Astro 101
Fall 2013
Lecture 9
Stars (continued) – Stellar evolution
T. Howard
Spectral Classes
Strange lettering scheme is a historical
accident.
Spectral Class
Examples
O
B
A
F
G
K
M
Surface Temperature
30,000 K
20,000 K
10,000 K
7000 K
6000 K
4000 K
3000 K
Rigel
Vega,
Sirius
Sun
Further subdivision: BO - B9, GO - G9, etc. GO hotter thanBetelgeus
G9. Sun is a
G2.
e
The Hertzsprung-Russell (H-R) Diagram
Red Supergiants
Red Giants
Increasing
Mass, Radius
on Main
Sequence
Sun
Main Sequence
White Dwarfs
A star’s position in the H-R diagram depends on its mass and
evolutionary state.
H-R Diagram of Nearby Stars
Note lines of constant radius!
H-R Diagram of Well-known Stars
Stellar Evolution:
Evolution off the Main Sequence
Main Sequence Lifetimes
Most massive (O and B stars):
millions of years
Stars like the Sun (G stars):
billions of years
Low mass stars (K and M stars): a trillion years!
While on Main Sequence, stellar core has H -> He fusion, by p-p
chain in stars like Sun or less massive. In more massive stars,
“CNO cycle” becomes more important.
Evolution of a Low-Mass Star
(< 8 Msun , focus on 1 Msun case)
- All H converted to He in core.
- Core too cool for He burning. Contracts.
Heats up.
- H burns in hot, dense shell around core:
"H-shell burning phase".
- Tremendous energy produced. Star must
expand.
- Star now a "Red Giant". Diameter ~ 1 AU!
- Phase lasts ~ 109 years for 1 MSun star.
- Example: Arcturus
Red Giant
Red Giant Star on H-R Diagram
Eventually: Core Helium Fusion
- Core shrinks and heats up to 108 K, helium can now burn into carbon.
"Triple-alpha process"
4He
+ 4He ->
8Be + 4He
->
8Be
+ energy
12C + energy
- Core very dense. Fusion first occurs in a runaway process: "the
helium flash". Energy from fusion goes into re-expanding and cooling
the core. Takes only a few seconds! This slows fusion, so star gets
dimmer again.
- Then stable He -> C burning. Still have H -> He shell burning
surrounding it.
- Now star on "Horizontal Branch" of H-R diagram. Lasts ~108 years
for 1 MSun star.
More massive
Horizontal branch star structure
Core fusion
He -> C
Shell fusion
H -> He
less massive
Helium Runs out in Core
- All He -> C. Not hot
enough
-for C fusion.
-
- Core shrinks and heats up, as
-does H-burning shell.
-
- Get new helium burning
shell (inside H burning shell).
- High rate of burning, star
expands, luminosity way up.
- Called ''Red Supergiant'' (or
Asymptotic Giant Branch) phase.
- Only ~106 years for 1 MSun star.
Red Supergiant
"Planetary Nebulae"
- Core continues to contract. Never hot
enough for C fusion.
- He shell dense, fusion becomes unstable
=> “He shell flashes”.
- Whole star pulsates more and more violently.
- Eventually, shells thrown off star altogether! 0.1 - 0.2 MSun
ejected.
- Shells appear as a nebula around star, called “Planetary Nebula”
(awful, historical name, nothing to do with planets).
White Dwarfs
- Dead core of low-mass star
after Planetary Nebula thrown
off.
- Mass: few tenths of a MSun
- Radius: about REarth
6
3
-- Density: 10 g/cm ! (a cubic
cm of it would weigh a ton on
Earth).
- Composition: C, O.
-
- White dwarfs slowly cool to
oblivion. No fusion.
Star Clusters
Open Cluster
Globular Cluster
Comparing with theory, can easily determine cluster age
from H-R diagram.
Luminosity
Following the evolution of a cluster on the H-R diagram
LSun
LSun
Temperature
100 LSun
LSun
LSun
LSun
Globular Cluster M80 and composite H-R diagram for similar-age clusters.
