ASTRO 101

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ASTRO 101

• Principles of Astronomy

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Instructor Jerome A. Orosz
(rhymes with boris)Contact

• Telephone [phone]
• E-mail orosz_at_sciences.sdsu.edu
• WWW http//mintaka.sdsu.edu/faculty/orosz/web/
• Office Physics 241, hours T TH 330-500

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Text Perspectives on Astronomy First
Editionby Michael A. Seeds Dana Milbank.
4
Astronomy Help Room Hours

• Monday 1200-1300, 1700-1800
• Tuesday 1700-1800
• Wednesday 1200-1400, 1700-1800
• Thursday 1400-1800, 1700-1800
• Friday 900-1000, 1200-1400
• Help room is located in PA 215

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Coming Up

• November 3 In-class review
• November 5 Exam 2
• November 10 Furlough day class cancelled
• Extra review session Wednesday, November 4 at
  330 pm in PA 216

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Review

• Thursday Exam 2 Chapters 5-8
• Bring the Scantron No. F-288-PAR-L

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Breakdown

• There will be three types of questions
• multiple choice questions (2 pts each)
• long answer (5 pts each)
• fill in the blank (1 pt each)

8
Highlights

• The Sun and Stars
• Basic properties
• Spectral type
• Temperature
• Mass and radius
• Luminosity
• Internal Structure

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Highlights

• Stellar Evolution
• Observational aspects
• lifetime depends on initial mass
• Observations of star clusters
• Theory, using stellar models
• outline of phases of stellar evolution, details
  depend on initial mass
• Formation in clouds of gas and dust
• Main sequence
• Expansion into a red giant
• Mass loss
• Planetary nebula (low mass stars)
• Supernova explosion (high mass stars)
• Remnant
• White dwarf (low mass stars)
• Neutron star (massive stars)
• Black hole (most massive stars)

10
Review Questions Chapter 5

• 6. Why cant you see deeper in the Sun than the
  photosphere?
• 7. What evidence can you give that granulation
  is caused by convection?
• 20. How are astronomers able to explore the
  layers of the Sun below the photosphere?
• 24. How can solar flares affect Earth?

11
Review Questions Chapter 6

• 1. Why are Earth-based parallax measurements
  limited to the nearest stars?
• 5. Why are hydrogen Balmer line strong in the
  spectra of medium-temperature stars and weak in
  the spectra of hot and cool stars?
• 7. Why does the luminosity of a star depend on
  both its radius and its temperature?
• 8. How can you be sure that giant stars really
  are larger than main-sequence stars?
• 9. Why do astronomers conclude that white
  dwarfs must be very small?

12
Review Questions Chapter 6

• 12. What observations would you make to study an
  eclipsing binary star?
• 13. Why dont astronomers know the inclination of
  a spectroscopic binary? How do they know the
  inclination of an eclipsing binary?

17. If all of the stars in the photo here
are members of the same star cluster, then they
all have about the same distance. Then why are
three of the brightest stars much redder than the
rest? What kind of star are they?
13
Review Questions Chapter 7

• 1. What opposing forces are balanced in a
  stable star?
• 3. How does the pressure-temperature thermostat
  control the nuclear reactions inside stars?
• 6. Why is there a lower limit to the mass of a
  main sequence star?
• 7. Why does a stars life expectancy depend on
  its mass?

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Review Questions Chapter 7

• What evidence can you cite that the space between
  the stars is not empty?
• Why would an emission nebula near a hot star look
  red, while a reflection nebula near its star look
  blue?
• 10. Why do astronomers rely heavily on infrared
  observations to study star formation?

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Review Questions Chapter 8

• 4. How can star clusters confirm astronomers
  theories of stellar evolution?
• Why cant a white dwarf star contract as it
  cools?
• How are neutron stars and white dwarfs similar?
  How do they differ?
• If neutron stars are hot, why arent they very
  luminous?
• 23. How can a black hole emit X-rays?

16
Review Questions Chapter 5

• 6. Why cant you see deeper in the Sun than the
  photosphere?
• 7. What evidence can you give that granulation
  is caused by convection?
• 20. How are astronomers able to explore the
  layers of the Sun below the photosphere?
• 24. How can solar flares affect Earth?

17
The Sun and the Stars

• The Sun is the nearest example of a star.
• Basic questions to ask
• What do stars look like on their surfaces? Look
  at the Sun since it is so close.
• How do stars work on their insides? Look at both
  the Sun and the stars to get many examples.
• What will happen to the Sun? Look at other stars
  that are in other stages of development.

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The Sun

• There are two broad areas of solar research
• The study of the overall structure of the Sun.
• The study of its detailed surface features.
• Think of the distinction of climate and
  weather on Earth
• Climate refers to global trends.
• Weather refers to local conditions.

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The Surface of the Sun

• The surface of the Sun can be complex.
• Surprisingly, observing the Sun can be quite
  difficult, owing to the immense heat.
• The study of the solar surface is usually done
  using many different wavelengths, from the X-rays
  to radio. Different features show up well in
  certain wavelengths.

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The Solar Surface

• The Sun has no solid surface. The part we see is
  called the photosphere.
• A visual light image captures different features
  than an ultraviolet light image.

21
The Solar Surface

• The Sun has no solid surface. The part we see is
  called the photosphere.
• High resolution images of the photosphere show
  granulation.

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Granulation

• From the measurement of Doppler shifts, we know
  that the granules are blobs of gas that are
  rising and falling.
• The granules are similar to what one sees in
  boiling water on Earth.
• Energy from the interior is being transported
  outwards by motions in the gas. This type of
  energy transport is called convection.

