1. HW1 is due Reading: Chapters 3 and 1
“The only thing that makes me believe in UFOs is that, sometimes I lose stuff.”
Jack Handy
Notices:
HW1 is due
Reading: Chapters 3 and 1

2. Composition: X,Y, and Z Spectral Classes: OBAFGKM(LST) Stellar motion:
Last Time:
Composition: X,Y, and Z
Spectral Classes: OBAFGKM(LST)
Stellar motion:
Radial Velocity: Doppler shift.
Proper Motion: Astrometry- across the line-of-sight.

3. But wait....
If I said that all stars are ~75%H, then why are G stars dominated by CaII and K stars dominated by Fe-group lines?

4. But wait....
If I said that all stars are ~75%H, then why are G stars dominated by CaII and K stars dominated by Fe lines?
We will calculate this later, but the answer is that absorption lines are created by atoms which can absorb available photons.
Cooler stars have photon energies in ranges ill- matched with H.

5. There are pulsating stars nearly everywhere!
This is good since seismology can probe their insides.

6. Irregulars: SN: end states of stars.
Supernova

7. Flare stars: life on exoplanets

8. Chapter 1: Our Sun. Read this chapter.
We will use the Sun as a proxy for the properties of stellar surfaces- atmospheres.
We will spend a LOT of time doing atmospheres- in more detail than what's in the book.

9. Stellar atmospheres

10. Depth from where sunlight's emitted
Depth from where sunlight's emitted. H=0 is where the Sun's optically thick.

11. We can see 0.07% into the Sun. Roughly the same is true for all stars.

12. The entire solar surface
Features: limb darkening and sunspots

13. Limb darkening is caused by our viewing angle into the Sun
Limb darkening is caused by our viewing angle into the Sun. The more directly you view, the deeper into
the Sun you can see.
The deeper in you see,
the hotter material
you see. Since
L~T4, the hotter
the material,
the brighter

14. Near the limb, the Sun is only 30% as bright as in the center.

15. Limb darkening laws:
A lot of work goes into parameterizing the limb darkening of various stars. Sun-like stars have photospheres 500km thick while in white dwarfs they are ~10m.

16. In this star, the pluses are the measurements (with errors)
In this star, the pluses are the measurements (with errors). f(x) is one parameterization and g(x) is another.

17. Limb darkening laws Linear: Im/Io=1-c(1-m)
Quadratic: Im/Io=1-c1(1-m)-c2(1-m)2
Square root: Im/Io=1-c1(1-m)-c2(1-m1/2)
Logarithmic: Im/Io=1-c1(1-m)-c2m ln m
With the coefficients determined from atmospheric models (and usually looked up in tables).
Square root and log are the 2 most commonly-used parameterizations.

18. e=2.718... and Io is the incident intensity
Optical depth.
Is a measure of transparency. A perfectly transparent medium has an optical depth of 0. An optically thick medium would have infinite optical depth (as all of a beam of light would be blocked).
I/Io = e-mt
e= and Io is the incident intensity

19. Side note: E-folding scales
E-folding is an important concept in many physical phenomena. Whenever an exponential decay law applies, scales are done in factors of e. These are then called e-folding scales. So 1 scale height would have a change by ~2.7.
In optical depth: an optical depth of 1 would have the incident light reduced by ~2.7.

20. Optical depth I/Io=e-mt Where m = 1/cosq where q is the zenith angle.
Stellar atmospheres are often considered as plane- parallel slabs with viewing angles from incident.
Then optical depth becomes
I/Io=e-mt
Where m = 1/cosq where q is the zenith angle.

21. Optical depth: plane parallel approximation. I/Io=e-mtq

22. plane parallel approximation

23. One of my favorite examples of optical depth.

24. However, because the pressure within stars increases with depth, you can actually see further in near the limb, but still not to the same temperature.

25. plane parallel approximationTT TB TT TB

26. Effective temperature
Is defined as the blackbody temperature at an optical depth of 1.

27. Sunspots
Sunspots are only dark compared to their surroundings. They are still over 4000K

28. Sunspots
Sunspots are not permanent, typically lasting a few weeks for our Sun.

29. But they last long enough to see them move across the Sun's surface.
Galileo used sunspots to determine the rotation period of the Sun.

30. Sunspots at different latitudes also indicate differential rotation with latitude.

31. The Sun is a differential rotator.
Spinning faster
at the equator.

32. Sunspots are regions where the Sun's magnetic field passes through the surface, preventing surface convection.

33. As the material radiates its heat to space, it appears cooler than the surrounding material.

34. Sunspots
What causes the magnetic field to pass through the surface of the Sun?
Differential rotation.

36. Sunspot numbers varies in a regular way
Sunspot numbers varies in a regular way. This is known as the solar cycle.
The Sun's magnetic field causes the solar cycle. Roughly every 11 years, the solar magnetic field switches polarity, that is the north magnetic pole becomes the south magnetic pole.

37. The magnetic field of the sunspots indicate the orientation of the magnetic field.

38. And show that a total solar cycle is about 22 years.

39. Other solar activity, such as prominences and flares roughly follow this cycle too.

40. Over the course of a solar cycle, sunspots migrate towards the equator.

41. Other stars have spots too!

42. Other stars have cycles too.

44. Another G2 V star,
…..and others

45. But all are late-type stars.
And relationships can be drawn with other stars.
But all are late-type stars.

46. So spot (activity) cycles in other stars is a multi-parameter problem.
A bit ahead, but.....
Cycles, spots, and activity is related to spin rate and magnetic field strength, both of which diminish with age (magnetic braking).
So spot (activity) cycles in other stars is a multi-parameter problem.

