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Capture of an alpha particle by carbon-12 makes oxygen-16. Competition between this reaction and the Triple-alpha process helps determine the carbon-to-oxygen ratio after core helium burning.

Core helium burning begins when a hydrogen-exhausted stellar core becomes hot enough for the Triple-alpha process. Subsequent alpha capture on carbon produces oxygen, leaving a carbon-oxygen core after central helium exhaustion.

For a nonresonant charged-particle thermonuclear reaction rate, the thermal high-energy tail favors low $E$ while the Coulomb barrier penetration factor favors high $E$. Their product peaks in an intermediate energy window. Resonant reactions such as the Triple-alpha process require an additional resonance treatment.

This excited carbon-12 resonance lies close to the three-alpha threshold and enables the Triple-alpha process to make carbon efficiently. A transient beryllium-8 nucleus captures an alpha particle into the resonance; electromagnetic decay then stabilizes carbon-12. A small radiative branching probability still matters because the resonance enhances formation.

An Asymptotic giant branch star has an approximately degenerate carbon-oxygen core, a helium-burning shell, a hydrogen-burning shell farther out, and a deep convective envelope. During an interpulse interval, the hydrogen-burning shell supplies most of the luminosity and deposits helium ash beneath it. The helium layer gradually grows and its temperature rises until Triple-alpha process heating becomes large.

The helium layer is geometrically thin. A thermal perturbation greatly increases its nuclear rate, but at first expansion of the layer does not provide sufficient cooling to offset the heating. This Härm–Schwarzschild instability causes a thermal pulse of an asymptotic-giant-branch star: a helium-shell flash with an enormous but brief increase in internal helium luminosity. It is a shell instability, not repeated ignition of the entire stellar core.

The flash creates an intershell convection zone, expands the layers above it and cools or extinguishes hydrogen burning temporarily. Much of the flash energy goes into expansion and internal rearrangement, so the huge peak shell luminosity need not immediately appear as a comparable surface luminosity. After the layer expands and cools, the helium flash subsides; hydrogen burning later resumes and replenishes the helium layer, repeating the cycle.

After a pulse, the convective envelope may penetrate into the intershell: third dredge-up transports newly formed carbon and slow neutron-capture process products to the surface. This helps explain carbon stars and heavy-element enrichment. Strong winds remove the envelope over successive pulses. When the envelope is too small to sustain the giant configuration, the star leaves the AGB and exposes a hot core that becomes a white dwarf. Pulse behavior, dredge-up efficiency and the number of cycles depend on core/envelope mass, composition and mass loss.

The elements have several complementary origins: primordial light nuclei, stellar and explosive fusion products, and nuclei built by neutron capture. Chemical enrichment also requires their ejection, rather than merely their production inside a star. Nucleosynthesis and transport into the interstellar medium must therefore be considered together.

Hydrogen and much of the helium are primordial. During Big Bang nucleosynthesis, a cooling, expanding plasma assembled surviving neutrons and protons into deuterium, helium-3 and especially helium-4, with small abundances of lithium-7 or its beryllium-7 progenitor. Unstable nuclei at mass numbers five and eight, together with the rapidly falling density and short available time, obstructed sustained production of heavier nuclei. The carbon, oxygen and heavier material in later generations consequently require other sites. Cosmic rays fragment heavier interstellar nuclei and contribute importantly to the light elements lithium, beryllium and boron, which ordinary stellar burning tends to destroy.

Burning stages depend on initial stellar mass. Stellar nuclear fusion can release energy when the products have greater nuclear binding energy than the reactants. The resulting stellar thermostat links nuclear burning to hydrostatic equilibrium: when fuel exhaustion lowers heating, contraction raises the central temperature until another fuel can ignite, if the core becomes hot enough. Higher nuclear charges bring larger Coulomb barriers, so later charged-particle burning generally requires progressively higher temperatures. Whether the core reaches them depends on its mass, electron degeneracy pressure, mixing and envelope loss.

An approximately solar-composition $1M_{\odot }$ star first spends most of its life on the main sequence, converting hydrogen into helium mainly through the proton–proton chain. The net conversion is four protons into one helium-4 nucleus, with positrons and neutrinos; the small CNO cycle contribution redistributes CNO catalyst abundances but is not a net source of carbon at this stage. Exhaustion of central hydrogen leaves a helium-rich core. A surrounding hydrogen-burning shell continues to add helium, while the core contracts and the envelope expands into a red giant.

