Test 3 Review
Test 3 Review
Review for Test #3 Nov 17
• The Sun
• The Interstellar medium
• Stellar Evolution and Stellar Death
• Neutron stars and pulsars
• Conceptual Review and Practice Problems Chapters 9 - 13
• Review lectures (on-line) and know answers to clicker questions
• Try practice quizzes on-line
• Review (time Sunday, Nov 15 starting at 3pm) mainly Q&A format
• Two Number 2 pencils
• Simple calculator (no electronic notes)
• UNM Student ID
Reminder: There are NO make-up tests for this class
Test #3 Review
How to take a multiple choice test
1) Before the Test:
• Study hard (~2 hours/day Friday through Monday)
• Get plenty of rest the night before
• Bring at least 2 pencils, UNM student ID, and a calculator
2) During the Test:
• Write out and bubble your last name, space, first name and Exam
color in the name space of the scantron form. Write out and
bubble your Banner ID in the ID space.
• Draw simple sketches to help visualize problems
• Solve numerical problems in the margin
• Come up with your answer first, then look for it in the choices
• If you can’t find the answer, try process of elimination
• If you don’t know the answer, Go on to the next problem and
come back to this one later
• TAKE YOUR TIME, don’t hurry
• If you don’t understand something, ask me.
Test #3 Useful Equations
parallactic distance d = 1/p where p is parallax in arcsec and
d is in parsecs
Lifetimes of stars (on the main sequence):
L = 1010/M2 years where M is the Mass in solar masses
and L is the Lifetime
Equivalence of Matter and Energy:
E = mc2
The Sun is a star: a shining ball of gas
powered by nuclear fusion.
Mass of Sun = 2 x 1033 g = 330,000 MEarth
= 1 MSun
Radius of Sun = 7 x 105 km = 109 REarth
= 1 RSun
Luminosity of Sun = 4 x 1033 erg/s = 1 LSun
(amount of energy put out each second in
form of radiation, = 1025 40W light bulbs)
The Sun in X-rays over several years
Temperature at surface = 5800 K => yellow (Wien’s Law)
Temperature at center = 15,000,000 K
Average density = 1.4 g/cm3
Density at center = 160 g/cm3
Composition: 74% of mass is H
1% the rest
Rotation period = 27 days at equator
31 days at poles
The Interior Structure of the Sun
(not to scale)
Let's focus on the core, where the Sun's energy is generated.
Core of the Sun
Temperature : 15 million
K (1.5 x 107 K)
Density: 160 gm/cm3, 160
times that of water, 10
times the density of lead
What Powers the Sun
Nuclear Fusion: An event where nuclei of two atoms join together.
Need high temperatures.
Energy is produced. Elements can be made.
nuc. 1 + nuc. 2 →
nuc. 3 + energy (radiation)
Mass of nuc. 3 is slightly less than mass of (nuc. 1 + nuc. 2). The
lost mass is converted to energy. Why? Einstein's conservation of
mass and energy, E = mc2. Sum of mass and energy always conserved
in reactions. Fusion reactions power stars.
Chain of nuclear reactions called "proton-proton chain" or p-p chain
occurs in Sun's core, and powers the Sun.
In the Sun's Core...
neutrino (weird particle)
deuteron (proton + neutron
positron (identical to electron
but positively charged)
proton + proton →
proton+neutron + neutrino + positron
2) deuteron + proton
He nucleus, only 1 neutron
+ 2 neutrinos + energy
proton + proton + energy
Mass of end products is less than mass of 4 protons by
0.7%. Mass converted to energy.
600 millions of tons per second fused. Takes billions of
years to convert p's to 4He in Sun's core. Process sets
lifetime of stars.
Hydrostatic Equilibrium: pressure from fusion reactions balances
gravity. Sun is stable.
