12 Stellar Evolution

1. Leaving the Main Sequence

Most of stars spend most of their lives on the MS
- Virtually all the low-mass stars that have ever formed still exist as stars
- Most of the high-mass stars that have ever existed perished long ago
On the MS
- fueling: star consumes Hydrogen and converts it to He ➤ core H burning
- equilibrium: GRAVITY ≣ PRESSURE
Balance changes when H is consumed
- Star leaves MS (ie. star starts to die)
- Mass of the star describes the end:
  - Low-mass stars die gently
  - High-mass stars ( > 8 M☉ ) die catastrophically

2. Evolution of a Sun-like Star

Solar Composition Change

Hydrogen (yellow) and helium (orange) abundances are shown

(a) at birth, just as the star arrives on the zero-age main sequence;
(b) after 5 billion years; and
(c) after 10 billion years.

At stage (b) only a few percent of the star’s total mass has been converted from hydrogen into helium. This change speeds up as the nuclear burning rate increases with time.

Hydrogen- Shell Burning

As a star’s core converts more and more of its hydrogen into helium, the hydrogen in the shell surrounding the non-burning helium “ash” burns ever more violently.

GRAVITY > PRESSURE

By the time shown in below figure,

the core has shrunk to a few tens of thousands of kilometers in diameter,
whereas the star’s photosphere is ten times the star’s original size.
Therefore star gets brighter too.

Stage8: The Sub-giant Branch

T decreases, L increases slightly
Tsurface decreases
- interior is opaque to radiation
- convection takes over
- constant Tsurface is maintained

Stage 9: The Red-giant Branch

MS to Red-giant: 100 x 106 years
As its helium core shrinks and its outer envelope expands, the star leaves the main sequence.
The star is well on its way to becoming a red giant.
The star continues to brighten and grow as it ascends the red-giant branch to stage 9.

Stage 10: Helium Fusion

He begins to burn in the core (Tcore ~ 108 K)
He ➤ C: through a three-alpha process (involves 3 × 4He atom)

Helium Flash

When He begins to burn, physics has to be changed from "classical" to "quantum":

electron degeneracy: two electrons cannot be in the same quantum state,
so the core cannot contract beyond a certain point.
This pressure is almost independent of temperature.
- T increases ➤ no increase in P ➤ no Expansion ➤ therefore no decrease in T : Therefore "no equilibrium".
- Instead, P remains almost the same as the nuclear reaction rate increases: T increases rapidly in a runaway condition: Helium Flash

Horizontal Branch

A large increase in luminosity occurs as a star ascends the red-giant branch, ending in the helium flash. The star then settles down into another equilibrium state at stage 10, on the horizontal branch.

Due to He burning
- Core is heated
- Equilibrium reached
- Thermal pressure takes over
- At core: He ➤ C @ T > 108 K
Due to He Flash
- Star terminates red-giant branch
- L doesn't increase;
- expands and cools the core ➤ energy is reduced
- Tsurface increases

Stage 11: Asymptotic Giant Branch

At core: He ➤ C
- the core becomes hotter and hotter, and
- the helium burns faster and faster.
The star is now similar to its condition just as it left the MS,
- except now there are two shells
The star has become a red-giant for the 2nd time.
Lack of nuclear fusion at the center causes the core to contract and the overlying layers to expand.
C core:
- too dense; cannot be compressed further (mass above is not enough)
- electrons are degenerate; core contraction stops

3. Death of a Low-Mass Star

This graphic shows the entire evolution of a Sun-like star. Such stars never become hot enough for fusion past carbon to take place.

Stage 12: Planetary Nebulae

Star has a C core ➤ No energy generation
At outer core ➤ burns H, He in a shell ➤ envelope increases
Burning is unstable
- He-burning in shell is explosive: He-shell flashes
- Fluctuations in intensity of radiation
- Pulsations
Surface layers are unstable too.
- Temperature decreases ➤ electrons can recombine w/ nuclei
- This produces more photons and they push outer layers further
In a few million years envelope is ejected (Veject ~ 10 km/s)

The end result

The star has two distinct parts
- Center:
  - core, mostly C ash, small, still He ➤ C fusion goes on
- Envelope:
  - cooler, low-density matter, ejected, size ~ solar system
Planetary Nebulae
- represent the end of stellar evolution
- not related to planets (early astronomers viewing the fuzzy envelope thought it resembled a planetary system).

(a) Abell 39, some 2100 pc away, a spherical shell of gas about 1.5 pc across.