The low-mass helium core becomes supported substantially by electron degeneracy pressure. At roughly $10^8\mathrm{K}$, the Triple-alpha process ignites, first making transient beryllium-8 and then carbon-12 through the Hoyle state. Because degeneracy initially weakens the usual expansion response, this ignition is a helium flash. It heats and lifts the degeneracy of the core, leading to a stable phase of core helium burning. The Triple-alpha process makes carbon; competing carbon-12 alpha capture makes oxygen:After central helium exhaustion, the star develops a carbon-oxygen core, a helium-burning shell and a more external hydrogen-burning shell. On the Asymptotic giant branch, recurrent thermal pulses of an asymptotic-giant-branch star arise from unstable helium-shell burning. Stellar dredge-up can bring processed material toward the surface, with its efficiency depending on mass and composition. The eventual stellar wind removes the envelope; the hot exposed core can illuminate a planetary nebula, and the remnant becomes a carbon-oxygen white dwarf. A usual isolated $1M_{\odot }$ star does not ignite carbon burning. In particular, an element synthesized in its core need not all escape: much of the carbon and oxygen remains locked in the white dwarf.

An approximately $5M_{\odot }$ star burns central hydrogen predominantly through the CNO cycle, usually in a convective core. The CNO nuclei act as catalysts; the slow nitrogen-14 proton-capture step tends to accumulate nitrogen-14 while converting hydrogen into helium. After central fuel exhaustion, a hydrogen-burning shell surrounds the contracting helium core. Unlike the $1M_{\odot }$ case, core helium burning normally begins before strong electron degeneracy, without a classical helium flash. The same Triple-alpha process and carbon-12 alpha capture create a carbon-oxygen core.

The $5M_{\odot }$ star then enters the Asymptotic giant branch, with hydrogen and helium burning in shells. Repeated thermal pulses and stellar dredge-up can enrich its envelope with freshly made carbon and s-process nuclei. Hot-bottom burning can occur when the base of the convective envelope is sufficiently hot: the CNO cycle processes dredged-up carbon into nitrogen, so a massive AGB star need not become carbon-rich despite making carbon below its envelope. Helium-shell reactions on neon-22 can also provide neutrons for the s-process. For an ordinary $5M_{\odot }$ model, strong envelope loss generally precedes carbon ignition, leaving a carbon-oxygen white dwarf. The exact threshold for carbon ignition and the size of these yields depend on metallicity, mass loss and mixing; they are not universal integers fixed solely by initial mass.

A $20M_{\odot }$ star reaches much more advanced stages. It starts with convective-core CNO cycle hydrogen burning, followed by core helium burning. After central helium exhaustion, contraction can ignite carbon burning at temperatures approaching $10^9\mathrm{K}$. Carbon-fusion channels make products including neon, sodium and magnesium. Neon burning then uses photodisintegration of neon-20 to release oxygen-16 and an alpha particle, followed by capture of that alpha particle on another neon-20 nucleus; the combined network releases energy and produces magnesium-24. Oxygen burning makes silicon-group nuclei through channels such asAt still higher temperature, silicon burning rearranges nuclei by photodisintegration and captures of protons, neutrons and alpha particles. It is not principally direct fusion of two silicon nuclei. Networks approach quasi-equilibrium and then nuclear statistical equilibrium, producing an iron-group core whose precise mixture depends on the electron fraction in stellar matter. Outer shells retain different stages of burning, giving an approximately layered structure. Increasing stellar neutrino energy loss makes advanced burning stages much shorter than hydrogen burning.

Near the iron group, nuclear binding energy per nucleon is close to its maximum. Further fusion cannot provide the sustained energy source required to support the core. As the core grows, electron capture reduces electron-pressure support and photodisintegration absorbs energy, assisting gravitational collapse. A successful core-collapse supernova ejects some of the envelope and processed shells, and leaves a neutron star or black hole. The shock also causes explosive burning, changing the pre-existing abundances. A $20M_{\odot }$ initial mass does not uniquely fix the explosion or remnant: envelope loss, rotation, composition and fallback all matter, and some collapses fail to eject much material.

Ejection determines the enrichment of the interstellar medium. Low- and intermediate-mass stars return helium, CNO-processed matter, dredged-up carbon and s-process products through stellar winds and envelope expulsion. Massive-star winds can expose hydrogen- or helium-burning products before collapse. Successful core-collapse supernovae eject substantial oxygen and other alpha-capture products, together with some iron-group matter formed in hydrostatic and explosive burning. Material that falls back or remains in a stellar remnant is withheld from the interstellar medium. Subsequent mixing, cooling and star formation distribute the escaped material into new stars. The distinction between production and ejection is why an internal burning inventory alone is not a stellar yield.