47. Spots are useful tools!

48. Main period = 0.6 days M4 V star
The main spot lasts for over 4 years! 2Nd spots are days.

49. Another example. Differential rotation seems to decrease in later spectral types (expected).

50. Solar granulation: each granule is the top of a small convective cell
Solar granulation: each granule is the top of a small convective cell. Each is about 1,000km across and last about 5-10 minutes.

51. Until recently, granulation could only be seen in the Sun
Until recently, granulation could only be seen in the Sun. Now, they can be measured (by their variability) in other stars.

52. The effects of faculae (plages; dotted line) and granulation (dashed line) on a solar-like pulsator.

53. Roughly a few thousand km thick.
Chromosphere: A colored layer of low-pressure gas surrounding the photosphere.
Roughly a few thousand km thick.

54. Chromospheric features.

55. Chromospheric features.
Plages: bright spots of hotter gas above the photosphere.

56. Filament: a prominence seen from above.

57. Prominence:

58. Spicules: stick up from the photosphere about 500km and last about 5-10 minutes.

59. Roughly a few thousand km thick.
Chromosphere: A colored layer of low-pressure gas surrounding the photosphere.
Roughly a few thousand km thick.

60. The corona: The Sun's upper atmosphere.
A very low density million K gas.

61. Temperature and density of the Sun's atmosphere (chromosphere and corona).

62. During coronal mass ejections, billions of tons of material is lost to space.

63. This sort of space weather effects us.

64. The solar wind: Particles (mostly electrons and protons) in the corona accelerated to escape velocity.

65. Coronal holes: where the magnetic field opens outward to space
Coronal holes: where the magnetic field opens outward to space. Major source of the solar wind.

66. To measure chromospheres in other stars, two calcium lines are used
To measure chromospheres in other stars, two calcium lines are used. Ionized Ca is often enhanced in active regions.
Used to measure solar cycles in other stars.

67. The Sun's spectrum is not quite that of a blackbody.

68. At this point, we are going to make a huge deviation to cover spectral features and atmospheric lines properly. Much of this is not in your book.

69. Light can be thought of as both a wave and a particle.

70. Light Associated with its 'wave' properties is wavelength, 
The 'particle' energy (that is, the energy of each photon) is related to its wavelength: E=hc/
Where h is Planck's constant and c is the speed of light. h=6.626x10-34J*s and c=3x108m/s

71. Light E=hc/ Where h is Planck's constant and c is the speed of light.
h=6.626x10-34J*s and c=3x108m/s
Another handy value: hc=1240 eV*nm for wavelengths in nm and energy in eV (the charge of an electron).

72. Light But what determines the wavelength? E=hc/
To answer this question, we have to know how light is emitted (created) or absorbed (destroyed).

73. Light
To answer this question, we have to know how light is emitted (created) or absorbed (destroyed).
The processes are:
1) bound-bound (atomic) transition
2) bound-free (ionization)
3) Free-free (Bremsstrahlung) absorption
4) Thomson (electron) scattering

74. Bound-Bound: Atomic Emission/Absorption
This is when a bound electron changes orbitals.

75. Only orbits that have integer wavelengths are allowed. The Bohr model
Only orbits that have integer wavelengths are allowed. The Bohr model. Modern QM sees these as wave packets.

76. Light is emitted (or absorbed) when an electron changes orbital.
But the energy of the light is quantized and can only have certain values.

77. DE=hc/l

78. Notation
Frequency: Most people write n, but the authors of your book usually use f. However, they are radio astronomers and so most astronomers use wavelength: l with the relationship n = c/l

79. The energy is determined by the exchange between electron 'orbitals.'
For H, it looks like this.

80. What is the energy (in eV) for a 2-4 transition
What is the energy (in eV) for a 2-4 transition? What wavelength does this correspond to?(hc=1240 eV.nm)

81. What is the energy (in eV) for a 2-4 transition
What is the energy (in eV) for a 2-4 transition? What wavelength does this correspond to?(hc=1240 eV.nm)
2.55eV is nm

82. This line corresponds to a commonly-detected feature in hot stars.

83. In a more general form, the equation is modified by the number of protons in the nucleus.
E= Z2 x 13.6eV (1/n2l-1/n2u)

84. What is the wavelength of light for an Iron n=2 to n=3 transition?
hc=1240 eV*nm, z=26.
E= Z2 x 13.6eV (1/n2l-1/n2u)

85. What is the wavelength of light for an Iron n=2 to n=3 transition?
hc=1240 eV*nm, z=26.
E= Z2 x 13.6eV (1/n2l-1/n2u)
hc=1240 eV*nm, z=26.
hc/l=(262)(13.6eV) (1/4-1/9)
l=1240/ = 0.97 nm

86. Note- this general form becomes less accurate as Z gets larger- this is caused by shielding from inner electrons.
E= Z2 x 13.6eV (1/n2l-1/n2u)

87. Transitions for hydrogen for the Bohr model

88. IR
Optical UV