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A post-helium-ignition stage of low-mass stellar evolution with core helium nuclear fusion and usually a hydrogen-burning shell. The branch spans a broad range of effective temperatures at comparatively similar luminosities, largely because envelope masses vary.

Hydrogen burning is the net conversion of hydrogen into helium through nuclear fusion. The proton–proton chain and CNO cycle provide different sequences with the same principal fuel and final helium product. In the CNO cycle, carbon, nitrogen and oxygen act as catalysts rather than being consumed as the principal fuel.

The released nuclear binding energy supplies the long-term luminosity of a main-sequence star, with some energy escaping in neutrinos. Core exhaustion ends that evolutionary phase even if the outer envelope still contains abundant hydrogen. A hydrogen-burning shell can subsequently sustain an evolved star. The word burning denotes nuclear reactions here; it does not require combustion with molecular oxygen.

The time a star spends with core hydrogen nuclear fusion as its principal energy source. If the usable fuel fraction $f$, conversion efficiency $ϵ$, and composition are comparable, the main-sequence lifetime scales as $M/L$. With a local mass-luminosity relation $L\propto M^{\alpha }$, the lifetime scales as $M^{1-\alpha }$. This is a scaling estimate: convective core size and changing luminosity affect detailed ages.

A nuclear reaction transforms one or more atomic nuclei through interactions with particles or other nuclei. Total energy, momentum, electric charge and nucleon number constrain ordinary low-energy reaction bookkeeping. Nuclear fusion, alpha capture, neutron capture and photodisintegration are important examples in stellar nucleosynthesis. Weak processes can also change the proton-to-neutron ratio.

In a hot radiation-supported stellar core, electron-positron thermal pair abundance can grow as radiation energy is converted into pair rest energy. The stellar adiabatic exponent can fall below $4/3$, permitting contraction and rapid heating. If the resulting explosive nuclear fusion releases enough energy, it disrupts the star in a pair-instability supernova. Weaker events can produce pulses rather than full disruption, and still heavier cores can collapse without an explosion. Thus the thermal relativity scale alone neither establishes the instability nor predicts its outcome.

A stellar polytrope approximates a spherical self-gravitating star by the structural relationwhere $K$ is constant and $n$ is the polytropic index. Combining hydrostatic equilibrium with mass conservation givesThe Lane-Emden variables for a stellar polytrope separate the dimensional scales from the profile:For $n>0$ these substitutions give the Lane-Emden equationThe central conditions express finite central mass density and spherical symmetry. If ${\xi }_1$ is the first zero, a zero-pressure surface hasthe Lane-Emden mass formula. For $0<n<5$ this surface is at finite radius. For example, the polytrope of index one has $\theta =\sin \xi /\xi$ and ${\xi }_1=\pi$, giving the density profile shown in the overview figure.

An isentropic ideal monatomic gas has $p\propto {\rho }^{5/3}$ and hence $n=3/2$, a useful approximation for a fully convective ideal-gas star. Nonrelativistic electron degeneracy pressure has the same density exponent. The exponent $4/3$, giving $n=3$, occurs for ultrarelativistic electron degeneracy and in appropriate radiation-dominated stellar models. The structural index should not be confused with the adiabatic index controlling a perturbation unless the model is actually isentropic.

Polytropes give useful mass-radius scalings and central concentration with very few parameters. They do not by themselves specify nuclear fusion, energy transport, or the star's thermal evolution. Nor does a structural profile alone establish dynamical stability; that requires the response of pressure to the perturbation.

On the main sequence, central hydrogen burning converts four protons into helium, positrons, neutrinos and released energy. The net reaction is $4p\to {}^4\mathrm{He}+2e^{+}+2{\nu }_e$, with positron annihilation contributing to the total roughly $26.7\mathrm{MeV}$ release before subtracting escaping neutrino energy. In the low-mass main-sequence stars of an old globular cluster, the proton–proton chain generally dominates. The CNO cycle makes the same net conversion and becomes important in hotter burning regions.

After central hydrogen exhaustion, a subgiant contracts its helium core and establishes a hydrogen-burning shell. On the red giant branch, that shell supplies most of the luminosity, commonly through the temperature-sensitive CNO cycle, while the inert helium core grows and becomes supported mainly by electron degeneracy pressure. The envelope expands and its surface cools. The helium core is not yet powered by helium nuclear fusion.

Helium ignition in a sufficiently low-mass degenerate core produces the helium flash, removing the strong electron degeneracy pressure dominance. A horizontal-branch star subsequently burns helium in its core through the Triple-alpha process, $3{}^4\mathrm{He}\to {}^{12}\mathrm{C}+\gamma$, and through ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$. A surrounding hydrogen-burning shell can continue simultaneously.

After central helium exhaustion, the Asymptotic giant branch has an inert carbon-oxygen core with a helium-burning shell and an outer hydrogen-burning shell. Alternation between quiescent burning and helium-shell thermal pulses drives mixing and substantial mass loss. Subsequent post-asymptotic giant branch evolution exposes a hot core that may ionize its expelled envelope as a planetary nebula. Finally a white dwarf cools mainly by loss of stored thermal energy, rather than sustained central nuclear fusion.

The common energetic principle behind nuclear fission and nuclear fusion is the nuclear binding energy. If the products are more tightly bound in total than the reactants, their smaller rest mass releasesThe two binding-energy expressions assume that the same numbers of protons and neutrons are counted on both sides; emitted free nucleons have zero nuclear binding. The energy appears mainly as product kinetic energy, with radiation and subsequent decays contributing according to the reaction.

