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Convection zone

A convection zone, convective zone, or convective region in a star is a layer which is unstable to convection, where energy is transported outward primarily by the bulk motion of plasma rather than radiation.^[1] In the Sun, the convection zone is the outermost layer of its interior, extending from a depth of approximately 200,000 kilometers below the photosphere to the visible solar surface, where plasma transports energy from the deeper radiative zone to the exterior through vigorous convective currents.^[2] This region comprises roughly the outer 30% of the Sun's radius and is characterized by boiling motions of ionized gas, similar to convection in a pot of heated water, forming large-scale cells known as granules and supergranules on the surface.^[3] Temperatures in the Sun's convection zone decrease from about 2 million degrees Celsius at its base to around 5,700 Kelvin at the top, with densities dropping dramatically to near-vacuum levels at the surface, enabling the rapid rise and fall of hot and cooler plasma parcels.^[2] Energy transfer in this zone occurs because the temperature gradient exceeds the adiabatic limit, causing instability that drives convection rather than radiative diffusion, which dominates in the underlying radiative zone.^[2] The opacity of the plasma here, due to heavier elements like carbon, nitrogen, and oxygen that trap photons, further promotes these convective flows by preventing efficient radiation outward.^[2] Convective motions also play a crucial role in solar dynamics, buoying magnetic fields from the tachocline—the boundary with the radiative zone—to the surface, where they manifest as sunspots, flares, and other phenomena that influence space weather.^[4] Observations of the convection zone have been advanced through helioseismology, which uses sound waves propagating through the Sun to map its internal structure, confirming the zone's depth and flow patterns via missions like the Solar Dynamics Observatory (SDO).^[5] These insights reveal overturning cells up to 30,000 kilometers across, with plasma velocities reaching several kilometers per second, underscoring the zone's importance in the Sun's differential rotation and overall energy budget.^[3]

Fundamentals

Definition and Characteristics

The convection zone is the outer layer in a star where convective motions dominate the transport of thermal energy, surpassing radiative diffusion as the primary mechanism for heat transfer. In this region, instability arises in the stratified plasma, leading to bulk displacement of material that efficiently carries energy outward from the stellar interior.^[6]^[7] Key characteristics of convection zones include highly turbulent plasma motions driven by buoyancy, resulting in the overturning of material within convective cells or granules, where hot, less dense plasma rises and cooler, denser plasma sinks. These zones exhibit nearly adiabatic stratification, with the temperature gradient slightly superadiabatic to sustain the instability, and their thickness varies significantly across stellar types—from approximately 30% of the solar radius in the Sun to encompassing nearly the entire volume in low-mass, fully convective stars.^[8]^[6] Unlike radiative zones, where energy is transported primarily by photon diffusion through stable stratification, convection zones feature superadiabatic temperature gradients that promote convective instability and turbulent mixing. This distinction ensures that convection zones form in regions where radiative opacity or temperature conditions favor fluid motion over radiation.^[7]^[8] The existence of convection zones was first inferred in the early 20th century, with Karl Schwarzschild deriving the quantitative criterion for convective instability in stellar atmospheres in 1906.^[9]^[10]

Physical Mechanism of Convection

Convection in stellar interiors manifests as the bulk motion of ionized plasma, where hotter, less dense regions rise due to buoyancy while cooler, denser regions sink, establishing a cyclic flow that transports thermal energy outward. This process is initiated when local temperature gradients exceed the adiabatic limit, causing density perturbations that drive the instability. The buoyancy force arises from these density differences, governed by the ideal gas law and hydrostatic equilibrium, where a temperature excess \Delta T in a fluid element leads to a relative density deficit \Delta \rho / \rho \approx -\Delta T / T for an ideal gas.^[11]^[6] In regions of high opacity, such as deep stellar envelopes, radiative energy transport becomes inefficient because photons are frequently scattered or absorbed, resulting in a steep temperature gradient that cannot be sustained by diffusion alone. Convection then dominates, carrying substantial energy fluxes that radiation cannot match; for instance, in the Sun's convection zone, it transports nearly the full solar luminosity of $3.828 \times 10^{26} \, \mathrm{W}, enabling efficient outward heat flow where radiative opacity would otherwise impede it.^[12]^[13] Unlike radiative transfer, which depends on microscopic photon interactions over mean free paths, or conduction via particle collisions without net mass displacement, convection relies on macroscopic fluid motions, allowing for rapid, large-scale energy advection in turbulent flows.^[14] The convective heat flux F_\mathrm{conv} quantifies this energy transport and can be approximated as

