3.2 Red Giants and Asymptotic Giant Branch Stars

Red Giant and AGB Evolution

Red giants and asymptotic giant branch (AGB) stars represent the dramatic late stages of stellar evolution for low- and intermediate-mass stars. During these phases, stars undergo radical structural changes: cores contract while envelopes expand enormously, fusion migrates to thin shells, and powerful mixing events dredge freshly synthesized elements to the surface. These stages also drive intense mass loss that shapes the star's final fate and seeds the interstellar medium with heavy elements.

Red Giant Branch and AGB Stages

Once a star exhausts hydrogen in its core, the inert helium core contracts and heats up while a hydrogen-burning shell ignites around it. The enormous energy output from this shell causes the envelope to expand, and the star ascends the red giant branch (RGB). A solar-mass star can swell to roughly 100 times its original radius during this phase.

After helium ignites in the core (either gradually for intermediate-mass stars or via the helium flash for stars below ~2 $M_\odot$), the star settles onto the horizontal branch, burning helium steadily. Once core helium is exhausted, the star enters the asymptotic giant branch (AGB) phase. The internal structure of an AGB star is layered:

• An inert carbon-oxygen core (the ash of helium burning)
• A helium-burning shell just above the core
• A hydrogen-burning shell farther out
• A deeply convective, hugely extended envelope

Luminosities on the AGB climb to $10^3$–$10^4 \, L_\odot$, with the most massive AGB stars approaching $\sim 5 \times 10^4 \, L_\odot$. The star's track on the HR diagram runs roughly parallel to (and brighter than) the RGB, which is why it's called "asymptotic."

Thermal Pulses and Dredge-up Events

On the AGB, the two burning shells don't operate smoothly together. The helium shell burns quiescently for long stretches, accumulating a thin layer of helium ash from the hydrogen shell above it. When this layer reaches a critical mass, helium ignition becomes thermally unstable and the shell ignites in a brief, explosive thermal pulse (also called a helium shell flash). Each pulse releases a burst of energy that drives a short-lived convective zone through the intershell region.

Between pulses, the base of the convective envelope can penetrate downward into layers enriched by the pulse, dragging freshly synthesized material to the surface. These are the dredge-up events, and they occur at distinct evolutionary stages:

• First dredge-up happens on the RGB. The deepening convective envelope mixes CNO-processed material (enhanced $^{13}\text{C}$ and $^{14}\text{N}$, depleted $^{12}\text{C}$) to the surface.
• Second dredge-up occurs at the base of the AGB in stars above ~4 $M_\odot$. It further enhances nitrogen and helium at the surface.
• Third dredge-up is the repeated mixing that follows individual thermal pulses on the thermally pulsing AGB (TP-AGB). This is the event that brings $^{12}\text{C}$ and s-process elements to the surface, progressively transforming the star's atmospheric chemistry.

Each successive third dredge-up episode ratchets up the surface carbon abundance, which is how oxygen-rich M-type giants eventually become carbon stars.

Evolution Timescales and Stellar Lifetimes

The time a star spends in these phases depends strongly on its initial mass:

• A ~1 $M_\odot$ star spends roughly 1 Gyr on the RGB but only a few million years on the AGB.
• Thermal pulse cycles repeat every ~$10^4$–$10^5$ years during the TP-AGB, so a star may experience only a few dozen pulses total.
• Stars above ~8 $M_\odot$ develop cores massive enough to ignite carbon and proceed through advanced nuclear burning stages toward core collapse. They do not become classical AGB stars.

The brevity of the AGB phase relative to the main sequence (roughly 0.1% of the total lifetime for a solar-mass star) means AGB stars are rare in any given stellar population, yet their outsized contribution to nucleosynthesis and mass return makes them disproportionately important.

AGB Star Composition

Carbon Stars and Their Characteristics

A star becomes a carbon star when third dredge-up episodes have delivered enough $^{12}\text{C}$ to the surface that the carbon-to-oxygen number ratio exceeds unity: $\text{C/O} > 1$. This threshold matters because carbon and oxygen lock each other up in CO molecules. When C/O < 1, leftover oxygen forms oxides (TiO, $\text{H}_2\text{O}$). When C/O > 1, leftover carbon forms carbon-bearing molecules instead.

Carbon star spectra show strong molecular absorption bands of CN, $\text{C}_2$, and CH, and their atmospheres are cool enough to form carbon-rich dust grains (amorphous carbon, SiC). This dust gives them a distinctly red appearance. Well-known examples include the Mira-type variable TX Piscium and the eruptive R Coronae Borealis variables (though R CrB stars likely have a different formation channel involving white dwarf mergers).

Carbon stars are among the most important sources of carbonaceous dust in the interstellar medium, directly contributing the raw material for organic chemistry in molecular clouds.

S-type Stars and Transitional Objects

S-type stars sit at the chemical boundary between oxygen-rich M giants and carbon stars, with C/O ratios close to unity (roughly 0.95–1.05). At this ratio, nearly all carbon and oxygen are bound in CO, leaving very little of either element free. The result is a distinctive spectral signature: strong ZrO bands replace the TiO bands of M giants, and lines of s-process elements like strontium, yttrium, barium, and zirconium are prominently enhanced.

