Download Review 3 (11-18-10)

• Review for Exam 3. The material is
difficult, most students have more trouble
with this exam than with exams 1and 2.
• Please Remember to fill out course
evaluations online
• Ch 10 through 14 will be on Exam 3
• Exam based on material covered in class,
i,e., study class notes and use book only to
help you understand the material covered in
class. Several questions presented in class
are included in the exam almost verbatim
• I will put up a list of formulas, you do not
need to memorize them, BUT you need to
understand how to use them.
• No calculators will be allowed
• About 1/3 to 1/2 of exam questions are on the
H-R diagram and the evolution of stars
• Come to my office hours, or see the tutors at
SARC
Outline of The Sun (Ch. 10)
I.
The Solar Spectrum: Sun’s
composition and surface temperature
II. Sun’s Interior: Energy source, energy
transport, structure, helioseismology.
III. Sun’s Atmosphere: Photosphere,
chromosphere, corona
IV. Solar Activity: Sunspots, solar magnetism,
solar cycle, prominences and flares.
Solar Spectrum
Hydrogen Fusion into Helium in the Sun’s Core
4 protons  one Helium nucleus + Energy
Hydrogen Fusion into Helium in the Sun’s Core
4 protons  one helium nucleus + Energy
The mass of the four protons is higher than
that of the helium nucleus where did the
missing mass go?
The mass became energy and E=mc2
So a little mass can produce a lot of energy
Sun’s Interior
Outline of The Sun (Ch. 10)
I.
The Solar Spectrum: Sun’s composition and
II.
Sun’s Interior: Energy source, energy transport, structure,
surface temperature
helioseismology.
III. Sun’s Atmosphere:
Photosphere, chromosphere,
corona
IV. Solar Activity: Sunspots, solar
magnetism, solar cycle,
prominences and flares.
Solar Granulation in the Photosphere
Sunspots
Solar Chromosphere
Solar Corona
IV. Solar Activity
I.
Sunspots: main indicator
II.
Prominences and flares: also indicators of
solar activity
III.
Solar cycle: 11-year cycle
Outline of Chapter 11 Part I
I.
Parallax and distance.
II.
Luminosity and brightness
Apparent Brightness
Absolute Brightness or Luminosity
Inverse-Square Law
III.
Stellar Temperatures
Color, Spectral lines, Spectral Classification:OBAFGKM
IV.
Stellar sizes (radius)
V.
Stellar Masses
Properties of Stars
Our Goals for Learning
• How far away are stars?
• How luminous are stars?
• How hot are stars?
• How massive are stars?
• How large (radius) are stars?
I. Parallax and distance.
p = parallax angle in
arcseconds
d (in parsecs) = 1/p
1parsec= 3.26 light
years
I. Parallax and distance.
Nearest Star: Alpha Centauri d = 4.3 light years
(since 1 parsec = 3.26 light years)
distance to in parsecs = 4.3/3.26 = 1.32
What is the parallax of this star?
d=1/p hence p=1/d
p for nearest star is 0.76 arcseconds
All other stars will have a parallax angle smaller
than 0.76 arcseconds
II. Luminosity and Brightness
1.
Apparent Brightness (how bright it looks in the
sky)
2.
Absolute Brightness or Luminosity (energy/sec)
3.
4.
Inverse-Square Law
 apparent brightness = (absolute
brightness)/d2
Examples: light bulbs at different distances
III. Stellar Temperatures
1.
Color ( hotter > bluer; cooler > redder)
2.
Spectral lines
3.
Spectral Classification:
OBAFGKM (from hottest to coldest)
Laws of Thermal Radiation
hotter  brighter, cooler  dimmer
hotter  bluer,
cooler  redder
(from Ch. 5)
IV. Stellar sizes (radius)
Luminosity is proportional to surface area x
temperature: L= 4R2T4
If we can measure the Luminosity and the
temperature of a star we can tell how large its
raduis is.
Summary of Ch 11a
Distance: If you know the parallax “p” (in arcseconds) you can
calculate the distance “d” (in parsecs) d=1/p (1parsec= 3.26
lightyears)
Apparent brightness: how bright a star looks in the sky
The inverse-square Law: light from stars gets fainter as the
inverse square of the distance (brightness proportional to 1/d2).
If we know the apparent brightness and the distance to a star
we can calculate its absolute (intrinsic) brightness: apparent
brightness = (absolute brightness)/d2
Luminosity (energy/sec) is equivalent to absolute brightness
L= 4R2T4
If we can measure the luminosity and the temperature of a star
we can tell how large it is.
 Binary stars allow us to determine stellar masses
Binary Stars
•
Definition:
When two stars are in orbit around their center of mass
•
Three main types of Binary Stars
•
•
•
•
Visual: orbits
Spectroscopic: Review of Doppler effect, spectral lines,
double and single lines
Eclipsing: masses and diameters of stars
Stellar Masses and Densities
Radial Velocity