The Solar Constant
If we placed a light detector (a.k.a. solar cell) above the Earth’s
atmosphere and perpendicular to the sun’s rays, we can measure how
much solar energy is received per square meter (Watts / m2)
This is the solar constant => 1400 Watts / m2
About 50-70% of this energy reaches earth
So assuming 50% of this energy reaches of this energy reaches earth
Every square meter receives 700 Watts
Solar cells - devices to convert light into electricity are about
So a square meter of solar cells generates 140 Watts
To power a 2,000 sq. ft. house in summer with energy to run
washer/dryer etc., need about 14, 000 Watts peak or 100 sq.
meter of solar cells
Solar neutrino problem
In 1960s Ray Davis and John Bahcall measured the neutrino flux
from the Sun and found it to be lower than expected (by 30-50%)
Confirmed in subsequent experiments
Theory of p-p fusion well understood
Solar interior well understood
Answer to the Solar neutrino problem
Theoriticians like Bruno Pontecorvo realized
There was more than one type of neutrino
Neutrinos could change from one type to another
Confirmed by Super-Kamiokande experiment in Japan in 1998
50,000 gallon tank
Total number of neutrinos
agrees with predictions
How does energy get from core to surface?
off nuclei and
"surface" or photosphere:
gas density low enough so
photons can escape into
some electrons bound to nuclei
=> radiation can't get through
=> heats gas, hot gas rises,
cool gas falls
Last ~2 months
Usually in pairs
Follow solar rotation
They are darker because they are cooler (4500 K vs. 5800 K).
Related to loops of the Sun's magnetic field.
radiation from hot gas flowing
along magnetic field loop at
limb of Sun.
The Solar Wind
At top of corona, typical gas speeds are close to escape speed => Sun
losing gas in a solar wind.
Wind escapes from "coronal holes", seen in X-ray images.
Wind speed 500 km/sec (takes a few days to reach Earth).
106 tons/s lost. But Sun has lost only 0.1% of its mass from solar wind.
Prominences: Loops of gas ejected from surface. Anchored in
sunspot pairs. Last for hours to weeks.
Flares: A more energetic eruption. Lasts for minutes. Less well understood.
Prominences and flares occur most often at maximum of Solar Cycle.
Measuring the Stars
How big are stars?
How far away are they?
How bright are they?
How old, and how long do they live?
What is their chemical composition?
How are they moving?
Are they isolated or in clusters?
By answering these questions, we not only learn about stars, but
about the structure and evolution of galaxies they live in, and the
How Far Away are the Stars?
Earth-baseline parallax useful in Solar System
Earth-orbit parallax - useful
for nearest stars
New distance unit: the parsec (pc).
Using Earth-orbit parallax, if a star has a parallactic angle of 1",
it is 1 pc away.
Remember 1" (arcsecond) = 1/60 arcmin = 1/3600 degrees
If the angle is 0.5", the distance is 2 pc.
Distance (pc) = Parallactic angle (arcsec)
Closest star to Sun is Proxima Centauri. Parallactic angle is 0.7”, so
distance is 1.3 pc.
1 pc = 3.3 light years
= 3.1 x 10 18 cm
= 206,000 AU
1 kiloparsec (kpc) = 1000 pc
1 Megaparsec (Mpc) = 10 6 pc
Strange lettering scheme is a historical accident.
Further subdivision: BO - B9, GO - G9, etc. GO hotter than G9.
Sun is a G2.
Stellar Sizes - Indirect Method
Almost all stars too far away to measure their radii directly. Need
indirect method. For blackbodies, use Stefan's Law:
Energy radiated per cm2 of area on surface every second T 4
(T = temperature at surface)
Luminosity = (energy radiated per cm2 per sec) x (area of surface in cm2)
Luminosity (temperature) 4 x (surface area)
Determine luminosity from apparent brightness and distance, determine
temperature from spectrum (black-body curve or spectral lines), then
find surface area, then find radius (sphere surface area is 4 p R2)
The Wide Range of Stellar Sizes
H-R Diagram of Nearby Stars
Note lines of constant radius!
H-R Diagram of Well-known Stars
The Hertzsprung-Russell (H-R) Diagram
Radius on Main
How Long do Stars Live
(as Main Sequence Stars)?
A star on Main Sequence has fusion of H to He in its core. How
fast depends on mass of H available and rate of fusion. Mass of H
in core depends on mass of star. Fusion rate is related to
luminosity (fusion reactions make the radiation energy).
mass of core
mass of star
Because luminosity (mass) 3,
So if the Sun's lifetime is 10 billion years, a 30 MSun star's lifetime is only
10 million years. Such massive stars live only "briefly".
