Stellar Neutrino Emission across the Mass–Metallicity Plane

We explore neutrino emission from nonrotating, single-star models across six initial metallicities and 70 initial masses from the zero-age main sequence to the final fate. Overall, across the mass spectrum, we find metal-poor stellar models tend to have denser, hotter, and more massive cores with lower envelope opacities, larger surface luminosities, and larger effective temperatures than their metal-rich counterparts. Across the mass–metallicity plane we identify the sequence (initial CNO → 14N → 22Ne → 25Mg → 26Al → 26Mg → 30P → 30Si) as making primary contributions to the neutrino luminosity at different phases of evolution. For the low-mass models we find neutrino emission from the nitrogen flash and thermal pulse phases of evolution depend strongly on the initial metallicity. For the high-mass models, neutrino emission at He-core ignition and He-shell burning depends strongly on the initial metallicity. Antineutrino emission during C, Ne, and O burning shows a strong metallicity dependence with 22Ne(α, n)25Mg providing much of the neutron excess available for inverse-β decays. We integrate the stellar tracks over an initial mass function and time to investigate the neutrino emission from a simple stellar population. We find average neutrino emission from simple stellar populations to be 0.5–1.2 MeV electron neutrinos. Lower metallicity stellar populations produce slightly larger neutrino luminosities and average β decay energies. This study can provide targets for neutrino detectors from individual stars and stellar populations. We provide convenient fitting formulae and open access to the photon and neutrino tracks for more sophisticated population synthesis models.

1. INTRODUCTION The next core-collapse (CC) supernova in the Milky Way or one of its satellite galaxies will be an opportunity to observe the explosion of a massive star across the electromagnetic, gravitational, and particle spectrums.For example, neutrinos with energies ≲ 10 MeV have played a prominent role in stellar physics (Hirata et al. 1987(Hirata et al. , 1988;;Bionta et al. 1987;Alekseev et al. 1987;Bahcall 1989;Borexino Collaboration et al. 2014, 2018, 2020) and particle physics (Bahcall 1989;Ahmad et al. 2002;Ackermann et al. 2022).Maps of ≥ 1 TeV neutrinos from the Galactic plane are consistent with a diffuse emission model of neutrinos whose analysis includes the Corresponding author: Ebraheem Farag ekfarag@asu.edusupernova remnant and pulsar wind nebula outcome(s) of CC events (IceCube Collaboration 2023).
Ongoing technological improvements in detector masses, energy resolution, and background abatement will allow the global SuperNova Early Warning System network (Al Kharusi et al. 2021) to observe new signals from different stages of the lifecycle of individual stars or the aggregate signal from a stellar population with multi-kiloton detectors such as SuperKamiokande (Simpson et al. 2019;Harada et al. 2023), SNO+ (Allega et al. 2023), KamLAND (Abe et al. 2023), Daya Bay (An et al. 2023), DUNE (Acciarri et al. 2016), JUNO (Yang & JUNO Collaboration 2022) and the upcoming HyperKamiokande (Abe et al. 2016).
Examples of ongoing stellar neutrino searches include pre-supernova neutrinos which allow new tests of stellar and neutrino physics (e.g., Odrzywolek et al. 2004;Kutschera et al. 2009;Odrzywolek 2009;Patton et al. 2017a,b;Kato et al. 2017Kato et al. , 2020a;;Kosmas et al. 2022) and enable an early alert of an impending CC supernova to the electromagnetic and gravitational wave communities (Beacom & Vogel 1999;Vogel & Beacom 1999;Mukhopadhyay et al. 2020;Al Kharusi et al. 2021).Other ongoing explorations include the diffuse supernova neutrino background (Hartmann & Woosley 1997;Bisnovatyi-Kogan & Seidov 1984;Krauss et al. 1984;Ando & Sato 2004;Horiuchi et al. 2009;Beacom 2010;Anandagoda et al. 2020;Suliga 2022;Anandagoda et al. 2023), and neutrinos from the helium-core nitrogen flash (Serenelli & Fukugita 2005), compact object mergers (Kyutoku & Kashiyama 2018;Lin & Lunardini 2020), tidal disruption of stars (Lunardini & Winter 2017;Winter & Lunardini 2022;Reusch et al. 2022), and pulsational pair-instability supernovae (Leung et al. 2020).Farag et al. (2020) introduced the idea of a neutrino Hertzsprung-Russell Diagram (νHRD) with a sparse grid of models.Each model started from the zero-age main sequence (ZAMS) and ended at a final fate but only at solar metallicity.They found all masses produce a roughly constant neutrino luminosity L ν during core H burning on the main-sequence (MS), and confirmed that low-mass (M ZAMS < 8 M ⊙ ) Red Giant Branch (RGB) models with M ZAMS ≤ 2 M ⊙ undergo large increases in L ν during the helium flash (nitrogen flash for neutrinos, Serenelli & Fukugita 2005) and subsequent subflashes.They also found He burning in asymptotic giant branch (AGB) models undergo sharp increases in L ν from thermal pulses (TPs), and significantly larger L ν from the hotter and denser cores of later evolutionary stages culminating at the onset of CC in high-mass (M ZAMS ≥ 8 M ⊙ ), non-rotating, single star models.A photon Hertzsprung-Russell Diagram (γHRD) provides information about the stellar surface, a νHRD can serve as a diagnostic tool of the stellar interior.
The coupling between these pieces of stellar physics and neutrino production from thermal (Itoh et al. 1996a) and weak reaction processes (Fuller et al. 1985;Oda et al. 1994;Langanke & Martínez-Pinedo 2000;Nabi et al. 2021) suggests that changes in Z can cause changes in a νHRD, and upon integration, the neutrino emission from a simple stellar population model.
This article is novel in exploring stellar neutrino emission across the mass-metallicity plane.This study can provide targets for neutrino detectors from individual stars and stellar populations.Section 2 describes the mass-metallicity grid and stellar physics, § 3 presents overall features and drivers across the mass-metallicity plane, § 4 analyzes low-mass tracks, § 5 details high-mass tracks, § 6 explores neutrino emission from a simple stellar population model, and § 7 summarizes our results.
Important symbols are defined in Table 1.Acronyms and terminology are defined in Table 2.

MASS-METALLICITY PLANE AND STELLAR PHYSICS
We model the evolution of single, non-rotating stars over a wide range of initial masses and metallicities, from the pre-main sequence (PMS) to the final fate. Figure 1 shows the mass-metallicity plane for 70 M ZAMS models distributed in the range 0.2 M ⊙ ≤ M ZAMS ≤ 150 M ⊙ for six initial metallicities log(Z/Z ⊙ ) = 0.5, 0, −0.5, −1, −2, −3, where we choose Z ⊙ = 0.0142 (Asplund et al. 2009).This mass-metallicity plane spans the range of single stars found in the Galaxy (Edvardsson et al. 1993;Ratcliffe et al. 2023;Almeida-Fernandes et al. 2023), and aids estimates of the neutrino emission from simple stellar population models.
For the low-mass models, we chose the Riemers wind mass loss scheme (Reimers 1977) with an efficiency of 0.5 on the RGB, and Blöckers wind mass loss scheme (Blöcker 2001) with an efficiency of 1.0 on the AGB.All low-mass models terminate as a white dwarf (WD) at L = 10 −3 L ⊙ , even if the evolution is longer than the age of the universe.
For the high-mass models, we choose the "Dutch" wind loss scheme (Nieuwenhuijzen & de Jager 1990;Nugis & Lamers 2000;Vink et al. 2001;Glebbeek et al. 2009) with an efficiency of 1.0 to generate stripped models.All models use an Eddington-grey iterated atmosphere as an outer boundary condition.We apply an extra pressure to the surface (see Section 6.1 of Jermyn et al. 2023) of our AGB and high-mass models to maintain stability of the surface layer in super Eddington regimes where the surface of the model can otherwise run away.The termination age for all high-mass models is at the onset of CC when the infall velocity of the Fe core reaches 100 km s −1 .A subset of our models halted prematurely: at core C-depletion (M ZAMS = 8-10 M ⊙ ), a stalled Ne/O flame in a degenerate core (M ZAMS = 11-14 M ⊙ ), the onset of pair-instability (C-ignition with M He ≳ 45 M ⊙ ), or due to numerical difficulties near the onset of CC.
We adopt a minimum chemical diffusive mixing coefficient of D min = 10 −2 cm 2 s −1 from C-ignition to the onset of CC to aid the convergence properties of our high-mass models (Farag et al. 2022).To reduce the numerical cost we use operator splitting to decouple the hydrodynamics from the nuclear burning for temperatures above T = 1×10 9 K (Jermyn et al. 2023).
We also adopt α = 1.5 for the convective mixing-length parameter, and f ov = 0.016, f 0,ov = 0.008 for the convective overshooting parameters in all convective regions (Herwig 2000;Choi et al. 2016).All stellar models use the MLT++ treatment for superadiabatic convection in the envelopes (Sabhahit et al. 2021).We also damp the velocities in the envelopes of our low-mass AGB models and high-mass models during the advanced burning stages to inhibit the growth of radial pulsations.
Figure 1 illustrates the 52 isotope nuclear reaction network used for low-mass stars and the 136 isotope reaction network used for high-mass models.Extended networks are required to accurately capture the nuclear energy generation, composition and stellar structure profiles, and the neutrino luminosity and spectra from βprocesses (Farmer et al. 2016;Patton et al. 2017a,b;