F_\mathrm{conv} \approx \rho c_p v \Delta T \frac{l}{H_p},

where \rho is the plasma density, c_p is the specific heat capacity at constant pressure, v is the characteristic convective velocity, \Delta T is the temperature excess of a rising fluid element, l is the mixing length (the typical distance a convective element travels before mixing), and H_p = -dr / d \ln P is the pressure scale height. This form arises from estimating the net enthalpy flux carried by buoyant elements across a horizontal layer.^[15] To derive this approximation, consider a fluid element displaced upward adiabatically by a distance l from its equilibrium position in a stratified atmosphere. The surrounding temperature decreases according to the actual gradient, but the element cools only along the adiabatic path, acquiring a temperature excess \Delta T \approx (\nabla - \nabla_\mathrm{ad}) T (l / H_p), where \nabla = d \ln T / d \ln P is the actual logarithmic temperature gradient and \nabla_\mathrm{ad} = (\gamma - 1)/\gamma \approx 0.4 for a monatomic ionized gas with adiabatic index \gamma = 5/3. The resulting buoyancy acceleration is a \approx g (\Delta \rho / \rho) \approx -g (\partial \ln \rho / \partial \ln T)_P (\Delta T / T) \approx g \delta (\Delta T / T), with \delta \approx 1 for an ideal gas and g the local gravitational acceleration. Assuming the element reaches a terminal velocity v after traveling l, energy balance gives v^2 / 2 \approx a l, so v \approx \sqrt{2 g \delta (\Delta T / T) l}. The heat flux then follows from the upward mass flux \sim \rho v / 2 (accounting for counterflowing downwelling elements) times the excess specific enthalpy c_p \Delta T, yielding F_\mathrm{conv} \approx (\rho v / 2) c_p \Delta T. The factor l / H_p enters to normalize for the fractional depth of the convective layer or the gradient scale over which \Delta T develops, providing an order-of-magnitude estimate for the total flux in efficient convection where \nabla \approx \nabla_\mathrm{ad} + \epsilon and \epsilon \ll 1. This mechanism ensures that convection adjusts the temperature profile to remain nearly adiabatic, efficiently balancing the stellar energy generation.^[11]^[14]

Theoretical Models

Stability Criteria

The onset of convective instability in stellar layers occurs when a displaced fluid element experiences buoyancy forces that amplify its motion rather than restoring it to equilibrium, a condition analyzed through specific stability criteria derived from hydrostatic equilibrium and energy transport equations. These criteria determine the boundaries between radiative and convective regions by comparing the actual temperature gradient to a critical threshold. The foundational Schwarzschild criterion, applicable to compositionally homogeneous layers, states that a stellar layer is unstable to convection if the actual temperature gradient ∇ exceeds the adiabatic gradient ∇_ad, where ∇ = d ln T / d ln P and ∇ad = (∂ ln T / ∂ ln P){S} represents the gradient for an isentropic displacement. In radiative zones, the actual gradient ∇ approximates the radiative gradient ∇_rad, defined from the radiative transfer equation as ∇rad = (d ln T / d ln P){rad}, which quantifies the temperature change required to transport luminosity by radiation alone under local thermodynamic equilibrium. For an ideal monatomic gas typical of ionized stellar interiors, ∇_ad ≈ 0.4, derived from ∇_ad = (γ - 1)/γ with γ = 5/3. This criterion emerges from considering a fluid "blob" displaced vertically in a star under hydrostatic equilibrium, dP/dr = -ρ g, where the blob adjusts pressure instantaneously to match its surroundings but evolves temperature adiabatically, preserving entropy. The surroundings follow the actual gradient, δ ln T_s / δ ln P = ∇, while the blob follows δ ln T_b / δ ln P = ∇ad. The resulting density perturbation in the blob relative to surroundings is δρ/ρ = -δ (δ ln T / T) + α (δ ln P / P), with thermal expansion coefficient δ = -(∂ ln ρ / ∂ ln T){P,μ} > 0. Buoyancy force on the blob is then f_b ∝ (∇_ad - ∇) δ ln P ⋅ ρ g, positive (upward acceleration) if ∇ > ∇_ad, leading to runaway instability and convection; conversely, ∇ < ∇_ad yields restoration and stability. In regions with varying chemical composition, such as near nuclear burning shells where mean molecular weight μ may increase inward, the Schwarzschild criterion overestimates instability; the Ledoux criterion accounts for this by incorporating a stabilizing μ-gradient term, stating the layer is stable if ∇ < ∇_ad + (φ/δ) ∇_μ, where ∇μ = (d ln μ / d ln P), φ = (∂ ln ρ / ∂ ln μ){P,T} > 0 is the composition response coefficient, and δ is as above. If ∇_μ > 0 (heavier elements deeper), the additional term (φ/δ) ∇_μ > 0 enhances stability, potentially preventing convection even if ∇ > ∇_ad; for uniform μ (∇_μ = 0), it reduces to the Schwarzschild case. The full Brunt-Väisälä frequency squared, N² ∝ g δ / H_p (∇_ad - ∇ + (φ/δ) ∇_μ) with scale height H_p, is positive for stability (oscillatory motion) and negative for instability (exponential growth). These criteria are essential for delineating convective zone boundaries in theoretical stellar models, where ∇_rad is computed from luminosity L, opacity κ, and local conditions, and compared against ∇_ad ± μ terms to define regions where radiative transport fails and convection must dominate.

