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Stellar core
Stellar core
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A stellar core is the extremely hot, dense region at the center of a star. For an ordinary main sequence star, the core region is the volume where the temperature and pressure conditions allow for energy production through thermonuclear fusion of hydrogen into helium. This energy in turn counterbalances the mass of the star pressing inward; a process that self-maintains the conditions in thermal and hydrostatic equilibrium. The minimum temperature required for stellar hydrogen fusion exceeds 107 K (10 MK), while the density at the core of the Sun is over 100 g/cm3. The core is surrounded by the stellar envelope, which transports energy from the core to the stellar atmosphere where it is radiated away into space.[1]

Main sequence

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High-mass main sequence stars have convective cores, intermediate-mass stars have radiative cores, and low-mass stars are fully convective.

Main sequence stars are distinguished by the primary energy-generating mechanism in their central region, which joins four hydrogen nuclei to form a single helium atom through thermonuclear fusion. The Sun is an example of this class of stars. Once stars with the mass of the Sun form, the core region reaches thermal equilibrium after about 100 million (108)[2][verification needed] years and becomes radiative.[3] This means the generated energy is transported out of the core via radiation and conduction rather than through mass transport in the form of convection. Above this spherical radiation zone lies a small convection zone just below the outer atmosphere.

At lower stellar mass, the outer convection shell takes up an increasing proportion of the envelope, and for stars with a mass of around 0.35 M (35% of the mass of the Sun) or less (including failed stars) the entire star is convective, including the core region.[4] These very low-mass stars (VLMS) occupy the late range of the M-type main-sequence stars, or red dwarf. The VLMS form the primary stellar component of the Milky Way at over 70% of the total population. The low-mass end of the VLMS range reaches about 0.075 M, below which ordinary (non-deuterium) hydrogen fusion does not take place and the object is designated a brown dwarf. The temperature of the core region for a VLMS decreases with decreasing mass, while the density increases. For a star with 0.1 M, the core temperature is about 5 MK while the density is around 500 g cm−3. Even at the low end of the temperature range, the hydrogen and helium in the core region is fully ionized.[4]

Logarithm of the relative energy output (ε) of proton–proton (p-p), CNO, and triple-α fusion processes at different temperatures (T). The dashed line shows the combined energy generation of the p-p and CNO processes within a star.

Below about 1.2 M, energy production in the stellar core is predominantly through the proton–proton chain reaction, a process requiring only hydrogen. For stars above this mass, the energy generation comes increasingly from the CNO cycle, a hydrogen fusion process that uses intermediary atoms of carbon, nitrogen, and oxygen. In the Sun, only 1.5% of the net energy comes from the CNO cycle. For stars at 1.5 M where the core temperature reaches 18 MK, half the energy production comes from the CNO cycle and half from the pp chain.[5] The CNO process is more temperature-sensitive than the pp chain, with most of the energy production occurring near the very center of the star. This results in a stronger thermal gradient, which creates convective instability. Hence, the core region is convective for stars above about 1.2 M.[6]

For all masses of stars, as the core hydrogen is consumed, the temperature increases so as to maintain pressure equilibrium. This results in an increasing rate of energy production, which in turn causes the luminosity of the star to increase. The lifetime of the core hydrogen–fusing phase decreases with increasing stellar mass. For a star with the mass of the Sun, this period is around ten billion years. At M the lifetime is 65 million years while at 25 M the core hydrogen–fusing period is only six million years.[7] The longest-lived stars are fully convective red dwarfs, which can stay on the main sequence for hundreds of billions of years or more.[8]

Subgiant stars

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Once a star has converted all the hydrogen in its core into helium, the core is no longer able to support itself and begins to collapse. It heats up and becomes hot enough for hydrogen in a shell outside the core to start fusion. The core continues to collapse and the outer layers of the star expand. At this stage, the star is a subgiant. Very-low-mass stars never become subgiants because they are fully convective.[9]

Stars with masses between about 0.4 M and 1 M have small non-convective cores on the main sequence and develop thick hydrogen shells on the subgiant branch. They spend several billion years on the subgiant branch, with the mass of the helium core slowly increasing from the fusion of the hydrogen shell. Eventually, the core becomes degenerate, where the dominant source of core pressure is electron degeneracy pressure, and the star expands onto the red giant branch.[9]