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Solar Oscillations

• By detailed analysis of the Doppler shifts of
  different parts of the photosphere, we know that
  the photosphere oscillates (i.e. it vibrates much
  like a bell).
• These vibrations are somewhat similar to sound
  waves in the air on Earth.
• Since the speed of sound in a gas depends on the
  temperature and density of the gas, the study of
  solar oscillations can reveal details about the
  solar interior.

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Sunspots

• Sunspots are darker regions on the Suns surface.
• They can be observed in the optical, and were
  first discovered by Galileo in 1610.

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Sunspots

• Note the complex structure in the spot and its
  surroundings.

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The Solar Cycle

• In the mid 1800s, a Swiss astronomer made
  detailed observations of sunspots in order to
  search for transits of a possible planet interior
  to Mercury.

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The Solar Cycle

• No planets were found, but it was discovered that
  the number of sunspots varies with an 11 year
  cycle.
• This is not fully understood.

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Sunspots

• Galileo used sunspots to track the rotation of
  the Suns surface

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Sunspots

• Galileo was the first to sunspots to track the
  rotation of the Suns surface.

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Sunspots

• Galileo was the first to sunspots to track the
  rotation of the Suns surface.
• The Sun does not rotate as a solid body. The
  equator rotates once every 25 days. At 45o
  latitude, it takes 27.8 days.

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The Sun and Space Weather

• Violent activity can occur in regions near
  sunspots.
• A solar flare is a giant eruption of particles
  and radiation.
• The radiation and particles can interact with the
  Earths upper atmosphere, disrupting satellite
  communications and power grids.

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The Sun and Space Weather

• Violent activity can occur in regions near
  sunspots.
• A solar flare is a giant eruption of particles
  and radiation.
• The cause of these giant flares is not
  understood, although magnetic fields are thought
  to play a role.

33
Review Questions Chapter 5

• 6. Why cant you see deeper in the Sun than the
  photosphere?
• 7. What evidence can you give that granulation
  is caused by convection?
• 20. How are astronomers able to explore the
  layers of the Sun below the photosphere?
• 24. How can solar flares affect Earth?

34
Review Questions Chapter 6

• 1. Why are Earth-based parallax measurements
  limited to the nearest stars?
• 5. Why are hydrogen Balmer line strong in the
  spectra of medium-temperature stars and weak in
  the spectra of hot and cool stars?
• 7. Why does the luminosity of a star depend on
  both its radius and its temperature?
• 8. How can you be sure that giant stars really
  are larger than main-sequence stars?
• 9. Why do astronomers conclude that white
  dwarfs must be very small?

35
Review Questions Chapter 6

• 12. What observations would you make to study an
  eclipsing binary star?
• 13. Why dont astronomers know the inclination of
  a spectroscopic binary? How do they know the
  inclination of an eclipsing binary?

17. If all of the stars in the photo here
are members of the same star cluster, then they
all have about the same distance. Then why are
three of the brightest stars much redder than the
rest? What kind of star are they?
36
The Distance

• How can you measure the distance to something?
• Direct methods, e.g. a tape measure. Not good for
  things in the sky.
• Sonar or radar send out a signal with a know
  velocity and measure the time it takes for the
  reflected signal. Works for only relatively
  nearby objects (e.g. the Moon, certain
  asteroids).
• Triangulation the use of parallax.

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The Parallax

• Parallax is basically the apparent shifting of
  nearby objects with respect to far away objects
  when the viewing angle is changes.
• Example hold out your finger and view it with
  one eye closed, then the other eye closed. Your
  finger shifts with respect to the background.

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The Parallax

• Example hold out your finger and view it with
  one eye closed, then the other eye closed. Your
  finger shifts with respect to the background.

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The Parallax

• A better example place an object on the table
  in front of the room and look at its position
  against the back wall as you walk by. In most
  practical applications you will have to change
  your position to make use of parallax.

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Triangulation

• Triangulation is based on trigonometry, and is
  often used by surveyors.
• Here is another diagram showing the technique.
  This technique can be applied to other stars!

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
41
Triangulating the Stars

• The largest baseline one can obtain is the orbit
  of the Earth!
• When viewed at 6 month intervals, a relatively
  nearby star will appear to shift with respect to
  distant stars.

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Triangulating the Stars

• The largest baseline one can obtain is the orbit
  of the Earth!
• When viewed at 6 month intervals, a relatively
  nearby star will appear to shift with respect to
  distant stars.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
43
Triangulating the Stars

• The largest baseline one can obtain is the orbit
  of the Earth!
• When viewed at 6 month intervals, a relatively
  nearby star will appear to shift with respect to
  distant stars.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
44
Triangulating the Stars

• Here are two neat Java tools demonstrating
  parallax

http//www.astro.ubc.ca/scharein/a310/Sim.htmlOn
eover
http//spiff.rit.edu/classes/phys240/lectures/para
llax/para1_jan.html
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Triangulating the Stars

• When viewed at 6 month intervals, a relatively
  nearby star will appear to shift with respect to
  distant stars.
• The angle p for the nearest star is 0.77
  arcseconds. One can currently measure angles as
  small as a few thousands of an arcsecond.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
46
Triangulating the Stars

• For very tiny angles, use the approximation that
  tan(p)p, when p is in radians.
• Then dB/tan(p) becomes dB/p.
• B1 astronomical unit (e.g. the Earth-Sun
  distance). Define a unit of distance such that
  d1/p, if the angle p is measured in arcseconds.
• This unit is the parsec, which is 3.26 light
  years.

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Stellar Distances

• Parallax angles as small as about 1/50 of an
  arcsecond can be measured from the ground. Thus
  the distance can be measured only for stars
  closer than 50 parsecs (163 light years).
• From space, parallax angles as small as about
  0.003 arcseconds can be measured, corresponding
  to distances closer than about 300 parsecs.

