Transcript Integrative Studies 410 Our Place in the Universe

Homework #10
• 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-BoltzmannLaw: L = b A T4, so use scaling arguments
to figure out L from R,T and R from L,T
Homework #10
• 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.
The Fundamental Problem in
studying the stellar lifecycle
• We study the subjects of our research for a
tiny fraction of its lifetime
• Sun’s life expectancy ~ 10 billion (1010)
years
• Careful study of the Sun ~ 370 years
• We have studied the Sun for only 1/27
millionth of its lifetime!
Suppose we study human beings…
• 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 and Experiment
• 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
Hydrostatic Equilibrium
• 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
Star Formation & Lifecycle
• 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
Example: Orion Nebula
• Orion Nebula is a place where stars are being born
Protostellar Evolution
• 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
Path in the Hertzsprung-Russell
Diagram
Gas cloud becomes smaller,
flatter, denser, hotter  Star
Protostellar Evolution
• 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
Path in the Hertzsprung-Russell
Diagram
Gas cloud becomes smaller,
flatter, denser, hotter  Star
A Newborn 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
Mass Matters
• 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
Mass and the Main Sequence
• 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
Stellar Lifetimes
• 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!
Main Sequence Lifetimes
Mass (in solar masses)
Lifetime
10 Suns
10 Million yrs
4 Suns
2 Billion yrs
1 Sun
10 Billion yrs
½ Sun
500 Billion yrs
Luminosity
10,000 Suns
100 Suns
1 Sun
0.01 Sun
Is the theory correct? Two Clues from
two Types of Star Clusters
 Open Cluster
Globular Cluster 
Star Clusters
• 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)
What do Open Clusters tell us?
•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
Why Do Stars Leave
the Main Sequence?
• Running out of fuel
Stage 8: Hydrogen Shell Burning
• 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
Stage 9: The Red Giant Stage
• Luminosity huge (~ 100
Suns)
• Surface Temperature lower
• Core Temperature higher
• Size ~ 70 Suns (orbit of
Mercury)
Lifecycle
• Lifecycle of a
main sequence G
star
• Most time is
spent on the
main-sequence
(normal star)
The Helium Flash and Stage 10
• 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
Stage 11
• 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
Deep Sky Objects: Globular Clusters
• 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
Type of Death depends on Mass
• 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
• 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
Duration: 100,000 years
Central Temperature: 300  106 K • A planetary nebula is formed
Surface Temperature: 100,000 K
Size: 0.1  Sun
Deep Sky Objects: Planetary Nebulae
• 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”
Stage 13: 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!
Stage 14: Black Dwarf
• Impossible to see in a telescope
• About the size of Earth
• Temperature very low
 almost no radiation
 black!