The binding energy per nucleon rises rapidly through light nuclei, has a broad maximum in the iron/nickel region, and decreases more slowly for heavier nuclei. Combining suitable light nuclei can therefore increase their total binding, whereas splitting a sufficiently heavy nucleus into moderately heavy fragments can do the same. This is an energy comparison, not a rule that every fusion or fission channel is exothermic: the actual nuclear masses fix the sign of $Q$.

In nuclear fission, the liquid-drop model illustrates the competition between attractive short-range nuclear cohesion and long-range proton repulsive Coulomb interaction. Deformation increases surface area and costs surface energy, but separating the charge can reduce nuclear Coulomb energy. Their competition creates a fission barrier. An excited nucleus may pass over the barrier; spontaneous fission can occur through quantum tunnelling. The resulting fragments are often excited and neutron-rich, so they may emit prompt neutrons and photons and undergo later beta decay. The typical total energy released by a heavy-nucleus fission is of order a few hundred MeV, rather than an electronic-scale energy. Its size follows from an approximately MeV-per-nucleon binding gain summed over a heavy nucleus. A neutron from one fission can induce another; a nuclear chain reaction is the repeated physical process, distinct from the energy-release condition for one event.

In nuclear fusion, the initial charged nuclei repel one another. Exothermicity does not remove this entrance Coulomb barrier. A reaction requires sufficient overlap of their wavefunctions, achieved by energetic encounters and quantum tunnelling. For nonresonant low-energy charged-particle fusion, a useful separation isThe astrophysical S factor isolates the nuclear part from much of the rapidly varying Coulomb penetration probability. In a thermal population, the competition between the decreasing high-energy population and increasing penetration produces the Gamow peak. This explains how fusion can proceed below the classical barrier without requiring the mean thermal energy to equal its height.

Both processes conserve total energy, charge, baryon number and angular momentum. Their very different entrance barriers and mass ranges explain why a favorable $Q$ value by itself does not specify a reaction rate. Short-range attraction gives approximately saturated nuclear binding, while surface, Coulomb, symmetry and pairing terms account for the broad trend and its isotope-dependent departures.

Using the stipulated $570\mathrm{nm}$ as a wavelength-density peak, Wien's displacement law givesThis is a rough estimate from the supplied characteristic wavelength, not an accurate measurement of the Sun's effective temperature. The Sun emits a broad, approximately thermal visible spectrum and appears white outside the atmosphere; its familiar yellow appearance does not identify a monochromatic thermal peak. A photospheric effective temperature near $5770\mathrm{K}$ instead corresponds to a wavelength-density maximum near $502\mathrm{nm}$.^[ref][ref]

The core must be much hotter to provide the pressure required for hydrostatic equilibrium and to sustain nuclear fusion. Outward energy transport through an opaque interior proceeds down a temperature gradient, by radiative diffusion and then convection through much of the outer envelope. The observable photosphere radiates to space at the temperature needed to carry the solar luminosity, $L_{\odot }=4\pi R_{\odot }^2\sigma T_{\mathrm{eff}}^4$; it is not an unobstructed view of the hot core. The printed core estimate above $20$ million degrees is also too high for the present Sun: the standard central temperature is about $1.56\times 10^7\mathrm{K}$. This correction leaves the large core-to-surface contrast and its explanation intact.^[ref]

The phase of stellar evolution in which hydrogen-shell nuclear fusion surrounds an inert helium core and the envelope expands and cools. Low-mass stars climb toward helium ignition with growing core mass and luminosity; their cores become supported by electron degeneracy pressure. A red giant is a broader observational category and need not be on this particular evolutionary branch.

A star is a self-gravitating astronomical body whose luminous life is governed by the competition between gravity, internal pressure, energy loss and nuclear fusion. A main-sequence star sustains core hydrogen burning; a pre-main-sequence star is still contracting toward that stage, while evolved stars can burn different fuels or in shells. The name therefore includes more than the currently hydrogen-burning phase.

Hydrostatic equilibrium relates the inward pull of gravity to an outward pressure gradient. Radiative transfer and convection carry energy through the interior, and the photosphere supplies much of the observed spectrum. Mass, composition, age and interactions determine the resulting stellar radius and luminosity. The Sun offers a nearby example in which resolved observations and solar neutrino detection test different parts of the same physical picture.

Stellar evolution is the change of a star's composition, structure and observable properties over time. Nuclear fusion changes the core's composition and available fuel; gravity, energy transport and mass loss then alter the stellar radius, luminosity and effective temperature. The initial mass strongly influences the sequence, but composition, rotation and binary mass transfer also matter.

The evolution of a solar-mass star connects the main sequence to giant phases and eventually a white dwarf. More massive stars can reach stellar core collapse. An evolutionary track in the Hertzsprung-Russell diagram makes these changes visible, while comparisons with coeval stellar populations test the predicted lifetimes. Two stars with similar present appearance can have different prior histories, especially after binary interaction.

Temperature-sensitive nuclear fusion can heat material faster than cooling and expansion can regulate it, accelerating the burning. In a classical nova, hydrogen accumulated on a white dwarf ignites; initial electron degeneracy pressure helps suppress the usual expansion response. The eruption can eject the envelope without destroying the underlying white dwarf.

A Type Ia supernova is a thermonuclear stellar explosion associated with the disruption of a carbon-oxygen white dwarf. Rapid nuclear fusion releases enough energy to unbind the compact body and eject newly processed material. Several progenitor routes are studied, including the Double-degenerate Type Ia supernova scenario; the observational class does not identify one unique prior binary history.

The subsequent radioactively powered Type Ia supernova light curve is strongly influenced by the amount and distribution of radioactive material and by photon escape through expanding ejecta. Its peak luminosity is therefore not identical in every event. Empirical standardization using light curve shape and colour makes the class useful for distances, while composition, extinction and population differences must be accounted for in precision applications.