Stars with higher masses have at least partially convective cores while on the main sequence, and they develop a relatively large helium core before exhausting hydrogen throughout the convective region, and possibly in a larger region due to convective overshoot. When core fusion ceases, the core starts to collapse and it is so large that the gravitational energy actually increases the temperature and luminosity of the star for several million years before it becomes hot enough to ignite a hydrogen shell. Once hydrogen starts fusing in the shell, the star cools and it is considered to be a subgiant. When the core of a star is no longer undergoing fusion, but its temperature is maintained by fusion of a surrounding shell, there is a maximum mass called the Schönberg–Chandrasekhar limit. When the mass exceeds that limit, the core collapses, and the outer layers of the star expand rapidly to become a red giant. In stars up to approximately 2 M, this occurs only a few million years after the star becomes a subgiant. Stars more massive than 2 M have cores above the Schönberg–Chandrasekhar limit before they leave the main sequence.[9]

Giant stars

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Differences in structure between a star on the main sequence, on the red giant branch, and on the horizontal branch

Once the supply of hydrogen at the core of a low-mass star with at least 0.25 M[8] is depleted, it will leave the main sequence and evolve along the red giant branch of the Hertzsprung–Russell diagram. Those evolving stars with up to about 1.2 M will contract their core until hydrogen begins fusing through the pp chain along with a shell around the inert helium core, passing along the subgiant branch. This process will steadily increase the mass of the helium core, causing the hydrogen-fusing shell to increase in temperature until it can generate energy through the CNO cycle. Due to the temperature sensitivity of the CNO process, this hydrogen fusing shell will be thinner than before. Non-core convecting stars above 1.2 M that have consumed their core hydrogen through the CNO process, contract their cores, and directly evolve into the giant stage. The increasing mass and density of the helium core will cause the star to increase in size and luminosity as it evolves up the red giant branch.[10]

For stars in the mass range 0.4–1.5 M, the helium core becomes degenerate before it is hot enough for helium to start fusion. When the density of the degenerate helium at the core is sufficiently high − at around 107 g cm−3 with a temperature of about 109 K − it undergoes a nuclear explosion known as a "helium flash". This event is not observed outside the star, as the unleashed energy is entirely used up to lift the core from electron degeneracy to normal gas state. The helium fusing core expands, with the density decreasing to about 103 − 104 g cm−3, while the stellar envelope undergoes a contraction. The star is now on the horizontal branch, with the photosphere showing a rapid decrease in luminosity combined with an increase in the effective temperature.[11]

In the more massive main-sequence stars with core convection, the helium produced by fusion becomes mixed throughout the convective zone. Once the core hydrogen is consumed, it is thus effectively exhausted across the entire convection region. At this point, the helium core starts to contract and hydrogen fusion begins along with a shell around the perimeter, which then steadily adds more helium to the inert core.[7] At stellar masses above 2.25 M, the core does not become degenerate before initiating helium fusion.[12] Hence, as the star ages, the core continues to contract and heat up until a triple alpha process can be maintained at the center, fusing helium into carbon. However, most of the energy generated at this stage continues to come from the hydrogen fusing shell.[7]

For stars above 10 M, helium fusion at the core begins immediately as the main sequence comes to an end. Two hydrogen fusing shells are formed around the helium core: a thin CNO cycle inner shell and an outer pp chain shell.[13]

See also

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References

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Bibliography

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from Grokipedia
The stellar core is the central region of a star where nuclear fusion reactions primarily occur, converting hydrogen into helium and generating the energy that powers the star and counteracts gravitational collapse. This dense, extremely hot zone, characterized by temperatures exceeding 10 million Kelvin and pressures sufficient to overcome electrostatic repulsion between atomic nuclei, constitutes a small fraction of the star's total radius—typically about 20-25% in main-sequence stars like the Sun—but contains a significant portion of its mass. In stellar evolution, the core's composition and activity define a star's lifecycle stages. During the main-sequence phase, which lasts billions of years for low-mass stars and mere millions for high-mass ones, hydrogen fusion dominates in the core, producing helium ash that accumulates at the center. As hydrogen depletes, the core contracts and heats, potentially igniting helium fusion in stars above about 0.5 solar masses, leading to phases like the red giant branch where shell burning occurs around an inert helium core. In more massive stars, successive fusion stages proceed through carbon, oxygen, and up to iron in the core, beyond which fusion becomes endothermic, culminating in core collapse and events such as supernovae. The structure and dynamics of the stellar core are governed by equations of hydrostatic equilibrium, energy transport, and nuclear reaction rates, influencing the star's luminosity, temperature, and eventual fate—ranging from white dwarfs for low-mass remnants to neutron stars or black holes for high-mass ones. Observations and models, including helioseismology for the Sun, reveal cores with near-uniform composition in radiative zones but convective mixing in massive stars, affecting element distribution and nucleosynthesis. These processes not only sustain individual stars but also contribute to the chemical enrichment of the universe.