Binary stars provide an additional major iron-group source. In a Type Ia supernova, a carbon-oxygen white dwarf in a binary undergoes thermonuclear disruption after an appropriate accretion or merger history. Explosive carbon and oxygen burning makes intermediate-mass and iron-group nuclei. Much initially synthesized nickel-56 decays through cobalt-56 into iron-56; this radioactive decay also powers the supernova light curve. Such explosions have delay times and yields different from those of massive-star collapse, and help explain why iron enrichment need not track oxygen enrichment exactly.

Neutron capture builds much of the material beyond iron. Charged-particle reactions encounter increasing Coulomb barriers as nuclear charge grows, but a neutral neutron does not encounter that barrier. Neutron capture raises mass number, and subsequent beta-minus decay can turn a neutron into a proton and raise atomic number. The relative capture and decay times select different paths through the nuclear chart.

In the slow neutron-capture process, most unstable intermediates decay before the next capture, so the path stays near stable nuclei. In Asymptotic giant branch stars, important neutron sources areThe carbon-13 source operates in suitable partially mixed layers, while the hotter helium-shell pulses can activate the neon-22 source. Captures on pre-existing seed nuclei produce elements such as strontium and barium and, under suitable conditions, lead. Stellar dredge-up and stellar winds return these products to the interstellar medium. Massive stars also have a weak s-process, notably using neon-22 during helium- and carbon-burning phases; it need not produce the same abundance range as the main AGB contribution.

In the rapid neutron-capture process, very high neutron densities permit many captures before typical beta-minus decays. The path moves to neutron-rich nuclei, which later decay toward stability, producing heavy nuclei including lanthanides and actinides. Neutron-rich ejecta from neutron star mergers provide an established site: a merger can eject dynamical material and disk outflows, and radioactive decay of the newly made nuclei powers a kilonova. Special neutron-rich outflows associated with some massive-star collapses are additional candidate sites. It would be unjustified to assume that every ordinary core-collapse supernova produces the full heavy r-process pattern; the required neutron richness and expansion history are restrictive.

The two neutron-capture processes do not make every isotope beyond iron. Some proton-rich isotopes bypass their main paths. Gamma-process nucleosynthesis, for example, uses photodisintegration of pre-existing heavy seed nuclei in hot explosive material. Other proton-rich reaction paths can matter in suitable environments. Thus “heavier than iron” describes a family of production mechanisms rather than a single further ordinary fusion stage.

Binaries change both stellar evolution and the delivery of elements. Roche-lobe overflow, wind transfer and mergers can strip a donor, rejuvenate a mass-gaining star, alter core and envelope masses, and change the timing and character of an eventual explosion. Binary stripping can remove the hydrogen envelope of a massive core-collapse supernova progenitor. Accretion onto a white dwarf can cause a classical nova, ejecting hydrogen-burning products and particular isotopes while ordinarily leaving the white dwarf intact; this differs from the destructive Type Ia supernova. Compact binary stars can lose orbital energy through gravitational radiation and merge, providing the neutron star merger route to heavy r-process material. Consequently chemical enrichment cannot be inferred entirely from isolated-star tracks, even when a simplified population calculation treats binary components as evolving independently.

A $5M_{\odot }$ star of roughly solar stellar composition begins on the zero-age main sequence with a hot convective core, a mostly radiative envelope, and hydrogen burning dominated by the CNO cycle. The strong temperature dependence of the CNO cycle concentrates the stellar energy-generation rate near the centre, helping produce the convective core. Core mixing replenishes hydrogen within that region; it does not homogenize the entire star. The nuclear fuel supply gives a stellar nuclear timescale of order $10^8$ years. For a numerical comparison, Table 2 of Ekström et al.'s solar-metallicity models gives core hydrogen burning lifetimes of about $88$ and $109$ million years for nonrotating and rotating $5M_{\odot }$ models, respectively.

After central hydrogen exhaustion, an inert helium core contracts and heats through Kelvin-Helmholtz contraction, while a hydrogen-burning shell supplies the growing luminosity. The envelope expands and cools: the track crosses the Hertzsprung gap toward the red giant region. Its deepening convective envelope causes first dredge-up, bringing material altered by hydrogen burning to the surface. The rapid structural crossing has a thermal timescale, roughly $10^5$–$10^6$ years for a star of this mass, rather than the full stellar nuclear timescale; an estimate follows from the Kelvin-Helmholtz cooling time $G{M}^2/(RL)$ with the evolving radius and luminosity.