Kato et al. 2020a
).The 136 isotope network is reliable up to the onset of Si-shell burning, T ≲ 4×10 9 K.At higher temperatures, the paucity of Fe group isotopes in this reaction network cannot fully capture the nuclear burning (Farmer et al. 2016;Patton et al. 2017a).
Nuclear reaction rates are a combination of NACRE (Angulo et al. 1999) and JINA REACLIB (Cyburt et al. 2010b).We use the median 12 C(α,γ) 16 O reaction rate from the experimental probability distribution function provided by deBoer et al. (2017), updated in Mehta et al. (2022), and publicly released in Chidester et al. (2022).Reaction rate screening corrections are from Chugunov et al. (2007), which includes a physical parameterization for the intermediate screening regime and reduces to the weak (Dewitt et al. 1973;Graboske et al. 1973) and strong (Alastuey & Jancovici 1978;Itoh et al. 1979) screening limits at small and large values of the plasma coupling parameter.Weak reaction rates are based, in order of precedence, on Langanke & Martínez-Pinedo (2000), Oda et al. (1994), andFuller et al. (1985).
Baryon number is conserved in nuclear reactions.Define the abundance of species Y i by where n i is the number density of isotope i and n B is baryon number density.The number of baryons in isotope i divided by the total number of baryons of all isotopes is the baryon fraction (mass fraction) where A i is the atomic mass number, the number of baryons in an isotope.The mean atomic number is the mean charge is the electron to baryon ratio (electron fraction) is where n e is the free electron number density and the second equality assumes full ionization.The related neutron excess is the mean ion molecular weight is the mean electron molecular weight is and the mean molecular weight is Across the mass-metallicity plane the dominant thermal neutrino processes in our models are plasmon decay (γ plasmon → ν + ν) which scales with the composition as Y 3 e , photoneutrino production (e − + γ → e − + ν + ν) which scales as Y e , and pair annihilation (e − + e + → ν + ν) which also scales as Y e .All else being equal, as material becomes more neutron rich the neutrino emission from these three dominant processes decrease.
Bremsstrahlung (e − + A Z → e − + A Z + ν + ν), which scales with the composition as Y e Z, and recombination (e − continuum → e − bound + ν + ν) , which scales as Z 14 /A, play smaller roles.Neutrino emission from these five processes are discussed in Itoh et al. (1989Itoh et al. ( , 1992Itoh et al. ( , 1996a,b),b); Kantor & Gusakov (2007) Dzhioev et al. (2023).Each of the 420 stellar models in the mass-metallicity grid use between 2000-3500 mass zones (lower values occur at ZAMS where there are no composition gradients) with ≃3000 mass zones over the evolution being typical.Each low-mass model uses 1×10 5 -3×10 5 timesteps depending on the number of thermal pulses (TPs), and each high-mass model uses 2×10 4 -5×10 4 timesteps.Each model executes on a 16 core node with 2 GHz AMD Epyc 7713 CPUs, with low-mass models consum-ing 14-21 days and high-mass models using 10-21 days.The uncompressed total data set size is ≃ 730 GB.
The MESA files to reproduce our models, and open access to the photon and neutrino tracks, are available at http://doi.org/10.5281/zenodo.8327401.

OVERALL MASS-METALLICITY FEATURES
Here we present features and drivers of the neutrino emission, first at one metallicity in Section 3.1 and then for all six metallicities in Section 3.2.

One Metallicity
Figure 2 shows the photon and neutrino light curves for all 70 calculated masses at Z = 1 Z ⊙ .Both plots begin at the ZAMS, defined when the luminosity from nuclear reactions L nuc is 99% of the total luminosity L, marking a transition from evolution on thermal timescale to a nuclear timescale.
Models with M ZAMS ≲ 1.2 M ⊙ have a central temperature T c ≲ 18×10 7 K and burn H in their cores primarily through the pp chains, with a small fraction from the CNO cycles.For example, based on observations of solar neutrinos CNO burning accounts for around 1.6% of the current energy generation of the Sun (Naumov 2011;Borexino Collaboration et al. 2020).Models with M ZAMS ≳ 1.2 M ⊙ have T c ≳ 18×10 7 K and maintain their stability primarily from the CNO cycles (Wiescher et al. 2010).Metal-poor models can produce their own carbon to begin CNO cycle H-burning (Mitalas 1985;Wiescher et al. 1989;Weiss et al. 2000;Tompkins et al. 2020).In addition, most of a model's initial Z comes from the CNO and 56 Fe nuclei inherited from its ambient interstellar medium.The slowest step in the CNO cycle is proton capture onto 14 N, resulting in all the CNO catalysts accumulating into 14 N during core H-burning.
All light curves in Figure 2 proceed to the terminal age main sequence (TAMS), defined by core H-depletion (X c ≤ 10 −6 ).The He-rich core contracts as a H-burning shell forms.The higher temperatures of shell H-burning can activate the Ne-Na, and Mg-Al cycles (Salpeter 1955;Marion & Fowler 1957;Arnould et al. 1999;José et al. 1999;Izzard et al. 2007;Boeltzig et al. 2022).The light curves then bifurcate depending on M ZAMS .
During He-burning the accumulated 14 N is converted into the neutron-rich isotope 22 Ne through the reaction sequence 14 N(α,γ) 18 F(,e + ν e ) 18 O(α,γ) 22 Ne, also shown in Figure 2.This sequence is the source of neutrinos powering L ν through all phases of He-burning (Serenelli & Fukugita 2005;Farag et al. 2020).
Usually the ashes of nuclear burning have a larger A and lie interior to the unburned fuel.For example, a He core is interior to a H-burning shell, and a carbon-oxygen (CO) core is interior to a He-burning shell.Exceptions occur when electron degeneracy and thermal neutrino losses lead to a temperature inversion with cooler temperatures in the central regions and hotter temperatures exterior to the core.The fuel ignites off-center and a burning front propagates towards the center.
For example, the 0.9 M ⊙ ≤ M ZAMS ≤ 2 M ⊙ light curves in Figure 2 undergo off-center He ignition, the He Flash (Thomas 1967;Bildsten et al. 2012;Gautschy 2012;Serenelli et al. 2017).The accompanying nitrogen flash for neutrinos (Serenelli & Weiss 2005) are prominent and labeled.In contrast, the M ZAMS ≥ 2 M ⊙ light curves undergo central He burning.The 0.9 M ⊙ ≤ M ZAMS ≤ 7 M ⊙ light curves undergo TPs on the AGB, generating neutrinos first from H burning, and subsequently from He burning.A few light curves show a late TP during the transition to a cool WD.
Neutrino emission from nuclear reactions dominate whenever H and He burn, otherwise neutrinos from thermal processes generally dominate (Farag et al. 2020).For example, light curves for M ZAMS ≥ 8 M ⊙ in Figure 2 have the minimum mass for C ignition and those for M ZAMS ≥ 10 M ⊙ have the minimum mass for Ne ignition (Becker & Iben 1979, 1980;García-Berro et al. 1997;Farmer et al. 2015;De Gerónimo et al. 2022).For these advanced burning stages L ν in Figure 2 become nearly vertical and greatly exceeds L γ .Thermal neutrinos from pair-production dominate until the last few hours before CC when neutrinos from nuclear processes contribute (Odrzywolek et al. 2004;Odrzywolek & Heger 2010;Patton et al. 2017a,b;Kato et al. 2020a,b).

