1. Introduction to Astronomy
Prof. Sébastien R. A. Foucaud
Department of Earth Sciences
National Taiwan Normal University
Unless noted, the course materials are licensed under Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Taiwan (CC BY-NC-SA 3.0)

2. Syllabus Astronomical techniques
Lecture 1: Finding its way on the night…
Lecture 2: Moving blindly and seeing the light…
Lecture 3: Eyes better than my eyes: the telescopes
The solar system
Lecture 4: Home: Earth
Lecture 5: Our close friend: The Moon
Lecture 6: Our neighborhood: Rocky Planets
Lecture 7: The good Monsters: Giant Planets
Lecture 8: Dwarf Planets, minor bodies and scenario of solar system formation
Stars and planets
Lecture 9: Our king: The Sun
Lecture 10: Shades of colors: so many stars…
Lecture 11: The life of a star: from its birth to its death
Lecture 12: The quest for another Earth: extrasolar planets
The Milky-Way, galaxies and our Universe
Lecture 13: The cosmic carrousel: galactic structure & Galaxy formation
Lecture 14: Hubble, the expansion of the Universe and the Big-Bang Theory
Lecture 15: Einstein and the relativity

3. Shades of colors: so many stars…
Lecture 10
Shades of colors: so many stars…

4. The Sun

5. The Sun: facts Average star Spectral type G2
Only appears so bright because so close Absolute
Visual magnitude = 4.83 (magnitude if at a distance of 32.6 light years)
109 times Earth’s diameter
333,000 times Earth’s mass
Spin rate: 26 days at equator - 36 days at the poles
Consists entirely of gas (av. density = 1.4 g/cm3)
5 billion years old
Central temperature = 15 million °K
Surface temperature = 5800 °K

6. Properties of Stars
Mass – The single most important property that determines other properties of the star.
Luminosity – The total amount of energy (light) that a star emits into space.
Temperature – surface temperature, closely related to the luminosity and color of the star.
Spectral type – closely related to the surface temperature
Size – together with temperature determine the luminosity

7. Properties of Stars What we can measure directly:
Surface temperature and color
Spectrum
Apparent magnitude or intensity
Diameter of a few nearby stars
Distance to nearby stars
What we usually cannot:
Distance to most stars
Luminosity (energy radiated per second)
Diameter and mass

8. Things Light Tells Us From black body spectrum From spectral lines
Temperature
From spectral lines
Chemical composition
From Doppler shift
Radial velocity
Speed of object toward or away from Earth
Whether an object is rotating, speed of rotation.
Whether an object is expanding or contracting
From Polarization
Presence and strength of magnetic fields.
Presence and strength of electric fields.
Atomic composition.
Surface temperature T of a remote object.
Whether object has an atmosphere, composition of the atmosphere.
Whether an object is expanding or contracting.

9. Color and Temperature Stars appear in different colors,
from blue (like Rigel)
via green/yellow (like our sun)
to red (like Betelgeuse).
These colors tell us about the star’s temperature!
Betelgeuse
Rigel
Orion
Wikipedia Mouser

10. Black body radiation Blackbody = absorbs all electromagnetic radiation
= irradiate thermal radiation(temperature)
Wikipedia 4C

11. Surface temperature and color indices
Color filters
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Michael Richmond
Michael Richmond
Color indices: B-V, U-B
Differences in apparent magnitudes observed through different filters

12. Energy, Luminosity and Temperature
Stefan-Boltzman Law
E = σ T4
E is the energy emitted per surface area per second
T is temperature in Kelvins
T4 = T x T x T x T
σ is the Stefan-Boltzmann constant
In words: “Hot stuff glows more”
Black-body Luminosity Law
L=PSemt=4πR2σT4
L is the total energy emitted per sec
π is pi = …
R is the radius of the body
In words: “Bigger and hotter stuffs glows more.”

13. Black-body Luminosity Law
L=4πR2σT4
Example:
Two stars have the same color (and hence T). One star is twice the radius R of the other.
Which star has higher luminosity L?
The bigger star
How much more?
Lbig/Lsmall=4πRbig2σTbig4 /4πRsmall2σTsmall4
= (Rbig/Rsmall) 2 = (2/1) 2 = 4.

