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Review for Test 3 Nov 17

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Methods Conceptual Review ... Others may be more stable. Magnetic fields and rotation also have some influence. ... Study hard (~2 hours/day Friday through Monday) ... – PowerPoint PPT presentation

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Title: Review for Test 3 Nov 17


1
Review for Test 3 Nov 17
  • Topics
  • The Sun
  • Stars
  • The Interstellar medium
  • Stellar Evolution and Stellar Death
  • Neutron stars and pulsars
  • Methods
  • 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 QA format
  • Bring
  • Two Number 2 pencils
  • Simple calculator (no electronic notes)
  • UNM Student ID
  • Reminder There are NO make-up tests for this
    class

2
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 cant find the answer, try process of
    elimination
  • If you dont know the answer, Go on to the next
    problem and come back to this one later
  • TAKE YOUR TIME, dont hurry
  • If you dont understand something, ask me.

3
Test 3 Useful Equations
parallactic distance d 1/p where p is
parallax in arcsec and
d is in parsecs
Schwarschild Radius
2 GM c2
R
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
4
The Sun
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
5
Temperature at surface 5800 K gt yellow
(Wiens 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
25 He 1 the rest
Rotation period 27 days at equator
31 days at poles
6
The Interior Structure of the Sun (not to scale)
Let's focus on the core, where the Sun's energy
is generated.
7
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
8
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.
9
In the Sun's Core...
neutrino (weird particle)
proton
deuteron (proton neutron bound together)
positron (identical to electron but positively
charged)
proton
photon

1) proton proton ? protonneutron
neutrino positron



(deuteron)
energy (photon)
10
2) deuteron proton ? 3He
energy
He nucleus, only 1 neutron
3) 3He 3He ? 4He
proton proton energy
Net result 4 protons ? 4He
2 neutrinos 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.
11
The Solar Constant
  • If we placed a light detector (a.k.a. solar cell)
    above the Earths atmosphere and perpendicular to
    the suns rays, we can measure how much solar
    energy is received per square meter (Watts / m2)
  • This is the solar constant gt 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 20 efficient
  • 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