48
Review Questions Chapter 6

• 1. Why are Earth-based parallax measurements
  limited to the nearest stars?
• 5. Why are hydrogen Balmer line strong in the
  spectra of medium-temperature stars and weak in
  the spectra of hot and cool stars?
• 7. Why does the luminosity of a star depend on
  both its radius and its temperature?
• 8. How can you be sure that giant stars really
  are larger than main-sequence stars?
• 9. Why do astronomers conclude that white
  dwarfs must be very small?

49
Observing Other Stars

• Recall there is basically no hope of spatially
  resolving the disk of any star (apart from the
  Sun). The stars are very far away, so their
  angular size as seen from Earth is extremely
  small.
• The light we receive from a star comes from the
  entire hemisphere that is facing us. That is, we
  see the disk-integrated light.

50
Observing Other Stars

• To get an understanding of how a star works, the
  most useful thing to do is to measure the
  spectral energy distribution, which is a plot of
  the intensity of the photons vs. their
  wavelengths (or frequencies or energies).
• There are two ways to do this
• Broad band, by taking images with a camera and
  a colored filter.
• High resolution, by using special optics to
  disperse the light and record it.

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Broad Band Photometry

• Despite the disadvantages, broad band photometry
  is useful.
• For example, it is immediately evident that
  different stars have different colors (the
  image on the left is a composite of three images
  taken in different filters.

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High Resolution Spectroscopy

• To obtain a high resolution spectrum, light from
  a star is passed through a prism (or reflected
  off a grating), and focused and detected using
  some complicated optics.

53
High Resolution Spectroscopy

• Using a good high resolution spectrum, you can
  get a much better measurement of the spectral
  energy distribution.
• The disadvantage is that the efficiency is lower
  (more photons are lost in the complex optics).
  Also, it is difficult to measure more than one
  star at a time (in contrast to the direct imaging
  where several stars can be on the same image).

54
Stellar Properties

• The Sun and the stars are similar objects.
• In order to understand them, we want to try and
  measure as many properties about them as we can
• Temperature at the surface
• Power output (luminosity)
• Radius
• Mass
• Chemical composition

55
Spectral Classification

• In the early 1800s, Joseph Fraunhofer observed
  the solar spectrum. He saw dark regions, known
  as spectral lines (these tell us what elements
  are there).
• Starting in the late 1800s, it became possible to
  take the spectra of stars with similar detail.

56
Spectral Classification

• At first, there was no physical understanding.
• The earliest classification scheme was based on
  the strength of the hydrogen lines, with classes
  of A, B, C, D, E, F, G, H, I, J, K, L, M, N, O.
• Class A had the strongest hydrogen lines, class O
  the weakest.
• Later on, only a few of these classes were kept.
  Then, subclasses were added (e.g. G2), based on
  other elements.

57
Spectral Classification

• At first, there was no physical understanding.
• The earliest classification scheme was based on
  the strength of the hydrogen lines, with classes
  of A, B, F, G, K, M, O.
• Eventually, physical understanding came. It was
  discovered that the spectral type was a
  temperature indicator. As a result, a more
  natural ordering of the spectral types became O,
  B, A, F, G, K, M (the old classes were retained).

58
Spectral Type Sequence Mnemonics

• Oh Boy, An F Grade Kills Me
• Oh, Be A Fine Girl, Kiss Me
• http//www.astro.sunysb.edu/fwalter/AST101/mnemoni
  c.html

59
Spectral Classification

• Here are digital plots of representative stars in
  the spectral sequence.
• Note the variation in the strength of the
  hydrogen lines.

60
Spectral Classification

• This is a computer simulation of the different
  types.

61
Spectral Classification

• Why do the spectral classes look different from
  one another?
• The temperature. The electrons in the atoms are
  responsible for the spectral lines, and the
  energies of the electrons are change with
  changing temperature. Example an O-star is so
  hot that the hydrogen atoms have lost their
  electrons, so no lines of hydrogen are seen.

62
Spectral Classification

• http//www.astronomynotes.com

63
Spectral Classification

• This is a computer simulation of the different
  types.

64
Spectral Classification

• A measurement of the spectral type gives the
  surface temperature of the star.
• O-stars are the hottest, with surface
  temperatures of up to 60,000 K.
• M-stars are the coolest, with temperatures of
  only 3000 K.
• The temperature of the Sun (a G2 star) is 5770 K.

65
Review Questions Chapter 6

• 1. Why are Earth-based parallax measurements
  limited to the nearest stars?
• 5. Why are hydrogen Balmer line strong in the
  spectra of medium-temperature stars and weak in
  the spectra of hot and cool stars?
• 7. Why does the luminosity of a star depend on
  both its radius and its temperature?
• 8. How can you be sure that giant stars really
  are larger than main-sequence stars?
• 9. Why do astronomers conclude that white
  dwarfs must be very small?

66
Stellar Properties

• The Sun and the stars are similar objects.
• In order to understand them, we want to try and
  measure as many properties about them as we can
• Temperature at the surface Use the spectral
  type
• Power output (luminosity)
• Radius
• Mass
• Chemical composition

67
The Luminosity of Stars

• An important physical characteristic of a star is
  its luminosity, which is a measure of the amount
  of energy emitted by the star at its surface per
  unit time.

68
The Luminosity of Stars

• An important physical characteristic of a star is
  its luminosity, which is a measure of the amount
  of energy emitted by the star at its surface per
  unit time.
• We can measure the amount of energy received from
  the star per unit time (we call this the flux).

69
The Luminosity of Stars

• An important physical characteristic of a star is
  its luminosity, which is a measure of the amount
  of energy emitted by the star at its surface per
  unit time.
• We can measure the amount of energy received from
  the star per unit time (we call this the flux).
• How do we relate the luminosity to the flux?