Mixing Length Theory

The mixing length theory (MLT) is a semi-empirical model that parameterizes convective energy transport in stellar interiors by assuming that fluid elements, or "blobs," rise or sink adiabatically over a characteristic distance known as the mixing length before mixing with their surroundings.^[16] This distance is typically taken as l = \alpha H_p, where H_p is the pressure scale height and \alpha is a dimensionless parameter of order 1 to 2, calibrated to match observed stellar properties such as the solar luminosity.^[16] Originally developed in the context of atmospheric turbulence, the concept was adapted for stellar convection in the 1950s. Ludwig Prandtl introduced the mixing length idea in 1925 to model turbulent viscosity in fluids, while Erika Böhm-Vitense extended it to stellar applications in 1953 for the solar convection zone and generalized it in 1958 for stars across a range of effective temperatures. This framework assumes local, blob-like motions without resolving the full turbulent cascade, making it computationally efficient for one-dimensional stellar evolution models.^[16] In MLT, the convective velocity v of a blob is derived from the buoyancy work done over the mixing length, yielding v \approx \left[ g \delta (\nabla_{\rm rad} - \nabla_{\rm ad}) \frac{l}{H_p} \right]^{1/2}, where g is the local gravitational acceleration, \nabla_{\rm rad} is the radiative temperature gradient required to carry the total energy flux by radiation alone, and \nabla_{\rm ad} is the adiabatic gradient.^[16] The factor \delta = -\left( \frac{\partial \ln \rho}{\partial \ln T} \right)_P accounts for the thermodynamic response of density to temperature changes at constant pressure, typically \delta \approx 1 for ideal gases but varying with composition and ionization.^[16] This velocity expression links the superadiabatic driving to the motion scale, assuming the blob accelerates due to the density contrast with surroundings and reaches terminal velocity over l.^[16] The resulting convective flux is then F_{\rm conv} \propto \rho c_P T v (\nabla - \nabla_{\rm ad}) l / H_p, balancing the total stellar luminosity with radiative contributions.^[16] The superadiabatic excess \Delta \nabla = \nabla_{\rm rad} - \nabla_{\rm ad} quantifies the instability driving convection, building on criteria like the Schwarzschild condition where \Delta \nabla > [0](/page/0) signals convective onset.^[16] In practice, stellar structure codes solve for \Delta \nabla iteratively: starting with an assumed temperature gradient, they compute v and F_{\rm conv} from MLT, adjust \nabla = \nabla_{\rm ad} + \Delta \nabla to ensure F_{\rm rad} + F_{\rm conv} matches the local energy generation or transport needs, and repeat until convergence, often involving a cubic equation for optically thick regimes.^[16] This process is nested within the overall stellar model integration, with \alpha fixed by solar calibration to reproduce the observed radius and luminosity at the Sun's age.^[16] Despite its widespread use, MLT has notable limitations stemming from its simplifying assumptions of isotropic, homogeneous blobs undergoing purely vertical, steady motions without entrainment or pressure effects.^[16] It treats convection as a local diffusion process, which breaks down in highly turbulent regimes where multi-scale eddies dominate or in overshoot zones beyond formal convective boundaries, leading to underestimation of mixing efficiency.^[16] These shortcomings are evident in discrepancies between MLT predictions and three-dimensional simulations, particularly near convective-radiative interfaces.^[16]

