• 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

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.

Outline of The Sun (Ch. 10)

Solar Spectrum

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

Hydrogen Fusion into Helium in the Sun’s Core

Sun’s Interior

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.

Outline of The Sun (Ch. 10)

Solar Granulation in the Photosphere

Sunspots

Solar Chromosphere

Solar Corona

I. Sunspots: main indicator

II. Prominences and flares: also indicators of solar activity

III. Solar cycle: 11-year cycle

IV. Solar Activity

I. Parallax and distance.

II. Luminosity and brightnessApparent Brightness Absolute Brightness or Luminosity Inverse-Square Law

III. Stellar TemperaturesColor, Spectral lines, Spectral Classification:OBAFGKM

IV. Stellar sizes (radius)

V. Stellar Masses

Outline of Chapter 11 Part I

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

1. Apparent Brightness (how bright it looks in the sky)

2. Absolute Brightness or Luminosity (energy/sec)

3. Inverse-Square Law apparent brightness = (absolute

brightness)/d2

4. Examples: light bulbs at different distances

II. Luminosity and Brightness

1. Color ( hotter > bluer; cooler > redder)

2. Spectral lines

3. Spectral Classification:OBAFGKM (from hottest to coldest)

III. Stellar Temperatures

hotter brighter, cooler dimmer

hotter bluer, cooler redder

Laws of Thermal Radiation

(from Ch. 5)

Luminosity is proportional to surface area x temperature: L= 4R2T4

If we can measure the Luminosity and the

temperature of a star we can tell how large its

raduis is.

IV. Stellar sizes (radius)

Summary of Ch 11aDistance: 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 skyThe 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 brightnessL= 4R2T4

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

• 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

Binary Stars

Approaching stars: more energy, spectral lines undergo a blue shift

Receding stars: less energy, spectral lines undergo a red shift

/ = v/c

Radial Velocity

Spectroscopic Binary

Eclipsing Binary: Masses and Radii

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

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

Outline of Ch 11 part II: The H-R Diagram (cont.)

Temperature

Lu

min

osi

ty

H-R diagram plots the luminosity vs. surface temperature of stars

Hydrogen-fusion stars reside on the main sequence of the H-R diagram

Luminosity proportional to surface area x temperature: L= 4R2T4

If we can measure the luminosity and the

temperature of a star we can tell how large its

raduis is.

Remember Stellar sizes (radius)

H-R Diagram: Radii of stars

Stellar Masses

For main sequence stars, the larger the

mass the higher the luminosity

This mass-luminosity relation is

valid only for the main sequence

Stellar Masses

For main sequence stars, the larger the

mass the higher the luminosity

This mass-luminosity 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 mass-luminosity 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

High

Same as water

Low

Stellar Densities

M.S. same density as

water

Giants and Supergiants: same

or lower density than air

W.D. very dense

Temperature

Lu

min

osi

tyH-R diagram depicts:TemperatureColor, Spectral Type,

Luminosit

y,

and

Radius of

stars

(*Mass,

*Lifespan,

*Density

of MS

stars only)

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)

Outline of Ch 11 part II: The H-R Diagram (cont.)

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 isA.     1 and 3B.     2 and 3C.     1, 2 and 4 D.     2, 3 and 4E.      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 class2.            Mass3.            Luminosity4.            Density5.            Radial velocity The correct answer isA.     1, 2, 3, 4 and 5B.     1 and 5C.     2 onlyD.    1, 3 and 5E.     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 stars2.            Very massive3.            Much denser than water4.            Very red5.            Not very old The correct answer isA.     2 and 3B.     1, 2, 3 and 4C.     1, 2, 3, 4 and 5D.    1, 2 and 5E.     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.     Very hotB.     Very massiveC.     Very blueD.    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 hydrogen-burning 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 stops1. 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 2What 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?

Temperature

Lu

min

osi

tyVery massive stars are rare

Low-mass stars are common

Equilibrium inside M.S. stars

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) fusionFaster and faster Core collapses Supernova Produces all elements heavier than Fe and blows

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

Leaving the Main Sequence: Hydrogen fusion stops

White Dwarfs

2. Intermediate mass stars (0.4 solar masses < M < 4 solar masses, including our Sun)He fusion, red giant, ejects outer layers white dwarf

I. Leaving the Main Sequence: Hydrogen fusion stops

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

3.High mass Stars (M > 4 solar masses)Fusion of He,C,O,…..but not Fe (Iron) fusionFaster and faster Core collapses Supernova Produces all elements heavier than Fe and blows up

I. Leaving the Main Sequence: Hydrogen fusion stops

3. High mass star (M > 4 solar masses)•Fusion of He,C,O,…..but not Fe (Iron) fusionFaster and faster Core collapses SupernovaProduces all elements heavier than Fe and blows envelope apart ejecting to interstellar space most of its mass• Supernova RemnantsCrab nebula and others

Supernovas

An evolved massive star (M > 4 Msolar)

Supernova Remnant: Crab Nebula

I. Death of Stars • White Dawrfs• Neutron Stars• Black Holes

II. Cycle of Birth and Death of Stars (borrowed in part from Ch. 14)

Outline of Chapter 13 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

I. Death of Stars

A white dwarf is about the same size as Earth

Neutron StarAbout 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

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

I. Death of Stars

Black Hole in a Binary SystemIf 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 OUTLINEShorter 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.

We see our galaxy edge-on

Primary features: disk, bulge, halo, globular clusters

The Shape of our Galaxy: a flattened disk

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?

Disk: blue stars star formation

Halo: no blue stars no star formation

Much of star formation in disk happens in spiral arms

The Whirlpool Galaxy

Emission NebulaeBlue StarsGas Clouds

Spiral arms are waves of star formation

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

Disk Stars: 2% heavy elements, stars of all ages

Halo stars formed first, then stopped

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

Stars continuously form in disk as galaxy grows older

Note: This model is oversimplified

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