Late evolution of low- and intermediate-mass stars

Ch. 11 of Notes by Onno Pols. HKT Chapter 2.

Day 16 - October, 21, 2025

Agenda:

• Reminders - Final Project Report Draft - Due: Nov. 11 (2m)
• Lecture (25m)
• ICA 14 - 3/4 Groups - Due: EoD, Tue. Oct 21. (25m)
• ICA 14 Report out (10m)

Recap -

The Horizontal Branch (HB)

• Described as the location in the HR diagram for stars that have just undergone helium flash and settled into stable burning and thermodynamic equilibrium.

  • For a fixed helium core ignition mass, the radius and effective temperature depends on the envelope mass.

• Stars with less envelope mass at the ZAHB can be substantially hotter than those with much more of their envelope remaining.

Recap -

The Horizontal Branch (HB)

• zero-age horizontal branch (think gray line) for a metallicity Z = 0.001 typical of globular clusters.
• models have the same core mass (0.489 ) but varying total (i.e. envelope) mass, which determines their position in the H-R diagram.

Recap -

• Recall that helium burning begins when the temparature in the core has reached K via the triple- reaction.

• Core helium burning proceeds in a stable fashion, causing a large focus of energy production near the center that leads to formation of a convective core that grows with time.

• We will explore the stages of core He-burning for these intermediate mass stars.

Recap -

Blue Loop: an evolved star changes from a cool star to a hotter one before cooling again.

• E - at the tip of the RGB, helium is ingnited in the core as stable.
  • luminosity decreases while the envelope is convective - the star moves along the Hayashi line.

The Asymptotic Giant Branch (AGB)

The AGB phase starts at the exhaustion of helium in the center.

We can identify 3 main phases of a star on the AGB:

• The early AGB phase - point H

Kippenhahn diagram for a 5 star during late evolutionary phases.

Q: Kippenhahn diagram??

Asymptotic Giant Branch (AGB) - The early AGB phase

This phase is characterized by a few key steps:

• After He-depletion, all the material below the H-shell contracts until burning proceeds in a He-shell surrounding the now CO core.
  • For a brief period of time, the star has two active burning shells.

We see this about at 106 Myr.

Asymptotic Giant Branch (AGB) - The early AGB phase

• expansion of the He-rich zone, the H-burning shell decreases and eventually extinguished.

  • the CO core contracts, the envelope expands.

• the main contribution to the stellar luminosity is primarily the He-burning shell. The ashes of He-shell burning build the mass of the CO core which becomes degenerate.

Asymptotic Giant Branch (AGB) - Second Dredge-Up (2DU)

• At a later time the envelope expands and cools and eventually penetrates to a depth of the previous now extinguished H-shell burning region.
  • This is the scenario for stars with initial mass (the boundary at which can be modified due to convective overshoot).

In our above example model above, the Second Dredge Up occurs at point K.

Asymptotic Giant Branch (AGB) - Second Dredge-Up (2DU)

Second Dredge Up: Primarily due to the expansion of the envelope, which leads to cooling and increase of the opacity, as well as the increasing energy production from the He-burning shell.

• For lower mass stars (), the H-shell is not extinguished and thus prevents the convective envelope from penetrating deeper into the star. The 2DU therfore does not occur for these models.

• The 2DU is similar to the 1DU but a larger effect. The primary material brought to the surface is helium and (CNO cycle).
  • In this example this is about 0.2 of material.

Asymptotic Giant Branch (AGB) - Thermally Pulsing - AGB phase (TP-AGB)

As the He-burning shell moves outward in mass its luminosity decreases as it runs out of fuel. As a result of this, the layers again contract and the H-burning shell is reignited leading again to a double shell burning scenario.

Schematic structure of an AGB star during its thermally pulsing phase.

Asymptotic Giant Branch (AGB) - Thermally Pulsing - AGB phase (TP-AGB)

double shell burning scenario: the He-shell burns in an unstable configuration and leads to thermal pulses.

Consequences of the TP-AGB Phase:

• The pulses are followed by mixing events leading to the production of unique nucleosynthesis events and making the envelope and atmosphere more carbon-rich.

Asymptotic Giant Branch (AGB) - Thermally Pulsing - AGB phase (TP-AGB)

Consequences of the TP-AGB Phase:

• Similar to the RGB luminosity relying on the core mass, the stellar properties on the AGB mainly depend on the size of the degenerate CO core:

Asymptotic Giant Branch (AGB) - Thermally Pulsing - AGB phase (TP-AGB)

Consequences of the TP-AGB Phase:

• Strong mass loss ( to ) driven by dynamical pulsations and increased radiation pressure on dust particles in the cool atmosphere.
  • This process gradually removes the envelope and replenishes the ISM.

Brief aside about "thin" shells

In Sec 7.5.2, secular stability - the stability of thermal equilibrium is discussed and in particular for a thin burning shell:

• We can define a burning shell of mass , in a star of radius . The shell is located at a fixed inner boundary and outer boundary with thickness .

• Now, consider a perturbation that causes an excess of energy generation to heat flowing out leading to an expansion of the shell to larger radius.

Brief aside about "thin" shells

• Now, we can say that the shell is stable if this expansion leads to a sufficient pressure drop leading to a temperature drop. That is, the shell is stable if:

• For an ideal gas , suggesting that a shell thinner than will be unstable even for an ideal gas.
  • That is, the increase in energy from a perturbation does not lead to an expansion to a pressure decrease to a temperature decrease to maintain TE, and runaway can occur.

Asymptotic Giant Branch (AGB) - TP-AGB and Dredge-Up

Let's look closer at the thermal pulse and mixing events:

• When the H-shell is reignited and the He-burning shell beneath it is geometrically thin and unstable for the reasons discussed above and leads to thermal pulses of the He-shell.

