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=mc 2 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 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 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)/d 2 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= 4  R 2  T 4 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 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/d 2). If we know the apparent brightness and the distance to a star we can calculate its absolute (intrinsic) brightness: apparent brightness = (absolute brightness)/d 2 Luminosity (energy/sec) is equivalent to absolute brightness L = 4  R 2  T 4 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~M 3.5 ) Lifetime on Main Sequence (T MS ~ 1/M 2.5 ) 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 Luminosity 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= 4  R 2  T 4 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(  R 3 )

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 Luminosity H-R diagram depicts: Temperature Color, Spectral Type, Luminosity, 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~M 3.5 ) Lifetime on Main Sequence (T MS ~ 1/M 2.5 ) Outline of Ch 11 part II: The H-R Diagram (cont.)

Lifetime on Main Sequence T MS ~ 1/M 2.5 M in solar masses T in units of Sun’s total lifetime on MS (10 billion years)

Mass- Luminosity of Main Sequence Stars L~ M 3.5 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. Very hot B. Very massive C. Very blue D. 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 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?

Temperature Luminosity Very 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) fusion Faster 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) fusion Faster 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) 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 Supernovas

An evolved massive star ( M > 4 M solar )

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 M o ) produce White Dawrfs Intermediate mass M.S. stars ( 0.4M o < M < 4 solar M o ) produce White Dawrfs High mass stars M.S. (M > 4 solar M o ) 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 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

 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 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 NebulaeExtinction 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.

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 Nebulae Blue Stars Gas Clouds Spiral arms are waves of star formation

What clues to our galaxy’s history do halo stars hold?

Halo Stars: % heavy elements (O, Fe, …), only old stars Disk Stars: 2% heavy elements, stars of all ages

Halo Stars: % heavy elements (O, Fe, …), only old stars Disk Stars: 2% heavy elements, stars of all ages Halo stars formed first, then stopped

Halo Stars: % 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?

Stars appear to be orbiting something massive but invisible … a black hole! Orbits of stars indicate a mass of about 4 million M Sun