The helium core reaches ignition before becoming strongly supported by electron degeneracy pressure. Thus a normal $5M_{\odot }$ star starts core helium burning without the helium flash characteristic of lower-mass stars. The Triple-alpha process produces carbon-12, and carbon-12 alpha capture produces oxygen-16; these reactions build a carbon-oxygen core. There is a convective core and continued hydrogen-burning shell activity. Core helium burning lasts order $10^7$ years: the same model table gives approximately $19$ and $18$ million years. The changing core and envelope structure can produce a blue loop in the Hertzsprung-Russell diagram; its extent depends on stellar composition, mixing and stellar rotation.

After central helium exhaustion, the carbon-oxygen core contracts and becomes increasingly supported by electron degeneracy pressure. A helium-burning shell forms above it, beneath the hydrogen-burning shell. The star returns to a cool, luminous Asymptotic giant branch configuration. On this early branch, helium-burning shell activity is an important energy source; the overlying hydrogen-burning shell can weaken during readjustment and resume later. At this mass, a deepening convective envelope can cause second dredge-up. This shell-supported evolution to the first AGB thermal pulse takes order $10^6$ years, with model-dependent duration. As the helium-burning shell becomes sufficiently thin, the thin-shell instability ends steady shell burning and marks the onset of AGB thermal pulses.

The original sketch shows the direction of stellar evolution, with higher effective temperature to the left. It illustrates a possible blue loop; its coordinates and loop shape are schematic, rather than a computed stellar model. The stages before the first AGB thermal pulse are the requested track; the later remnant evolution is described below.

In the usual final evolution, stellar winds and an AGB superwind remove the envelope before the carbon-oxygen core can ignite substantial carbon burning. Once shell fuel is exhausted, the exposed core contracts and heats, potentially ionizing the expelled gas as a planetary nebula, and finally becomes a carbon-oxygen white dwarf that loses its stored thermal energy by cooling. The relevant competition is between the AGB envelope-loss and core-growth timescales, not just the total initial mass.

Much higher late-stage mass loss strips the envelope sooner, shortens the Asymptotic giant branch phase, and allows less core growth, usually producing a smaller carbon-oxygen white dwarf. Much lower mass loss prolongs shell burning and permits greater core growth. In an extreme hypothetical case, retention of the envelope could let a degenerate carbon-oxygen core approach the Chandrasekhar mass and undergo explosive carbon burning: the proposed type 1.5 supernova channel. This is not an inevitable fate for a $5M_{\odot }$ star. Doherty et al.'s evolutionary calculations emphasize the uncertainty of that channel and find that their adopted mass loss removes carbon-oxygen envelopes before such ignition. If carbon burning instead proceeds without disruption, the possible further evolution depends on the resulting core and continued envelope retention; lowering mass loss alone does not establish an electron-capture supernova outcome.

Stellar nucleosynthesis and the subsequent return of matter explain most elements heavier than the primordial hydrogen and helium. Big Bang nucleosynthesis supplied predominantly those two elements, with small light-isotope abundances; stars do not make every element from an initially metal-free mixture. Different stellar masses reach different central temperatures and leave different remnants. The mass comparisons below describe representative isolated, near-solar-composition stars; mass loss and binary interaction can alter the final core. A nucleus contributes to later generations only if it is eventually expelled into the interstellar medium, rather than remaining locked in a remnant.

A $1M_{\odot }$ star spends its main sequence life converting hydrogen to helium, predominantly through the proton–proton chain. After core hydrogen burning ends, a hydrogen-burning shell supplies an expanding red giant envelope and builds an electron-degenerate helium core. First dredge-up exposes material whose CNO cycle has redistributed the original carbon and nitrogen abundances. The helium flash starts core helium burning: the Triple-alpha process makes carbon, and carbon-12 alpha capture makes oxygen. Once core helium is exhausted, the Asymptotic giant branch has a carbon-oxygen core with helium-burning shell and hydrogen-burning shell. Shell instability causes AGB thermal pulses; subsequent third dredge-up, where efficient enough, can bring carbon and neutron-capture products into the envelope. Its efficiency at such low mass depends on composition and mixing. The star does not ordinarily ignite core carbon burning. Stellar winds remove the envelope, a hot remnant may illuminate a planetary nebula, and a carbon-oxygen white dwarf retains much of the core's synthesized matter.

