063/PT.3.4341
  * Paxton et al. (2011) Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192, 3, doi: 10.1088/0067-0049/192/1/3
  * Paxton et al. (2013) Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4, doi: 10.1088/0067-0049/208/1/4
  * Paxton et al. (2015) Paxton, B., Marchant, P., Schwab, J., et al. 2015, ApJS, 220, 15, doi: 10.1088/0067-0049/220/1/15
  * Paxton et al. (2018) Paxton, B., Schwab, J., Bauer, E. B., et al. 2018, ApJS, 234, 34, doi: 10.3847/1538-4365/aaa5a8
  * Paxton et al. (2019) Paxton, B., Smolec, R., Schwab, J., et al. 2019, ApJS, 243, 10, doi: 10.3847/1538-4365/ab2241
  * Pignatari et al. (2016) Pignatari, M., Herwig, F., Hirschi, R., et al. 2016, ApJS, 225, 24, doi: 10.3847/0067-0049/225/2/24
  * Planck Collaboration et al. (2020) Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6, doi: 10.1051/0004-6361/201833910
  * Prantzos (2012) Prantzos, N. 2012, A&A, 542, A67, doi: 10.1051/0004-6361/201219043
  * Prantzos et al. (1993) Prantzos, N., Casse, M., & Vangioni-Flam, E. 1993, ApJ, 403, 630, doi: 10.1086/172233
  * Prantzos, N. et al. (2017) Prantzos, N., de Laverny, P., Guiglion, G., Recio-Blanco, A., & Worley, C. C. 2017, A&A, 606, A132, doi: 10.1051/0004-6361/201731188
  * Romano & Matteucci (2003) Romano, D., & Matteucci, F. 2003, MNRAS, 342, 185, doi: 10.1046/j.1365-8711.2003.06526.x
  * Romano et al. (1999) Romano, D., Matteucci, F., Molaro, P., & Bonifacio, P. 1999, A&A, 352, 117, doi: 10.48550/arXiv.astro-ph/9910151
  * Romano et al. (2001) Romano, D., Matteucci, F., Ventura, P., & D’Antona, F. 2001, A&A, 374, 646, doi: 10.1051/0004-6361:20010751
  * Rood et al. (1992) Rood, R. T., Bania, T. M., & Wilson, T. L. 1992, Nature, 355, 618, doi: 10.1038/355618a0
  * Rukeya et al. (2017) Rukeya, R., Lü, G., Wang, Z., & Zhu, C. 2017, PASP, 129, 074201, doi: 10.1088/1538-3873/aa6b4d
  * Schatzman (1951) Schatzman, E. 1951, Annales d’Astrophysique, 14, 294
  * Selvelli et al. (2018) Selvelli, P., Molaro, P., & Izzo, L. 2018, MNRAS, 481, 2261, doi: 10.1093/mnras/sty2310
  * Shafter (2017) Shafter. 2017, ApJ, 834, 196, doi: 10.3847/1538-4357/834/2/196
  * Shafter (1997) Shafter, A. W. 1997, ApJ, 487, 226, doi: 10.1086/304609
  * Shafter (2002) Shafter, A. W. 2002, in American Institute of Physics Conference Series, Vol. 637, Classical Nova Explosions, ed. M. Hernanz & J. José, 462–471, doi: 10.1063/1.1518246
  * Shara (1980) Shara, M. M. 1980, ApJ, 239, 581, doi: 10.1086/158144
  * Shara et al. (1986) Shara, M. M., Livio, M., Moffat, A. F. J., & Orio, M. 1986, ApJ, 311, 163, doi: 10.1086/164762
  * Sharov (1972) Sharov, A. S. 1972, Soviet Ast., 16, 41
  * Shen & Bildsten (2009) Shen, K. J., & Bildsten, L. 2009, ApJ, 692, 324, doi: 10.1088/0004-637X/692/1/324