Occurrence in Stars

Main Sequence Stars

In main sequence stars, the structure and location of convection zones exhibit a strong dependence on stellar mass. For low-mass stars with masses below approximately 1.5 solar masses (M < 1.5 M_⊙), the interiors feature radiative cores surrounded by convective envelopes, where the outer layers become unstable to convection due to the inefficient radiative transport in cooler, denser regions. In contrast, higher-mass main sequence stars (M > 1.5 M_⊙) possess convective cores that facilitate rapid mixing of nuclear-processed material, while their envelopes remain radiative owing to higher central temperatures and lower opacities that allow efficient photon diffusion. This dichotomy arises from the interplay between energy generation rates, opacity profiles, and temperature gradients, with the transition mass varying slightly with metallicity but generally occurring around 1.2–1.5 M_⊙ for solar composition.^[17]^[18] The depth of the convection zone boundary also varies with mass, becoming shallower in higher-mass stars. In solar-type stars (G-type, ~1 M_⊙), the base of the convective envelope lies at about 0.70 R_⊙ (where R_⊙ is the solar radius), corresponding to a depth of roughly 200,000 km from the surface. For more massive F-type stars, this envelope convection zone is thinner, with the base lying at a larger fractional radius, approximately 0.9 R from the center.^[2]^[19]^[20]^[21] In the Sun (a G2V star), convection dominates energy transport throughout much of this zone, carrying nearly 100% of the outward flux in the outermost layers near the photosphere, but this fraction drops to approximately 1% near the base, where radiative diffusion contributes the majority of the energy flow.^[2]^[19]^[20] The extent of these convection zones is primarily influenced by opacity variations, particularly in ionization zones of hydrogen and helium, which are prominent in F, G, and K stars. These partial ionization regions increase opacity by factors of 10–100, steepening the temperature gradient beyond the adiabatic limit and triggering convective instability in the envelopes of lower-mass stars. Metallicity and composition further modulate this, with higher metal content enhancing opacity and deepening the convective layers.^[22]^[23] During the hydrogen-burning phase on the main sequence, convection zones remain evolutionarily stable, with minimal changes in their depths or extents. The stellar structure adjusts slowly to core composition shifts from hydrogen fusion, but the overall configuration—radiative cores with convective envelopes in low-mass stars, or vice versa in high-mass ones—persists without significant boundary migration, ensuring consistent energy transport throughout this prolonged phase.^[24]^[25]

Evolved Stars

In post-main-sequence evolution, stars develop dramatically altered convection zones due to core contraction and envelope expansion. For low- to intermediate-mass stars ascending the red giant branch (RGB), the outer convective envelope deepens substantially, often encompassing a large fraction of the stellar radius—up to approximately 80-90%—as the helium core contracts and the hydrogen-burning shell's luminosity destabilizes the overlying layers. This structural shift occurs rapidly once the stellar radius approaches red giant dimensions, with the convection zone extending inward to the base of the envelope just above the hydrogen-burning shell.^[26] The deepening of the convective envelope in red giants enables the first dredge-up, where the convection base reaches the chemically processed layers from prior hydrogen burning, transporting fusion products like lithium depletion and enhanced carbon and nitrogen abundances to the surface. As the star ascends the RGB, the convection zone progressively extends deeper in mass, driven by ongoing envelope dilation and radiative instability, with the full RGB phase lasting approximately 1–2 billion years for solar-mass stars.^[18]^[27] In asymptotic giant branch (AGB) stars, following helium core ignition on the horizontal branch and subsequent second dredge-up, the convective envelope penetrates even deeper during thermal pulses, facilitating the third dredge-up that mixes helium-shell products—such as carbon and s-process elements—into the envelope for surface enrichment. Overshooting at the envelope base enhances this penetration, with dredge-up efficiency increasing to values of λ ≈ 0.7-1.6 over multiple pulses, enabling the formation of carbon stars at lower luminosities than previously thought. The AGB phase, marked by these recurrent deepenings of the convection zone, typically lasts about 10^6 years for solar-mass stars.^[28]^[29] In contrast, horizontal branch stars, which burn helium in a degenerate core after the RGB tip, generally feature shallow or absent convective envelopes, with convection confined to thin superficial layers in cooler examples due to the contracted structure and radiative dominance in the interior. In hotter horizontal branch stars (T_eff > 11,500 K), the superficial convection zone vanishes entirely, allowing atomic diffusion processes to alter surface compositions without convective mixing. This limited convection persists throughout the horizontal branch phase, which bridges the RGB and AGB for low-mass stars.^[30]