70
The Inverse Square Law

• The received flux from a source depend inversely
  on the square of the distance.

71
The Inverse Square Law

• Here is a neat Java tool demonstrating the
  inverse square law

http//www.astro.ubc.ca/scharein/a310/Sim.htmlOn
eover
72
The Inverse Square Law

• The received flux from a source depend inversely
  on the square of the distance.
• If you want to know the intrinsic luminosity of
  your source, you must measure the flux and the
  distance.

73
Stellar Properties

• The Sun and the stars are similar objects.
• In order to understand them, we want to try and
  measure as many properties about them as we can
• Temperature at the surface Use the spectral
  type
• Power output (luminosity) Measure the flux
  distance
• Radius
• Mass
• Chemical composition

74
Stellar Properties

• We can measure the apparent brightnesses of stars
  relatively easily (e.g. broad-band photometry).
• We can measure the color index and/or the
  spectral type of stars. This gives us the
  temperatures.
• We can measure the distances to the relatively
  nearby stars. Thus we can compute intrinsic
  brightnesses or luminosities for these stars.
• What do you do with these data?

75
Temperature-Luminosity Diagrams

• When you have a large number of objects, each
  with several observed characteristics, look for
  correlations between the observed properties.

76
Correlations

• You might plot the horsepower of a cars engine
  vs. the weight of the car.
• Most cars would fall along a single sequence, but
  some would deviate.

77
Temperature-Luminosity Diagrams

• When you have a large number of objects, each
  with several observed characteristics, look for
  correlations between the observed properties.
• Henry Norris Russell and Ejnar Hertzsprung were
  the first to do this with stars in the early
  1900s.
• Some measure of the temperature is plotted on the
  x-axis of the plot, and some measure of the
  intrinsic luminosity is plotted on the y-axis.

78
Temperature-Luminosity Diagrams

• The stars do not fall on random locations in this
  diagram!

79
Temperature-Luminosity Diagrams

• The stars do not fall on random locations in this
  diagram!

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
80
Temperature-Luminosity Diagrams

• The stars do not fall on random locations in this
  diagram!
• What does this mean?

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
81
Temperature-Luminosity Diagrams

• The stars do not fall on random locations in this
  diagram!
• What does this mean?
• This diagram gives us clues to inner workings of
  stars, and how they evolve.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
82
Temperature-Luminosity Diagrams

• The stars do not fall on random locations in this
  diagram!
• There is some specific physical process that
  limits where a star can be on this diagram.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
83
Temperature-Luminosity Diagrams

• The stars do not fall on random locations in this
  diagram!
• Furthermore, the location of a star on this
  diagram is an indicator of its size.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
84
Review Black Body Radiation

• Recall the discussion of the ideal radiator,
  aka the black body.

85
Review Black Body Radiation

• For a given size, hotter objects give off more
  energy than cooler objects, and are bluer.

86
Black Body Radiation

• For a given temperature, larger bodies give off
  more energy than smaller bodies, in direct
  proportion to their surface areas.

87
Black Body Radiation

• The luminosity (energy loss per unit time) of a
  black body is proportional the surface area times
  the temperature to the 4th power

88
Black Body Radiation

• What does this equation tell us?

89
Black Body Radiation

• What does this equation tell us?
• The luminosity, radius, and temperature of a
  black body are related measure any two values,
  you can compute the third one.

90
Black Body Radiation

• The luminosity, radius, and temperature of a
  black body are related measure any two values,
  you can compute the third one.
• Since stars are approximately black bodies, their
  location in the CMD indicates their radii.

91
Temperature-Luminosity Diagrams

• Temperature is on the x-axis hotter stars are on
  the left, cooler ones on the right.
• Luminosity is on the y-axis, more luminuous ones
  are at the top, the less luminuous ones are at
  the bottom.

92
Temperature-Luminosity Diagrams

• Temperature is on the x-axis hotter stars are on
  the left, cooler ones on the right.
• Luminosity is on the y-axis, more luminuous ones
  are at the top, the less luminuous ones are at
  the bottom.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
93
Temperature-Luminosity Diagrams

• Lines of constant radius go something like this

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
94
Temperature-Luminosity Diagrams

• Lines of constant radius go something like this

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
95
Temperature-Luminosity Diagrams

• Lines of constant radius go something like this
• Cool and luminous stars large radii.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
96
Temperature-Luminosity Diagrams

• Lines of constant radius go something like this
• Cool and luminous stars large radii.
• Hot and faint stars small radii.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
97
Temperature-Luminosity Diagrams

• Lines of constant radius go something like this
• Cool and luminous stars large radii.
• Hot and faint stars small radii.
• Most stars are here, and there is not a large
  variation in radius.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
98
Temperature-Luminosity Diagrams

• This diagram shows some well-known stars. Most
  of the bright stars you see without a telescope
  are giants.

99
Review Questions Chapter 6

• 1. Why are Earth-based parallax measurements
  limited to the nearest stars?
• 5. Why are hydrogen Balmer line strong in the
  spectra of medium-temperature stars and weak in
  the spectra of hot and cool stars?
• 7. Why does the luminosity of a star depend on
  both its radius and its temperature?
• 8. How can you be sure that giant stars really
  are larger than main-sequence stars?
• 9. Why do astronomers conclude that white
  dwarfs must be very small?

100
Review Questions Chapter 6

• 12. What observations would you make to study an
  eclipsing binary star?
• 13. Why dont astronomers know the inclination of
  a spectroscopic binary? How do they know the
  inclination of an eclipsing binary?

17. If all of the stars in the photo here
are members of the same star cluster, then they
all have about the same distance. Then why are
three of the brightest stars much redder than the
rest? What kind of star are they?
101
Binary Stars

• A binary system is when two stars are bound
  together by gravity. They orbit their common
  center of mass.