Six Metallicities
The top panel of Figure 3 shows the total energy emitted in photons E γ and neutrinos E ν , obtained by integrating L γ and L ν over the lifetime of a model.Metal-poor models tend to have larger E γ and E ν than the metal-rich models.Homology relations with power-law expressions for a bound-free Kramers opacity κ ∝ Z(1 + X)ρT −3.5 , pp-chain energy generation rate ϵ pp ∝ X 2 ρT 4 , and mean molecular weight µ ∝ X −0.57lead to (Sandage 1986;Hansen et al. 2004) where τ MS is the MS lifetime.Similarly, for a Thomson electron scattering opacity κ ∝ 1 + X and CNO cycle energy generation rate ϵ CNO ∝ XZρT 17 , These expressions suggest that displacement on the MS due to a lower Z is partially offset by a shift to a larger X (Demarque 1960).In addition, a lower Z requires higher T c to produce the same L γ and L ν .This is mainly why the low-Z high-mass models in Figure 3 produce only a marginally larger L γ and L ν on the MS while possessing larger T c .In turn, a larger L γ implies a larger radiative gradient, and thus a larger core mass.
L γ and L ν in the core is primarily set by the mass of the model.Envelope opacities affect the rate of nuclear reactions in the core insofar as the envelope has a large mass.The hotter the model is overall (e.g., the more massive), the less mass in the envelope will be cold enough to provide bound-free or bound-bound opacity.The largest differences due to the opacity occur in the low-mass models because they are colder, both in the core and the envelope.The models adjust the structure to accommodate a change in Z at a fixed luminosity.
Overall, across the mass spectrum, metal-poor stellar models tend to have denser, hotter and more massive cores with lower envelope opacities, larger surface luminosities and larger effective temperatures T eff than their metal-rich counterparts (Demarque 1960;Iben 1963;Demarque 1967;Iben & Rood 1970;Vandenberg 1983;Sandage 1986;Hansen et al. 2004;Georgy et al. 2013;Young 2018;Groh et al. 2019;Kemp et al. 2022).These are the main drivers of changes to the thermal and nuclear reaction neutrino emission as the initial Z changes.
The bottom panel of Figure 3 shows the ratio E γ /E ν .A maximum of E γ /E ν ≃ 20 at M ZAMS ≃ 0.9 M ⊙ occurs at the transition between models that ignite He and those that do not, between the most massive He WD and the least massive CO WD.As M ZAMS increases the resulting electron degenerate cores, first CO then ONeMg, become progressively more massive, denser, and hotter (also see Woosley & Heger 2015).This increases production of thermal neutrinos from the plasmon, photoneutrino, and pair annihilation channels faster than the production of reaction neutrinos or photons.Thus E γ / E ν decreases with M ZAMS as shown in Figure 3. 3 occurs at the transition between models that produce the most massive WD and those that go to CC.As M ZAMS further increases, thermal neutrinos from pair annihilation increases slower than reaction neutrinos or photons, and thus E ν is smaller than E γ in more massive models (pulsational pair-instability supernovae models are suppressed).The ratio E γ /E ν thus rises from the minimum and develops a roughly linear trend for M ZAMS ≳ 12 M ⊙ .Overall, both extrema of E γ /E ν of Figure 3 correlate with transitions in the final fate.
Another trend in the bottom panel of Figure 3 is the metallicity dependence of M ZAMS models that become CO WD, the blue shaded region.More metal-rich models have a larger E γ /E ν than metal-poor models.A larger initial Z produces a larger accumulation of 14 N during CNO cycle H-burning, thus a larger mass fraction of 22 Ne during He-burning, and hence a smaller Y e as the CO WD becomes more neutron-rich.Plasmon neutrino rates scale as Y 3 e leading to a smaller E ν , hence more metal-rich models have a larger E γ /E ν than metalpoor models in this M ZAMS range.The dependence of CO WD on the 22 Ne mass fraction, the degree of neutronization, may have implications for the progenitors Type Ia supernova (Timmes et al. 2003;Townsley et  2009; Bravo et al. 2010;Piersanti et al. 2022) and the pulsation periods of variable WD (Campante et al. 2016;Chidester et al. 2021;Althaus & Córsico 2022).Farag et al. (2020) showed L γ /L ν ≃ 40 for a standard solar model.As this model evolves off the MS the inert He core becomes denser, more electron degenerate, thermal neutrino production rise, L ν increases, and thus L γ /L ν decreases.Integrated over the lifetime of the model, E γ /E ν decreases to ≃ 20 as shown in Figure 3.
For any M ZAMS , what is the impact of changing Z on the neutrino emission at any evolutionary stage?
Figure 4 compares L ν to L ν of the Z = 1 Z ⊙ model across the mass-metallicity plane at three evolutionary stages in the top three panels.As for Figure 3, at the ZAMS there is generally a small dependence on the ini- tial Z but there are interesting features.For example, the dip at M ZAMS ≃ 1.2 M ⊙ corresponds to the transition from pp-chain dominated to CNO cycle dominated H-burning.Another feature is the stronger Z dependence for M ZAMS models that become CO WD.As low-Z models tend to have denser, hotter and more massive H-burning cores, thermal and reaction neutrino contributions to L ν is larger relative to high-Z models.At the TAMS, the 0.2 M ⊙ ≤ M ZAMS ≤ 8.0 M ⊙ models in Figure 4 have a partially degenerate He-rich core.As low-Z models have denser, hotter and more massive cores than high-Z models, the thermal plasmon neutrino contributions to L ν are larger.More massive M ZAMS models do not develop degenerate He-rich cores, and the small dependence on the initial Z continues.The most metal-rich track decreases due to the larger mass loss.
At core He-depletion (CHeD), the 0.9 M ⊙ ≤ M ZAMS ≤ 8.0 M ⊙ models have a partially electron-degenerate COrich core.The denser, hotter and more massive cores of the low-Z models means larger thermal neutrino contributions, and thus L ν is larger in lower Z models.
The M ZAMS ≥ 60 M ⊙ models at CHeD in Figure 4 show sawtooth profiles with the lowest Z models disrupting a metallicity trend.This occurs because the convective boundary mixing model, exponential overshooting (Herwig 2000), is based on the pressure scale height H = P/(ρg) ≃ k B T /(µ ion g), where P is the pressure, k B is the Boltzmann constant, and g is the gravitational acceleration.All else being equal, a smaller Z means a smaller µ ion , a larger H, and thus the chemical mixing region in low-Z models is larger than in high-Z models.If two burning shells are within H, they are mixed.For masses with low L ν , the H-shell mixes into the burning He core repeatedly.This delays core He burning until there is a homogeneous stripped CO core with a little He on the surface.By CHeD there is no H-shell to undergo CNO burning and all the 14 N is depleted, ergo L ν is very low.
Overall, for fixed overshooting parameters, metal-poor models have larger amounts of chemical mixing.This is a secondary driver of changes to the thermal and nuclear reaction neutrino emission as the initial metallicity changes.Other specific examples of overshooting dominating are shown for low-mass models in Section 4 and for high-mass models in Section 5.The overshooting prescription may have an additional metallicity dependence that is not captured by these models.
Figure 4 also compares E ν at each M ZAMS to E ν of the Z = 1 Z ⊙ model on a linear scale at three evolutionary stages in the bottom three panels.At the TAMS, models across the mass spectrum reflect the Z dependence of L ν shown in the top two panels.At CHeD, the denser, hotter and more massive cores of the low-Z models, plus contributions from the conversion of 14 N into 22 Ne, also show larger E ν with decreasing Z.
Tracks in the bottom panel of Figure 4 are the same neutrino tracks in Figure 3 but normalized to the solar metallicity track.The M ZAMS range for He WD and CO WD have the metallicity signature of having had an inert, electron-degenerate core during their evolution.The ONeMg WD region shows a sawtooth pattern because these models had numerical challenges completing the propagation of their off-center, convectively bounded flame fronts to the center.The M ZAMS region for CC events show a weak dependence of E ν on Z.

LOW-MASS STARS
Here we analyze the neutrino emission from the lowmass stellar tracks at one metallicity in Section 4.1, and then for all six metallicities in Section 4.2.

