Transcript Lecture 12, PPT version

Selected Questions from Minute Papers
Black Holes:
• Will all the material in the Milky Way eventually be sucked into the BH
at the center?
• Does the star that “gives up” mass to a BH eventually get pulled in to
the BH?
Star properties:
• If Betelgeuse is so much more luminous than the sun, why isn’t it
hotter than the sun?
• Is it more difficult to measure the distances that are farther away
(because the parallax is very small)?
Binary Stars:
• How do you know there are 2 stars (since you can’t see 2 stars)?
• Why are binary stars so very common?
• Can binary stars have planets around them?
Outline - March 2, 2010
•
Stellar properties recap
• “Spectral Type” for stars (pgs. 525-527)
• Hertzsprung-Russel Diagram (pgs. 530-533)
• How does the sun shine? (pgs. 495-497, 499-503)
• Lifetimes of stars: gas guzzlers vs. econoboxes (pgs. 533-534)
• Where are the oldest known stars? (pgs. 536-538)
Stellar Properties Recap
Luminosity (from L = 4 b d2)
factor of about 10 billion: 10-4 Lsun to 106 Lsun
Temperature (from T = 0.29 / max)
factor of about 10: 3,000 K to 30,000 K
Radius (from R = {L / 4 T4}1/2)
factor of about 50,000: 0.01 Rsun (white dwarf) to 500 Rsun (supergiant)
Mass (from “spectroscopic” binary stars)
factor of about 1,800: 0.08 Msun (smaller = can’t run nuclear fusion) to
150 Msun (larger = pressure overwhelms gravity)
Stellar Properties
Just because a star has a radius that is bigger than the sun doesn’t
necessarily mean that it is more massive than the sun!
Just because a star is more luminous than the sun doesn’t necessarily mean
that it is more massive than the sun!
Just because a star is hotter than the sun, doesn’t necessarily mean that it is
more massive than the sun!
It turns out that this is due to the fact that the radius, temperature and
luminosity of stars evolve over time…
Patterns to the Stars
Stellar Spectra
Depending upon the surface temperature of the star, you see different absorption lines.
The hottest stars show strong Helium lines, stars with T = 10,000 K show the strongest
Hydrogen lines, and the very coolest stars show strong lines due to molecules (like
titanium oxide).
This is really is a temperature effect, it is not reflective of different chemical
composition for the different stars!
Spectral Type
(Astronomers like to classify things / put them in bins)
The letters O, B, A, F, G, K,
M are called the “spectral
type” of the star and describe
the appearance of the
spectrum (i.e., strong helium
lines but weak hydrogen
lines, strong hydrogen lines
but no helium lines).
The spectral type classifications are historical and come from a time
when we didn’t know that the different spectra were due to different
stellar temperatures. The notation persists today, though!
Time-honored mnemonic: “Oh Be A Fine Girl/Guy, Kiss Me”
Hertzprung-Russel (H-R) Diagram for Stars
Take a huge random sample of stars
and plot up their luminosity (vertical)
and their surface temperature /
spectral type (horizontal, with T
increasing to the LEFT).
Remarkably, you don’t get a random
plot at all!
Roughly 90% of all stars fall on “the
Main Sequence”. These are stars that
produce energy by fusion of hydrogen
(E = mc2).
Any star that is not on the Main
Sequence is getting close to the end
of its life.
How do stars shine?
Sun as a typical example
Ideas that don’t work:
1. Flame (like coal or wood) - can’t
account for sun’s observed
luminosity and can’t produce
energy for very long
2. Gravitational contraction
(“shrinking sun”) - could only last
for 25 million years, plus violates
observations of the sun
Sun has been generating about 3.84x1026 W of power (more or less)
every day for about 4.5 billion years!!
Sun cannot be solid
slower
faster
slower
Rotation time is 30 days at the poles and 25 days at the equator (“differential rotation”)
Solar Properties
Radius = 696,000 km (about 109 times radius of Earth)
Mass = 2x1030 kg (about 300,000 times mass of Earth)
Luminosity = 3.8x1026 W
Composition (by mass) = 70% hydrogen, 28% helium, 2% heavier elements
Surface temperature = 5,800 K
Core temperature = 15x106 K
Core average density = 36 g / cm3 (about 3 times density of lead)
Core pressure = about 200 billion “atmospheres” (pressure at sea level is 1 atmosphere;
pressure deep in the ocean is hundreds of atmospheres)
All “Main Sequence” Stars are Stable
(not expanding or contracting by large amounts)
Pressure pushing out exactly
balancing gravity pulling in:
“gravitational equilibrium”
Energy generation takes place in
the core only for main sequence
stars (e.g., the sun)
In the sun, the core is about 25% of
the diameter and contains about
40% of the total mass.
Only in the core is it sufficiently
hot and dense for nuclear fusion
(“nuclear burning”) to occur!!