102
Detour The Two-Body Problem

• Use Newtons Laws to describe the behavior of two
  objects under the influence of their mutual
  gravity.
• We will apply it to binary star systems (e.g. a
  system consisting of two stars).

103
Center of Mass

• For two point masses, the center of mass is along
  the line joining the two masses.
• The center of mass is closer to the more massive
  body.

104
Center of Mass

• Why is this useful? Two bodies acting under their
  mutual gravity will orbit in a plane about their
  center of mass.
• Here is the case for equal masses.

105
Center of Mass

• Why is this useful? Two bodies acting under their
  mutual gravity will orbit in a plane about their
  center of mass.
• Here is the case for M1 2M2.

106
Center of Mass

• Why is this useful? Two bodies acting under their
  mutual gravity will orbit in a plane about their
  center of mass.
• Here is the case for M1 gtgt M2, for example
  the Sun and Earth.

107
Binary Stars

• A binary system is when two stars are bound
  together by gravity. They orbit their common
  center of mass.
• In some cases, you can see two stars move around
  each other on the sky.

108
Binary Stars

• A binary system is when two stars are bound
  together by gravity. They orbit their common
  center of mass.
• In some cases, you can see two stars move around
  each other on the sky.
• These are visual binaries.

109
Binary Stars

• A binary system is when two stars are bound
  together by gravity. They orbit their common
  center of mass.
• In a visual binary, you can see two stars.
• However, for most binary stars, their separation
  is very small compared to their distance, and
  from Earth they appear to be a single point.
• How do you observe these types of binaries? Use
  spectroscopy!

110
Center of Mass

• A star will appear to wobble when it is
  orbiting another body.
• If the other body is another star, the wobble
  will be relatively large.
• If the other body is a planet, the wobble will be
  very small.

111
Detecting the Wobble
112
Detecting the Wobble

• In Astronomy, any motion can be broken down into
  two groups
• Motion in the plane of the sky (e.g. east-west
  and north-south motion).

113
Detecting the Wobble

• In Astronomy, any motion can be broken down into
  two groups
• Motion in the plane of the sky (e.g. east-west
  and north-south motion).
• Motion towards or away from us (e.g. radial
  velocities).

114
Detecting the Wobble

• In Astronomy, any motion can be broken down into
  two groups
• Motion in the plane of the sky (e.g. east-west
  and north-south motion).
• Motion towards or away from us (e.g. radial
  velocities).
• For a binary star, the decomposition depends on
  the orientation of the orbit

115
Detecting the Wobble

• In Astronomy, any motion can be broken down into
  two groups
• Motion in the plane of the sky (e.g. east-west
  and north-south motion).
• Motion towards or away from us (e.g. radial
  velocities).
• For a binary star, the decomposition depends on
  the orientation of the orbit
• For an orbit seen face-on, all motion is in the
  plane of the sky.
• For an orbit seen edge-on, the motion is also in
  the radial direction. The size of the radial
  velocity variations depend on the inclination of
  the orbit (the radial velocity is the true
  velocity times the sine of the inclination.)

116
Viewing Angle

• The plane of the orbit is two dimensional, so
  depending on how that plane is tilted with
  respect to your line of sight you can see
  different things.

117
Detecting the Wobble

• In Astronomy, any motion can be broken down into
  two groups
• Motion in the plane of the sky (e.g. east-west
  and north-south motion).
• Motion towards or away from us (e.g. radial
  velocities).
• Motions in the plane of the sky are usually
  small, and typically one has to wait many years
  to see a relatively big shift.

118
Detecting the Wobble

• In Astronomy, any motion can be broken down into
  two groups
• Motion in the plane of the sky (e.g. east-west
  and north-south motion).
• Motion towards or away from us (e.g. radial
  velocities).
• Motions in the plane of the sky are usually
  small, and typically one has to wait many years
  to see a relatively big shift. One can see
  Sirius wobble over the course of decades (it has
  a very massive, but dark, companion).

119
Detecting the Wobble

• In Astronomy, any motion can be broken down into
  two groups
• Motion in the plane of the sky (e.g. east-west
  and north-south motion).
• Motion towards or away from us (e.g. radial
  velocities).
• Motions in the plane of the sky are usually
  small, and typically one has to wait many years
  to see a relatively big shift. We cant detect
  this motion in most binaries.

120
Detecting the Wobble

• In Astronomy, any motion can be broken down into
  two groups
• Motion in the plane of the sky (e.g. east-west
  and north-south motion).
• Motion towards or away from us (e.g. radial
  velocities).
• Motions in the plane of the sky are usually
  small, and typically one has to wait many years
  to see a relatively big shift. We cant detect
  this motion in most binaries.

121
Detecting Radial Velocities

• Recall that radial velocities can be measured
  from Doppler shifts in the spectral lines

122
Detecting Radial Velocities

• Recall that radial velocities can be measured
  from Doppler shifts in the spectral lines

Motion towards us gives a shorter observed
wavelength.
123
Detecting Radial Velocities

• Recall that radial velocities can be measured
  from Doppler shifts in the spectral lines

Motion towards us gives a shorter observed
wavelength. Motion away from us gives a longer
observed wavelength.
124
Spectroscopic Binaries

• Recall that radial velocities can be measured
  from Doppler shifts in the spectral lines
• Here are two spectra of Castor B, taken at two
  different times. The shift in the lines due to a
  change in the radial velocity is apparent.

125
Spectroscopic Binaries

• The radial velocity of each star changes smoothly
  as the stars orbit each other.
• These changes in the radial velocity can be
  measured using high resolution spectra.