Definition and Basic Properties

Physical Characteristics

The stellar core is the central region of a star where nuclear fusion dominates energy production. It typically comprises 10-25% of the star's radius but over 50% of its mass, owing to the elevated central density compared to the outer layers. For main-sequence stars, core temperatures generally range from about 4 to 40 million Kelvin, enabling hydrogen fusion, while central densities range from about 10 g/cm³ in massive stars to over 1000 g/cm³ in low-mass stars. The initial composition is dominated by hydrogen at 70-75% by mass and helium at 25-30%, with minor metals making up the remainder. Physical characteristics vary significantly with stellar mass. Low-mass stars feature partial contributions from degenerate electron pressure in their cores where quantum effects supplement thermal support against gravity, whereas high-mass stars possess convective cores that facilitate mixing of fusion products. In low-mass stars, the core pressure balances gravitational compression through a combination of thermal and degeneracy contributions, expressed as P=ρkTμmH+PdegP = \frac{\rho k T}{\mu m_H} + P_{\rm deg} where the first term represents the ideal gas pressure and the second the electron degeneracy pressure.

Role in Stellar Structure

The stellar core occupies the central region of a star, where its immense gravitational pull is counterbalanced by the outward pressure generated primarily through nuclear fusion reactions. This balance establishes hydrostatic equilibrium throughout the star, with the core's high density and temperature driving the pressure gradient that supports the overlying layers against collapse. In this configuration, the core's fusion processes provide the thermal energy necessary to maintain the star's structural integrity, preventing gravitational implosion while allowing the star to remain stable over its lifetime. The core is responsible for generating approximately 99% of a star's total luminosity, as nearly all nuclear fusion occurs within this compact volume, with the resulting energy subsequently transported to the surface. This dominant energy production underscores the core's pivotal role in determining the star's overall brightness and evolutionary path, as variations in core fusion efficiency directly influence the star's observable properties. The boundary of the stellar core is typically defined as the radial point where the nuclear fusion rate diminishes to a negligible level, often corresponding to the location where about 99% of the total energy generation has occurred, marking the transition to less active outer layers such as the radiative or convective zones. High central densities, exceeding 100 g/cm³ in main-sequence stars like the Sun, further delineate this boundary by concentrating fusion activity inward. A fundamental relation governing the core's dynamics is the , which for a self-gravitating system in equilibrium states that twice the total KK (arising from thermal motions and fusion-driven pressure) plus the gravitational potential energy WW equals zero: 2K+W=02K + W = 0 This equation illustrates how the core's thermal , fueled by fusion, offsets the negative , ensuring long-term stability.

Formation and Initial Conditions

Protostellar Collapse

The protostellar collapse phase marks the initial formation of a stellar core, triggered by gravitational instability within a fragment of a molecular cloud. These fragments, typically ranging from approximately 0.01 to 1 solar masses, become unstable when their mass exceeds the Jeans mass, allowing self-gravity to overcome internal thermal pressure and initiate collapse. Cooling primarily occurs through radiation from dust grains, which efficiently emits infrared photons and prevents excessive heating during the early stages, enabling the cloud to contract without immediate fragmentation. The collapse proceeds in distinct stages, beginning with free-fall dynamics where the core density increases rapidly as material falls inward under gravity. As angular momentum conservation comes into play, the infalling gas flattens into an accretion disk around the central protostar, facilitating continued mass infall onto the core. Throughout this process, the central temperature rises progressively, reaching approximately 10610^6 K due to compressional heating, setting the stage for subsequent structural evolution. The Jeans criterion provides the theoretical foundation for this instability, defined by the Jeans length: λJ=πcs2Gρ\lambda_J = \sqrt{\frac{\pi c_s^2}{G \rho}}
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