Approaching stars: more
energy, spectral lines undergo a
blue shift

Receding stars: less energy,
spectral lines undergo a red
shift

/ = v/c
Spectroscopic Binary
Eclipsing Binary: Masses and Radii
Outline of Ch 11 part II: The H-R
Diagram
I.
The Hertzprung-Russell (H-R) Diagram:

Surface Temperature vs Luminosity

Analogy: horsepower vs weight
II.
Where Stars plot in the H-R diagram

Main Sequence: 90% of all stars

Why? stars spend 90% of their lives fusing hydrogen

Main sequence  Hydrogen fusion

Giants, Supergiants, White Dwarfs
III.
Main Sequence Stars
(cont.)
Outline of Ch 11 part II: The H-R
Diagram (cont.)
III. Main Sequence Stars
•
Stellar Masses and Densities along main sequence
•
Mass-Luminosity Relation (L~M3.5)
•
Lifetime on Main Sequence (TMS~ 1/M2.5)
•
Main sequence Thermostat
IV.
Star Clusters
•
What is so special about Star Clusters?
•
Open and Globular Clusters
•
Ages of Clusters
Luminosity
H-R
diagram
plots the
luminosity
vs. surface
temperature
of stars
Temperature
Hydrogenfusion stars
reside on the
main
sequence of
the H-R
diagram
Remember Stellar sizes (radius)
Luminosity proportional to surface area x temperature:
L= 4R2T4
If we can measure the luminosity and the
temperature of a star we can tell how large its
raduis is.
H-R Diagram: Radii of stars
Stellar Masses
For main
sequence stars,
the larger the
mass the
higher the
luminosity
This massluminosity
relation is
valid only for
the main
sequence
Stellar Masses
For main
sequence stars,
the larger the
mass the
higher the
luminosity
This massluminosity
relation is
valid only for
the main
sequence
How do we
know the
masses of
these stars?
Stellar Masses
For main
sequence stars,
the larger the
mass the
higher the
luminosity
This massluminosity
relation is
valid only for
the main
sequence
How do we
know the
masses of
these stars?
Binary
Stars
Stellar Densities
Density = Mass/Volume
V= 4/3(R3)
Stellar Densities
Low
High
Stellar Densities
Giants and
Supergiants: same
or lower density
than air
M.S. same
density as
W.D. very water
dense
Luminosity
H-R diagram
depicts:
Temperature
Color,
Spectral Type,
Luminosity,
and Radius
of stars
(*Mass,
*Lifespan,
*Density of
MS stars only)
Temperature
Outline of Ch 11 part II: The H-R
Diagram (cont.)
III. Main Sequence Stars
•
Main sequence Thermostat
•
Stellar Masses and Densities along main sequence
•
Mass-Luminosity Relation (L~M3.5)
•
Lifetime on Main Sequence (TMS~ 1/M2.5)
Lifetime on Main Sequence
TMS~ 1/M2.5
M in solar masses
T in units of Sun’s total lifetime on MS (10 billion
years)
Mass- Luminosity of Main Sequence Stars
L~ M3.5
M in solar masses
L in units of Sun’s Luminosity
Main Sequence Thermostat:
In the Sun, and in all main
sequence stars gravity is
balanced by outward
pressure due to the outflow
of energy.
1.
Which of the following correctly fills in the blank?
A main-sequence star of spectral class B is _____
than a main-sequence star of spectral class G.
1. More massive 2. Hotter 3. Longer lived 4. More
luminous
The correct answer is
A. 1 and 3
B. 2 and 3
C. 1, 2 and 4
D. 2, 3 and 4
E.
1, 2, 3 and 4
2.
Which of the following correctly fills in the blank?
