Transcript charts_set_8

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, Betelgeus
etc. GO
e
hotter than G9. Sun is a G2.
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
- Density: 106 g/cm3! (a cubic
cm of it would weigh a ton on
Earth).
-
-
- Composition: C, O.
- White dwarfs slowly cool to
oblivion. No fusion.
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.
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
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) ->
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.
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.
Examples:
1) Bending of light. If light travels in straight lines in free space, then
gravity causes light to follow curved paths.
Observed! In 1919 eclipse.
Gravitational lensing. The gravity of a foreground cluster of
galaxies distorts the images of background galaxies into arc shapes.
Saturn-mass
black hole
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
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
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 .