One Metallicity
Figure 5 shows the 0.2 M ⊙ ≤ M ZAMS ≤ 7.0 M ⊙ tracks in a γHRD and a νHRD for Z = 1 Z ⊙ .The cores are progressively enriched with the ashes of H-burning as the models begin to evolve beyond the MS.The H-burning reactions increase µ and thus ρ in the core.To maintain hydrostatic equilibrium the central temperature T c rises with the central density ρ c , increasing the rate of nuclear fusion and thus L γ and L ν .This slow increase of T c is reflected in the γHRD and νHRD of Figure 5 as an increase in their respective luminosities until core Hdepletion at the terminal-age main-sequence (TAMS).
The He-rich core contracts as an H-burning shell forms and the tracks in Figure 5 evolve across both HRDs on a thermal timescale.Both L γ and L ν increase along the RGB until core He-ignition at the tip of the RGB.All tracks that reach this point have a semi electron degenerate He core with 0.5 M ⊙ ≤ M He ≤ 1.7 M ⊙ , and a similar L γ , L ν , and T eff (Cassisi & Salaris 2013;Serenelli et al. 2017).Photons from the tip of the RGB provide a standard candle distance indicator (Da Costa & Armandroff 1990; Lee et al. 1993;Madore et al. 2023), and offer constraints on the neutrino magnetic dipole moment (Capozzi & Raffelt 2020;Franz et al. 2023).
He ignition by the triple-α process in the 0.9 M ⊙ ≤ M ZAMS ≤ 2.1 M ⊙ tracks of Figure 5 occur off-center (on-center in the 2.1 M ⊙ ) and under semi-electrondegenerate conditions in a helium flash (Thomas 1967;Bildsten et al. 2012;Gautschy 2012;Serenelli et al. 2017).A He burning front propagates towards the center by conduction, with burning behind the front driving convection.The helium flash and the sub-flashes that follow burn very little He; the nuclear energy generated mainly goes into lifting the electron degeneracy in the core.The last sub-flash reaches and heats the center allowing stable convective core He-burning under nondegenerate conditions.During each helium flash, a nitrogen flash also occurs from the conversion of all of the accumulated 14 N to 22 Ne, sharply increasing L ν via 18 F(,e + ν e ) 18 O (Serenelli & Weiss 2005).For example, Figure 6 shows that a M ZAMS = 1 M ⊙ , Z = 1 Z ⊙ track undergoes 7 flashes.The first flash is the strongest, occurring at M ≃ 0.2M ⊙ and reaches L ν ≃ 2 × 10 7 L ⊙ for ≃ 3 days.
Tracks with M ZAMS ≥ 2.1 M ⊙ reach a high enough T c at the tip of the RGB to ignite He in the center quiescently under non-degenerate conditions.For exam-  ple, Figure 6 shows a M ZAMS = 3 M ⊙ , 1 Z ⊙ track produces a smoother L ν signature during core He burning than a M ZAMS = 1 M ⊙ , 1 Z ⊙ track.Tracks in this massmetallicity range also experience a blue loop (Hayashi et al. 1962;Hofmeister et al. 1964;Xu & Li 2004;Zhao et al. 2023) in the γHRD and νHRD of Figure 5.
Post He ignition, the tracks in Figure 5 migrate to the horizontal branch (HB), becoming less luminous with larger T eff .All the He cores have approximately the same mass, regardless of the total stellar mass, and thus about the same helium fusion luminosity L He .These stars form the red clump at T eff ≃ 5,000 K, L γ ≃ 50 L ⊙ and L ν ≃ 20 L ⊙ (Alves & Sarajedini 1999;Sarajedini 1999;Girardi 1999;Hawkins et al. 2017;Wang & Chen 2021).Less massive H envelopes shift the tracks to hotter T eff and smaller L γ on the HB.This effect occurs more readily at lower Z (see §4.2) with old metal-poor clusters showing pronounced HB in a γHRD (Casamiquela et al. 2021;Dondoglio et al. 2021).
Core He-burning produces an electron-degenerate CO core with a semi-electron-degenerate He shell encased in a larger H-rich envelope.These AGB stars are the final stage of evolution driven by nuclear burning, characterized by H and He burning in geometrically thin shells on top of the CO core (Herwig 2005).Larger M ZAMS yield super-AGB models, where an Oxygen-Neon-Magnesium (ONeMg) core forms from a convectively bounded carbon flame propagating toward the center (Becker & Iben 1979, 1980;Timmes et al. 1994;García-Berro et al. 1997;Siess 2007;Denissenkov et al. 2015;Farmer et al. 2015;Lecoanet et al. 2016).
During the AGB phase a thin He shell grows in mass as material from the adjacent H-burning shell is processed, causing the He shell to increase in temperature and pressure.When the mass in the He shell reaches a critical value (Schwarzschild & Härm 1965;Giannone & Weigert 1967;Siess 2010;Gautschy 2013;Lawlor 2023), He ignition causes a thermal pulse (TP).
For example, Figure 6 shows the L ν of a 3 M ⊙ , 1 Z ⊙ track experiencing a series of 21 TPs, with an interpulse period of ≃ 10 5 yr.Like the helium flash, each TP is composed of a primary flash followed by a series of weaker sub-flashes.These TP sequences appear as spikes in the νHRD of Figure 5.The primary flash produces the largest L ν ≃ 4.6×10 4 L ⊙ from 18 F(,e + ν e ) 18 O.The sub-flashes do not produce neutrino emissions from this process, as nearly all of the 14 N is converted to 22 Ne during the primary flash.The number of TPs a track undergoes is uncertain as the number is sensitive to the mass and time resolution, the stellar mass loss rate, and the treatment of convective boundaries.

Six Metallicities
Figure 7 shows the evolution of M ZAMS = 1 M ⊙ and 3 M ⊙ in a γHRD and a νHRD across all six metallicities.Overall, the low-Z models show the trend of having denser, hotter and more massive cores with lower envelope opacities, larger surface luminosities and larger effective temperatures T eff than the high-Z counterparts.Features in the νHRD between core H depletion and the end of the TP-AGB phase are analyzed below.
The tracks in Figure 7 leave the TP-AGB phase when the envelope mass above the H and He burning shells is reduced to ≃ 0.01 M ⊙ by stellar winds.All the tracks then evolve toward larger T eff at nearly constant L ν and L γ .The M ZAMS = 1 M ⊙ and 3 M ⊙ tracks, in both the γ-HRD and ν-HRD, show late TPs for some metallicities.These are the result of a strong He flash (and nitrogen flash) that occurs after the AGB phase but before the WD cooling phase (Iben et al. 1983;Bloecker & Schoenberner 1997;Lawlor 2023).A candidate late TP star is V839 Ara, the central star of the Stingray Nebula (Reindl et al. 2017;Peña et al. 2022).The more dramatic very late TP stars, also visible in Figure 7, include Sakurai's Object, V605 Aql, and perhaps HD 167362 the central star of planetary nebula SwSt 1 (Clayton & De Marco 1997;Herwig 2002;Miller Bertolami & Althaus 2007;Hajduk et al. 2020;Lawlor 2023).
Plasmon neutrino emission then dominates the energy loss budget in Figure 7 for average-mass ≃ 0.6 M ⊙ CO WDs with T eff ≳ 25,000 K (Vila 1966;Kutter & Savedoff 1969;Bischoff-Kim & Montgomery 2018).As the WD continues to cool, photons dominate the cooling as the electrons transition to a strongly degenerate plasma (van Horn 1971;Córsico et al. 2019).The tracks in Figure 7 are arbitrarily chosen to terminate when the WD reaches L ≤ 10 −3 L ⊙ .This is sufficient (see Figure 5 of Timmes et al. 2018) for calculating the integrated neutrino background from a simple stellar population.
Figure 8 shows the fraction of L ν from specific reaction sequences and weak reactions over the lifetime of the 1 M ⊙ models for all six metallicities.Fractions whose components do not sum to unity indicate the contribution of thermal neutrinos to L ν .
The green shaded regions correspond to shell Hburning.The fraction of L ν from the CNO cycles in this phase steadily increases with metallicity from the Z = 10 −3 Z ⊙ in the bottom panel to Z = 10 0.5 Z ⊙ in the top panel.Since the CNO nuclei catalyze H-burning, L γ and L ν depend directly on the initial metallicity.