126
Spectroscopic Binaries

• Recall from that radial velocities can be
  measured from Doppler shifts in the spectral
  lines

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
127
Spectroscopic Binaries

• In some cases, you can see both stars in the
  spectrum.
• In most cases, you can only see one star changing
  its radial velocity in a periodic way.

128
Binary Stars

• A binary system is when two stars are bound
  together by gravity. They orbit their common
  center of mass.
• In some cases, we can use binary stars to measure
  precise masses and radii for stars.

129
Center of Mass

• Recall that m1r1m2r2
• Also, note that velocity of the star is
  proportional to the distance to the center of
  mass since a star further from the COM has a
  greater distance to cover in the same amount of
  time.

130
Center of Mass

• Recall that m1r1m2r2
• Also, note that velocity of the star is
  proportional to the distance to the center of
  mass since a star further from the COM has a
  greater distance to cover in the same amount of
  time. This implies m1v1m2v2, or m1/m2v2/v1

131
Center of Mass

• Recall that m1r1m2r2
• Also, note that velocity of the star is
  proportional to the distance to the center of
  mass since a star further from the COM has a
  greater distance to cover in the same amount of
  time. This implies m1v1m2v2, or m1/m2v2/v1
• The ratio of the velocities in inversely
  proportional to the mass ratio.

132
Center of Mass

• Recall that m1r1m2r2
• Also, note that velocity of the star is
  proportional to the distance to the center of
  mass since a star further from the COM has a
  greater distance to cover in the same amount of
  time. This implies m1v1m2v2, or m1/m2v2/v1
• The ratio of the velocities in inversely
  proportional to the mass ratio. Also, the same
  is true for radial velocities.

133
Center of Mass

• If you can see both stars in the spectrum, then
  you may be able to use Doppler shifts to measure
  the radial velocities of both stars. This gives
  you the mass ratio, regardless of the viewing
  angle (e.g. nearly face-on, nearly edge-on, etc.).

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
134
Stellar Masses

• If you can see both stars in the spectrum, then
  you may be able to use Doppler shifts to measure
  the radial velocities of both stars. This gives
  you the mass ratio, regardless of the viewing
  angle (e.g. nearly face-on, nearly edge-on,
  etc.). This is usually useful information.

135
Stellar Masses

• If you can see both stars in the spectrum, then
  you may be able to use Doppler shifts to measure
  the radial velocities of both stars. This gives
  you the mass ratio, regardless of the viewing
  angle (e.g. nearly face-on, nearly edge-on,
  etc.). This is usually useful information.
• If you can find the viewing angle, then you can
  compute true orbital velocities and use Keplers
  Laws and Newtons theory to find the actual
  masses.

136
Viewing Angle

• The plane of the orbit is two dimensional, so
  depending on how that plane is tilted with
  respect to your line of sight you can see
  different things.

137
Stellar Masses

• If you can see both stars in the spectrum, then
  you may be able to use Doppler shifts to measure
  the radial velocities of both stars. This gives
  you the mass ratio, regardless of the viewing
  angle (e.g. nearly face-on, nearly edge-on,
  etc.). This is usually useful information.
• If you can find the viewing angle, then you can
  compute true orbital velocities and use Keplers
  Laws and Newtons theory to find the actual
  masses. How do you find the viewing angle?

138
Stellar Masses

• If you can see both stars in the spectrum, then
  you may be able to use Doppler shifts to measure
  the radial velocities of both stars. This gives
  you the mass ratio, regardless of the viewing
  angle (e.g. nearly face-on, nearly edge-on,
  etc.). This is usually useful information.
• If you can find the viewing angle, then you can
  compute true orbital velocities and use Keplers
  Laws and Newtons theory to find the actual
  masses. Find eclipsing systems!

139
Definition

• An eclipse, occultation, and transit essentially
  mean the same thing one body passes in front of
  another as seen from earth.

140
Eclipsing Systems and Stellar Radii

• Eclipsing systems must be nearly edge-on, since
  the stars appear to pass in front of each other
  as seen from Earth.

141
Eclipsing Systems and Stellar Radii

• The relative radii can be found by studying how
  much light is blocked, and for how long.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
142
Eclipsing Systems and Stellar Radii

• The light curve depends on the relative sizes
  and brightnesses of the stars, and on the
  orientation.

143
Eclipsing Systems and Stellar Radii

• The light curve depends on the relative sizes
  and brightnesses of the stars, and on the
  orientation.
• Algol was known to be variable for a long time,
  and its periodic nature was established in 1783.

144
Accurate Masses and Radii From Binary Stars

• The ideal binary systems are ones where both
  stars are seen in the spectrum (double-lined),
  and where eclipses are seen.

145
Accurate Masses and Radii From Binary Stars

• The ideal binary systems are ones where both
  stars are seen in the spectrum (double-lined),
  and where eclipses are seen. Masses and radii
  accurate to a few percent can be derived from
  careful observations of these systems.

146
Accurate Masses and Radii From Binary Stars

• The ideal binary systems are ones where both
  stars are seen in the spectrum (double-lined),
  and where eclipses are seen. Masses and radii
  accurate to a few percent can be derived from
  careful observations of these systems.
• There are on the order of 100 such well-studied
  systems with main sequence stars. What do you
  do with this information?

147
Mass-Luminosity Relation

• The stars form a tight sequence. This is another
  clue to the inner workings of stars!

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
148
Stellar Properties

• The Sun and the stars are similar objects.
• In order to understand them, we want to try and
  measure as many properties about them as we can
• Temperature at the surface ---use spectral
  types
• Power output (luminosity) --- flux and distance
• Radius --- eclipsing binary stars
• Mass --- eclipsing binary stars
• Chemical composition

149
Review Questions Chapter 6

• 1. Why are Earth-based parallax measurements
  limited to the nearest stars?
• 5. Why are hydrogen Balmer line strong in the
  spectra of medium-temperature stars and weak in
  the spectra of hot and cool stars?
• 7. Why does the luminosity of a star depend on
  both its radius and its temperature?
• 8. How can you be sure that giant stars really
  are larger than main-sequence stars?
• 9. Why do astronomers conclude that white
  dwarfs must be very small?