A $5M_{\odot }$ star generally uses the more temperature-sensitive CNO cycle for main-sequence hydrogen burning, with a substantial convective core. Its hotter helium core ignites core helium burning without the low-mass degeneracy-driven helium flash, producing carbon and oxygen. After core helium exhaustion it develops double-shell Asymptotic giant branch burning and a degenerate carbon-oxygen core. Second dredge-up and repeated third dredge-up alter the envelope composition. In sufficiently hot models, hot-bottom burning at the base of the convective envelope converts dredged-up carbon into nitrogen through the CNO cycle; consequently a carbon-producing shell need not produce a carbon-rich final envelope. Hot helium-shell pulses can activate the ${}^{22}\mathrm{Ne}(\alpha ,n){}^{25}\mathrm{Mg}$ neutron source. Strong stellar winds expel these processed layers. A conventional isolated five-solar-mass model ends as a carbon-oxygen white dwarf, below the mass range that normally develops sustained core carbon burning; mass loss and mixing govern the exact boundaries between outcomes.

A $32M_{\odot }$ star has core CNO cycle hydrogen burning, followed by core helium burning. The core then contracts through carbon burning, neon burning, oxygen burning and silicon burning, with active shells outside the successive exhausted cores. Carbon burning produces chiefly nuclei such as neon and magnesium. Neon burning combines photodisintegration and alpha capture; oxygen burning makes silicon-group nuclei. Silicon burning is a network of captures and photodisintegration approaching nuclear statistical equilibrium, rather than simply fusion of pairs of silicon nuclei. It produces an iron-group mixture governed by temperature, density and weak reactions. The maximum in nuclear binding energy per nucleon near the iron group prevents continued exothermic fusion from supplying ordinary hydrostatic support. Stellar neutrino energy loss accelerates the advanced stages; electron capture and photodisintegration help remove support during iron-core collapse.

The massive star can return products both before and during collapse. Radiation-driven stellar winds may expose and expel layers enriched in helium, nitrogen, carbon and oxygen. A successful core-collapse supernova ejects additional hydrostatic products and creates further nuclei by shock-driven explosive burning, including alpha-rich and iron-group products. The nickel-56 decay chain converts radioactive nickel into iron through cobalt. Initial mass alone does not fix the explosion or remnant: substantial fallback or a failed supernova can leave a black hole and retain much of the core material. Thus the possible core-collapse supernova contribution is not a guarantee that a thirty-two-solar-mass star ejects every element it made.

For nuclei well beyond the iron group, neutron capture is a principal assembly mechanism, avoiding the large Coulomb barrier for charged-particle fusion. Beta-minus decay converts captured neutrons into protons and raises the atomic number. In the s-process, captures are slower than relevant beta decays, so the sequence usually follows nuclei near stability. The main site is the Asymptotic giant branch: ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ is an important neutron source in low-mass intershell material, while ${}^{22}\mathrm{Ne}(\alpha ,n){}^{25}\mathrm{Mg}$ becomes important in hotter pulses and in massive-star helium/carbon burning. Third dredge-up and stellar winds make these products available to the interstellar medium. Barium and lead illustrate heavy products; the detailed yield depends on seed abundance, neutron exposure and branching at unstable nuclei.

In the r-process, neutron captures outrun beta decays, building very neutron-rich nuclei before they decay toward stable heavy isotopes. This needs much larger neutron densities than the s-process and can produce very heavy nuclei, including uranium. Neutron-rich ejecta from neutron star mergers provide an established site: observed kilonova emission and spectroscopy support heavy-element synthesis in such ejecta. Rare magnetically driven stellar-collapse outflows are additional candidate sites. An ordinary core-collapse supernova cannot automatically be assumed to supply a complete heavy r-process pattern.

Not every heavy isotope belongs to the two capture sequences. Gamma-process nucleosynthesis in hot supernova material uses photodisintegration on pre-existing heavy seed nuclei through neutron, proton and alpha-emission channels, helping produce proton-rich isotopes bypassed by the main capture paths. This is distinct from simply using charged-particle fusion to build every element beyond the iron group.

Finally, binary stars change both production and delivery. Roche-lobe overflow and wind mass transfer in a binary star strip envelopes, change subsequent core growth, and expose processed layers. Mass transfer from an Asymptotic giant branch donor can enrich a surviving companion in carbon and s-process products, as in a barium star; this redistributes existing yields rather than creating them in the recipient. Accretion onto a white dwarf can trigger a classical nova with explosive hydrogen-burning products. Thermonuclear disruption of a carbon-oxygen white dwarf in a Type Ia supernova, through suitable accretion or the Double-degenerate Type Ia supernova scenario, supplies a major delayed iron-group contribution, including iron; it is not the same event as collapse of a massive iron core. Compact binaries containing two neutron stars can later merge and eject r-process material. Thus binaries affect stellar mass histories, enrich companions, open thermonuclear explosion channels, and create heavy-element-producing compact-remnant mergers.