1) Open Clusters
-Example: The Pleiades
-10's to 100's of stars
-Few pc across
-Loose grouping of stars
-Tend to be young (10's to 100's of millions of
years, not billions, but there are exceptions)
2) Globular Clusters
- few x 10 5 or 10 6 stars
- size about 50 pc
- very tightly packed, roughly
- billions of years old
Clusters are crucial for stellar evolution studies because:
1) All stars in a cluster formed at about same time (so all have same age)
2) All stars are at about the same distance
3) All stars have same chemical composition
The Interstellar Medium (ISM) of the Milky Way Galaxy
Or: The Stuff (gas and dust) Between the Stars
Why study it?
Stars form out of it.
Stars end their lives by returning gas to it.
The ISM has:
a wide range of structures
a wide range of densities (10-3 - 107 atoms / cm3)
a wide range of temperatures (10 K - 107 K)
Compare density of ISM with Sun or planets:
Sun and Planets: 1-5 g / cm3
1 atom / cm3
Mass of one H atom is 10-24 g!
So ISM is about 1024 times as tenuous as a star or planet!
ISM consists of gas (mostly H, He) and dust. 98% of mass is in gas, but
dust, only 2%, is also observable.
Effects of dust on light:
Blocks out light
Blocks out short wavelength light better than
long wavelength light => makes objects appear redder.
Grain sizes typically 10-5 cm. Composition uncertain,
but probably silicates, graphite and iron.
Gas Structures in the ISM
Emission Nebulae or H II Regions
Regions of gas and dust near stars just formed.
The Hydrogen is essentially fully ionized.
Temperatures near 10,000 K
Sizes about 1-20 pc.
Hot tenuous gas => emission lines
Red color comes from one
emission line of H atoms
(tiny fraction of H is atoms,
Why is the gas ionized?
Remember, takes energetic UV photons to ionize H. Hot, massive
stars produce huge amounts of these.
Such short-lived stars spend all their lives in the stellar nursery of their
birth, so emission nebulae mark sites of ongoing star formation.
Many stars of lower mass are forming too, but make few UV photons.
Why "H II Region?
H I: Hydrogen atom
H II: Ionized Hydrogen
O III: Oxygen missing two electrons
H I Gas and 21-cm radiation
Gas in which H is atomic.
Fills much (most?) of interstellar space. Density ~1 atom / cm3.
Too cold (~100 K) to give optical emission lines.
Primarily observed through radiation of H at wavelength of 21 cm.
H I accounts for almost half the mass in the ISM: ~2 x 109 MSun !
HI in IC 342
Galaxy IC 342 in visible light
Origin of 21-cm photon:
The proton and electron each have “spin”. A result from quantum
mechanics: if both spinning the same way, atom's energy is slightly higher.
Eventually will make transition to state of opposite spins. Energy difference
is small -> radio photon emitted, wavelength 21-cm.
It's in the form of cold (~10 K) dense (~103 - 107 molecules / cm3)
Molecular cloud masses: 103 - 106 MSun !
Sizes: a few to 100 pc.
1000 or so molecular clouds in ISM. Total mass about equal to H I
Optically, seen as dark dust clouds.
=> Molecular Clouds important
because stars form out of them!
They tend to be associated with
We can observe emission from molecules. Most abundant is H2 (don't
confuse with H II), but its emission is extremely weak, so other "trace"
etc. . .
These emit photons with wavelengths near 1 mm when they make a
rotational energy level transition. Observed with radio telescopes.
Stars form out of molecular gas clouds. Clouds must collapse
to form stars (remember, stars are ~1020 x denser than a
Probably new molecular clouds form continually out of less dense
gas. Some collapse under their own gravity. Others may be more
stable. Magnetic fields and rotation also have some influence.
Gravity makes cloud want to
Outward gas pressure resists collapse,
like air in a bike pump.
When a cloud starts to collapse, it should fragment. Fragments then
collapse on their own, fragmenting further. End product is 100’s or
1000’s of dense clumps each destined to form star, binary star, etc.
Hence a cloud gives birth to a cluster of stars.
As a clump collapses, it heats up. Becomes very luminous.
Now a protostar. May form proto-planetary disk.
Protostar and proto-planetary disk in Orion
Eventually hot and dense
enough => spectrum
Can place on HR diagram.
Protostar follows “Hayashi
Finally, fusion starts, stopping collapse: a star!
