Stellar EvolutionChapter 12

Stars form from the interstellar medium and reach stability fusing hydrogen in their cores. This chapter is about the long, stable middle age of stars on the main sequence and their old age as they swell to become giant stars. Here you will answer three essential questions:

• What happens as a star uses up its hydrogen?

• What happens when a star exhausts its hydrogen?

• What evidence do astronomers have that stars really do evolve?

Guidepost

Stars evolve over billions of years because of changes deep inside. That raises an interesting question about how scientists can understand such processes:

• How can astronomers study the inside of stars?

This chapter is about how stars live. The next two chapters are about how stars die and the strange objects they leave behind.

Guidepost (continued)

I. Main-Sequence StarsA. Stellar ModelsB. Why is there a Main Sequence?C. The Upper End of the Main SequenceD. The Lower End of the Main SequenceE. The Life of a Main-Sequence StarF. The Life Expectancies of Stars

II. Post-Main-Sequence EvolutionA. Expansion into a GiantB. Degenerate Matter (簡併物質 )C. Helium FusionD. Fusing Elements Heavier than Helium

Outline

III. Evidence of Evolution: Star ClustersA. Observing Star ClustersB. The Evolution of Star Clusters

IV. Evidence of Evolution: Variable StarsA. Cepheid and RR Lyrae Variable StarsB. Pulsating StarsC. Period Changes in Variable Stars

Outline (continued)

The structure and evolution of a star is determined by the laws of

Stellar Models

• Hydrostatic equilibrium

• Energy transport

• Conservation of mass

• Conservation of energy

A star’s mass (and chemical composition) completely determines its properties.

That’s why stars initially all line up along the main sequence.

Maximum Masses of Main-Sequence Stars

a) More massive clouds fragment into smaller pieces during star formation.

b) Very massive stars lose mass in strong stellar winds

Example: Eta Carinae: Binary system of a 60 Msun and 70 Msun star Dramatic mass loss; major eruption in 1843 created double lobes

Mmax ~ 100 solar masses

Minimum Mass of Main-Sequence Stars

Mmin = 0.08 Msun

At masses below 0.08 Msun, stellar

progenitors do not get hot enough to

ignite thermonuclear fusion.

Brown Dwarfs

Brown DwarfsHard to find because they are very faint

and cool; emit mostly in the infrared.

Many have been detected in star forming regions like the Orion Nebula.

Evolution on the Main Sequence (1)

Zero-Age Main Sequence (ZAMS)

Main-Sequence stars live by

fusing H to He.

Finite supply of H => finite life time

Evolution on the Main Sequence (2)

Luminosity L ~ M3.5

A star’s life time T ~ energy reservoir / luminosity

T ~ M/L ~ 1/M2.5

Energy reservoir ~ M

Massive stars have short

lives!

Evolution off the Main Sequence: Expansion into a Red Giant

When the hydrogen in the core is completely converted into He:

H burning continues in a shell around the core.

He Core + H-burning shell produce more energy than needed for pressure support

Expansion and cooling of the outer layers of the

star Red Giant

“Hydrogen burning” (i.e. fusion of H into He) ceases in the core.

Expansion onto the Giant Branch

Expansion and surface cooling during the phase of an inactive He core and a H- burning shell

Sun will expand beyond Earth’s orbit!

Degenerate MatterMatter in the He core has

no energy source left.

Not enough thermal pressure to resist and

balance gravity

Matter assumes a new state, called

degenerate matter:

Pressure in degenerate core is due to the fact that

electrons can not be packed arbitrarily close together and have small

energies.

Red Giant Evolution

4 H → He

He

H-burning shell keeps dumping He

onto the core.

He-core gets denser and hotter until the

next stage of nuclear burning can begin in

the core:

He fusion through the

“Triple-Alpha Process”

4He + 4He 8Be + 8Be + 4He 12C +

Red Giant Evolution (5 solar-mass star)

Main Sequence

Expansion to red giant

Red giant

Helium ignition in the core

Development of Carbon-Oxygen

Core

Helium in the core exhausted;

development of He-burning shell

Fusion Into Heavier Elements

Fusion into heavier elements than C, O requires very high

temperatures; occurs only in very massive

stars (more than 8 solar masses).

The Life “Clock” of a Massive Star (> 8 Msun)

Let’s compress a massive star’s life into one day…

12 12

3

45

67

8

9

1011

12 12

3

45

67

8

9

1011

Life on the Main Sequence

+ Expansion to Red Giant: 22 h, 24 min.

H burning

H He

H He

He C, O

He burning:

(Red Giant Phase) 1 h, 35 min, 53 s

The Life “Clock” of a Massive Star (2)

H HeHe C, O

C Ne, Na, Mg, O

Ne O, Mg

H He He C, O

C Ne, Na, Mg, O12 1

23

4567

8

910

11

C burning:

6.99 s

Ne burning:

6 ms 23:59:59.996

The Life “Clock” of a Massive Star (3)

H HeHe C, O

C Ne, Na, Mg, ONe O, Mg

O burning:

3.97 ms 23:59:59.99997

O Si, S, P

H HeHe C, O

C Ne, Na, Mg, ONe O, Mg

Si burning:

0.03 ms

The final 0.03 msec!!

O Si, S, PSi Fe, Co, Ni

Summary of Post Main-Sequence Evolution of Stars

M > 8 Msun

M < 4 Msun

Evolution of 4 - 8 Msun stars is still uncertain.

Fusion stops at formation of C,O core.

Mass loss in stellar winds may reduce them all to < 4 Msun stars.

Red dwarfs: He burning never ignites

M < 0.4 Msun

Supernova

Fusion proceeds; formation of Fe core.

Evidence for Stellar Evolution: Star Clusters

Stars in a star cluster all have approximately the same age!

More massive stars evolve more quickly than less massive ones.

If you put all the stars of a star cluster on a HR diagram, the most massive stars

(upper left) will be missing!

HR Diagram of a Star Cluster

Example: HR diagram of the star cluster M3

Estimating the Age of a Cluster

The lower on the MS the turn-off point,

the older the

cluster.

Evidence for Stellar Evolution: Variable Stars

Some stars show intrinsic brightness variations not caused by eclipsing in binary systems.

Most important example:

Cephei

Light curve of Cephei

Cepheid Variables: The Period-Luminosity Relation

The variability period of a Cepheid variable is

correlated with its luminosity.

=> Measuring a Cepheid’s period, we

can determine its absolute magnitude!

The more luminous it is, the more slowly it

pulsates.

Cepheid Distance MeasurementsComparing absolute and apparent magnitudes of Cepheids,

we can measure their distances (using the 1/d2 law)!

The Cepheid distance measurements were the first distance determinations that worked out to distances beyond our Milky Way!

Cepheids are up to ~ 40,000 times more luminous than our sun

=> can be identified in other galaxies

Pulsating Variables: The Instability Strip

For specific combinations of radius and temperature, stars can maintain periodic oscillations.

Those combinations correspond to locations in the Instability Strip

Cepheids pulsate with radius changes of ~ 5 – 10 %.

Period Changes in Variable Stars

Periods of some Variables are not constant over time

because of stellar evolution. Another piece of evidence for stellar evolution