The key distinction is between making nuclei and ejecting them: ordinary low/intermediate-mass stars mainly return processed envelopes, massive stars add advanced and explosive burning products when those layers escape, and neutron-capture environments supply much of the material beyond iron.

For a slowly evolving spherical star, use a Lagrangian enclosed mass coordinate $m$. Let $u$ be specific thermal internal energy and $D/Dt$ follow a mass element. The stellar energy balance equation isThe outward luminosity is energy transported through the mass shell, ${ϵ}_{\mathrm{nuc}}$ is nuclear rest-mass energy released per unit mass and time, and ${ϵ}_{\nu }$ is escaping neutrino power per unit mass. Define the gravothermal stellar energy generation by ${ϵ}_{\mathrm{grav}}=-Du/Dt-PD(1/\rho )/Dt$. At fixed composition it is $-TDS/Dt$ by the first law of thermodynamics. During composition changes the full internal-energy derivative must use the appropriate equation of state, with nuclear rest-mass changes counted only once. If a tabulated nuclear rate already subtracts reaction-neutrino energy, that loss must not be subtracted a second time in ${ϵ}_{\nu }$.

In a nearly steady main sequence star, stellar nuclear fusion supplies most of the luminosity. Before stable hydrogen ignition, Kelvin-Helmholtz contraction releases gravitational energy. In a gas-supported hydrostatic star the stellar virial theorem gives $U\simeq -\Omega /2$, so about half the change in gravitational binding energy heats the star and half is available for radiation. The associated timescale is $G{M}^2/(RL)$. After nuclear burning ends, a white dwarf can shine by losing stored thermal energy; crystallization releases latent heat, and composition separation can add gravitational energy. These are heat and gravitational reservoirs rather than sustained hydrogen fusion.

Stellar nuclear fusion is possible because lighter nuclei can combine into products with larger nuclear binding energy. The energy per reaction is $Q=(m_{\mathrm{initial}}-m_{\mathrm{final}})c^2$, including the relevant particles consistently. Although thermal energies are below the Coulomb barrier, quantum tunnelling permits fusion. The thermonuclear reaction rate averages a cross-section over the thermal relative-speed distribution:For nonresonant charged-particle reactions the energy weighting contains $\exp [-E/(kT)-\sqrt{E_G/E}]$; the compromise between the thermal tail and penetration produces the Gamow peak. A resonance can greatly enhance the rate. Density, abundances and temperature therefore all affect the stellar energy-generation rate, and power laws such as $T^4$ or $T^{16}$ are local approximations.

For the proton–proton chain, first produce deuterium and helium-3:The initial reaction is slow because it converts a proton to a neutron through the weak interaction. It is the bottleneck that allows long hydrogen-burning lifetimes. The alternative pep reaction $p+e^{-}+p\to {}^2\mathrm{H}+{\nu }_e$ also feeds the same chain. There are three principal proton-proton chain branches. In pp I, two helium-3 nuclei terminate the chain:In pp II, helium-3 first captures an existing helium-4 nucleus, then electron capture and proton capture finish the branch:In pp III, the beryllium-7 instead captures a proton:Relative branch weights change with temperature and composition. All branches convert four protons into a net helium-4 nucleus, with two weak conversions and two neutrinos, allowing for the electron consumed in pp II. After including positron annihilation, the atomic-mass energy budget is approximately $26.7\mathrm{MeV}$ per net helium-4 nucleus, but the deposited heat is smaller by the branch-dependent escaping-neutrino energy. Near ordinary low-mass main-sequence conditions, ${ϵ}_{pp}\propto \rho X_H^2{T}^4$ is a useful local approximation.

The CNO cycle provides an alternative catalyzed hydrogen burning route in hotter cores. The CNO-I cycle, also called the CN cycle, consists ofThe carbon seed is regenerated: the net reaction again consumes four protons and produces one helium-4 nucleus, two positrons and two neutrinos. The slow ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction governs the ordinary cycle and causes nitrogen-14 to accumulate. The CNO-II cycle branches through ${}^{15}\mathrm{N}(p,\gamma ){}^{16}\mathrm{O}$, ${}^{16}\mathrm{O}(p,\gamma ){}^{17}\mathrm{F}$, ${}^{17}\mathrm{F}\to {}^{17}\mathrm{O}+e^{+}+{\nu }_e$, and ${}^{17}\mathrm{O}(p,\alpha ){}^{14}\mathrm{N}$, after which the main cycle continues. Thus CNO nuclei are catalytic in the closed cycles, although their relative abundances change. A local rate is ${ϵ}_{\mathrm{CNO}}\propto \rho X_H{X}_{\mathrm{CNO}}{T}^{\eta }$ with a much steeper exponent than the PP chain; the preceding homology problem specifies $\eta =16$. The concentration of this heating near the centre favors a convective core in hotter, more massive hydrogen-burning stars.