12
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
13
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
14
How does energy get from core to surface?
core
"radiative zone" photons scatter off nuclei and
electrons, slowly drift outwards "diffusion".
15
Sunspots
Roughly Earth-sized Last 2 months Usually in
pairs Follow solar rotation
16
Sunspots
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.
17
The Solar Wind
At top of corona, typical gas speeds are close to
escape speed gt 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.
18
Active Regions
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.
Solar Flare Video
Prominences and flares occur most often at
maximum of Solar Cycle.
19
Measuring the Stars
How big are stars? How far away are they? How
bright are they? How hot? 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
universe.
20
How Far Away are the Stars?
Earth-baseline parallax - useful in Solar System
Earth-orbit parallax - useful for nearest stars
21
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.
1 Parallactic angle (arcsec)
Distance (pc)
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
22
Spectral Classes
Strange lettering scheme is a historical accident.
Spectral Class Surface
Temperature Examples
Rigel Vega, Sirius Sun Betelgeuse
30,000 K 20,000 K 10,000 K 7000 K 6000 K 4000
K 3000 K
O B A F G K M
Further subdivision BO - B9, GO - G9, etc.
GO hotter than G9. Sun is a G2.
23
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 a T 4 (T
temperature at surface)
And Luminosity (energy radiated per
cm2 per sec) x (area of surface in cm2)
So
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)
24
The Wide Range of Stellar Sizes
25
H-R Diagram of Nearby Stars
H-R Diagram of Well-known Stars
Note lines of constant radius!
26
The Hertzsprung-Russell (H-R) Diagram
Red Supergiants
Red Giants
Sun
Main Sequence
White Dwarfs
27
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).
So,
mass of star luminosity
mass of core fusion rate
lifetime ?
?
Because luminosity ? (mass) 3,
mass (mass) 3
1 (mass) 2
or
lifetime ?
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".
28
Star Clusters
Two kinds 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)
29
2) Globular Clusters - few x 10 5 or 10 6
stars - size about 50 pc - very tightly packed,
roughly spherical shape - 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
30
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)
31
Compare density of ISM with Sun or planets
Sun and Planets 1-5 g / cm3
ISM average 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!
32
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 1)
"Extinction" Blocks out
light 2) "Reddening"
Blocks out short wavelength light better than
long wavelength light gt makes
objects appear redder.
Grain sizes typically 10-5 cm. Composition
uncertain, but
probably silicates, graphite and iron.
33
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 gt emission lines
(Kirchhoff's Laws)
34
Rosette Nebula
Lagoon Nebula
Tarantula Nebula
Red color comes from one emission line of H atoms
(tiny fraction of H is atoms, not ionized).
35
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
etc.
36
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 !
37
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 -gt radio photon emitted,
wavelength 21-cm.
38
Molecular Gas
It's in the form of cold (10 K) dense (103 -
107 molecules / cm3) clouds. 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 mass. Optically,
seen as dark dust clouds.
gt Molecular Clouds important because stars form
out of them! They tend to be associated with
Emission Nebulae.
39
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"
molecules observed CO
(carbon monoxide) H2O (water
vapor) HCN (hydrogen
cyanide) NH3 (ammonia)
etc. . .
These emit photons with wavelengths near 1 mm
when they make a rotational energy level
transition. Observed with radio telescopes.
40
Star Formation
Stars form out of molecular gas clouds. Clouds
must collapse to form stars (remember, stars are
1020 x denser than a molecular cloud).
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.
41
When a cloud starts to collapse, it should
fragment. Fragments then collapse on their own,
fragmenting further. End product is 100s or
1000s of dense clumps each destined to form
star, binary star, etc. Hence a cloud gives birth
to a cluster of stars.
42
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
1700 AU
Eventually hot and dense enough gt
spectrum approximately black-body. Can place on
HR diagram. Protostar follows Hayashi tracks
43
Finally, fusion starts, stopping collapse a star!
Star reaches Main Sequence at end of Hayashi Track
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.
44
Brown Dwarfs
Some protostars not massive (lt 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?
45
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 -gt He
fusion, by p-p chain in stars like Sun or less
massive. In more massive stars, CNO cycle
becomes more important.
46
Evolution of a Low-Mass Star (lt 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 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
47
Red Giant Star on H-R Diagram
48
Eventually Core Helium Fusion
- Core shrinks and heats up to 108 K, helium can
now burn into carbon.
"Triple-alpha process"
4He 4He -gt 8Be energy 8Be 4He
-gt 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 -gt C burning. Still have H -gt
He shell burning surrounding it. - Now star on
"Horizontal Branch" of H-R diagram. Lasts 108
years for 1 MSun star.
49
More massive less massive
Horizontal branch star structure
Core fusion He -gt C
Shell fusion H -gt He
50
Helium Runs out in Core
  • All He -gt 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.
Red Supergiant
51
"Planetary Nebulae"
- Core continues to contract. Never gets hot
enough for carbon fusion. - Helium shell burning
becomes unstable -gt "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).
52
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53
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54
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). - White dwarfs slowly
cool to oblivion. No fusion.
55
Evolution of Stars gt 8 MSun
Eventual state of gt 8 MSun star
Higher mass stars evolve more rapidly and fuse
heavier elements. Example 20 MSun star lives
"only" 107 years. Result is "onion" structure
with many shells of fusion-produced elements.
Heaviest element made is iron.
56
Fusion Reactions and Stellar Mass
In stars like the Sun or less massive, H -gt
He most efficient through proton-proton
chain. In higher mass stars, "CNO cycle" more
efficient. Same net result 4 protons -gt He
nucleus Carbon just a catalyst. Need Tcenter gt
16 million K for CNO cycle to be more efficient.
Sun
(mass) -gt
57
Following the evolution of a cluster on the H-R
diagram
T
58
Final States of a Star
No Explosive Event Planetary Nebula (Possible
Nova from Carbon Flash) Supernova ejecta GRB
Hypernova ejecta
1. White Dwarf (WD) If initial star mass lt
8 MSun or so (Max WD mass is 1.4 MSun ,
radius is about that of the Earth) 2.
Neutron Star (NS) 8 MSun lt initial star
mass lt 25 Msun (1.4 MSun lt NS mass lt 3?
Msun radius is 10 km - city sized) 3.
Black Hole (BH) If initial mass gt 25 MSun
(For BH with mass 3 Msun radius 9 km)
59
Stellar Explosions
Novae
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 gt recurrent novae.
60
Death of a High-Mass Star
M gt 8 MSun Iron core Iron fusion doesn't
produce energy (actually requires energy) gt core
collapses in lt 1 sec.
T 1010 K, radiation disrupts nuclei, p
e gt n neutrino
Collapses until neutrons come into contact.
Rebounds outward, violent shock ejects rest of
star gt A Core-collapse or Type II Supernova
Such supernovae occur roughly every 50 years in
Milky Way.
Ejection speeds 1000's to 10,000's of
km/sec! (see DEMO) Remnant is a neutron star
or black hole.
61
Example Supernova 1998bw
62
Remember, core collapse (Type II) and
carbon-detonation (Type I) supernovae have very
different origins
63
Making the Elements
Universe initially all H (ps and es). 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 didnt discuss, like Cl, Na, made in
reactions that arent 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.
64
Neutron Stars
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 per second!!! Magnetic field
1012 x Earth's!
A neutron star over the Sandias?
65
The Lighthouse model of a pulsar
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