Globular clusters formed 12-14 billion years ago. Useful info for
studying the history of the Milky Way Galaxy.
Schematic Picture of Cluster Evolution
Massive, hot, bright,
blue, short-lived stars
Time 0. Cluster
looks blue
Low-mass, cool, red,
dim, long-lived stars
Time: few million years.
Cluster redder
Time: 10 billion years.
Cluster looks red
Evolution of Stars > 12 MSun
Low mass stars never got
past this structure:
Eventual state of > 12 MSun star
Higher mass stars fuse heavier
elements.
Result is "onion" structure with
many shells of fusion-produced
elements. Heaviest element
made is iron. Strong winds.
They evolve more rapidly.
Example: 20 MSun star lives
"only" ~107 years.
Fusion Reactions and Stellar Mass
In stars like the Sun or less massive, H -> He
most efficient through proton-proton chain.
In higher mass stars, "CNO cycle" more
efficient. Same net result:
4 protons -> He nucleus
Carbon just a catalyst.
Need Tcenter > 16 million K for CNO cycle to
be more efficient.
Sun
(mass) ->
Endpoints of Massive Stars
• Stars with mass >~ 8 Msun  Supernovae
• Massive stellar explosions
• Remnant core collapses (usually much less than 50% mass)
• In most cases, core  neutron star
• Electrons and protons “crushed together” creating neutrons
• Many neutrinos emitted  these escape the star completely
• Neutron stars often end up forming pulsars
• What about even more massive stars?
• Mass >~ 25 Msun  collapse to a Black Hole
Supernovae – extremely violent stellar explosions
• Several types & subtypes (called type “I”, “Ia”, “II”, etc.)
• Different types arise from
pre-explosion stellar
conditions
• We can use the change
in brightness
over time to
distinguish them
Example supernova remnant—
Crab nebula in Taurus
Two major classifications of Supernovae
 Tycho’s
supernova
Supernova remnant in Vela 
Light Curves of Supernovae Types
Neutron Stars
If star has mass 12-25 MSun , remnant of supernova expected to be a
tightly packed ball of neutrons.
Diameter: 10 km only!
Mass: 1.4 - 3(?) MSun
Density: 1014 g / cm3 !
Rotation rate: few to many times
per second!!!
Magnetic field: 1010 x typical bar
A neutron star over the Sandias?
magnet!
Please read about observable neutron stars: pulsars.
Pulsars discovered 1967 by
Jocelyn Bell Burnell & Anthony
Hewish.
Pulsars – “Lighthouse” model
Crab nebula in X-rays (Chandra)
 “Blinking” of the Crab pulsar
Off
A brief digression -- Relativity
1905: Special Theory of Relativity
1915: General Theory of Relativity
Relativity stars with assigning “frames of reference” (coordinates) to
the Observer and the Event (or Thing) in question
z
z
y
x
y
x
Special Relativity  covers situations where velocities may be
very high, but frames of reference are not
accelerated
General Relativity  as it says, the more general case: acceleration
between frames of reference is included
A fundamental postulate of relativity:
The speed of light, c, in free (empty) space is a universal constant.
It does not get added to or subtracted from the frame of reference.
c =
(approx.) 3 x 108 meters/sec
Note: the speed of light can be slower in solid, gaseous, or liquid media
(glass, water, air), but never faster than c.
This effect actually accounts for the bending of light rays in lenses,
when entering or leaving a body of water, etc.
Black Holes and General Relativity
General Relativity: Einstein's (1915) description of
gravity (extension of Newton's). It begins with:
The Equivalence Principle
Here’s a series of thought experiments and arguments:
1) Imagine you are far from any source of gravity, in free space,
weightless. If you shine a light or throw a ball, it will move in a
straight line.
2. If you are in freefall, you are also
weightless. Einstein says these are
equivalent. So in freefall, light and ball
also travel in straight lines.
3. Now imagine two people in freefall on
Earth, passing a ball back and forth.