  * Smith & Lambert (1989) Smith, V. V., & Lambert, D. L. 1989, ApJ, 345, L75, doi: 10.1086/185556
  * Smith, Verne V. and Lambert, David L. (1990) Smith, Verne V. and Lambert, David L. 1990, ApJS, 72, 387, doi: 10.1086/191421
  * Spergel et al. (2003) Spergel, D. N., Verde, L., Peiris, H. V., et al. 2003, ApJS, 148, 175, doi: 10.1086/377226
  * Spite & Spite (1982) Spite, M., & Spite, F. 1982, Nature, 297, 483, doi: 10.1038/297483a0
  * Starrfield et al. (2020) Starrfield, S., Bose, M., Iliadis, C., et al. 2020, ApJ, 895, 70, doi: 10.3847/1538-4357/ab8d23
  * Starrfield et al. (2024) Starrfield, S., Bose, M., Iliadis, C., et al. 2024, Hydrodynamic Simulations of Oxygen-Neon Classical Novae as Galactic 7Li Producers and Potential Accretion Induced Collapse Progenitors.  https://arxiv.org/abs/2401.02307
  * Starrfield et al. (2016) Starrfield, S., Iliadis, C., & Hix, W. R. 2016, PASP, 128, 051001, doi: 10.1088/1538-3873/128/963/051001
  * Starrfield et al. (2009) Starrfield, S., Iliadis, C., Hix, W. R., Timmes, F. X., & Sparks, W. M. 2009, ApJ, 692, 1532, doi: 10.1088/0004-637X/692/2/1532
  * Starrfield et al. (1978) Starrfield, S., Truran, J. W., Sparks, W. M., & Arnould, M. 1978, ApJ, 222, 600, doi: 10.1086/156175
  * Starrfield et al. (1998) Starrfield, S., Truran, J. W., Wiescher, M. C., & Sparks, W. M. 1998, MNRAS, 296, 502, doi: 10.1046/j.1365-8711.1998.01312.x
  * Tajitsu et al. (2015) Tajitsu, A., Sadakane, K., Naito, H., Arai, A., & Aoki, W. 2015, Nature, 518, 381, doi: 10.1038/nature14161
  * Tajitsu et al. (2016) Tajitsu, A., Sadakane, K., Naito, H., et al. 2016, ApJ, 818, 191, doi: 10.3847/0004-637X/818/2/191
  * Thoul et al. (1994) Thoul, A. A., Bahcall, J. N., & Loeb, A. 1994, ApJ, 421, 828, doi: 10.1086/173695
  * Townsley & Bildsten (2004) Townsley, D. M., & Bildsten, L. 2004, ApJ, 600, 390, doi: 10.1086/379647
  * Travaglio et al. (2001) Travaglio, C., Randich, S., Galli, D., et al. 2001, ApJ, 559, 909, doi: 10.1086/322415
  * Yan et al. (2018) Yan, H.-L., Shi, J.-R., Zhou, Y.-T., et al. 2018, Nature Astronomy, 2, 790, doi: 10.1038/s41550-018-0544-7
  * Yaron et al. (2005) Yaron, O., Prialnik, D., Shara, M. M., & Kovetz, A. 2005, ApJ, 623, 398, doi: 10.1086/428435
  * Yu et al. (2021) Yu, J., Zhang, X., & Lü, G. 2021, MNRAS, 504, 2670, doi: 10.1093/mnras/stab1063
  * Yu et al. (2019) Yu, J., Li, Z., Zhu, C., et al. 2019, ApJ, 885, 20, doi: 10.3847/1538-4357/ab44b5
  * Zhu et al. (2021) Zhu, C., Liu, H., Wang, Z., & Lü, G. 2021, A&A, 654, A57, doi: 10.1051/0004-6361/202039692
  * Życzkowski et al. (1998) Życzkowski, K., Horodecki, P., Sanpera, A., & Lewenstein, M. 1998, Phys. Rev. A, 58, 883, doi: 10.1103/PhysRevA.58.883