This week at Astro 233

• Melissa and I will read your papers, write comments and give them back to you.

• You’ll then have time to consult with Melissa and write your revisions.

• In class, we’ll be talking about the stellar evolution.

• For next Thursday’s class, read the short paper by Hans Bethe, “Energy Production in Stars”; it is linked on the A233 website.

The H-R diagram

• Stars on the Main Sequence (MS) are burning H to He in their cores.

• A star’s location on the MS is determined by its mass.

• Red supergiants and giants have the same surface temperature as low mass main sequence stars but are much bigger.

• Therefore, they are more luminous than Main Sequence stars of the same surface temperature

L ∝ R2 T4

The method of “spectroscopic parallax”1. Observe the star’s

apparent brightness.

2. Observe the star’s spectrum; determine its spectral class and luminosity class.

3. Place the star on the H-R diagram; estimate its luminosity.

4. Use luminosity and apparent brightness to get distance.

What is the Sun like?Corona: • seen at eclipse• Rarefied; very hot -

1.8 million degrees• Extends millions of km

Photosphere: • “Surface” we see• T ~ 5600 – 6000 °K• Region from which

photons escape

Core: • T ~ 15 million °K• Inner ¼ radius• Region where nuclear

fusion (“hydrogen burning”) takes place

Stellar birth• Stars are born out of clouds in the interstellar medium,

when the clouds collapse because of their own gravity.

• When a gas becomes denser, it heats up.

• When the core of the collapsing cloud fragment becomes hot enough, hydrogen burning ignites.

• The star then shines, burning hydrogen. It resides at the proper location, for its mass, on the Main Sequence of the H-R diagram… until it exhausts its fuel supply.

Stellar birth

• Stars are born when cold molecular clouds (mostly molecular hydrogen but also CO, methanol, formaldehyde etc) collapse under their own weight and fragment into pieces.

Star formation: cloud collapse

Collapse of an Interstellar Cloud

Evolution of a star like the SunI. Contraction of a fragment of an interstellar cloud

• Density and temperature in core rise.• Star has large radius, but cool temperature so it is bright

(high Lum) but very red (infrared).• Short-lived phase.• Collapses along axis of rotation; formation of disk possible.• When the core becomes hot enough, hydrogen burning

ignites.II. Stable existence on the Main Sequence

• Sustained, controlled hydrogen burning the core• Energy generation balanced by energy radiated• Long-lived phase

L ∝ R2 T4

but alsoL ∝ M4

The Main Sequence

• Stars on the “Main Sequence”are burning hydrogen into helium in their cores.

• The mass of a star determines its location on the Main Sequence of the H-R diagram

• Stars in other parts of the H-R diagram are not shining by other processes, not (just) hydrogen burning.

Thermonuclear fusion in the Sun

• The temperature in the Sun’s core reaches 15 million °K•This is hot enough for hydrogen nuclei to fuse together to form helium.

•At 15 million degrees, only hydrogen fusion takes place.

•The requirement that these reactions provide a stable “burning lifetime” greater than 3.5 billion years implies that the Sun must consist mostly of hydrogen.

•By their number, ~90% of the nuclei in the Sun are hydrogen (H), while ~9% are helium (He) and ~1% is everything else (C, N, O, Fe, Mg, Al, etc.)

Fusion of H into He

1H + 1H 2H + e+ + νe1H + 1H 2H + e+ + νe

2H + 1H 3He + photons2H + 1H 3He + photons

3He + 3He 4He + 2 1H

• 6 H nuclei are involved.• Neutrinos are also produced.• 4 H nuclei are converted into 1 He nucleus.• In other stars (of different mass), the sequence of

reactions is different, but the outcome is the same.

Proton-proton chain

Main Sequence phase

Hydrogen burning in core

photosphere

Star like the Sun: core temp: 15 million °K

II. Main Sequence (long-lived; stable)• Shines by controlled, stable hydrogen fusion

Controlled thermonuclear fusion• The Sun has been burning more or less constantly over the past

>4.5 billion years.• So the process of thermonuclear fusion in the Sun must be stable:

not too much; not too little.• Hydrostatic equilibrium: balance of potential energy and thermal

energy generated by fusion reactions.

core

Energy generation in core

Photons escape from surface, giving star’s luminosity

Stellar evolution: Life and Death• Stars along the Main Sequence are burning hydrogen to

helium in the cores.• Hydrogen burning is a stable process. • The location of a star on the M.S. is determined by its mass.

The length of time a star remains on the M.S. and what happens afterwards is strongly dependent on its mass.