If a star is on the main-sequence and one knows its
temperature, then one can estimate its ____.
1.
Spectral class
2.
Mass
3.
Luminosity
4.
Density
5.
Radial velocity
The correct answer is
A. 1, 2, 3, 4 and 5
B. 1 and 5
C. 2 only
D. 1, 3 and 5
E. 1, 2, 3 and 4
3.
Which of the following correctly fills in the blank?
If a star of class O is on the main-sequence, that star
must be ____.
1.
Hotter than most stars
2.
Very massive
3.
Much denser than water
4.
Very red
5.
Not very old
The correct answer is
A. 2 and 3
B. 1, 2, 3 and 4
C. 1, 2, 3, 4 and 5
D. 1, 2 and 5
E. 4 and 5
4. Which of the following correctly fills in the blank?
If a star of class M is on the main-sequence, that star
must be ____.
A.
B.
C.
D.
Very hot
Very massive
Very blue
None of the other answers are correct
What have we learned?
• What are the two types of
star clusters?
 Open clusters contain up to
several thousand stars and are
found in the disk of the galaxy.
 Globular clusters contain
hundreds of thousands of stars,
all closely packed together.
They are found mainly in the
halo of the galaxy.
What have we learned?
 How do we measure the
age of a star cluster?
 Because all of a cluster’s
stars we born at the same
time, we can measure a
cluster’s age by finding the
main sequence turnoff
point on an H–R diagram of
its stars. The cluster’s age is
equal to the hydrogenburning lifetime of the
hottest, most luminous stars
that remain on the main
sequence.
Chapter 12. Star Stuff
I.
Birth of Stars from Interstellar Clouds
•Young stars near clouds of gas and dust
•Contraction and heating of clouds
• Hydrogen fusion stops collapse
II. Leaving the Main Sequence: Hydrogen fusion stops
1. Low mass stars (M < 0.4 solar masses)
Not enough mass to ever fuse any element heavier than
Hydrogen → white dwarf
2.Intermediate mass stars (0.4 solar masses < M < 4 solar masses,
including our Sun)
He fusion, red giant, ejects outer layers → white dwarf
3.High mass Stars (M > 4 solar masses)
Fusion of He,C,O,…..but not Fe (Iron) fusion
Faster and faster → Core collapses → Supernova
produces all elements heavier than Fe and blows up
Chapter 12. Star Stuff Part I Birth of Stars
I.
Birth of Stars from Interstellar Clouds
•Young stars near clouds of gas and dust
•Contraction and heating of clouds
• Hydrogen fusion stops collapse
I. Birth of Stars and Interstellar Clouds
•Young stars are always found near clouds of gas and dust
•Stars are born in intesrtellar molecular clouds
consisting mostly of hydrogen molecules and dust
Summary of Star Birth
1. Gravity causes gas cloud to shrink
2. Core of shrinking cloud heats up
3. When core gets hot enough (10
millon K), fusion of hydrogen
begins and stops the shrinking
4. New star achieves long-lasting
state of balance (main sequence
thermostat)
Question 2
What happens after an interstellar cloud of gas
and dust is compressed and collapses:
A. It will heat and contract
B. If its core gets hot enough (10 million K) it
can produce energy through hydrogen
fusion
C. It can produce main sequence stars
D. All of the answers are correct
Main Sequence ( Hydrogen Fusion)