14. Light and Matter
Spectra of stars more complicated than pure blackbody spectra  characteristic lines, (absorption).
Need to understand atomic structure and interactions between light and atoms.
Wikipedia D-Kuru

15. Absorption vs. Emission+ + + +
wrong energy
right energy
absorption
emission
National Taiwan Normal University Sébastien R. A. Foucaud
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Wikipedia Jon Chui

16. Absorption Spectrum dominated by Balmer lines
National Taiwan Normal University Sébastien R. A. Foucaud
Intensity
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400
500
600
700
National Taiwan Normal University Sébastien R. A. Foucaud
Wavelength (nm)
Wikipedia Jan Homann

17. Lines of Hydrogen Wikipedia Szdori
Wikipedia Szdori

18. Emission nebula, dominated by the red Ha line.
Wisps Surrounding the Horsehead Nebula
Credit & Copyright: Star Shadows Remote Observatory
APOD: 2006 February 21
Emission nebula, dominated by the red Ha line.

19. The Balmer Thermometer
Balmer line strength is sensitive to temperature:
Hydrogen
Most hydrogen atoms are ionized => weak Balmer lines
Almost all hydrogen atoms in the ground state (electrons in the n = 1 orbit) => few transitions from n = 2 => weak Balmer lines
Intensity
10000
8000
6000
4000
Temperature(K)
National Taiwan Normal University Sébastien R. A. Foucaud

20. Measuring the Temperatures of Stars
Hydrogen
Ionized calcium
Ionized Helium
Titanium oxide
Ionized iron
Helium
Intensity
10000
8000
6000
4000
Temperature(K)
National Taiwan Normal University Sébastien R. A. Foucaud
Comparing line strengths, we can measure a star’s surface temperature!

21. Spectral Type of Stars Class Surface temperature (kelvin)
Conventional color
Apparent color
Mass(solar masses)
Radius(solar radii)
Luminosity (bolometric)
Hydrogen lines
Fraction of all main-sequence stars O
≥ 33,000 K
blue
≥ 16 M☉
≥ 6.6 R☉
≥ 30,000 L☉
Weak
~ % B
10,000–33,000 K
white to blue white
blue white
2.1–16 M☉
1.8–6.6 R☉
25–30,000 L☉
Medium
0.13% A
7,500–10,000 K
white
1.4–2.1 M☉
1.4–1.8 R☉
5–25 L☉
Strong
0.6% F
6,000–7,500 K
yellowish white
1.04–1.4 M☉
1.15–1.4 R☉
1.5–5 L☉ 3% G
5,200–6,000 K
yellow
0.8–1.04 M☉
0.96–1.15 R☉
0.6–1.5 L☉
7.6% K
3,700–5,200 K
orange
yellow orange
0.45–0.8 M☉
0.7–0.96 R☉
0.08–0.6 L☉
Very weak
12.1% M
≤ 3,700 K
red
orange red
≤ 0.45 M☉
≤ 0.7 R☉
≤ 0.08 L☉
76.45%
Wikipedia

22. O B A F G K M Stellar Spectral Types: OBAFGKM
Credit & Copyright: KPNO 0.9-m Telescope, AURA, NOAO, NSF
APOD: 2004 April 18

23. Stellar Spectra O B A Surface temperature F G K M Hα He Hδ Hγ Hβ
ADD COPYRIGHTXANADU OBSERVATORY G K M
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TiO
TiO
TiO
TiO

24. Spectral Type of Stars Oh Only Be Boy, Bad A An Astronomers Fine F
Wikipedia Kieff Oh
Only Be
Boy,
Bad A An
Astronomers
Fine F
Forget
Girl/Guy
Grade
Generally
Kiss
Kills
Known Me
Mnemonics

25. Distances to the stars Parallax (only for stars within ~1500 ly)
From stellar motions
For moving clusters
Using “standard candles” (model-dependent)
Using mass-luminosity relation (for main-sequence stars) or period-luminosity relations (for binaries and variable stars; model-dependent)

26. Parallax Parallax is used to measure the distance to the nearest stars
d (parsec) = 1 / p (arcsec)
Parsec is 3.26 light years