Once hydrogen is exhausted in a core, contraction can raise its temperature enough for core helium burning. The Triple-alpha process overcomes the absence of stable mass-5 and mass-8 nuclei by maintaining a tiny transient beryllium-8 population:The Hoyle state, an excited carbon-12 resonance near the three-alpha threshold, makes the second capture efficient enough despite beryllium-8's very short lifetime. The net conversion is $3{}^4\mathrm{He}\to {}^{12}\mathrm{C}$, releasing about $7.27\mathrm{MeV}$. Because three alpha particles are required, the specific rate scales as ${\rho }^2{Y}^3$; a schematic resonant rate isIts local temperature exponent is $-3+44/T_8$, of order forty near $T_8=1$. A degenerate core cannot expand promptly to regulate this increase, giving a helium flash; in a nondegenerate core the stellar thermostat permits stable helium burning. The competing ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction determines much of the eventual carbon-oxygen mixture.

If the core becomes hot enough, carbon burning follows, for example through ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}\to {}^{20}\mathrm{Ne}+\alpha$ and ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}\to {}^{23}\mathrm{Na}+p$. Neon burning begins with photodisintegration, ${}^{20}\mathrm{Ne}+\gamma \to {}^{16}\mathrm{O}+\alpha$, followed by alpha capture such as ${}^{20}\mathrm{Ne}+\alpha \to {}^{24}\mathrm{Mg}+\gamma$. The first step consumes heat, but the combined rearrangement can release net energy. Oxygen burning includes ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}\to {}^{28}\mathrm{Si}+\alpha$ and channels producing phosphorus and other nearby nuclei. At still higher temperatures, silicon burning proceeds through photodisintegration and particle captures in a reaction network approaching quasi-statistical equilibrium, producing iron-group nuclei. It is not simply direct silicon-plus-silicon fusion; the products depend on the electron fraction and weak-interaction timescale.

The increasing nuclear binding energy per nucleon supplies progressively less energy as products approach the iron group. Further fusion past that region cannot provide sustained net heat to support a core. Massive stars can therefore end with an unstable iron-group core; lower-mass stars do not attain all these burning stages and instead leave remnants such as carbon-oxygen white dwarfs. Heavy-element neutron captures can synthesize nuclei beyond the iron group without being the principal hydrostatic power source.

Finally, stellar neutrino energy loss competes with every heat source. Reaction neutrinos accompany the proton–proton and CNO chains. Hot or dense material also emits neutrino pairs through $e^{-}+e^{+}\to \nu +\bar{\nu }$, plasmon decay, $e^{-}+\gamma \to e^{-}+\nu +\bar{\nu }$, and electron-ion bremsstrahlung. These neutrinos usually escape, unlike the photons whose transport is diffusive; neutrino trapping requires much more extreme collapse conditions. Late burning has smaller fuel-energy reservoirs and strong neutrino cooling, so its duration is much shorter than core hydrogen burning. The surface luminosity is the escaping photon power, $L=4\pi R^2\sigma T_{\mathrm{eff}}^4$, not the sum of photons and unobserved neutrino power. Radiative diffusion in a star, convection and electron conduction redistribute energy, while the energy-balance equation distinguishes true sources, losses and storage. Accretion or mass loss adds boundary energy and mechanical work when present, rather than changing the nuclear reaction budget.

Assume an isolated star of initial mass five solar masses of approximately solar stellar metallicity. Rotation, convective overshooting and mass loss change numerical ages and the extent of a blue loop, so the ages below are estimates. Take zero age at the zero-age main sequence; the pre-main-sequence star phase adds a much shorter contraction time.

The original schematic Hertzsprung-Russell diagram marks the stages discussed below. The strip denotes the approximate Cepheid instability strip; the track is illustrative, rather than a computed stellar model.

The main sequence lasts roughly $8\times 10^7$–$10^8$ years. CNO cycle hydrogen burning is concentrated in a mixed convective core. Its declining hydrogen mass fraction and rising helium mass fraction are nearly uniform there, while the retreating core leaves a composition gradient. The unprocessed envelope remains hydrogen rich. At the terminal-age main sequence, core hydrogen is exhausted and a hydrogen-burning shell takes over.