Observational Evidence

Surface Manifestations

The surface manifestations of convection in the Sun are most prominently observed as granulation, a pattern of small-scale convective cells visible in the photosphere. These granules appear as bright, hot upwelling regions surrounded by darker intergranular lanes where cooler plasma descends, with typical diameters of approximately 1,000 km.^[31] The turnover time for these structures is short, lasting about 5–10 minutes, reflecting the rapid convective cycle driven by buoyancy and radiative cooling near the solar surface.^[32] High-resolution images from space-based observatories, such as the Solar and Heliospheric Observatory (SOHO), and the Daniel K. Inouye Solar Telescope (DKIST) on the ground, which has resolved granulation features as small as 30 km since its first light in 2020, capture solar granulation with sufficient detail to reveal brightness contrasts of around 10% in visible light between the bright granule centers and dark lanes.^[33]^[34]^[35] On larger scales, supergranulation manifests as expansive cellular flows covering the solar surface, with cell diameters of about 30,000 km and characteristic lifetimes of roughly 24 hours.^[36] These structures are associated with convection originating from deeper layers of the convection zone, producing horizontal flows that influence the overall dynamics of the quiet Sun.^[36] An intermediate scale, mesogranulation, features cellular patterns with horizontal extents of 5,000–10,000 km, bridging the gap between granular and supergranular motions and contributing to the hierarchical organization of surface convection.^[37] Spectroscopic observations of these surface features reveal Doppler shifts indicative of vertical velocities in granules, typically ranging from 1 to 2 km/s, with upflows in bright regions and downflows in intergranular lanes.^[38] These velocity signatures allow researchers to map convective motions through line profile asymmetries and shifts in spectral lines formed in the photosphere, providing insights into the energy transport at the solar surface.^[38]

Internal Probing Techniques

Internal probing techniques for the convection zone primarily rely on helioseismology and asteroseismology, which analyze stellar oscillations to infer interior structures inaccessible to direct observation. These methods exploit acoustic waves generated within the star, whose propagation is influenced by density, pressure, and temperature gradients in the convective layers, allowing mapping of zone boundaries and dynamics.^[39]^[40] Helioseismology focuses on the Sun, using pressure modes or p-modes—acoustic waves trapped in the solar interior—to probe the convection zone. By observing these oscillations via Doppler shifts in spectral lines from instruments like the Global Oscillation Network Group (GONG) and the Solar Dynamics Observatory (SDO), researchers invert frequency data to reconstruct sound-speed profiles, revealing the convection zone extends from the surface to approximately 0.7 solar radii (R_\odot) at its base, where it transitions to the radiative zone via the tachocline—a thin shear layer of about 0.05–0.09 R_\odot thick.^[41]^[42]^[43] Key advancements came from the Solar and Heliospheric Observatory (SOHO) mission in the 1990s, whose Michelson Doppler Imager (MDI) and Global Oscillation at Low Frequency (GOLF) instruments provided high-precision p-mode data, confirming the convection zone's thickness at around 0.29 R_\odot from the surface and identifying the tachocline's role in dynamo processes.^[44]^[39] These observations exposed discrepancies between standard solar models using mixing-length theory (MLT) and seismic data, particularly in sound-speed profiles near the base, prompting revisions to models incorporating non-local convection effects and adjusted opacities to better match inferred helium abundances and convective overshoot. In 2025, helioseismology has enabled direct inference of solar radiative opacity, finding values about 10% higher than theoretical models near 2 million K, aiding further refinements to convection zone models.^[45]^[46]^[47] The core technique involves inverting observed p-mode frequencies through linear perturbation methods, solving integral equations that relate frequencies to interior properties like sound speed c. A fundamental dispersion relation governs wave propagation, given by