The classification sequence runs M → MS → S → SC → C, tracing the progressive enrichment of carbon through successive dredge-up episodes:

• MS stars show mild ZrO alongside TiO
• SC stars are on the verge of becoming carbon stars

Notable S-type stars include χ Cygni (also a Mira variable) and R Andromedae. Observing the relative populations of M, S, and C stars in a stellar system provides constraints on dredge-up efficiency and AGB models.

Chemical Evolution and Nucleosynthesis in AGB Stars

AGB stars are the dominant site of the slow neutron capture process (s-process), which is responsible for producing roughly half of all elements heavier than iron. During thermal pulses, the convective intershell region reaches temperatures where neutron-producing reactions operate. The two main neutron sources are:

• $^{13}\text{C}(\alpha, n)^{16}\text{O}$, which operates in a thin "$^{13}\text{C}$ pocket" during the interpulse period (the dominant source in low-mass AGB stars)
• $^{22}\text{Ne}(\alpha, n)^{25}\text{Mg}$, which activates at higher temperatures during the thermal pulse itself (more important in intermediate-mass AGB stars)

Neutrons released by these reactions are captured by iron-seed nuclei, building up heavier elements along the valley of stability: Sr, Y, Zr (first s-process peak), Ba, La, Ce (second peak), and Pb (third peak).

Additional nucleosynthetic signatures include:

• Hot bottom burning (HBB) in AGB stars above ~4–5 $M_\odot$, where the base of the convective envelope is hot enough for CNO and even some NeNa/MgAl cycling. HBB can produce $^7\text{Li}$ via the Cameron-Fowler mechanism and convert $^{12}\text{C}$ back to $^{14}\text{N}$, preventing carbon star formation in the most massive AGB stars.
• Isotopic ratios like $^{12}\text{C}/^{13}\text{C}$ and $^{16}\text{O}/^{17}\text{O}$ serve as sensitive diagnostics of mixing depth and nucleosynthetic history.

Through their winds, AGB stars return this chemically enriched material to the ISM, making them key contributors to galactic chemical evolution.

Mass Loss Mechanisms

Stellar Winds and Their Driving Forces

Mass loss on the AGB is enormous compared to main-sequence winds. Rates range from ~$10^{-7}$ to $10^{-4} \, M_\odot \, \text{yr}^{-1}$, with the highest rates occurring during the final "superwind" phase. The wind-driving mechanism operates in a two-step process:

1. Pulsations and convection levitate material from the photosphere into the cool, extended upper atmosphere, where temperatures drop below ~1500 K.
2. Dust grains condense in this levitated gas (silicates in O-rich stars, carbonaceous grains in C-rich stars).
3. Radiation pressure on the dust transfers momentum to the grains, which drag the surrounding gas outward via collisions, accelerating a slow but dense wind.

Typical AGB wind velocities are 5–30 km/s, far slower than the fast winds of hot stars but carrying vastly more mass per unit time. During the final superwind phase, mass-loss rates spike to $\sim 10^{-4} \, M_\odot \, \text{yr}^{-1}$, stripping the envelope on a timescale of $\sim 10^4$ years and exposing the hot core. This marks the transition to the planetary nebula phase.

Mira Variables and Pulsation-driven Mass Loss

Mira variables are the most prominent class of long-period variable (LPV) AGB stars. Their properties:

• Pulsation periods: 100–1000 days, driven by the κ-mechanism operating in the hydrogen and helium ionization zones
• Visual amplitude: up to ~8 magnitudes (though bolometric variations are much smaller, typically ~1 mag, because the flux shifts between optical and infrared as the temperature changes)
• Pulsation mode: fundamental mode for classical Miras; overtone pulsators tend to have smaller amplitudes (semiregulars)

Pulsations enhance mass loss by generating shock waves that propagate outward through the atmosphere, compressing and heating gas in discrete shells. This periodic compression creates favorable conditions for dust nucleation. The prototype is Mira (ο Ceti), with a period of ~332 days. R Leonis is another well-studied example.

Many Mira variables exhibit OH, $\text{H}_2\text{O}$, and SiO maser emission from their circumstellar envelopes. These masers trace different radial zones in the outflow and provide direct measurements of wind kinematics and mass-loss geometry.

Consequences of Mass Loss on Stellar Evolution

Mass loss is the single most important factor determining the final fate of an AGB star. Its consequences include:

• Final fate: Mass loss controls whether the core remains below the Chandrasekhar limit (~1.4 $M_\odot$), producing a white dwarf, or whether the star retains enough mass for further nuclear burning stages. The initial-final mass relation (IFMR) maps a star's birth mass to its white dwarf remnant mass, and this relation is governed almost entirely by how much envelope mass is lost on the AGB.
• Circumstellar structures: The mass-loss history is recorded in circumstellar shells and detached envelopes visible in CO emission and infrared imaging. Objects like AFGL 3068 show beautiful spiral patterns caused by binary orbital motion modulating the outflow geometry.
• ISM enrichment: AGB winds inject dust and heavy elements into the interstellar medium, contributing to the raw material for the next generation of stars and planets.
• Planetary nebula shaping: The interaction between the slow AGB wind and the fast wind from the newly exposed hot core sculpts the morphology of the resulting planetary nebula (the "interacting stellar winds" model of Kwok, Purton & Fitzgerald 1978).