150
Review Questions Chapter 6

• 12. What observations would you make to study an
  eclipsing binary star?
• 13. Why dont astronomers know the inclination of
  a spectroscopic binary? How do they know the
  inclination of an eclipsing binary?

17. If all of the stars in the photo here
are members of the same star cluster, then they
all have about the same distance. Then why are
three of the brightest stars much redder than the
rest? What kind of star are they?
151
Review Questions Chapter 7

• 1. What opposing forces are balanced in a
  stable star?
• 3. How does the pressure-temperature thermostat
  control the nuclear reactions inside stars?
• 6. Why is there a lower limit to the mass of a
  main sequence star?
• 7. Why does a stars life expectancy depend on
  its mass?

152
Models of the Solar Interior

• The interior of the Sun is relatively simple
  because it is an ideal gas, described by three
  quantities
• Temperature
• Pressure
• Mass density

153
Models of the Solar Interior

• The interior of the Sun is relatively simple
  because it is an ideal gas, described by three
  quantities
• Temperature
• Pressure
• Mass density
• The relationship between these three quantities
  is called the equation of state.

154
Ideal Gas

• For a fixed volume, a hotter gas exerts a higher
  pressure

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
155
Hydrostatic Equilibrium

• The Sun does not collapse on itself, nor does it
  expand rapidly.

156
Hydrostatic Equilibrium

• The Sun does not collapse on itself, nor does it
  expand rapidly. Gravity and internal pressure
  balance

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
157
Hydrostatic Equilibrium

• The Sun does not collapse on itself, nor does it
  expand rapidly. Gravity and internal pressure
  balance. This is true at all layers of the Sun.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
158
Hydrostatic Equilibrium

• The Sun (and other stars) does not collapse on
  itself, nor does it expand rapidly. Gravity and
  internal pressure balance. This is true at all
  layers of the Sun.
• The temperature increases as you go deeper and
  deeper into the Sun!

159
Models of the Solar Interior

• The pieces so far
• Energy generation (nuclear fusion).
• Ideal gas law (relation between temperature,
  pressure, and volume.
• Hydrostatic equilibrium (gravity balances
  pressure).

160
Models of the Solar Interior

• The pieces so far
• Energy generation (nuclear fusion).
• Ideal gas law (relation between temperature,
  pressure, and volume.
• Hydrostatic equilibrium (gravity balances
  pressure).
• Continuity of mass (smooth distribution
  throughout the star).

161
Models of the Solar Interior

• The pieces so far
• Energy generation (nuclear fusion).
• Ideal gas law (relation between temperature,
  pressure, and volume.
• Hydrostatic equilibrium (gravity balances
  pressure).
• Continuity of mass (smooth distribution
  throughout the star).
• Continuity of energy (amount entering the bottom
  of a layer is equal to the amount leaving the
  top).

162
Models of the Solar Interior

• The pieces so far
• Energy generation (nuclear fusion).
• Ideal gas law (relation between temperature,
  pressure, and volume.
• Hydrostatic equilibrium (gravity balances
  pressure).
• Continuity of mass (smooth distribution
  throughout the star).
• Continuity of energy (amount entering the bottom
  of a layer is equal to the amount leaving the
  top).
• Energy transport (how energy is moved from the
  core to the surface).

163
Models of the Solar Interior

• Solve these equations on a computer
• Compute the temperature and density at any layer,
  at any time.
• Compute the size and luminosity of the star as a
  function of the initial mass.
• Etc.

164
Stellar Models
165
Review Questions Chapter 7

• 1. What opposing forces are balanced in a
  stable star?
• 3. How does the pressure-temperature thermostat
  control the nuclear reactions inside stars?
• 6. Why is there a lower limit to the mass of a
  main sequence star?
• 7. Why does a stars life expectancy depend on
  its mass?

166
Nuclear Fusion

• Summary 4 hydrogen nuclei (which are protons)
  combine to form 1 helium nucleus (which has two
  protons and two neutrons).
• Why does this produce energy?
• Before the mass of 4 protons is 4 proton masses.
• After the mass of 2 protons and 2 neutrons is
  3.97 proton masses.
• Einstein E mc2. The missing mass went into
  energy! 4H ---gt 1He energy

167
Controlled Fusion in the Sun

• First, note that the rate of the p-p chain or CNO
  cycle is very sensitive to the temperature.
• Rate (temperature)4 for p-p chain.
• Rate (temperature)15 for the CNO cycle.
• Small changes in the temperature lead to large
  changes in the fusion rate.
• Suppose the fusion rate inside the Sun increased

168
Controlled Fusion in the Sun

• First, note that the rate of the p-p chain or CNO
  cycle is very sensitive to the temperature.
• Rate (temperature)4 for p-p chain.
• Rate (temperature)15 for the CNO cycle.
• Small changes in the temperature lead to large
  changes in the fusion rate.
• Suppose the fusion rate inside the Sun increased
• The increased energy heats the core and expands
  the star. But the expansion cools the core,
  lowering the fusion rate. The lower rate allows
  the core to shrink back to where it was before.

169
Odds and Ends

• Why does L vary like (mass)4? E.g., why is an
  O-star about 10,000 times more luminous than the
  Sun when its mass is only 20 times the solar mass?