Main sequence Thermostat : very stable
phase
How massive are newborn stars?
Luminosity
Very
massive
stars are
rare
Low-mass
stars are
common
Temperature
Equilibrium inside M.S. stars
Ch. 12 Part II. Leaving the Main Sequence:
Hydrogen fusion stops
1. Low mass stars (M < 0.4 solar masses)
Not enough mass to ever fuse any element heavier than
Hydrogen  white dwarf
2.Intermediate mass stars (0.4 solar masses
< M < 4 solar masses, including our Sun)
He fusion, red giant, ejects outer layers  white dwarf
3.High mass Stars (M > 4 solar masses)
Fusion of He,C,O,…..but not Fe (Iron) fusion
Faster and faster  Core collapses  Supernova
 Produces all elements heavier than Fe and blows
Leaving the Main Sequence:
Hydrogen fusion stops
1. Low mass stars (M < 0.4 solar masses)
Not enough mass to ever fuse any element heavier than
Hydrogen  white dwarf
White Dwarfs
I. Leaving the Main Sequence:
Hydrogen fusion stops
2. Intermediate mass stars (0.4 solar
masses < M < 4 solar masses, including
our Sun)
He fusion, red giant, ejects outer layers  white
dwarf
Stars like our Sun become Red Giants after they
leave the M.S. and eventually White Dwarfs
Most red giants stars eject their outer layers
I. Leaving the Main Sequence:
Hydrogen fusion stops
3.High mass Stars (M > 4 solar masses)
Fusion of He,C,O,…..but not Fe (Iron) fusion
Faster and faster  Core collapses  Supernova
 Produces all elements heavier than Fe and blows up
Supernovas
3. High mass star (M > 4 solar masses)
•Fusion of He,C,O,…..but not Fe (Iron) fusion
Faster and faster  Core collapses  Supernova
Produces all elements heavier than Fe and blows
envelope apart ejecting to interstellar space most of its
mass
• Supernova Remnants
Crab nebula and others
An evolved massive star (M > 4 Msolar)
Supernova Remnant: Crab Nebula
Outline of Chapter 13 Death of Stars
I.
Death of Stars
• White Dawrfs
• Neutron Stars
• Black Holes
II.
Cycle of Birth and Death of Stars (borrowed in
part from Ch. 14)
I. Death of Stars
•Low mass M.S. stars (M < 0.4 solar Mo) produce White
Dawrfs
•Intermediate mass M.S. stars ( 0.4Mo < M < 4 solar Mo)
produce White Dawrfs
•High mass stars M.S. (M > 4 solar Mo) can produce
Neutron Stars and Black holes
I. Death of Stars
• White Dawrfs: very dense, about mass of Sun in
size of Earth. Atoms stop further collapse. M less
than 1.4 solar masses
• Neutron Stars: even denser, about mass of Sun in
size of Orlando. Neutrons stop further collapse. M
between 1.4 and 3 solar masses. Some neutron
stars can be detected as pulsars
• Black Holes: M more than 3 solar masses. Nothing
stops the collapse and produces an object so
compact that escape velocity is higher than speed of
light; hence, not even light can escape.
•NOTE: these are the masses of the dead stars NOT
the masses they had when they were on the main
sequence
A white dwarf is about the same size as Earth
Neutron Star
About the
size of NYC
or Orlando
Neutron Star
Pulsar (in Crab Nebula)
This is a
confirmation
of theories
that predicted
that neutron
stars can be
produced by a
supernova
explosion,
because the
Crab Nebula
was produced
by a SN that
exploded in
the year 1054
I. Death of Stars