The inert helium core grows through shell burning. The Schönberg-Chandrasekhar limit is approximatelyBeyond this limit an isothermal nondegenerate core cannot remain in thermal equilibrium with its envelope. Core contraction and envelope expansion carry the star across the Hertzsprung gap. An initial slower shell-burning interval can precede the rapid crossing; the crossing itself is governed by Kelvin-Helmholtz contraction, with a representative $G{M}^2/(RL)\sim 10^5$–$10^6$ years. First dredge-up then mixes hydrogen-processed material into the convective envelope, lowering its hydrogen mass fraction and increasing helium and nitrogen, while leaving a composition discontinuity where the envelope later retreats.

At an age still of order $10^8$ years, core helium burning begins quietly: the core is nondegenerate, so there is no helium flash. The Triple-alpha process and subsequent alpha capture build a carbon-oxygen core. Core helium burning lasts roughly $1.6\times 10^7$–$2.2\times 10^7$ years in representative solar-composition models. Pols's stellar-evolution notes illustrate the substantial dependence of these lifetimes on convective overshooting.

During a blue loop the envelope contracts and effective temperature increases, before the star returns redward. The loop depends on core and envelope structure and the hydrogen discontinuity left by first dredge-up. A loop reaching the Cepheid instability strip produces two further crossings, blueward and redward, in addition to the earlier rapid crossing of the Hertzsprung gap. Cepheid variables pulsate through the opacity mechanism, involving helium ionization. Neither loop extent nor all three strip crossings are guaranteed for every composition or mixing prescription. The hydrogen-burning shell continues moving outward in enclosed mass while central helium is depleted. Lattanzio's five-solar-mass tutorial shows these composition changes.

After helium exhaustion, at an age roughly $1.0\times 10^8$–$1.2\times 10^8$ years, the star ascends the Asymptotic giant branch. An inert carbon-oxygen core is surrounded by helium-rich material and a hydrogen-rich envelope. Second dredge-up mixes helium and hydrogen burning products into the envelope and reduces the hydrogen-exhausted core mass. Subsequently a helium-burning shell and hydrogen-burning shell alternate in importance. A thermal pulse of an asymptotic-giant-branch star causes intershell convection, expansion and temporary quenching of hydrogen burning; third dredge-up can carry carbon and slow neutron-capture process products outward. Between pulses hydrogen burning rebuilds the helium layer. These mechanisms are illustrated in Lattanzio's AGB tutorial.

The following original stellar composition profile sketches distinguish hydrogen exhaustion from helium exhaustion; their mass boundaries are illustrative.

The final giant phases add at most a few million years at this level of accuracy. Strong stellar winds remove the envelope; the hot remnant can illuminate a planetary nebula and then cool as a carbon-oxygen white dwarf. A typical remnant is of order one solar mass. The ordinary isolated $5M_{\odot }$ case does not reach sustained carbon burning and core collapse. Thus the usual endpoint is a carbon-oxygen white dwarf, at a total age of order $10^8$ years, with its subsequent cooling age added separately.

A $6$--$8M_{\odot }$ main sequence star burns hydrogen mainly through the CNO cycle. Its strong temperature sensitivity produces a convective core, which leaves a helium-rich core with a relatively sharp composition discontinuity as it retreats. After central hydrogen exhaustion, hydrogen burning continues in a shell while the helium core contracts and the envelope expands toward the red-giant branch.

When the core becomes hot enough, the Triple-alpha process starts core helium burning. Alpha capture on the newly made carbon also produces oxygen, so central helium exhaustion leaves a carbon-oxygen core. The star then enters the Asymptotic giant branch with an inert core, a helium-burning shell, a hydrogen-burning shell, and a deep convective envelope. At the high-mass end, off-centre carbon burning converts the carbon-oxygen core into an oxygen-neon-magnesium core.

Hydrogen-shell burning deposits helium onto a geometrically thin helium layer. Once helium ignites, the strong temperature dependence of the Triple-alpha process and the shell's initially weak expansion response produce the Härm–Schwarzschild instability. The resulting AGB thermal pulse drives a short-lived intershell convection zone, expands the layers above it, and temporarily extinguishes the hydrogen-burning shell before the cycle restarts.

Toward the upper end of the mass range, neutrino cooling keeps the centre cooler than an off-centre shell, so carbon burning can ignite off-centre under partial electron degeneracy pressure. Repeated flashes and an inward-moving carbon flame consume most carbon and leave a degenerate oxygen-neon-magnesium core, surrounded by helium- and hydrogen-burning shells.