• What happens when a star “burns” all its hydrogen?• Energy generation in the core declines• Hydrostatic equilibrium is broken; instability sets in.• Star moves off the Main Sequence• Details also depend on the mass of the star.

Let’s start out with the evolution of the Sun

Post-Main SequenceIII. After all the hydrogen in the core is converted into helium, heat

continues to leak out, and the core collapses because of gravity.• A gas that contracts heats up.• A shell around the core is heated until it gets hot enough so that

hydrogen burning is ignited in the shell.• This new source of heat injects energy into the outer star, which

then expands.• Because the star’s radius increases, its luminosity increases => Moves

off the M.S. to higher luminosity

IV. The core contracts until Helium nuclei cannot be packed any closer together => “degenerate core”• Helium “ash” from the hydrogen burning shell falls onto the core,

increasing its mass, density and temperature until… the temperature reaches ~100 million degrees K.

• Helium burning in the core ignites.• This happens suddenly: helium flash• Helium burning is not a stable process

• The star becomes a “red giant” as the new burst of energy causes its envelope to expand.

“Post Main Sequence”

Hydrogen burning in core

photosphere

Hydrogen burning shell

Star like the Sun

“Red Giant”

Helium burning in core

photosphere

Hydrogen burning shell

R ~ 50 RStar like the Sun: core temp: ~100 million °K

“Helium burning”

Star like the Sun in helium burning phase:core temp: ~100 million °K

Helium burning: “triple alpha process”

3 4He 12 C + photons

Three helium nuclei fuse to form a carbon nucleus.

“Horizonal Branch” PhaseV. Helium burning in the core => carbon nuclei form• Short lived phase• All helium in core is quickly burned to form C

• Some of the carbon that is formed combines with helium to make oxygen (0)

12C + 4He 16O• End up with a core containing C and O only.• Surrounding it is a shell of helium which ignites in a

“flash” => envelope expands• What happens next depends on the star’s mass!

“Horizontal Branch”

Helium burning in core

photosphere

Hydrogen burning shell

R ~ 5 RStar like the Sun: core temp: ~100 million °K

Inert helium shell

“Red Supergiant”

All helium in core converted to carbon

photosphere

Hydrogen burning shell

R ~ 5 RStar like the Sun: core temp: ~100 million °K

Inert helium shell

End up with carbon core…

Death Throes of a Star

Carbon-Oxygen in core does notburn

photosphere

Hydrogen burning shell

R ~ 500 R ~1 A.U.

Star like the Sun: core temp: ~100 million °K

Helium burning in shell

Planetary Nebula Phase

Carbon-oxygen core

Envelope blows offShell of outward moving

material

“Planetary Nebula” PhaseVI. In the case of a star like the Sun (or of lower mass), the

helium burning in the shell will ignite suddenly, increasing the energy in the star so fast and furiously that its outer envelope will expand outward and effectively blow off.

=> Planetary nebula

Planetary Nebulae

White dwarf• End state of the evolution of a low mass star

• When helium is all fused into carbon and oxygen, no more burning takes place.

• The C-0 core collapses under its own gravity.

• But eventually, the electrons in the core cannot be packed any more closely together (“electron generacy”).. The collapse is halted.

• Mass of a white dwarf ≤ 1.4 M Chandrasekar limit

• Radius of a white dwarf ~ 1 REarth ~ 0.01 R ~ 104 km

• Surface Temperature ~ 10,000 °K (white)

White dwarf• A white dwarf is a very strange object

• 1 teaspoon of white dwarf material weighs 5 tons• The star is “held up” against gravitational collapse by

“electron degeneracy pressure”, the property of electrons that does not allow them to be packed too closely together.

• Pauli exclusion principle• Chandrasekhar limit: if a white dwarf had a mass greater

than 1.4 M , electron degeneracy could not halt the collapse of the core and it would collapse further.

White dwarfs must have masses less than 1.4 M .

The Sun will eventually become a white dwarf.

Evolution of the Sun

Evolution of Low Mass Stars1. Proto-stellar Collapse (short-lived; unstable)

• Shines by gravitational energy2. Main Sequence (long-lived; stable)

• Shines by controlled, stable hydrogen fusion3. Post Main Sequence (short-lived; unstable)

• Succession of phases of fusion a. Red giant: hydrogen burning in shellb. Horizontal branch: He burning in corec. Red Supergiant: He burning in shell

4. Planetary Nebula (short-lived; unstable)• Star’s outer layers blow off• Star therefore loses some of its mass

5. White dwarf (final remnant)• Shines due to its heat; eventually fades