c^2 = \frac{\gamma P}{\rho},

where \gamma is the adiabatic index, P is pressure, and \rho is density; this adiabatic sound speed is derived from frequency inversions using asymptotic approximations and regularized least-squares optimizations to minimize trade-offs between resolution and error.^[40]^[48]^[49] Asteroseismology extends these principles to other stars, leveraging space-based photometry from the Kepler and Transiting Exoplanet Survey Satellite (TESS) missions to detect p-modes and mixed modes in evolved stars like red giants, enabling inferences of convective envelope depths. In red giants, the deepening convection zone during the first dredge-up mixes material to the surface, and seismic scaling relations from dipole and quadrupole modes estimate zone extents reaching up to 0.1–0.3 stellar radii in lower red giants, providing constraints on mass-loss rates and evolutionary paths.^[50]^[51]^[52] As of 2025, previews of the PLAnetary Transits and Oscillations (PLATO) mission, slated for launch in 2026, promise enhanced resolution for asteroseismology of exoplanet-hosting Sun-like stars, with its array of 26 telescopes targeting brighter fields to achieve precisions below 1% in radius and density for probing shallow convection zones in main-sequence hosts.^[53]^[54]

Implications for Stellar Physics

Energy Transport Role

In the Sun, the convection zone is responsible for transporting the majority of the outward energy flux in the outer approximately 30% of the solar radius, where radiative diffusion becomes inefficient due to elevated opacities. This region features high opacity values on the order of 10^2 to 10^3 cm²/g, primarily arising from the formation of H⁻ ions in the cooler, partially ionized layers near the surface.^[55] These opacities trap photons, making radiative transport inadequate to carry the required flux, thereby necessitating convective motions to efficiently move heat from the deeper radiative interior to the photosphere.^[56] At the boundaries between convective and radiative zones, the energy flux carried by convection matches that of radiation, ensuring continuity and preserving the star's total luminosity as defined by the surface relation L = 4\pi R^2 \sigma T_{\rm eff}^4. In solar models, this matching occurs at the base of the convection zone, where the convective flux transitions smoothly to radiative flux without discontinuities, maintaining global energy balance throughout the stellar interior.^[57] Convection enforces a nearly adiabatic temperature profile (\nabla \approx \nabla_{\rm ad}) within the zone, which significantly influences the overall stellar structure by expanding the envelope, altering the radius, and modifying temperature gradients compared to purely radiative configurations. Without convection, standard solar models fail to reproduce observed properties, predicting a luminosity lower than the actual value by a factor of approximately 10 due to the inability of radiative transport alone to adequately handle the envelope's energy demands.^[58] Convective overshooting, involving brief penetration of plumes beyond formal convective boundaries, further enhances energy transport by allowing additional flux in adjacent stable layers, though its contribution is typically small compared to the primary convective region.^[59]