The blue shaded regions represent core He-burning.In this phase, the fraction of L ν from the 19 F → 18 O reaction dominates during the nitrogen flash.Neutrino emission from the H-burning pp-chain and CNO cycles appear during this phase of evolution for all six metallicities due to convective boundary mixing processes ingesting fresh H-rich material into the hotter core region.For the Z ≥ 10 −0.5 Z ⊙ tracks, the convective boundary mixing processes and hotter temperatures drive the Hburning Mg-Al cycles (red curves) and the appearance of 26 Al → 26 Mg between sub-flashes.
Shell He-burning and the TP-AGB phase of evolution are shown by the pink shaded regions in Figure 8.The Z = 10 −1,−0.5,0Z ⊙ tracks show traditional TPs, with the fractions contributing to L ν oscillating between successive TPs.Neutrino emission is initially from CNO burning before a TP, and then from 19 F → 18 O during the ensuing He-burning TP.
The Z = 10 −3 Z ⊙ and Z = 10 −2 Z ⊙ tracks in Figure 8 do not show traditional TPs.Instead they show a single event from a merger of their H-shells and He-shells that is driven by convective boundary mixing.As analyzed in Section 3.2, this is because metal-poor models have larger chemical convective boundary mixing regions than metal-rich models for fixed overshooting parameters.The Z = 10 0.5 Z ⊙ tracks in Figure 8  Figure 9 is the same as Figure 8 but for the lifetime of the 3 M ⊙ models for all six metallicities.The fraction of L ν from CNO processing during shell H-burning (green regions) is larger for the 3 M ⊙ tracks than the corresponding 1 M ⊙ tracks of Figure 8 at all metallicities.Core He-burning (blue shaded regions) proceeds smoothly under non-degenerate conditions at all metallicities.The spikes from 19 F → 18 O in the Z = 10 0.5 Z ⊙ track during core He-burning are due to overshooting injecting fresh H-rich fuel into the core.Shell He-burning and the TP-AGB phase of evolution (pink regions) show a trend of stronger and more numerous TPs as the metallicity increases from Z = 10 −3 Z ⊙ to Z = 10 0.5 Z ⊙ .Hotter temperatures in the 3 M ⊙ models cause neutrino emission from 26 Al → 26 Mg during the H burning Ne-Na cycle (red curves) and from the inverse beta decay 24 Na → 24 Mg reaction (purple curves).While 24 Na is not part of the H burning Mg-Al cycle, this isotope is synthesized at low abundance levels during the Mg-Al .Neutrino targets for the nitrogen flash in 1 M⊙ models for all six metallicities.The x-axis is the time since the first, and strongest, nitrogen flash.The y-axis is a luminosity relative to L⊙ = 3.828 ×10 33 erg s −1 (Prša et al. 2016).Colored curves show the ν, γ, and He-burning luminosity.The red circle marks the maximum Lν and the red label gives the value of Lν,max and the average neutrino energy.Labelled are the maximum flux at a distance d in parsec, and the duration for the Lν to be larger than 1/2 and 1/3 Lν,max.Metal-rich models have larger Lν,max and longer periods between flashes.
cycle.A late TP occurs during the WD cooling phase (purple regions) for the Z = 10 0,−1 Z ⊙ tracks.
Figure 10 shows L ν , L γ , and the He-burning luminosity L He during the nitrogen flash in 1 M ⊙ models.Across all metallicities the first flash has the largest L ν and L He with L He > L ν .The maximum neutrino luminosity L ν,max , marked by the red circles and labels, spans ≃ 2 orders of magnitude as the initial metallicity varies from Z = 10 −3 Z ⊙ to Z = 10 0.5 Z ⊙ .Note L ν,max is larger for the Z = 1 Z ⊙ model than the Z = 10 0.5 model.This is due to mass loss.If the metallicity was 10 0.3 Z ⊙ , then L ν,max at the He flash would be larger than the Z = 1 Z ⊙ model.At Z = 10 0.5 Z ⊙ , mass-loss hampers the strength of the He flash.The Z = 10 0.5 Z ⊙ model has M = 0.6 M ⊙ at the onset of He-flash, while the Z = 1 Z ⊙ model has M = 0.66 M ⊙ .The smaller shell burning temperatures is sufficient to weaken L ν,max .Note the duration of the peak in the Z = 10 0.5 Z ⊙ model is significantly longer than in the Z = 1 Z ⊙ model, ensuring more neutrinos are produced overall from the larger 14 N reservoir, but with a L ν,max of similar magnitude.
Figure 10 shows the average neutrino energy at L ν,max is insensitive to the initial Z.The neutrino fluxes at L ν,max span ≃ 2 orders of magnitude across metallicity and can serve as target values for neutrino observations of the nitrogen flash.The duration where L ν ≥ 1/2 L ν,max increases steadily from ≃ 0.8 days at Z = 10 −3 Z ⊙ to ≃ 11 days at Z = 10 0.5 Z ⊙ .The duration where L ν ≥ 1/3 L ν,max increases from ≃ 1.2 days at Z = 10 −3 Z ⊙ to ≃ 17 days at Z = 10 0.5 Z ⊙ .In addition, the time period between sub-flashes increases from ≃ 10 5 yr at Z = 10 −3 Z ⊙ to ≃ 2×10 5 yr at Z = 10 0.5 Z ⊙ while the number of sub-flashes ranges between 8 at the lowest initial Z to 5 at the largest initial Z.
Figure 11 shows L ν , L γ , and L He during the TP-AGB phase of evolution in 1 M ⊙ models for all six metallicities.As discussed for Figure 8, the tracks for the lowest initial Z show a single H-shell and He-shell merger event instead of a traditional TP.For these models L ν is dominated by 13 N → 13 C from non-equilibrium hot CNO cycle burning.At the peak of the merger T ≃ 2×10 8 K and ρ ≃ 10 4 g cm −3 .At these conditions the first half of the CNO cycle, 12 C(p,γ) 13 N(,e + ν) 13 C(p,γ) 14 N, is sufficiently energetic to cause a rapid expansion that self-quenches the second half of the CNO cycle, 14 N(p,γ) 15 O(,e + ν) 15 N(p,α) 12 C.For example, the stellar radius R of the Z = 10 −3 Z ⊙ model rapidly increases from 68 R ⊙ to 465 R ⊙ during the merger and the number of reactions per second from 13 N → 13 C is ≃ 3 orders of magnitude larger than from 15 O → 15 N. Thus, these 1 M ⊙ low-Z models do not undergo a TP because a violent shell merger causes the model to quickly lose most of the H envelope.These mergers, driven by convective boundary mixing, produce the largest L ν,max events over the entire evolution.They are also prominent and labeled in the νHRD of Figure 7.The Z = 10 0.5 Z ⊙ track also does not show TPs due to their thinner envelopes from wind mass loss.For the other metallicities, L ν,max during the TPs is ≃ 3 orders of magnitude smaller than L ν,max from the nitrogen flash shown in Figure 10.
Figure 12 shows L ν , L γ , and L He during the TP-AGB phase in the 3 M ⊙ models.The number of L ν peaks (6 to 21), the L ν peaks (2×10 3 L ⊙ to 2×10 5 L ⊙ ), and time between L ν peaks (2×10 4 yr to 4×10 4 yr) increase with Z, with evidence of saturation by Z = 1 Z ⊙ .Each successive TP releases more nuclear energy, thus L ν,max occurs at the end of the tracks (red circles and labels) across all metallicities.The Z = 10 −3 Z ⊙ model has a larger L ν,max than the Z = 10 −2 Z ⊙ model due to 13 N → 13 O (instead of the usual 18 F → 18 O) from a shell merger that is driven by convective boundary mixing.
Figure 13 compares the fraction of the total energy emitted by neutrinos at five phases of evolution across the mass-metallicity plane.Models with 0.2 M ⊙ ≤ M ZAMS ≤ 0.8 M ⊙ emit ≃ 80% of their neutrinos during shell H-burning (second panel) with a slight trend towards high-Z tracks making larger contributions than low-Z tracks.A ≃ 10% contribution originates from core H-burning (top panel), and a ≃ 10% contribution occurs during the He WD cooling phase (bottom panel).These models do not go through shell He-burning phase, as indicated by the empty region in the fourth panel, and the shorter tracks in the γHRD and νHRD of Figure 7. Models whose final fate is a CO WD emit ≃ 20-80% of their neutrinos during core H-burning, ≃ 20-40% during core He-burning, and ≃ 10-30% during the TP-AGB phase.The percentages increase with M ZAMS , and with Z for more massive models.