27. Trigonometric Parallax
A star is observed against a background of distant stars at 6-month intervals t1
Trig Parallax = p p p
Earth’s orbit
Nearby Star t2
National Taiwan Normal University Sebastien Foucaud
2 x p
Very Distant Background Stars t2 t1
On photographic plates, the nearby star appears to shift back and forth with respect to the distant background stars

28. Trigonometric Parallax
A star is observed against a background of distant stars at 6-month intervals t1
Trig Parallax = p p
Earth’s orbit
More Distant Star t2
National Taiwan Normal University Sebastien Foucaud
2 x p
Very Distant Background Stars t2 t1
A somewhat more distant star presents a smaller back and forth with respect to the distant background stars

29. Distances of stars The Five Nearest Stars Some of the Brightest Stars
Star Parallax Distance
arcsec pc
a Centauri
Barnard’s Star
Wolf
Lalande
Sirius
Some of the Brightest Stars
Star Parallax Distance
arcsec pc
Sirius
Canopus
a Centauri
Arcturus
Vega
Capella
Betelgeuse
Deneb

30. Proper Motion
Proper motion of Barnard's Star, showing position every 5 years 1985–2005.
Nearby stars show continuous motions across the sky, related to the actual motion of the stars throughout the Milky Way, and are called proper motion.
Star Proper Motion Distance
arcsec/year pc
Sirius
a Centauri
Capella
Betelgeuse
Deneb

31. Measuring Proper Motion
Wikipedia Brews ohare

32. Doppler Shift RADIAL velocity!! Wikipedia Lookang Wikipedia Lookang
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Wikipedia Charly Whisky 18:20, 27 January 2007 (UTC)
RADIAL velocity!!

33. Doppler Shift Wikipedia Georg Wiora
Wikipedia Georg Wiora

34. The Doppler effect allows us to measure the source’s radial velocity.Vr Vt
Δλ/λ0=Vr/c
Earth 34
National Taiwan Normal University Sébastien R. A. Foucaud

35. Luminosity and brightness
Luminosity of some object is the total energy emitted per second (power), has units of watts (W).
Apparent brightness is the amount of energy being received per second per unit area of measuring device. Apparent brightness is easily measured.
If the star emits energy uniformly in all direction, then :
The total area of the sphere with a radius of r is 4d2
National Taiwan Normal University Sébastien R. A. Foucaud

36. Luminosity and brightness
Wikipedia Borb

37. Classifying stars?
Hipparchus (200 BC): catalog listing 1080 of the brightest stars;
classified into 6 classes with faintest stars in the 6th class
Only classification: measure the brightnesses of the stars?

38. The Magnitude System Apparent magnitude: Logarithmic scale:
relative brightness of objects as appear in sky
Higher magnitude means dimmer
Counterintuitive, outdated, but standard!
Only the differences in mag are defined
0th mag. picked arbitrarily (Vega)
Logarithmic scale:
5 magnitudes means a factor of 100
mag 0 star 100 times brighter than mag 5 star
1 mag = factor of 2.51 difference in brightness
Negative magnitude = brighter than positive magnitude

39. Apparent visual magnitudes mV
App. Mag. (V)
Celestial object
–26.74
Sun (398,359 times brighter than mean full moon)
–12.92
Maximum brightness of full Moon (mean is –12.74)
–6.50
The total integrated magnitude of the night sky as seen from Earth
–2.50
Minimum brightness of new Moon
3 to 4
Faintest stars visible in an urban neighborhood with naked eye
31.50
Faintest objects observable in visible light with Hubble Space Telescope

40. Magnitudes and Intensities
Definition:
the magnitude scale so that two stars that differ by
5 magnitudes have an intensity ratio of 100.

41. The Absolute Magnitude
Absolute magnitude Mv:
apparent magnitude if at a distance of 10 parsecs (32.6 light-years) from Earth.
Sun: Mv = 4.8
Sirius: Mv = +1.4
Betelgeuse: Mv = -5.1
Apparent magnitude tells us nothing about the luminosity of the objects, but it tell us how difficult it is to see the objects in the sky.
Absolute magnitude, on the other hand, is directly related to the luminosity of the object. But it does not tell us how bright they appear in the sky.

