• Cosmic distance ladder III: Use formula and descriptions given in question text
• Q7: Luminosity, temperature and area of a star are related by the Stefan-Boltzmann-
Law: L = b A T 4 , so use scaling arguments to figure out L from R,T and R from L,T

• Q9: Estimate life expectancy from energy production rate and available fuel (mass)
– Example: Star with 4L and 3M uses 4 times more mass for energy production, but has 3 times more mass, so it life time is a factor
¾=0.75 compared to the sun: 7.5 billion years
• Q8: Given are m and M, so use the distance formula d(m,M) from Q5.

• We study the subjects of our research for a tiny fraction of its lifetime
• Sun’s life expectancy ~ 10 billion (10 10 ) years
• Careful study of the Sun ~ 370 years
• We have studied the Sun for only
1/27 millionth of its lifetime!

• Human life expectancy ~ 75 years
• 1/27 millionth of this is about 74 seconds
• What can we learn about people when allowed to observe them for no more than 74 seconds ?

• Theory:
– Need a theory for star formation
– Need a theory to understand the energy production in stars
 make prediction how bight stars are when and for how long in their lifetimes
• Experiment: observe how many stars are where when and for how long in the Hertzsprung-Russell diagram
•  Compare prediction and observation

• Two forces compete: gravity (inward) and energy pressure due to heat generated (outward)
• Stars neither shrink nor expand, they are in hydrostatic equilibrium, i.e. the forces are equally strong
Gravity
Heat Gravity

• Contraction of a cold interstellar cloud
•
Cloud contracts/warms, begins radiating; almost all radiated energy escapes
•
Cloud becomes dense
 opaque to radiation
 radiated energy trapped
 core heats up

• Orion Nebula is a place where stars are being born

• increasing temperature at core slows contraction
– Luminosity about 1000 times that of the sun
– Duration ~ 1 million years
– Temperature ~ 1 million K at core, 3,000 K at surface
• Still too cool for nuclear fusion!
– Size ~ orbit of Mercury

Gas cloud becomes smaller, flatter, denser, hotter

Star

• increasing temperature at core slows contraction
– Luminosity about 1000 times that of the sun
– Duration ~ 1 million years
– Temperature ~ 1 million K at core, 3,000 K at surface
• Still too cool for nuclear fusion!
– Size ~ orbit of Mercury

Gas cloud becomes smaller, flatter, denser, hotter

Star

•
Main-sequence star; pressure from nuclear fusion and gravity are in balance
– Duration ~
10 billion years (much longer than all other stages combined)
– Temperature ~ 15 million K at core, 6000
K at surface
– Size ~ Sun

• Larger masses
– higher surface temperatures
– higher luminosities
– take less time to form
– have shorter main sequence lifetimes
• Smaller masses
– lower surface temperatures
– lower luminosities
– take longer to form
– have longer main sequence lifetimes

• The position of a star in the main sequence is determined by its mass

All we need to know to predict luminosity and temperature!
• Both radius and luminosity increase with mass

• From the luminosity, we can determine the rate of energy release, and thus rate of fuel consumption
• Given the mass (amount of fuel to burn) we can obtain the lifetime
• Large hot blue stars: ~ 20 million years
• The Sun: 10 billion years
• Small cool red dwarfs: trillions of years

The hotter, the shorter the life!

Mass
(in solar masses)
Lifetime
Luminosity
10 Suns 10,000 Suns
10 Million yrs
4 Suns 100 Suns
2 Billion yrs
1 Sun 1 Sun
10 Billion yrs
½ Sun 0.01 Sun
500 Billion yrs

Is the theory correct? Two Clues from two Types of Star Clusters

Open Cluster
Globular Cluster


• Group of stars formed from fragments of the same collapsing cloud
• Same age and composition; only mass distinguishes them
• Two Types:
– Open clusters (young  birth of stars)
– Globular clusters (old  death of stars)

•Hypothesis:
Many stars are being born from a interstellar gas cloud at the same time
•Evidence:
We see
“associations” of stars of same age

Open Clusters

• Running out of fuel

• Cooler core  imbalance between pressure and gravity
 core shrinks
• hydrogen shell generates energy too fast
 outer layers heat up
 star expands
• Luminosity increases
• Duration ~ 100 million years
• Size ~ several Suns

• Luminosity huge (~ 100
Suns)
• Surface Temperature lower
• Core Temperature higher
• Size ~ 70 Suns (orbit of
Mercury)

• Lifecycle of a main sequence G star
• Most time is spent on the main-sequence
(normal star)

• The core becomes hot and dense enough to overcome the barrier to fusing helium into carbon
• Initial explosion followed by steady (but rapid) fusion of helium into carbon
• Lasts: 50 million years
• Temperature: 200 million
K (core) to 5000 K
(surface)
• Size ~ 10  the Sun

• Helium burning continues
• Carbon “ash” at the core forms, and the star becomes a Red Supergiant
•Duration: 10 thousand years
•Central Temperature: 250 million K
•Size > orbit of Mars

• Classic example: Great Hercules Cluster (M13)
• Spherical clusters
• may contain millions of stars
• Old stars
• Great tool to study stellar life cycle

Observing Stellar Evolution by studying Globular Cluster HR diagrams
• Plot stars in globular clusters in
Hertzsprung-Russell diagram
• Different clusters have different age
• Observe stellar evolution by looking at stars of same age but different mass
• Deduce age of cluster by noticing which stars have left main sequence already

Catching Stellar Evolution “ red-handed
”
Main-sequence turnoff

• Light stars like the Sun end up as
White Dwarfs
• Massive stars (more than 8 solar masses) end up as Neutron Stars
• Very massive stars (more than 25 solar masses) end up as Black Holes

Reason for Death depends on Mass
• Light stars blow out their outer layers to form a
Planetary Nebula
• The core of a massive star (more than 8 solar masses) collapses, triggering the explosion of a
Supernova
• Also the core of a very massive stars (more than
25 solar masses) collapses, triggering the explosion Supernova

Light Stars: Stage 12 - A Planetary
Nebula forms
• Inner carbon core becomes
“dead” – it is out of fuel
Duration: 100,000 years
Central Temperature: 300

10 6 K
• Some helium and carbon burning continues in outer shells
• The outer envelope of the star becomes cool and opaque
• solar radiation pushes it outward from the star
• A planetary nebula is formed
Surface Temperature: 100,000 K
Size: 0.1

Sun

• Classic Example: Ring nebula in Lyra (M57)
• Remains of a dead,
• exploded star
• We see gas expanding in a sphere
• In the middle is the dead star, a
“ White Dwarf”

• Core radiates only by stored heat, not by nuclear reactions
• core continues to cool and contract
• Size ~ Earth
• Density: a million times that of Earth – 1 cubic cm has 1000 kg of mass!

• Impossible to see in a telescope
• About the size of Earth
• Temperature very low
 almost no radiation
 black!