How do we detect Neutron Stars and Black
Holes?
Neutron Stars:
•As pulsars
•As compact objects in binary stars
Black Holes:
•As compact objects in binary stars
How do we distinguish Neutron Stars
from Black holes?
The mass of the object
How do we measure the masses of
Stars? Binary Stars
Black Hole in a Binary System
If the mass of the compact object is more
than 3 solar masses, it is a black hole
A black hole is an object whose gravity is so
powerful that not even light can escape it.
If the Sun shrank
into a black hole, its
gravity would be
different only near
the event horizon.
At the orbits of the
planets the gravity
would stay the same
Black holes don’t suck!
II. Cycle of Birth and Death of Stars: Interstellar
Medium
A. Interstellar Matter: Gas (mostly hydrogen) and
dust
•Nebulae •Extinction and reddening
•Interstellar absorption lines •Radio observations
B. Nebulae
• Emission • Reflection • Dark
C. Cycle of Birth and Death of Stars
Interstellar Medium
I.
Interstellar Matter: Gas (mostly hydrogen) and dust
How do we know that Interstellar Matter is there:
•Nebulae
•Extinction and reddening
•Interstellar absorption lines
•Radio observations
Extinction and Reddening: interstellar
dust will make stars look fainter and redder
Interstellar Absorption Lines
Radio Observations: some molecules
can be detected with radiotelescopes
II. Nebulae
• Emission Nebulae
• Reflection Nebulae
• Dark Nebulae
Emission Spectrum
Emission Nebula (Eagle Nebula)
Hubble Space
Telescope Image
Ch. 14 OUTLINE
Shorter than book
 14.1 The Milky Way Revealed
 14.2 Galactic Recycling (closely related to
Ch. 13)
 14.3 The History of the Milky Way
 14.4 The Mysterious Galactic Center
14.1 The Milky Way Revealed
 Our Goals for Learning (not exactly like
book)
• What does our galaxy look like?
• Where do stars form galaxy?
Dusty gas
clouds obscure
our view
because they
absorb visible
light
This is the
interstellar
medium that
makes new
star systems
All-Sky View at visible wavelengths
All-Sky View at infrared wavelengths
Remember Extinction and Reddening:
interstellar dust will make stars look fainter and
redder. Dust will affect more the shorter (bluer)
wavelengths and less the longer (redder)
wavelengths. By looking at infrared wavelengths we
can see through most of the dust.
The Shape of our Galaxy: a flattened disk
We see our galaxy edge-on
Primary features: disk, bulge, halo, globular clusters
If we could view the Milky Way from above the
disk, we would see its spiral arms
How do we know what our galaxy would look like if viewed
from the top? Infrared and Radio observations penetrate
dark interstellar clouds
Stellar Populations
 Turns out that there are two types of stars
in the Galaxy
• Population I: Relatively young. Similar to the
Sun. Tend to be in the galactic disk. Richer in
heavy elements
• Population II: Few heavy elements, very old
(12-14 billion years), tend to be in the center of
the galaxy or in globular clusters
Two types of star clusters
 Open clusters: young,
contain up to several
thousand stars and are
found in the disk of the
galaxy (Population I).
 Globular clusters: old,
contain hundreds of
thousands of stars, all
closely packed together.
They are found mainly in
the halo of the galaxy
(Population II).
14.2 Galactic Recycling
 Our Goals for Learning
• How does our galaxy recycle gas into stars?
• Where do stars tend to form in our galaxy?
Star-gas-star
cycle
Recycles gas
from old stars
into new star
systems
14.2 Galactic Recycling
• Where do stars tend to form in our
galaxy? In the Disk
How does our galaxy recycle gas
into stars?
Cycle of Birth and Deaths of Stars
 Interstellar cloud of gas and dust is
compressed and collapses to form stars
 After leaving the main sequence red giants
eject their outer layers back to the
interstellar medium
 Supernovae explode and eject their outer
layers back to the interstellar medium
 Supernova explosions and other events can
compress an interstellar cloud of gas and
dust that collapses to form stars ………..
Remember the Sun’s Evolutionary Process
Remember mass loss in Intermediate Mass
Stars
Remember Supernova explosions
Star-gas-star
cycle
Recycles gas
from old stars
into new star
systems
14.3 The History of the Milky Way
 Our Goals for Learning
• What clues to our galaxy’s history do halo stars
hold?
• How did our galaxy form?
Halo: no blue stars  no star formation
Disk: blue stars  star formation
Much of star
formation in disk
happens in spiral
arms
Emission Nebulae
Blue Stars
Gas Clouds
Spiral arms are waves of
star formation
The Whirlpool Galaxy
What clues to our galaxy’s
history do halo stars hold?
Halo Stars:
0.02-0.2% heavy elements (O, Fe, …),
only old stars
Disk Stars:
2% heavy elements,
stars of all ages
Halo Stars:
0.02-0.2% heavy elements (O, Fe, …),
only old stars
Disk Stars:
2% heavy elements,
stars of all ages
Halo stars
formed first,
then stopped
Halo Stars:
0.02-0.2% heavy elements (O, Fe, …),
only old stars
Halo stars
formed first,
then stopped
Disk Stars:
2% heavy elements,
stars of all ages
Disk stars
formed later,
kept forming
How did our galaxy form?
Our galaxy probably formed from a giant gas cloud
Halo stars formed first as gravity caused cloud to contract
Note: This
model is
oversimplified
Stars continuously form in disk as galaxy grows older
What have we learned?
• What clues to our galaxy’s history do halo
stars hold?
 The halo generally contains only old, low-mass
stars with a much smaller proportion of heavy
elements than stars in the disk. Thus, halo stars
must have formed early in the galaxy’s history,
before the gas settled into a disk.
14.4 The Mysterious Galactic Center
 Our Goals for Learning
• What lies in the center of our galaxy?
What lies in the center of our
galaxy?
Stars appear to
be orbiting
something
massive but
invisible … a
black hole!
Orbits of stars
indicate a mass
of about 4
million MSun