42. Absolute Magnitude and Distance
Star’s absolute and apparent magnitudes, infer distance!
mv-Mv d(pc)
Distance Modulus
= mV – MV
= log10(d [pc])
Distance in units of parsec
Equivalent:
d = 10(mV – MV + 5)/5 pc

43. Absolute Magnitude and Distance
Recall that for two stars 1 and 2
Let star 1 be at a distance d pc
and star 2 be the same star brought to the distance 10 pc.
Then
m1 = m
m2 = M
Inverse:

44. Absolute Magnitude Orion Betelgeuse Rigel mV 0.41 0.14 MV -5.5 -6.8 d
152 pc
244 pc
Rigel
Orion
Wikipedia Mouser

45. Size of the Stars Direct measurements
Extremely challenging, as angular size very small (size as seen from the Earth)
Interferometry
If angular size and the distance star known:
Size of star = angular size [radian]  distance
Physical size of Betelgeuse (red supergiant) ~ 500 × size of Sun (4.6 AU or 345 million km).
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Haubois/Perrin (LESIA, Observatoire de Paris)
Image of hot spots on Betelgeuse using interferometric technique.
This work is licensed by Astronomy and Astrophysics, Thierry Forveille at A&A Editorial Office for the use of “Course Database of General Education TW” ONLY. The copyright belongs to the above mentioned entity and GET does not have the right to sub-license. Copyright privileges have to be negotiated with the copyright owner(s) for separately.

46. Size of the Stars Indirect measurements
flux increases with surface temperature (~ T4); hotter stars are brighter
But luminosity also increases with size (L ~ R2)
Star B brighter than star A. B A
National Taiwan Normal University Sebastien Foucaud
Quantitatively: L = 4 p R2 s T4
Surface flux due to a blackbody spectrum
Surface area of the star
Same spectral type (same temperature) derive relative size

47. Size of the Stars
Polaris has just about the same spectral type (and thus surface temperature) as our sun, but it is 10,000 times brighter than our sun.
Thus, Polaris is 100 times larger than the sun.
This causes its luminosity to be 1002 = 10,000 times more than our sun’s.
However, star radius is not a convenient parameter to use for classification, because it is not directly measured.
Surface temperature, or spectral class is more convenient!

48. The Hertzsprung-Russell Diagram
Stars have different temperatures, different luminosities, different sizes and different masses.
Is there any correlation between stellar luminosities, radii, temperature, and masses???
To bring some order into that zoo of different types of stars: organize them in a diagram:
Luminosity
versus
Temperature (or spectral type)
Absolute mag.
Hertzsprung-Russell Diagram
Luminosity or
Temperature
Spectral type: O B A F G K M

49. The Hertzsprung-Russell Diagram
10000
Rigel
100
Sun 1
Absolute magnitude
0.01
Sirius B
0.0001
40000
20000
10000
5000
2500
Temperature(K)
National Taiwan Normal University Sébastien R. A. Foucaud

50. The Hertzsprung-Russell Diagram
Stars in the vicinity of the Sun
62 pc
10000
100
Earth 1
Absolute magnitude
0.01
90% of the stars are on the Main Sequence!
0.0001
40000
20000
10000
5000
2500
Temperature(K)
National Taiwan Normal University Sébastien R. A. Foucaud

51. The Hertzsprung-Russell Diagram
Check whether all stars are of the same radius:
Total radiated power (luminosity) L = T4 4R2 J/s
r =10r (Sun)
10000
100
r = r (Sun) 1
No, they are not of the same radius
Absolute magnitude
r = 0.1r (Sun)
0.01
0.0001
40000
20000
10000
5000
2500
Temperature(K)
National Taiwan Normal University Sébastien R. A. Foucaud

52. The Hertzsprung-Russell Diagram
All stars visible to the naked eye + all stars within 25 pc
ADD COPYRIGHT TO NICK STROBEL
This page was copied from Nick Strobel's Astronomy Notes. Go to his site at  the updated and corrected version.
This work is from “Nick Strobel” It is used subject to the fair use doctrine of:
Taiwan Copyright Act Articles 52 & 65
This page was copied from Nick Strobel's Astronomy Notes. Go to his site at for the updated and corrected version.
Nick Strobel
This page was copied from Nick Strobel's Astronomy Notes. Go to his site at for the updated and corrected version.