From their perspective, they pass it in a
straight line. From a stationary
perspective, it follows a curved path. So
will a flashlight beam, but curvature of
light path small because light is fast (but
not infinitely so).
The different perspectives are called
frames of reference.
4. Gravity and acceleration are equivalent. An apple falling in
Earth's gravity is the same as one falling in an elevator
accelerating upwards, in free space.
5. All effects you would observe by being in an accelerated frame
of reference you would also observe when under the influence of
gravity.
Some Consequences of General Relativity:
1. Mass “warps” space  i.e., the amount of mass introduces
a “curvature” to what would otherwise be perfectly linear
(Euclidean) space.
2. This curvature of space is a different way of thinking about
gravity. It works, and explains a lot of things.
3. The curvature of space causes things to move in curved lines.
 Even rays of light!
“Matter tells space how to curve. Space tells matter how to move.”
(Misner, Thorne, and Wheeler, 1973)
The “rubber sheet” analogy.
Curvature of light Observed! In 1919 eclipse.
Einstein
Sir Arthur Eddington
Gravitational lensing. The gravity of a foreground cluster of
galaxies distorts the images of background galaxies into arc shapes.
Other consequences of General Relativity:
Gravitational Waves – caused by massive violent events
(e.g., coalescence of binary pulsars, formation of Bl. Holes)
– cause asymmetric warping of space
The “ripples” move at speed c thru the universe.
Might be detectable (but very weak).
We are searching for them now.
USA:
LIGO Project
Elsewhere:
Virgo, GEO, others
Proposed Space-based GW Observatory: LISA
LIGO Facility at Hanford, WA (2nd facility is at Livingston, LA)
Proposed LISA mission (NASA-ESA)
This is just a schematic diagram. The spacecraft will be
~ 5 million km apart.
Other consequences of General Relativity
2. Gravitational Redshift
later, speed > 0
light received when
elevator receding at
some speed.
Consider accelerating elevator in
free space (no gravity).
Received light has longer wavelength
because of Doppler Shift ("redshift").
Gravity must have same effect!
Verified in Pound-Rebka experiment.
time zero, speed=0
light emitted when
elevator at rest.
3. Gravitational Time Dilation
Direct consequence of the redshift. Observers disagree on rate of
time passage, depending on strength of gravity they’re in.
Escape Velocity
Velocity needed to escape an object’s gravitational pull.
vesc =
2GM
R
Earth's surface: vesc = 11 km/sec.
If Earth shrunk to R=1 cm, then vesc = c, the speed of light!
Then nothing, including light, could escape Earth.
This special radius, for a particular object, is called the
Schwarzschild Radius, RS.
RS  M.
Black Holes
If core with about 3 MSun or more collapses, not even neutron
pressure can stop it (total mass of star about 25 MSun ?).
Core collapses to a point, a "singularity".
Gravity is so strong that not even light can escape.
RS for a 3 MSun object is 9 km.
Event horizon: imaginary sphere around object, with radius RS .
Event horizon
Anything crossing the event horizon,
including light, is trapped
RS
Saturn-mass
black hole
Black hole achieves this by severely curving space. According to General
Relativity, all masses curve space. Gravity and space curvature are
equivalent.
Like a rubber sheet, but in three dimensions, curvature dictates how all
objects, including light, move when close to a mass.
Curvature at event horizon is so great that space “folds in on itself”.
Effects around Black Holes
1) Enormous tidal forces.
2) Gravitational redshift. Example,
blue light emitted just outside event
horizon may appear red to distant
observer.
3) Time dilation. Clock just outside
event horizon appears to run slow to a
distant observer. At event horizon, clock
appears to stop.
Do Black Holes Really Exist? Good Candidate: Cygnus X-1
- Binary system: 30 MSun star with unseen companion.
- Binary orbit => companion > 7 MSun.
- X-rays => million degree gas falling into black hole.
Final States of a Star (simplified)
1. White Dwarf
If initial star mass < 8-12 Msun .
2. Neutron Star
If initial mass > 12 MSun and < 25 ? MSun .
3. Black Hole
If initial mass > 25 ? MSun .