1. “Snow and adolescence are the only problems that disappear if you ignore them long enough.”
Earl Wilson

2. Notices: HW1 is on-line now and due next Tuesday.
Reading: Chapters 3 and 1

4. Stars are exceptionally remote laboratories.
Yet they contain extremely interesting physics.
All our information comes from 1 source: light (electromagnetic radiation).

9. The 5 basic physical properties of stars:
Luminosity,
Mass, Radius (combined as surface gravity),
Surface Temperature (Teff)
Surface chemical composition (X,Y,Z)
Distance, via parallax;
Radial velocity via Doppler shift; and
Proper motion,

10. Luminosities
L=4R2T4
Lap=(R2/d2)(T4)
Labs=[R2/(d=10pc)2](T4)

12. Definition of magnitude
A difference of 5 magnitudes is a brightness ratio of 100.
For every 5 magnitudes multiply factors of 100.
For every ratio of 100, add 5 magnitudes.

13. Distance (3 ways)
Method 1) Stellar Parallax: d=1/p for distance in parsecs and parallax angles in arcseconds.
1pc = 3.26ly or 3.086x1016m

14. Example: a Cen A has a parallax of p=0.742”, what's its distance?
Method 1) Stellar Parallax: d=1/p for distance in parsecs and parallax angles in arcseconds.
1pc = 3.26ly or 3.086x1016m
Example: a Cen A has a parallax of p=0.742”, what's its distance?

15. Example: a Cen A has a parallax of p=0.742”, what's its distance?
Method 1) Stellar Parallax: d=1/p for distance in parsecs and parallax angles in arcseconds.
1pc = 3.26ly or 3.086x1016m
Example: a Cen A has a parallax of p=0.742”, what's its distance?
d=1/p = 1/0.742” = 1.35pc (4.4ly)

16. Method 2) Apparent and total luminosity: Lap = L/d2
Distance
Method 2) Apparent and total luminosity: Lap = L/d2

17. Method 3) in magnitudes. Absolute magnitude (M) is the magnitude an object would be at 10pc.

18. How far away is an object with a distance modulus of 15?

19. How far away is an object with a distance modulus of 15?

20. How far away is an object with a distance modulus of 15?
Note that you pick up a factor of 10 in distance for every 5 magnitudes!

21. Method 1: If you can measure the angular size (a) of the star, then
Radius (4 methods)
Method 1: If you can measure the angular size (a) of the star, then
R=(a/2)d.

22. Betelgeuse

24. Method 1: If you can measure the angular size (a) of the star, then
Radius (4 methods)
Method 1: If you can measure the angular size (a) of the star, then
R=(a/2)d.
If Betelgeuse has a diameter 700 times that of our Sun, and is at a distance of 197pc, what is a?

25. Radius (4 methods) Method 1: R=(a/2)d.
If Betelgeuse has a diameter 700 times that of our Sun, and is at a distance of 197pc, what is a?
a= 2R/d.
a is unitless, so R and d have to be in the same units, the easiest is probably m.
R=700*6.96x108m
D = 197*3.09x1016m
a= 1.60x10-7 rads = 0.033” (33mas)

26. Radius
Method 2: (And far more likely!) If you can measure a star's distance:
Lap=L/(4pd2) and L=4pR2sT4.
If you can get parallax, you can surely get a spectrum, so T is not a problem.

27. Radius- Method 3: eclipsing binary Ds=v(t2-t1) or v(t4-t3) and DL=v(t3-t1) or v(t4-t2)

28. L from the line widths, which gives luminosity class.
Radius
Method 4: Luminosity class and spectral type.
R=[L/(4psT4)]1/2
L from the line widths, which gives luminosity class.

29. Mass Method 1 (and only!): Binary stars F=GMm/R2
Where M and m are the masses and R is the distance between their centers. However, for non-circular orbits, R → a, which is the semimajor axis.
WE WILL DO A COMPLETE BINARY STAR SECTION LATER. FOR NOW, I WILL JUST BUZZ THROUGH THESE.