Asymptotic Giant Branch (AGB) - TP-AGB and Dredge-Up

Schematic evolution of an AGB star through two thermal-pulse cycles.

• Note the time axis is highly non-linear: the He shell-flash and dredge-up phases (lasting 100 years) are expanded relative to the interpulse phase (10 − 10 years). Mass range depicted is .

Asymptotic Giant Branch (AGB) - TP-AGB and Dredge-Up

We can discuss a few key epochs over the course of these events:

• H-shell burning adds mass (He) to the intershell region
• Once a critical intershell mass is reached, helium is ignited in an unstable fashion leading to thermonuclear runaway called a Helium Shell Flash.

Asymptotic Giant Branch (AGB) - TP-AGB and Dredge-Up

• Values of occur due to the flash over about 1 year and drive an intershell convective zone (ICZ) leading to dredge up event that mixes synthesized material upward.

• The energy from the flash mostly goes into the expansion of the intershell region, allowing the He-shell to expand and cool.

  • The flash fizzle out and dies, the H-shell is extinguished and a phase of stable He-shell burning further grows the CO core.

Asymptotic Giant Branch (AGB) - TP-AGB and Dredge-Up

• Expansion and cooling can allow for a third dredge up (3DU) event to further bring ashes of the flash to the surface. 3DU is a term used for dredge up following thermal pulses even for stars without a 2DU event.

• Following 3DU, the He-shell is extinguished, the H-shell is reignited and the process repeats until the critical He mass is again reached.

  • The "interpulse period" depends of the core mass and can last from 50,000 years to less than 1000 years.

Asymptotic Giant Branch (AGB) - TP-AGB and Dredge-Up

• the pulse cycle can repeat many times
• the pulse amplitude (the maximum ) increases with each pulse
• 3DU might not occur until after several pulses
• 3DU is unique that it not only brings up H-burning products but also He-burning products to the surface

Asymptotic Giant Branch (AGB) - TP-AGB and Dredge-Up

We can also define the efficiency for a dredge up event as:

efficient dredge up, can limit the maximum growth of the CO core and thus the WD mass.

Nucleosynthesis and abundance changes on the AGB

Production of heavy elements: the s-process

• Spectroscopic observations show that many AGB stars are enriched in elements, such as Zr, Y, Sr, Tc, Ba, La and Pb.

These elements can be formed in AGB stars via the slow neutron-capture process (s-procss). This process requires free neutrons.

• It is thought that the necessary free neutrons are formed in the intershell region via He-burning reactions or during the He-shell flash itself if the temperature is sufficiently high in more massive AGB stars.

Nucleosynthesis and abundance changes on the AGB

Production of heavy elements: the s-process

• Spectroscopic observations show that many AGB stars are enriched in elements, such as Zr, Y, Sr, Tc, Ba, La and Pb.

• In less massive AGB stars, a C pocket can form between the intershell region and H-shell to provide the seed nuclei for the thus providing the seed free nuetrons.

  • The free are later mixed into the surrounding intershell region after the next pulse. The carbon and -process products are then brought to the surface during the next 3DU event.

Hot bottom burning (HBB)

Stars with , the temperature at the base of the convective shell during the interpulse phase can lead to H-burning on material in the convective envelope, known as Hot Bottom Burning.

The two outcomes of this burning are:

• increase in the luminosity away from the relation earlier.
• transforming the dredged up C into N, preventing the stars from becoming carbon stars.

Mass loss and termination of the AGB phase

• Stars on the TP-AGB phase can experience many pulses, limited by the decreasing mass of the H-envelope and the mass of the core.
  • the duration of this phase ( years) is primarily determined by the mass loss rate.

AGB mass loss: The mechanisms driving such strong mass loss are not yet completely understood, but a combination of dynamical pulsations and radiation pressure on dust particles formed in the atmosphere probably plays an essential role.

Mass loss and termination of the AGB phase

Mass loss of AGB stars. The observed correlation between the pulsation period of Mira variables and mass-loss rate (in /yr). Credit: Vassiliadis & Wood 1993, ApJ 413, 641.

• As the star evolves towards larger radii, the pulsation period increases and so does the mass-loss rate.

• Observationally, the mass loss rate reaches a maximum value of about /yr, this phase is called the superwind phase.

Mass loss and termination of the AGB phase

Mass loss of AGB stars.

• At this phase, the H-envelope is rapidly removed marking the end of the AGB phase.

• Once a majority of the H-envelope is removed, down to to remaining, the envelope shrinks and the star leaves the AGB.

Post-AGB Evolution

We can identify a few next epochs:

• The decrease in radius occurs at nearly constant via the H-burning shell and follows the core-mass relationship.

• increase in effective temperautre is driven by the decrease of the envelope mass (yrs)

  • via weak mass loss at the surface
  • and at the bottom by the H-shell burning

Post-AGB evolution

• At K:
  • the star develops a weak, fast wind driven by radiation pressure from UV absorption lines
  • the strong UV radiation
    • destroys the dust in the cirumstellar envelope,
    • dissacociates the molecules and
    • fully ionizes the gas

Post-AGB evolution

the circumstellar envelope becomes and HII (singly-ionized H) region radiating in recombination lines (formed ion and an electron combine) as a Planetary Nebula.

• Once the H-envelope has decreased to 10 (usually at about K), the H-burning shell is finally extinguished and the star cools as a white dwarf.

In-Class Assignment 14

In class: Work on ICA here with groups per usual. Discuss conceptual questions together and prepare answers to share at the end of class.

• Choose someone that will report out the groups responses ahead of time!

After Class: Due: End of Day to D2L

Note: ICAs will be shorter with the goal of: reducing focus on coding, increasing time for discussion and interpretation of results / plots in groups and as a class.