170
Odds and Ends

• Why does L vary like (mass)4? E.g., why is an
  O-star about 10,000 times more luminous than the
  Sun when its mass is only 20 times the solar
  mass?
• More massive stars need hotter interiors to be
  stable. The increased temperature leads to large
  increase in energy generation (the rate varies
  like (temperature)15.)

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
171
Odds and Ends

• Why are there no stars more massive than about
  100 solar masses, and no stars with masses less
  than about 1/10 of a solar mass?

172
Odds and Ends

• Why are there no stars more massive than about
  100 solar masses, and no stars with masses less
  than about 1/10 of a solar mass?
• At the high end, the pressure rises rapidly with
  mass, and is stronger than gravity when the mass
  gets near 100 solar masses.

173
Odds and Ends

• Why are there no stars more massive than about
  100 solar masses, and no stars with masses less
  than about 1/10 of a solar mass?
• At the high end, the pressure rises rapidly with
  mass, and is stronger than gravity when the mass
  gets near 100 solar masses. The star is no longer
  stable!

174
Odds and Ends

• Why are there no stars more massive than about
  100 solar masses, and no stars with masses less
  than about 1/10 of a solar mass?
• At the low end, the core temperature does not get
  high enough to fuse hydrogen since the
  gravitational force is relatively weak.

175
Odds and Ends

• Why are there no stars more massive than about
  100 solar masses, and no stars with masses less
  than about 1/10 of a solar mass?
• At the low end, the core temperature does not get
  high enough to fuse hydrogen since the
  gravitational force is relatively weak. Brown
  dwarfs are such low-mass objects.

176
Review Questions Chapter 7

• 1. What opposing forces are balanced in a
  stable star?
• 3. How does the pressure-temperature thermostat
  control the nuclear reactions inside stars?
• 6. Why is there a lower limit to the mass of a
  main sequence star?
• 7. Why does a stars life expectancy depend on
  its mass?

177
Review Questions Chapter 7

• What evidence can you cite that the space between
  the stars is not empty?
• Why would an emission nebula near a hot star look
  red, while a reflection nebula near its star look
  blue?
• 10. Why do astronomers rely heavily on infrared
  observations to study star formation?

178
Side Bar Observing Clouds

• Ways to see gas
• By reflection of a nearby light source. Blue
  light reflects better than red light, so
  reflection nebulae tend to look blue.
• By emission at discrete wavelengths. A common
  example is emission in the Balmer-alpha line of
  hydrogen, which appears red.

179
Side Bar Observing Clouds

• Ways to see dust
• If the dust is warm (a few hundred degrees K)
  then it will emit light in the long-wavelength
  infrared region or in the short-wavelength radio.
• Dust will absorb light blue visible light is
  highly absorbed red visible light is less
  absorbed, and infrared light suffers from
  relatively little absorption. Dust causes
  reddening.

180
Interstellar Dust

• The dust is composed of tiny slivers of graphite
  and silicates, possibly coated with water ice.
• Note that the scale on this diagram is 10-7
  meters!

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
181
Interstellar Dust

• Light passing through an interstellar dust cloud
  will be dimmed.
• However, the amount of dimming depends on the
  wavelength of the light blue light is scattered
  more easily than red light. The object appears
  redder.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
182
Why is the Sky Blue?

• Blue light travels a relatively short distance
  before it is scattered by molecules in the air.
  Red light goes much further before being
  scattered.

Image from Nick Strobels Astronomy Notes
(http//www.astronomynotes.com)
183
Intersteller Dust

• Interstellar dust makes a star appear dimmer and
  redder if that star is behind a cloud of dust.

184
Interstellar Dust

• Interstellar dust makes a star appear dimmer and
  redder if that star is behind a cloud of dust.

185
Giant Molecular Clouds

• This nebula is in the sword of Orion. It is
  about 29 light years across and 1500 light years
  away.
• Dark regions are apparent (obscuration by dust),
  as well as regions of glowing gas (heated by a
  nearby hot star). Image from Nick
  Strobels Astronomy Notes (http//www.astronomynot
  es.com)

186
Giant Molecular Clouds

• This nebula is in the belt of Orion. Dark dust
  lanes and also glowing gas are evident.

187
Giant Molecular Clouds
188
Giant Molecular Clouds

• Interstellar dust makes stars appear redder.

189
Giant Molecular Clouds
190
Review Questions Chapter 7

• What evidence can you cite that the space between
  the stars is not empty?
• Why would an emission nebula near a hot star look
  red, while a reflection nebula near its star look
  blue?
• 10. Why do astronomers rely heavily on infrared
  observations to study star formation?

191
Review Questions Chapter 8

• 4. How can star clusters confirm astronomers
  theories of stellar evolution?
• Why cant a white dwarf star contract as it
  cools?
• How are neutron stars and white dwarfs similar?
  How do they differ?
• If neutron stars are hot, why arent they very
  luminous?
• 23. How can a black hole emit X-rays?

192
Stellar Groupings

• One way to get around sample biases is to study
  groups of stars bound by gravity. Why?
• The distance across a group is relatively small,
  which means the stars in the group have roughly
  the same distance from us. This in turn means
  that ratios in apparent brightness are the same
  as the ratios of intrinsic luminosities.

193
Stellar Groupings

• One way to get around sample biases is to study
  groups of stars bound by gravity. Why?
• The groups are loosely bound, meaning that the
  stars must have formed together, rather than
  being captured after formation.

194
Stellar Groupings

• One way to get around sample biases is to study
  groups of stars bound by gravity. Why?
• The groups are loosely bound, meaning that the
  stars must have formed together, rather than
  being captured after formation. This means the
  stars in the group all have the same age and the
  same chemical composition.

195
Star Clusters

• Star clusters can be roughly classified based on
  how tight they are.

196
Star Clusters

• Star clusters can be roughly c