Chemical Mixing Effects

In red giant stars, the deepening convective envelope during the first dredge-up process transports nuclear-processed material from the hydrogen-burning shell to the stellar surface, significantly altering surface compositions. This mixing brings enhanced abundances of isotopes such as ^3He, produced via the pp-chain, and products of the CNO cycle, including ^{14}N and ^{13}C, which are depleted in ^{12}C.^[60]^[61] These changes occur as the convective zone penetrates to depths of approximately 0.1-0.2 M_\odot, homogenizing the composition in the envelope and diluting fragile elements like lithium.^[62] Convection within these zones efficiently mixes isotopes on timescales much shorter than the star's evolution, leading to uniform abundances throughout the convective region and observable modifications in surface elemental ratios. For instance, the ^{12}C/^{13}C ratio decreases due to CNO processing, which is detectable through spectroscopic analysis of red giant atmospheres.^[63] This homogenization erases initial composition gradients in the mixed layers, providing a diagnostic of convective penetration depth.^[64] In the Sun, the outer convection zone thoroughly mixes the plasma from the surface down to the tachocline at about 0.7 R_\odot, resulting in uniform helium abundance in the envelope but halting further mixing into the radiative interior. This boundary preserves a helium abundance gradient established by gravitational settling in the core, with the envelope ^4He mass fraction around 0.24-0.25, distinct from the higher core value.^[65] Helioseismic inversions confirm this sharp transition, underscoring the tachocline's role in limiting chemical transport.^[66] In asymptotic giant branch (AGB) stars, recurrent thermal pulses drive episodic convection in the helium intershell, producing ^{12}C via the triple-α process. Subsequent third dredge-up events bring this helium-burning material, including ^{12}C, to the surface. These mixing episodes also facilitate s-process nucleosynthesis through the formation of a ^{13}C pocket in the intershell via partial mixing, where the ^{13}C(α,n)^{16}O reaction provides neutrons, enriching the surface in heavy elements like barium and strontium during later dredge-ups.^[63]^[67] The efficiency of chemical mixing in convection zones is often parameterized in stellar models using a diffusion coefficient D \sim v \ell / 3, where v is the convective velocity and \ell the mixing length, capturing the turbulent transport of elements on eddy timescales.^[68] This approximation allows quantification of abundance changes, with typical D values reaching $10^{10}-10^{12} cm^2 s^{-1} in solar-like envelopes.^[69]