E = mc2
There is a tremendous amount of energy associated with mass!
For about the first 90% of a star’s lifetime, it lives on the Main
Sequence of the H-R diagram, “burning” hydrogen.
Properly, the star converts hydrogen into helium through nuclear
fusion (but astronomers are notoriously casual about the language).
In the core, it is too hot and too dense for “atoms” to exist. Instead,
you have “bare nuclei swimming in a sea of electrons”
Pause to reflect…
What are the nuclei of atoms made of?
What actually holds them together?
Gravity is MUCH too weak to overcome mutual repulsion of protons!!
The Strong Force
The “strong force” is truly the strongest force
in nature, but it is extremely short-range.
Strong force is only effective over lengths
comparable to the size of atomic nuclei
(10-15 m or so); actually limits how big nuclei
of atoms can be!
If you can get 2 protons within about 10-15 m
of each other, the strong force can “bind”
them together (“nuclear fusion”).
Key: high temperature (protons moving
FAST) and high density (many, many
protons all in the same place).
Proton-Proton Chain
(all stars with M < 8 Msun)
Net result: 4 protons are fused, producing 1 helium nucleus
So where does the energy come from????
The mass of 4 protons is greater than the mass of 1 helium nucleus.
The mass that is lost is converted into energy (in the form of light).
The sun (and all stars that are not white dwarfs or “neutron stars”) are
very slowly losing mass in order to power themselves.
Note: only a tiny amount of mass is actually lost. By the end of its
lifetime the sun will have lost about about 10% of its total mass to
energy generation.
In principle, how long could the sun last by “burning” hydrogen at its
present rate?
Mass of 4 protons = 6.690x10-27 kg
Mass of 1 helium nucleus = 6.643x10-27 kg
Mass lost (mlost) = 0.047x10-27 kg
Energy gained = mlost c2 = (0.047x10-27)(3.0x108)2 = 4.23x10-12 J
Energy produced by the sun every second = 3.8x1026 J
Sun must run this fusion reaction 8.9x1037 times every second or it would collapse
under gravity!!!!
In other words, the sun must fuse 6.0x1011 kg of hydrogen every single second.
That’s a lot of hydrogen, but the sun has a lot of mass…
In principle, how long could the sun last by “burning”
hydrogen at its present rate?
The sun must fuse 6.0x1011 kg of hydrogen every single second.
The sun’s mass is 1.99x1030 kg, and at a current age of 4.5x109 years, we know
that 70% of that mass is in hydrogen, or 1.39x1030 kg of hydrogen remains.
If the sun converted ALL of it remaining hydrogen into helium (at today’s
rate of “nuclear burning”), how much longer could the sun live?
Remaining lifetime in seconds = remaining H mass / rate of H fusion
Remaining lifetime in seconds = 1.39x1030 / 6.0x1011 = 2.32x1018 seconds
Remaining lifetime in years = 73.4 billion years!!
In principle, how long could the sun last by “burning” hydrogen at its
present rate?
So, if the sun could turn ALL of its hydrogen into helium at its present rate,
you would think the sun would live a total of (4.5 + 73.4) = 77.9 billion years.
But, sadly, the sun’s lifetime is limited to only about 10 billion years because
it can’t actually convert all of its hydrogen into helium.
HUGE structural changes will happen to the star long before it can “burn up”
all of its hydrogen.
What determines a star’s Main Sequence lifetime?
It’s all about MASS.
The more massive is a star, the hotter and denser is the star in its core.
The hotter and denser it is in a star’s core, the FASTER the conversion of
hydrogen to helium happens.
High-mass (> 8 Msun) stars are “gas guzzlers”
Low-mass (< 2 Msun) are “economy cars”
Main Sequence is a MASS Sequence
The highest mass stars live
only a few million years.
They have a lot of fuel and
they’re burning it really
fast.
The lowest mass stars live
for 100’s of billions of
years. They have very
little fuel, but they’re
burning it extremely
efficiently.
Estimating the Age of the Universe
(What are stars “good for”?)
It stands to reason that you are younger than your mother.
It therefore stands to reason that the objects within the universe
cannot be older that the universe itself.
The ages of the oldest stars puts a limit on the minimum age
of the universe!!
The Oldest Stars in the Milky Way
Globular Star Clusters
Spherical groupings of 10,000 to 1 million stars (about 158 known in our
Galaxy). All of the stars formed at roughly the same time. Globular
clusters have lots of RED stars, but no BLUE stars (because they
died long ago and were not “replenished”).
Globular Cluster H-R Diagram
Globular Cluster M55
Globular clusters have short, stubby main sequences that “turn off” to the
red giant region. The “turn off” point tells you the approximate age.
Oldest Stars in the Milky Way
Globular cluster M4 is one of the oldest known star clusters (about 13 billion
years old), and contains many white dwarfs (the dead cores of low-mass stars
that used up all their fuel).