53. The Hertzsprung-Russell Diagram
Betelgeuse
Rigel
10,000 times the sun’s radius
Polaris
100 times the sun’s radius
Sun
As large as the sun
Wikipedia Rursus

54. The Hertzsprung-Russell Diagram
High
Racing cars
Sports cars
Horsepower
Normal cars
Economy cars
Low
Heavy
Light
Weight
National Taiwan Normal University Sébastien R. A. Foucaud

55. The Hertzsprung-Russell Diagram
Sizes scale
1 Rsun
10 Rsun
100 Rsun
1000 Rsun
Properties of Stars in the H-R Diagram:
Luminosity.
Temperature and spectral type
Size
Mass of the main sequence
Lifetime
Wikipedia Rursus

56. The Hertzsprung-Russell Diagram
Sizes scale
1 Rsun
10 Rsun
100 Rsun
1000 Rsun
Increasing size
Wikipedia Rursus

57. The Hertzsprung-Russell Diagram
Sizes scale
1 Rsun
10 Rsun
100 Rsun
1000 Rsun
Increasing mass
Wikipedia Rursus

58. Classification Main sequence Giants Supergiants White dwarfs
Sizes scale
1 Rsun
10 Rsun
100 Rsun
1000 Rsun
Main sequence
Giants
Supergiants
White dwarfs
Wikipedia Rursus

59. Distribution of stars Near stars Bright stars 60% 50% 40% 30% Percent
20%
10% M K G F A B O
Type 59
National Taiwan Normal University Sébastien R. A. Foucaud

60. Distribution of stars
90% of the stars on the main sequence of the H-R diagram
Giants larger radii
Supergiants largest radii
White dwarfs peculiar spectra
Wikipedia Rursus

61. Luminosity Classes Ia: Bright Supergiants Ib: Supergiants
II: Bright giants
III: Giants
IV: Subgiants
V: Main-sequence stars
Spectral type: OBAFGKM
Full classification:
Sun: G2 V
Polaris: G2 Ib
Proxima Centauri: M5 V
Betelgeuse: M2 Ib
Sirius A: A1 V
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Wikipedia HR-diag-w-text.svg : Rursus/RicHard-59

62. Puzzles of H-R diagram Why > 90% of stars are on the main sequence?
Reason for mass-luminosity dependence and mass cutoff
Same stars at different stages of life or just different stars?
Wikipedia Rursus 62

63. Thanks!

64. Copyright Declaration
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NASA
2012/03/06 visited
Wikipedia NASA/SDO
2012/06/14 visited
Wikipedia Mouser
Wikipedia 4C
Michael Richmond

65. Copyright Declaration
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2012/06/14 visited
NASA/Nigel Sharp (NSF), FTS, NSO, KPNO, AURA, NSF
National Taiwan Normal University Sébastien R. A. Foucaud
Wikipedia Jon Chui
Wikipedia Jan Homann

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2012/06/14 visited
NASA/Star Shadows Remote Observatory
National Taiwan Normal University Sébastien R. A. Foucaud
Wikipedia: Author Unknown
NASA/KPNO 0.9-m Telescope, AURA, NOAO, NSF

67. Copyright Declaration
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This work is from XANADU OBSERVATORY It is used subject to the fair use doctrine of:
Articles 52& 65 of Taiwan Copyright Act.
The "Code of Best Practices in Fair Use for OpenCourseWare 2009 ( by A Committee of Practitioners of OpenCourseWare in the U.S. The contents are based on Section 107 of the 1976 U.S. Copyright Act
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Wikipedia Booyabazooka
National Taiwan Normal University Sebastien Foucaud
Wikipedia Steve Quirk

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2012/06/14 visited
Wikipedia Lookang
Wikipedia Charly Whisky 18:20, 27 January 2007 (UTC)
Wikipedia Tkarcher, improved by Tatoute
Wikipedia Georg Wiora

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Wikipedia: Author Unknown
This work is licensed by Astronomy and Astrophysics, Thierry Forveille at A&A Editorial Office for the use of “Course Database of General Education TW” ONLY. The copyright belongs to the above mentioned entity and GET does not have the right to sub-license. Copyright privileges have to be negotiated with the copyright owner(s) for separately.

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