HIGH-MASS STARS
We present features of the neutrino emission from high-mass models for one metallicity in Section 5.1, and then for all six metallicities in Section 5.2.

One Metallicity
Tracks from the ZAMS to the onset of CC for the 8 M ⊙ ≤ M ZAMS ≤ 150 M ⊙ models in a γHRD and νHRD is shown in Figure 14.All tracks evolve at roughly constant L γ and L ν during core H-burning and He-burning as the tracks evolve from ZAMS to cooler T eff .Neutrinos from the CNO cycles and 14 N → 22 Ne power L ν through these phases of evolution.From CHeD onwards, the dominance of L ν from the core over L γ from the surface results in a rapid reduction in evolutionary timescales from years to hours to seconds (Fowler & Hoyle 1964;Deinzer & Salpeter 1965;Woosley et al. 2002).This escalating rapidity appears in the νHRD as the nearly vertical curves at approximately constant T eff .
For M ZAMS ≲ 50 M ⊙ , the nearly vertical tracks at cooler T eff in the νHRD end their lives as red supergiants (RSG).The M ZAMS ≳ 50 M ⊙ models evolve through the advanced stages at increasingly hotter T eff with thinner H envelopes, until wind driven mass-loss strips the Henvelope, creating a Wolf-Rayet model.The nearly vertical tracks at hotter T eff in the νHRD end their lives as a blue supergiants.This transition mass is the Humphrey-Davidson limit in our models (Humphreys & Davidson 1979;Davies et al. 2018;Davies & Beasor 2020;Sabhahit et al. 2021).The conversion of a mass limit to a luminosity limit depends on assumptions.For example, Sabhahit et al. (2021) adopt the luminosity limit as the luminosity above which a massive star model spends 10 −1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 t cc [hr]  <5% of it's lifetime or above the luminosity limit while the model is a yellow/red supergiant.This transition mass is sensitive to the mass and time resolution, massloss prescription, and treatment of super adiabatic convection in the outer envelope (Sabhahit et al. 2021).
Another feature in the νHRD of Figure 14 is the radial pulsations in the 35 M ⊙ ≲ M ZAMS ≲ 50 M ⊙ tracks that develop during He shell or C-burning, models with thin H envelopes, and 3.9 ≲ log(T eff ) ≲ 4.1.
C-burning sets the entropy for the continued evolution to CC, by proceeding either convectively or radiatively (Murai et al. 1968;Arnett 1972;Lamb et al. 1976).If the energy released by nuclear reactions is slightly larger than pair production neutrino losses, then net energy produced is transported by convection (e.g., Cristini et al. 2017).Otherwise, the core burns carbon radiatively in balanced power (Woosley et al. 2002;El Eid et al. 2004;Limongi & Chieffi 2018), where the mass averaged nuclear energy release nearly balances the mass averaged neutrino losses.For Z = 1 Z ⊙ , tracks for M ZAMS ≤ 20 M ⊙ burn carbon convectively (black circles in Figure 14) and tracks with M ZAMS ≥ 21 M ⊙ burn carbon radiatively (red circles in Figure 14).
The decrease in entropy from thermal neutrino emission that occurs during convective core C-burning is missing during radiative core C-burning (Weaver & Woosley 1993).For the M ZAMS ≥ 21 M ⊙ tracks that undergo radiative C-burning, the subsequent burning phases occur at higher entropy, s ∝ T 3 /ρ ∝ (M/M ⊙ ) 2 , at higher temperatures and lower densities.The larger entropy, in turn, drives shallower and more extended density gradients, larger effective Chandrasekhar masses at core-collapse, smaller compactness parameters, and thus are more challenging to explode as CC events (Woosley & Weaver 1986;Nomoto & Hashimoto 1988;Sukhbold & Woosley 2014;Sukhbold et al. 2016Sukhbold et al. , 2018;;Limongi & Chieffi 2018;Sukhbold & Adams 2020;Burrows & Vartanyan 2021).This entropy bifurcation at C-burning may seed a bimodal compact object distribution for single stars that undergo convective C-burning forming one peak in the compact object initial mass function (neutron stars) and single stars that undergo radiative C-burning forming a second peak (black holes) (e.g., Timmes et al. 1996;Heger et al. 2003;Zhang et al. 2008;Piro et al. 2017;Sukhbold et al. 2018;Vartanyan et al. 2018;Takahashi et al. 2023).
In the terminal phases Y e and µ act as guides to the evolution and culminating fate.A dwindling Y e , catalyzed by electron captures, hastens the core's contraction and amplifies energy depletion through neutrino emissions, thereby altering the core's structural equilibrium.Concurrently, as Y e ∝ 1/µ, an ascending µ signifies a shift towards fusing isotopically heavier nuclei, requiring ever larger core temperatures and densities to maintain hydrostatic equilibrium.
In addition, dynamical large-scale mixing on nuclear burning timescales can occur, as can mergers between the He, C, Ne, O, and Si shells.These shell mergers are sensitive to the mixing scheme adopted and particularly the treatment of convective boundary mixing across shell boundaries (e.g., Ritter et al. 2018;Fields & Couch 2021).An approximate location of these shell mergers is labeled in the νHRD of Figure 14.Strong coupling between nuclear burning and turbulent convection develop during late O-burning which requires 3D simulations to establish the fidelity of the 1D convection approximations (Meakin & Arnett 2007;Couch et al. 2015;Müller et al. 2017;Fields & Couch 2020, 2021).As the Fe core approaches its effective Chandrasekhar mass, electron capture and photodisintegration of nuclei drive the onset of CC. Figure 15 shows the components L ν for each phase of evolution in the M ZAMS = 20 M ⊙ Z = 1 Z ⊙ model, from shell He-burning on the left to CC on the right.After CHeD the CO core cools and contracts as a convective He-burning shell forms.The first panel on the left shows the energy budget becomes increasingly dominated by photoneutrino production with L ν ≃ 10 5 L ⊙ .
At t cc ≃ 574 yr, carbon ignites with L ν ≃ 10 6 L ⊙ and the energy budget becomes dominated by pair annihilation (second panel) .Thermal neutrinos from plasmon decay, bremsstrahlung, and recombination have luminosities several orders of magnitude smaller.
At t cc ≃ 13.6 yr the C-shell ignites (third panel), with a sharp increase in L ν,nuc = L ν,β+ + L ν,β − ≃ 10 6.7 L ⊙ .At t cc ≃ 1.5 yr Ne ignites (fourth panel) also with a second sharp increase in L ν,β− and L ν,nuc /L ν ≃ 5%.At t cc ≃ 0.5 yr (fifth panel) core O ignites.Convection mixes some of the Ne-shell into the core inducing a third spike in L ν,β− and L ν,nuc /L ν ≃ 15%.At t cc ≃ 11.5 day (sixth panel) the O-Neon shell ignites, producing a fourth spike with L ν,nuc ∼ 10 9 and L ν ∼ 10 11 , followed shortly by a subdued fifth spike marking the depletion of the Neshell and the ignition of shell O-burning.The common reason for these sharp increases ( 22 Ne) is analyzed in detail below.At t cc ≃ 11.5 day (seventh panel) the Si-core ignites, yielding another phase where L ν,nuc /L ν ≃ 15%.At t cc ≃ 10 hr (last panel) the Si-shell ignites and 56 Fe begins to form through α-capture channels.Shortly af-ter, electron capture and endothermic burning in the Fe core leads to the onset of CC.
Overall, Figure 15 shows thermal processes are the dominant form of neutrino production until Si-depletion, when neutrinos from β-processes in Fe-group nuclei become a comparable portion of energy-loss budget until CC.In models which include more Fe-group nuclei in the nuclear network than we do here, neutrinos from β-processes surpass thermal neutrino production at the onset of CC (Patton et al. 2017a,b;Farag et al. 2020).
We calculate an approximate pair-neutrino spectrum (Misiaszek et al. 2006b;Leung et al. 2020) from where ϕ(ϵ) is the number of emissions with energy ϵ, and the fitting parameters are α = 3.180657028, a = 1.018192299,A = 0.1425776426.This expression assumes the matter is relativistic and non-degenerate.We also assume all of the neutrinos are produced at the T c of a model, so our estimates serve as upper limits.The average pair-neutrino energy is then where the integral limits are in MeV.We also cumulatively integrate over the pair-neutrino spectrum to find the lower 10% and upper 90% of neutrino energies of the pair-neutrino spectrum.
We also calculate the average electron neutrino energy ϵ νe from β + processes and average electron antineutrino energy ϵ νe from β − processes as the sum of the energy released per second εi of each weak reaction i divided by the number luminosity L N,i where N =40 for the low-mass reaction network and N =148 for the high-mass reaction network of Figure 1.
During C and Ne burning β + processes are dominated by 21,22 Na→ 21,22 Ne from the Ne-Na cycle, 26 Al→ 26 Mg from the Mg-Al cycle, and supplemented by 23 Mg→ 23 Na.These reactions decrease Y e in the core, and produce ν e with average energies ϵ νe ≃ 1.6, 1.8, and 1.7 MeV respectively.During this phase β − decays are dominated by 28 Si← 28 Al, 24 Mg← 24 Na, and 27 Al← 27 Mg, producing νe with average energies ϵ νe ≃ 1.6, 2.7, and 0.9 MeV respectively.The total β − neutrino emission grows from ≃ 20% of the total β emission during C burning to ≃ 50% during Ne burning, with ϵ νe between 1.6-2 MeV independent of M ZAMS .
During Ne and O-burning there are windows where the ϵ νe exceeds the ≃ 1.8 MeV detection threshold to inverse beta decay of current neutrino detectors (e.g., Simpson et al. 2019;Harada et al. 2023).Table 3 lists the dominant electron anti-neutrino luminosity sources for the M ZAMS = 20M ⊙ model during the windows where νe exceeds current detector thresholds.
Core and shell Si-burning are the last exothermic burning stages and produce the Fe-peak nuclei.Initially 31,32 S→ 31,32 P and 35,36 Ar→ 35,36 Cl are the main β-decay channels, but are quickly replaced by 53,54,55 Fe→ 53,54,55 Mn, 51,52,53,54 Mn→ 51,52,53,54 Cr, 51,52,53,54 Mn→ 51,52,53,54 Cr, 55,56,57 Co→ 55,56,57 Fe, 48,49 Cr→ 48,49 V, and 556,57,58,60 Ni→ 56,57,58,60 Co.Many of the isotopes formed during the final stages undergo βprocesses that continue to make the core more neutronrich (e.g., Heger et al. 2001;Odrzywolek 2009;Patton et al. 2017b) with ϵ νe ≃ 2.2 MeV and ϵ νe ≃ 1.8 MeV. Figure 17 shows the tracks of a M ZAMS = 20 M ⊙ model in a γHRD and a νHRD across all six metallicities.Overall, the low-Z models show the trend of having denser, hotter and more massive cores with lower envelope opacities, larger surface luminosities and larger effective temperatures T eff than the high-Z counterparts.The hotter yet more massive H cores extends their MS lifetimes.High-Z models show significantly shorter lifetimes than low-Z models due to their smaller H abundance at the ZAMS.For example, at the ZAMS, X = 0.75 for Z = 10 −3 Z ⊙ and X = 0.637 for Z = 10 0.5 Z ⊙ .The Z = 10 0.5 Z ⊙ model also possesses a significantly smaller H reservoir to burn, due to the large line-driven wind mass-loss prescription ( Ṁ ∝ Z) which drives the already less massive H-burning region to retreat further inward during the MS evolution, resulting in a significantly shorter MS lifetime than any other model.Metalpoor tracks have lower envelope opacities and do not evolve to as low an T eff as their metal-rich counterparts.This behavior is especially prominent in the Z = 10 −3 Z ⊙ model, the purple curve in Figure 17, which has a much shorter track in the γHRD and is prominently offset from the lower-Z models in the νHRD.