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Variations of the solar granulation motions with height using the ...
We show that the granulation clearly evolves with height in the photosphere but does not present any significant variation with the activity cycle.
[33]
[PDF] Giant Convection Cells Found on the Sun - NASA Solar Physics
Dec 6, 2013 · These cells are expected to span the 200,000-km-deep solar convection zone, to have diameters of ~200,000 km and life- times of ~1 month ...
[34]
[PDF] ASTRONOMY AND ASTROPHYSICS Is solar mesogranulation a ...
The mesogranules have horizontal extents of 5,000–10,000 km. ... generation of global solar oscillations and smaller-scale acoustic ... granular features are ...
[35]
The Sun's Supergranulation | Living Reviews in Solar Physics
The Sun's supergranulation refers to a physical pattern covering the surface of the quiet Sun with a typical horizontal scale of approximately 30000.
[36]
Helioseismology: Probing the interior of a star - PNAS
May 11, 1999 · The first important result regarding the internal structure of the Sun was the determination of the depth of the surface convection zone (6). It ...
[37]
Inversion methods in helioseismology and solar tomography
Most of these techniques are based on a perturbation analysis which results in linear integral relations between the measured properties of solar oscillations ...
[38]
[PDF] Imaging the Solar Tachocline by Time-Distance Helioseismology
The solar tachocline at the bottom of the convection zone is an important region for the dynamics of the Sun and the solar dynamo. In this region, the sound ...
[39]
Helioseismology challenges models of solar convection - PNAS
At the base of the convection zone is a zone of rotational shear, known as the tachocline, which now plays a central role in theories of the solar dynamo (4).
[40]
Angular Velocity Gradient in Solar Convection Zone - IOP Science
1990 at the Big Bear Solar Observatory, we have found that the thickness of the transitional layer is 0.09 ± 0.04 solar radii (63 ± 28 Mm), and that most of the ...
[41]
The First Results from SOHO - European Space Agency
Three helioseismology instruments are providing unique data for the study of the structure and dynamics of the solar interior, from the very deep core to the ...
[42]
Sound-speed Inversion of the Sun Using a Nonlocal ... - NASA ADS
Nov 1, 2012 · We demonstrate that this discrepancy is caused by the inherent shortcomings of the local mixing-length theory adopted in the standard solar ...
[43]
Solar Models and New Helioseismic Constraints. I. - IOP Science
The standard mixing-length theory (MLT) (Böhm-Vitense 1958) is used to describe the convective transport of the energy, taking into account the optical ...
[44]
[PDF] Inversion methods in helioseismology and solar tomography
In this review, I discuss the basic mathematical and computational techniques of helioseismology. Most of these techniques are based on a perturbation analysis ...
[45]
Helioseismology - an overview | ScienceDirect Topics
There are four basic speeds in flux tubes: (1) the Alfvén speed v A = B 0 / 4 π ρ 0 , (2) the sound speed c s = γ P 0 / ρ 0 , (3) the cusp or tube speed c T = ...
[46]
[2107.05831] TESS asteroseismology of the Kepler red giants - arXiv
Jul 13, 2021 · Here, we seek to detect oscillations in TESS data of the red giants in the Kepler field using the 4-yr Kepler results as benchmark.
[47]
TESS Subgiant and Lower-red-giant Asteroseismology in the ...
Oct 28, 2025 · TESS Subgiant and Lower-red-giant Asteroseismology in the Continuous Viewing Zones ... convection depths and subsequently altering oscillations.
[48]
Giant star seismology | The Astronomy and Astrophysics Review
Jun 15, 2017 · ... convection zone is located too deep in red giants to be measured. Furthermore, the helium I and hydrogen ionisation zones are located close ...
[49]
The PLATO mission | Experimental Astronomy
Apr 21, 2025 · PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic ...
[50]
[2406.05447] The PLATO Mission - arXiv
Jun 8, 2024 · PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic ...
[51]
[PDF] PHYS-633: Introduction to Stellar Astrophysics
luminosity L, mass M, and radius R. But because the radius cancels in the ... For a fixed stellar flux F = L/4πr2 of stellar luminosity L that needs to be.
[52]
[PDF] Chapter 5 - Energy transport in stellar interiors - Astrophysics
CV VT, we can write this as an equation for heat conduction,. F = −K VT with ... flux of a star by convection, i.e. Fconv = l/4πr2? To make a rough ...
[53]
[PDF] STELLAR STRUCTURE AND EVOLUTION
This course aims to understand the structure and evolution of stars, their physics, and observational properties, using known laws of physics. A star radiates ...Missing: c_p H_p
[54]
Solar structure and evolution | Living Reviews in Solar Physics
Apr 26, 2021 · Here I provide a brief overview of the theory of stellar structure and evolution, including the physical processes and parameters that are involved.
[55]
Stellar Convective Penetration: Parameterized Theory and ...
Feb 22, 2022 · We present 3D numerical simulations that exhibit penetration zones: regions where the entire luminosity could be carried by radiation, but where the ...
[56]
COMPULSORY DEEP MIXING OF 3He AND CNO ISOTOPES IN ...
Giant-branch convection homogenizes this region, in an episode known as the first dredge-up or FDU, raising the surface 3He abundance by a factor of 80 (see Fig ...
[57]
CNO Isotopes in Red Giants - IOP Science
For the CNO isotopes, we have computed estimates of the enrichment of the interstellar medium from first and second dredge-up and CBP in stars of near-solar ...
[58]
Characterizing Observed Extra Mixing Trends in Red Giants using ...
Dec 20, 2022 · This inflection in the convection zone's movement is known as the first dredge-up. The RGBB occurs when the outward-propagating hydrogen ...
[59]
s-Process Nucleosynthesis in Asymptotic Giant Branch Stars
As a result of this intershell dredge-up, the neutron fluxes have a higher efficiency, both during the interpulse periods and within thermal pulses. The s ...
[60]
[PDF] CNO dredge-up in a sample of APOGEE/Kepler red giants - arXiv
Jun 7, 2021 · called first dredge-up), the pristine material in the stellar envelope ... (3He, 2p)4He in the outermost layers of the H-burning shell. This ...
[61]
[PDF] arXiv:astro-ph/0401568v1 27 Jan 2004
In our computations, the rotation-induced mixing and the tachocline parameters have been chosen to reproduce the smooth diffusion-induced helium-gradient below ...
[62]
SEISMIC STUDY OF THE CHEMICAL COMPOSITION OF THE ...
Bahcall et al. (2005b) suggested a change by factor of between 2.5 and 3.5 to bring the convection- zone base and the convection zone helium abundance ...
[63]
[PDF] arXiv:0708.3864v2 [astro-ph] 15 May 2008
May 15, 2008 · We consider a process with a diffusion coefficient Dmix = vl/3. At the present stage we leave. Dmix unspecified, and simply solve for the ...
[64]
Convective Overshooting in the Envelopes of A-type Stars Using the ...
Mar 24, 2021 · In order to study the convective mixing in. A-type stars, we show the profiles of the diffusion coefficient Dt in the 2.3 Me stellar model by ...Missing: vl / | Show results with:vl /