30. General Form of Kepler's 3rd Law.

31. Mass
What you can determine depends on the type of binary. So a quick review of binary types:
1) Visual Binary
2) Eclipsing Binary
3) Spectroscopic Binary
4) Double-lined (spectrum) Binary

32. Visual Binary: One or both stars are seen and proper motion is used to determine binarity.
Where d is distance, i is the inclination and a is the angular distance of 2a.

33. Eclipsing binary

34. Single-line binary

35. Circular orbits make sine waves, eccentric orbits do not.

36. Double-lined spectroscopic binary: the motion of both stars is observed.

38. Eclipsing, spectroscopic, and double-lined (spectrum) binaries
For all these, you can measure velocities in their spectra.
What is d in this case? P?

39. Single-lined binaries
Only 1 velocity. The right hand side contains the measurable quantities and is called the mass function.
To get actual masses, one mass must be assumed.

40. Double-lined binaries
With 2 velocities you get a complete solution.
2 unknowns (M1 and m2) requires 2 equations.

41. Double-lined binaries
With 2 velocities you get a complete solution.
If v2/v1=3 and M1+m2=12M*, what are M1 and m2?

42. Double-lined binaries
With 2 velocities you get a complete solution.
If v2/v1=3 and M1+m2=12M*, what are M1 and m2?
Since M1=3m2, m2=3 and M1=9.

43. Double-lined binaries
With 2 velocities you get a complete solution.
In reality there is a sin i in here as well.

44. Inclination i Face on is 0o Edge on is 90o
Astrometric binaries use cosine (so cosi=1 for face on)
Velocity binaries use sine (so sini=1 for edge on)

45. Surface composition: X, Y, Z X + Y + Z = 1
X is the mass fraction of H
Y is the mass fraction of He
Z is the mass fraction of everything else

46. Surface composition: X, Y, Z X + Y + Z = 1
X is the mass fraction of H
Y is the mass fraction of He
Z is the mass fraction of everything else
For the Sun, X=0.73, Y=0.25, Z=0.02

47. Surface composition: X, Y, Z X + Y + Z = 1
Composition is determined spectroscopically.
WE WILL DO THIS IN MORE DETAIL LATER USING LINE STRENGTHS.
For now:
Population III stars: By Mass: 75%H, 25%He, 0%Z
Population II stars: Z<0.01 (roughly)
Population I stars: Z>0.01 (roughly)

48. Surface composition: X, Y, Z
For now:
Population III stars: By Mass: 75%H, 25%He, 0%Z
Population II stars: Z<0.01 (roughly)
Population I stars: Z>0.1 (roughly)
NOTE: 75%H by mass is 92% by NUMBER of atoms.

49. Surface composition: X, Y, Z
What do we actually measure and how do we measure this?

50. Surface composition: X, Y, Z Spectral lines provide the # of atoms making a transition, not mass.

51. Spectral Classification
O, B, A, F, G, K, M
(Oh Boy, Astronomy Faculty Get Killed Monday)
Was originally an alphabetic sequence
Spectral classification began when Fraunhoffer discovered dark lines in the spectrum of the Sun.

52. Spectral Classification
O, B, A, F, G, K, M
In 1866, Angelo Secchi created Classes I (with a subtype for stars in Orion), II, and III where I had hydrogen lines, II had calcium and sodium lines, and III had complex bands.

53. Spectral Classification
O, B, A, F, G, K, M
Secchi classes I, II, and III
In the 1890s, a spectroscopic survey added to this classification:
I: A, B, C, D
II: E, F, G, H, I, K, L
III: M
Soon ofter these were added?
O- spectra with bright lines.
P- planetary nebulae.
Q- other spectra

54. Spectral Classification
O, B, A, F, G, K, M
Secchi classes I, II, and III
Pickering classification:
I: A, B, C, D
II: E, F, G, H, I, K, L
III: M
O- spectra with bright lines.
P- planetary nebulae.
Q- other spectra
In 1901, Annie Jump Cannon simplified it into our current system.

55. Spectral Classification
O, B, A, F, G, K, M
In 1901, Annie Jump Cannon simplified it into our current system.
In the 1920s, Cecilia Payne mathematically showed that a star's spectral class is determined by its temperature.