Six Metallicities
The first and second vertical panels in Figure 18 show the primary source of neutrinos during H-burning and He-core burning in a 20 M ⊙ model is CNO β + decays.At CHeD and the onset of shell He-burning (third vertical panel) L ν from β decays decreases while the CO core contracts and heats up.In higher Z models, the dominant source of β neutrinos are from  MeV detection threshold to inverse beta decay of current neutrino detectors (e.g., Simpson et al. 2019;Harada et al. 2023).The average electron neutrino and anti-neutrino energies are to first-order independent of Z.
the growing He-burning shell.In lower Z models where less 14 N is present, the dominant source of β neutrinos continues to be from CNO β + decays in the active H-burning shell.In all models, thermally excited photoneutrinos in the hot contracting CO core begin to dominate the neutrino emission until temperatures are high enough, T c ≥ 7 × 10 8 K, for pair-neutrinos to become the dominant energy loss mechanisms.
The fate of neutron-rich 25 Mg evolves during Cburning (Raiteri et al. 1991a), which is the fusion of two 12 C nuclei to form an excited 24 Mg * nucleus which decays in three channels (e.g., Woosley et al. 2002) 12 C + 12 C → 24 Mg * → 20 Ne + α + γ The α-and p-channels occur at similar rates while the n−channel branching ratio of ∼ 1 % (Dayras et al. 1977).Uncertainties in the branching ratios and temperature dependant rates can alter the nucleosynthetic yields during C-burning through the Ne-Na or Mg-Al cycles and the amount 20 Ne available for Ne-melting (Bennett et al. 2012;Pignatari et al. 2013;Zickefoose et al. 2018;Tan et al. 2020;Monpribat et al. 2022).
The fourth vertical panel in Figure 18 shows 26 Al→ 26 Mg (red curve) makes a primary contribution to L ν from nuclear reactions at all metallicities during C-burning.The p-channel powers the Ne-Na cycle, producing a neutrino signal through The larger T c of low-Z models results in a stronger expression of 21,22 Na→ 21,22 Ne during C-burning.High-Z models also show a larger β − luminosity during Cburning than their low-Z counterparts.This results from differences in the neutron excess across metallicities.High-Z models enter C-burning with a larger 22 Ne abundance available for 22 Ne(α,n) 25 Mg, which provides most of the free neutrons for an s-process (Raiteri et al. 1991a;The et al. 2007;Choplin et al. 2018).
Another feature during C-burning is the β − luminosity declines from ≃ 50% of the total β neutrino luminosity in the Z = 10 0.5 Z ⊙ model, to ≃ 25% in the Z = 1 Z ⊙ model, and ≤ 10% in lower Z models.Independent of metallicity, these β − decays are primarily 28 Al→ 28 Si, 27 Mg→ 27 Al, and 24 Na→ 24 Mg.
Neon melting is characterized by photodisintegration of Neon into α particles, which recapture onto a second Neon nucleus to form 16 O and 24 Mg.The fifth vertical panel in Figure 18 shows α-capture onto the remaining 22 Ne in the core provides a spike in the β − luminosity, and a neutron source for an s-process.A metallicity dependence on the initial 22 Ne content of the core affects the strength of β − decays at the onset of Nemelting.A significant fraction of the 26 Mg also undergoes 26 Mg(α,n) 30 P which then decays to 30 P→ 30 Si.
O-burning is the fusion of two 16 O nuclei to form an excited state of 32 S * , which promptly decays to Branching ratios for the α, p n, and d channels are ≃ 34%, 56%, 5%, and ≤ 5% respectively, and the products of O-burning include 28 Si, 32,33,34 S, 35,36,37 Cl,  36,37,38 Ar, 39,40,41 K, and 40,41,42 Ca (Woosley et al. 2002).The limited extent of neutron rich isotopes in the highmass nuclear reaction network of Figure 1 means we do not capture all these isotopes, including 35 S and 33 P.
The sixth vertical panel in Figure 18 shows 31 S→ 31 P makes a primary contribution to L ν from nuclear reactions at all metallicities during O-burning.The accumulation of 36 Ar leads to a growing neutrino signal from 36 Ar→ 36 Cl.After core O-depletion, shell Ne-melting occurs before O-shell burning.The α-captures onto the remaining 22 Ne nuclei in the shell provides a second spike in the β − luminosity in Figure 18.
From Si burning (Si-α) until CC, the seventh and eighth vertical panel in Figure 18, there are little differences in the relative strength of individual β decays.At this stage of evolution, the expression of Fe-group β decays is metallicity independent, and β − decays remain subdominant until t cc ≲ 10 −1 hr (Patton et al. 2017a,b;Kato et al. 2017Kato et al. , 2020a;;Kosmas et al. 2022).
In Figure 19 the average neutrino and anti-neutrino energies are, to first-order, similar across metallicities for β + and β − decays in a 20 M ⊙ model.The largest differences in anti-neutrino energies occur during C-shell and Ne-core burning, when the neutron excess provided by 22 Ne is most important.Metal-poor tracks possess lower L β − , but higher overall average anti-neutrino energy, since the signal is increasingly dominated by 24 Mg← 24 Na as opposed to 28 Si← 28 Al.Windows where νe exceeds current detector thresholds are listed in Table 3 for the Z = 1 Z ⊙ model.
Figure 20 shows the fraction of the total neutrino energy produced during different phases of evolution in the mass-metallicity plane.The spread reflects the different fates experienced by stellar models of differing massmetallicity.Larger spreads occur for the high-mass models where wind-driven mass-loss and shell-core mergers contribute.
Across metallicities in Figure 20, the chief nuclear neutrino production in high-mass models come from the CNO cycle during H-burning, accounting for ≃ 40-90% of the total neutrino emission with a trend towards larger fractions with increasing M ZAMS .Typical fractions for He-burning are ≲ 8%, with an exception for some very massive models that produce ≃ 10-20% from recurrent mixing of the shell-H into the He core before CHeD.Typical fractions for C-burning and O-burning are ≃ 5-20% and ≃ 5 − 30% respectively, with a negative trend toward higher masses.From core-Si ignition to CC, ≃ 2-10% of the total neutrino emission occurs with a negative trend toward increasing masses.Overall, most neutrinos are produced during H and He burning from β + decays, especially in the most massive models.

INTEGRATED STELLAR PHOTON AND NEUTRINO EMISSION
We explore the time-integrated photon and neutrino emission of a simple stellar population model.We assume a burst cluster population where all models are born at the same time and evolve together.
We adopt the normalized broken power law initial mass function (IMF) from Kroupa (2001) for the number of stars per unit mass dN /dm.We integrate over the IMF in Equation 19 to solve for a normalization coefficient such that a cluster of mean mass 1 M ⊙ is formed in the burst of star formation.The minimum mass M min0 = 0.01 M ⊙ and the maximum mass M max = 150 M ⊙ of the IMF set the integration limits for the 1 M ⊙ stellar cluster.We then solve Equation 20for Φ(t) the resultant integrated quantity, where ϕ(t)  is the quantity we source along an isochrone.The minimum mass M min0 = 0.2 M ⊙ and the maximum mass M max = 150 M ⊙ of the mass-metallicity plane set the integration limits.
Figure 21 shows L γ and L ν light curves for each population synthesis model, sampled at 600,000 points in log(Age) for each metallicity.We overlay a quadratic power law for each population synthesis model to provide a convenient fitting formulae for L γ and L ν as a function of the stellar cluster age and mass where the fit coefficients (a,b,c) are listed in Table 4.
Figure 22 shows the cluster L γ and L ν light curves and their ratio of L γ /L ν .Both L γ and L ν are slightly larger in low-Z models until ∼ 10 10.5 Gyr when low-Z models are depleted of most H-burning and He-burning stellar tracks, and L γ and L ν become comparable across all metallicities (except for Z = 10 0.5 Z ⊙ ).Low-Z stellar population fits show an overall larger L γ /L ν than high-Z fits until ∼ 10 10.5 Gyr, when the population synthesis models are dominated by very low-mass models M ZAMS ≤ 0.8 M ⊙ .Figure 23 shows the ϵ νe , ϵ νe , B-V color, V-K color, and the light to mass ratio in the V-band versus cluster age for all six metallicities.Photon and neutrino emission at early times ≃ 10 7 yr is indicative of high-mass model emissions.By ≃ 10 8 yr, all high-mass models have reached their final fate, leaving only low-mass models in the stellar population.Most of a star's life is spent during H and He burning in which neutrino emission is dominated by β processes, therefore it is reasonable to approximate the average neutrino energy of a simple stellar population by β processes alone.
The top panel in Figure 23 shows the average neutrino energy from a simple stellar population model ranges from 0.5-1 MeV.Average neutrino energies show a slight metallicity trend, with low-Z models producing up to 0.5 MeV larger signal than high-Z models between ages of 10 7 -10 9.5 yr, then decreasing to ≃ 0.5 MeV at 10 10.5 yr.The second panel shows the average anti-neutrino energy ranging from 0.6 -1.8 MeV.The anti-neutrino emission at early times, ≃ 10 7 yr, is dominated by highmass models reaching up to ∼ 1.8 MeV.By ≃ 10 8 yr, the anti-neutrino energy has reduced to ≃ 0.6 MeV, and remains roughly constant until 10 10.5 yr.
The third and fourth panels in Figure 23 shows the Johnson-Cousins B-V and V-K colors respectively, calculated using the tabulations from Lejeune et al. (1998).At early times, ≃ 10 7 yr, there is a slight excess in B-V and a relatively large jump in V-K from the high-Z population models, roughly at the onset of the RSG phase in the high-mass models (Choi et al. 2016).The bump in V-K is suppressed in the lowest metallicity models, which do not evolve toward the RSG branch and instead remain relatively blue, with RSG color spectra similar to the MS.At late times, ≳ 10 9 yr when the population contains only low-mass stars, the B-V and V-K colors show an overall reddening in high-Z stellar populations.
The V band light to mass ratio in the bottom panel of Figure 23 shows a weak but distinct metallicity trend.At early times, L V /M is larger in the lower metallicity populations.This is due to the increased L γ in low-Z models.At late times, the trend is inverted with larger L V /M the high-Z population models.This is due to the longer MS lifetimes in the high-Z population models.