Star reaches Main Sequence at end of
One cloud (103 - 106 MSun)
forms many stars, mainly in clusters,
in different parts at different times.
Massive stars (50-100 MSun) take about 106 years to form, least massive
(0.1 MSun) about 109 years. Lower mass stars more likely to form.
In Milky Way, a few stars form every year.
Some protostars not massive (< 0.08 MSun) enough to begin fusion.
These are Brown Dwarfs or failed stars. Very difficult to detect because
so faint. First seen in 1994 with Hubble. How many are there?
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.
- H burns in shell around core: "H-shell
- Tremendous energy produced. Star must
- Star now a "Red Giant". Diameter ~ 1 AU!
- Phase lasts ~ 109 years for 1 MSun star.
- Example: Arcturus
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.
+ 4He ->
8Be + 4He
12C + energy
- 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
- Now star on "Horizontal Branch" of H-R diagram. Lasts ~108 years
for 1 MSun star.
Horizontal branch star structure
He -> C
H -> He
Helium Runs out in Core
All He -> C. Not hot enough
-for C fusion.
- Core shrinks and heats up.
- 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.
- Core continues to contract. Never gets hot enough for carbon fusion.
- Helium shell burning becomes unstable -> "helium 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).
- 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).
- White dwarfs slowly cool to
oblivion. No fusion.
Evolution of Stars > 8 MSun
Higher mass stars evolve
more rapidly and fuse heavier
Example: 20 MSun star lives
"only" ~107 years.
Result is "onion" structure
with many shells of fusionproduced elements. Heaviest
element made is iron.
Eventual state of > 8 MSun star
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.
Following the evolution of a cluster on the H-R diagram
Final States of a Star
1. White Dwarf (WD)
If initial star mass < 8 MSun or so
(Max WD mass is 1.4 MSun ,
radius is about that of the Earth)
No Explosive Event +
(Possible Nova from
2. Neutron Star (NS)
8 MSun < initial star mass < 25 Msun
(1.4 MSun < NS mass < 3? Msun
radius is ~ 10 km - city sized)
Supernova + ejecta
3. Black Hole (BH)
If initial mass > 25 MSun
(For BH with mass = 3 Msun
radius ~ 9 km)
GRB + Hypernova +
White dwarf in
close binary system
WD's tidal force stretches out companion, until parts of outer envelope
spill onto WD. Surface gets hotter and denser. Eventually, a burst of
fusion. Binary brightens by 10'000's! Some gas expelled into space.
Whole cycle may repeat every few decades => recurrent novae.
Death of a High-Mass Star
M > 8 MSun
Iron fusion doesn't produce energy (actually
requires energy) => core collapses in < 1 sec.
T ~ 1010 K, radiation disrupts nuclei,
p + e => n + neutrino
Collapses until neutrons come into contact.
Rebounds outward, violent shock ejects rest
of star => A Core-collapse or Type II
Ejection speeds 1000's to 10,000's of km/sec!
Remnant is a “neutron star” or “black hole”.
Such supernovae occur
roughly every 50 years
in Milky Way.
Example Supernova: 1998bw
Remember, core collapse (Type II) and carbon-detonation (Type I)
supernovae have very different origins
Making the Elements
Universe initially all H (p’s and e’s). Some He made soon
after Big Bang before stars, galaxies formed. All the rest
made in stars, and returned to ISM by supernovae.
Solar System formed from such "enriched" gas 4.6
billion years ago. As Milky Way ages, the abundances
of elements compared to H in gas and new stars are
increasing due to fusion and supernovae.
Elements up to iron (56Fe, 26 p + 30 n in nucleus)
produced by steady fusion (less abundant elements we
didn’t discuss, like Cl, Na, made in reactions that aren’t
important energy makers).
Heavier elements (such as lead, gold, copper, silver,
etc.) by "neutron capture" in core, even heavier ones
(uranium, plutonium, etc.) in supernova itself.
Leftover core from Type II supernova
- a tightly packed ball of neutrons.
Diameter: 20 km only!
Mass: 1.4 - 3(?) MSun
Density: 1014 g / cm3 !
Surface gravity: 1012 higher
Escape velocity: 0.6c
Rotation rate: few to many times
A neutron star over the Sandias?
The Lighthouse model of a pulsar