(b) The brightened appearance around the edge of Abell 39 is caused by the thinness of the shell of glowing gas around the central core. Very little gas exists along the line of sight between the observer and the central star (path A), so that part of the shell is invisible. Near the edge of the shell, however, more gas exists along the line of sight (paths B and C), so the observer sees a glowing ring.

a) The Eskimo Nebula clearly shows several “bubbles” (or shells) of material being blown into space (distance ~1500 pc).

(b) The Cat’s Eye Nebula possibly produced by a pair of binary stars (unresolved at center) that have both shed envelopes (about 1000 pc away and 0.1 pc across).

(c) M2-9 shows surprising twin lobes (or jets) of glowing gas emanating from a central, dying star and racing out at speeds of about 300 km/s (some 600 pc away and 0.5 pc end-to-end).

Stage 13: White Dwarfs

The nebula has gone
The remaining core is visible now
- extremely dense
- extremely hot
- but quite small (~ size of Earth).
It is luminous only due to its high temperature.

As the white dwarf cools,
- its size does not change significantly;
- it simply gets dimmer and dimmer,
- and finally ceases to glow becoming black dwarfs

4. Evolution of Stars More Massive than the Sun

Evolutionary tracks for stars massive then the Sun differ very much from the Sun's evolutionary track.
The Sun-like stars ascend the giant branch almost vertically
- whereas higher-mass stars move roughly horizontally across the H–R diagram from the main sequence into the red-giant region.
The most massive stars experience smooth transitions into each new burning stage.
No helium flash occurs for stars more massive than about 2.5 solar masses.
In the figure, some points are labeled with the element that has just started to fuse in the inner core.
Eventually massive stars dies in a violent explosion called a supernova

5. Stellar Evolution in Star Clusters

Star Clusters are test sites for theory of evolution:
- stars are created at the same time
- stars are created from the same interstellar cloud
- stars are created from the same composition
- but stars will have different masses

(a) Initially, stars on the upper main sequence (MS) are already burning steadily while the lower MS is still forming.

(b) At 107 years, O-type stars have already left the MS (as indicated by the arrows), and a few red giants (RGs) are visible.

(c) By 108 years, stars of spectral type B have evolved off the MS. More RGs are visible, and the lower MS is almost fully formed.

(d) At 109 years, the MS is cut off at about spectral type A. The subgiant and RG branches are just becoming evident, and the formation of the MS is complete. A few white dwarfs may be present.

(e) At 1010 years, only stars less massive than the Sun still remain on the MS. The cluster’s subgiant, red-giant, horizontal, and asymptotic-giant branches are all visible. Many white dwarfs have now formed.

Young Cluster H–R Diagram

(a) The Hyades cluster is found 46 pc away.

(b) The H–R diagram for this cluster is cut off at about spectral type A, implying an age of about 600 million years. A few massive stars have already become white dwarfs.

Old Cluster H–R Diagram

(a) The southern globular cluster 47 Tucanae.

(b) Fitting its main-sequence turnoff and its giant and horizontal branches to theoretical models gives 47 Tucanae an age of between 12 and 14 billion years, making it one of the oldest-known objects in the Milky Way Galaxy.

The inset shows many blue stragglers (massive stars lying on the MS above the turnoff point, resulting perhaps from the merging of binary-star systems). The thickness of the lower main sequence is due almost entirely to observational limitations.

6. Evolution of Binary-Star Systems

Most stars are members of binary systems
Single star: evolves as usual (theory is known)
Multiple stars:
- stars widely separated:
  - their evolution proceeds much as it would have if they were not companions.
- stars are closer:
  - it is possible for material to transfer from one star to another, leading to unusual evolutionary paths.

Stellar Roche Lobes

Each star in a binary system is surrounded by a “zone of influence,” or Roche lobe, inside of which matter may be thought of as being “part” of that star.
The two Roche lobes meet at the Lagrangian point between the two stars.
Outside the Roche lobes, matter may flow onto either star with relative ease.

(a) In a detached binary, each star lies within its respective Roche lobe.

(b) In a semidetached binary, one of the stars fills its Roche lobe and transfers matter onto the other star, which still lies within its own Roche lobe.

(c) In a contact, or common-envelope, binary, both stars have overflowed their Roche lobes, and a single star with two distinct nuclear-burning cores results.

The evolution of the binary star Algol.

(a) Initially, Algol was probably a detached binary made up of two MS stars: a relatively massive blue giant and a less massive companion similar to the Sun.

(b) As the more massive component (star 1) left the MS, it expanded to fill, and eventually overflow, its Roche lobe, transferring large amounts of matter onto its smaller companion (star 2).

(c) Today, star 2 is the more massive of the two, but it is on the MS. Star 1 is still in the subgiant phase and fills its Roche lobe, causing a steady stream of matter to pour onto its companion.

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