SUMMARY
We explored the evolution of stellar neutrino emission with 420 models spanning the initial mass 0.2 M ⊙ ≤ M ZAMS ≤150 M ⊙ and initial metallicity −3 ≤ log(Z/Z ⊙ ) ≤ 0.5 plane.We found lower metallicity models are more compact, hotter, and produce larger L ν with two exceptions.At He-core ignition on the RGB and He-shell burning on the AGB, the birth metallicity determines the amount of 14 N available for the nitrogen flash 14 N(α,γ) 18 F(,e + ν e ) 18 O.In high-mass models, the birth metallicity determines the amount of 14 N and therefore 22 Ne available for 22 Ne(α,n) 25 Mg, providing a neutron excess to power anti-neutrino emission during C, Ne and O burning.Overall, across the massmetallicity plane we identify the sequence (Z CNO → 14 N → 22 Ne → 25 Mg → 26 Al → 26 Mg → 30 P → 30 Si) as making primary contributions to L ν at different phases of evolution.
Simple stellar populations with lower birth metallicities have higher overall L ν than their metal-rich counterparts.We find that most neutrinos from simple stellar populations are emitted in the form of electron-neutrinos through β + decays, with average energies in the range 0.5 -1.2 MeV.Lastly, we find that metal-poor stellar populations produce larger average β + neutrino energies (up to 0.5 MeV), though this trend is much weaker, if resolved, for β − neutrino emission.
We close this article by pointing out that there are many potential sensitivities that we have not investigated.Examples include choosing different convective mixing prescriptions, mass loss algorithms, and nuclear reaction rate probability distribution functions (especially 12 C(α,γ) 16 O and triple-α).We also neglected rotation, their associated magnetic fields, and binary interactions.Future uncertainty quantification studies could also explore potential couplings between simultaneous variations in uncertain parameters.We caution that these uncertainties, or missing physics, could alter the neutrino emission properties of our models.

Figure 1 .
Figure1.Coverage in the mass-metallicity plane (center).The x-axis is the initial Z of a model relative to solar, and the y-axis is MZAMS of a model relative to solar.Six metallicities, each marked with a different color, and 70 masses at each metallicity (circles) span the mass-metallicity plane.The nuclear reaction network for low-mass (left) and high-mass (right) models is illustrated.These x-axes are the difference in the number of neutrons and protons in an isotope.Positive values indicate neutron-rich isotopes, the zero value is marked by the red vertical line, and negative values indicate proton-rich isotopes.These y-axes are the number of protons in an isotope, labelled by their chemical element names.Isotopes in the reaction network are shown by purple squares.Reactions between isotopes are shown by gray lines.Note Fe in the low-mass reaction network does not react with other isotopes.Fe is included for a more consistent specification of the initial composition, hence any microphysics that depends upon the composition including the opacity, equation of state, element difffusion, and neutrino emission.

Figure 2 .
Figure 2. Light curves for photons (left) and neutrinos (right).Tracks span 0.2-150 M⊙ for Z = 1 Z⊙ and are labeled.Key phases of evolution including the ZAMS (black circles), TAMS (black circles), core He flashes (light green), thermal pulses, and pre-supernova stage are also labeled.The PMS light curves are suppressed for visual clarity.Lν during the nitrogen flash (He flash for photons) and thermal pulses for the M < 8 M⊙ light curves can exceed Lγ.At and beyond core C-burning Lν dominates the evolution of the M ≥ 8 M⊙ light curves.Luminosities are normalized to L⊙ = 3.828 × 10 33 erg s −1 (Prša et al. 2016).

Figure 3 .
Figure 3.Total energy emitted in photons and neutrinos over the lifetime of a model (top) and their ratio (bottom) across the mass-metallicity plane.Transition between different final fates occur at local extrema, indicated by the colored panels and labels.

Figure 4 .
Figure 4. Ratio of Lν to Lν of the Z = 1 Z⊙ model versus MZAMS for all six metallicities at ZAMS (top panel), TAMS (second panel) and CHeD (third panel).The ratio of Eν to Eν of the Z = 1 Z⊙ model versus MZAMS for all six metallicities at TAMS (fourth panel), CHeD (fifth panel) and final fate (bottom panel).Each panel is colored by the final fate given by the legend.

Figure 5 .
Figure 5. Low-mass tracks in a γHRD (left panels) and a νHRD (right panels) for Z = 1 Z⊙ over 0.2-2.0M⊙ (top row) and 2.0-7.0M⊙(bottom row).Tracks are colored by evolutionary phase and labeled.WD cooling tracks are suppressed for visual clarity.Luminosities are normalized to L⊙ = 3.828 × 10 33 erg s −1 (Prša et al. 2016).The 1 M⊙ and 3 M⊙ tracks are highlighted in black as they are analyzed in detail as examples of low-mass models that do and do not undergo the He flash, respectively.

Figure 6 .
Figure6.Components of Lν over the lifetimes of a 1 M⊙, 1 Z⊙ model (top) and a 3 M⊙, 1 Z⊙ model (bottom).The x-axis is the sequential model number, a non-linear proxy for time, which begins on the left at core H-depletion and ends on the right as a cool WD at each metallicity.Phases of evolution are marked by the colored regions and the time spent in each phase is labeled.Curves show the luminosities from nuclear and thermal processes and their sub-components, and are smoothed with a 50 model moving average filter.Luminosities are normalized to L⊙ = 3.828 × 10 33 erg s −1(Prša et al. 2016).

Figure 8 .
Figure 8. Components of Lν from nuclear reactions over the lifetime of a MZAMS = 1 M⊙ model for all six metallicities.The x-axis is the sequential model number, a proxy for time, beginning at core H-depletion (left) and ending as a cool WD (right).Curves are smoothed with a 50 model moving average filter.Evolutionary phases are shown by the colored regions and labelled.Reactions emitting neutrinos in the pp-chain and CNO cycles are listed in Section 3.1.regions) late TPS are visible in the Z = 10 −1,0 Z ⊙ tracks by the rise of L ν from CNO burning and subsequently 19 F → 18 O.
Figure10.Neutrino targets for the nitrogen flash in 1 M⊙ models for all six metallicities.The x-axis is the time since the first, and strongest, nitrogen flash.The y-axis is a luminosity relative to L⊙ = 3.828 ×10 33 erg s −1(Prša et al. 2016).Colored curves show the ν, γ, and He-burning luminosity.The red circle marks the maximum Lν and the red label gives the value of Lν,max and the average neutrino energy.Labelled are the maximum flux at a distance d in parsec, and the duration for the Lν to be larger than 1/2 and 1/3 Lν,max.Metal-rich models have larger Lν,max and longer periods between flashes.

Figure 11 .
Figure 11.Same format as Figure 10 but for the TP-AGB phase of evolution.

Figure 12 .
Figure 12.Same format as Figure 11 but for 3 M⊙ models across all six metallicities.

Figure 13 .
Figure13.Fraction of Eν emitted at different phases of evolution for all six metallicities (colored circles).From top to bottom, the panels show [E/Etot]ν for core H-burning, shell H-burning, core He-burning prior to any TP-AGB phase, He-burning through the TP-AGB phase, and during the WD cooling phase.

Figure 15 .
Figure 15.Components of Lν for each phase of evolution of a MZAMS = 20 M⊙, 1 Z⊙model.The x-axis is the time to the onset of CC.Curves show the contributions from nuclear and thermal neutrinos, and are smoothed with a 50 timestep moving average filter.Phases of evolution are shown by the colored regions and labeled above the plot.Boundaries between phases are defined by the ignition of the next fuel source, when the central mass fraction of the next fuel source decreases by 10 −3 .

Figure 16 .
Figure16.Average electron neutrino energy for beta decays (top), and average electron anti-neutrino energy for inverse-beta decays (bottom) for the 1 Z⊙ models across a range of MZAMS.Curves are smoothed with a 50 timestep moving average filter.The average pair-neutrino energy is shown by the black curve, with the gray band giving the lower 10% and upper 90% of pair-neutrino energies.Phases of evolution are shown by the colored panels and labeled.The horizontal dashed line shows a representative ≃ 1.8 MeV detection threshold to inverse beta decay of current neutrino detectors (e.g.,Simpson et al. 2019;Harada et al. 2023).The average electron neutrino and anti-neutrino energies are approximately independent of MZAMS.

Figure 17 .
Figure 17.Tracks in a γHRD (left) and νHRD (right) from ZAMS to the onset of CC for the MZAMS = 20 M⊙ models across all six metallicities.Approximate locations of evolutionary phases are labeled or marked with a black dashed line.Luminosities are normalized to L⊙ = 3.828 ×10 33 erg s −1 (Prša et al. 2016).

Figure 18 .Figure 19 .
Figure 18.Components of Lν from nuclear reactions over the lifetime of a MZAMS = 20 M⊙ model for all six metallicities.The x-axis is the time to the onset of CC.Evolutionary phases are shown by the colored regions and labelled.Curves show the largest contributions by the burning processes and weak reactions listed in the legend.

Figure 20 .
Figure20.Fraction of Eν emitted at different phases of evolution for all six metallicities (colored circles).From top to bottom, the panels show [E/Etot]ν for H-burning, He-burning, C-burning, O-burning and Si-burning to the onset of CC.

Figure 21 .
Figure21.Cluster Lγ and Lν light curves from the evolution models for all six metallicities.Overlayed are quadratic fitting functions with the coefficients for each metallicity listed (see Equation21).

Figure 23 .
Figure23.Average electron neutrino energies for beta decay processes (top panel), average electron anti-neutrino energies for inverse-beta decay processes (second panel), Johnson-Cousins B-V and V-K colors (third and fourth panels), and neutrino light to mass ratio for a simple stellar population (bottom panel) for all six metallicities.