1. Chap. 2 An Overview of Stellar Evolution
Jan 28, 2009
CSI661/ASTR530
Spring, 2009
Jie Zhang
Copyright ©

2. Outline Basics (from “Universe” by Freedman & Kaufmann)
Young Stellar Objects
Zero-Age Main Sequence
Leaving the Main Sequence
Red Giants and Supergiants
Helium Flash
Later Phase and Advanced Phase
Core Collapse and Nucleosynthesis
Variable Stars
Novae and Supernovae
White dwarfs, neutron stars and black holes
Binary Stars
X=0,y=0,z=1
X=-1,y=-1,z=e^-2=
X=0,y=1,y=e^-1=
e=2.718

3. 3

4. Parallax
The apparent displacement of a nearby object against a distant fixed background from two different viewpoints.

5. Stellar Parallax
The apparent position shift of a star as the Earth moves from one side of its orbit to the other (the largest separation of two viewpoints possibly from the Earth)

6. Stellar Parallax and Distance
1 pc = 3.26 ly
1 pc = 206,265 AU = 3.09 X 1013 km
Distances to the nearer stars can be determined by parallax, the apparent shift of a star against the background stars observed as the Earth moves along its orbit

7. Once a star’s distance is known ….. Luminosity and brightness
A star’s luminosity (total light output), apparent brightness, and distance from the Earth are related by the inverse-square law
If any two of these quantities are known, the third can be calculated

8. Luminosity, Brightness and Distance
Many visible stars turn out to be more luminous than the Sun

9. Magnitude Scale to Denote brightness
Apparent magnitude scale is a traditional way to denote a star’s apparent brightness (~ 200 B.C. by Greek astronomer Hipparchus)
First magnitude, the brightest
Second magnitude, less bright
Sixth magnitude, the dimmest one human naked eyes see

11. Apparent Magnitude and Absolute Magnitude
Apparent magnitude is a measure of a star’s apparent brightness as seen from Earth
the magnitude depends on the distance of the star
Absolute magnitude is the apparent magnitude a star would have if it were located exactly 10 parsecs from Earth
This magnitude is independent of the distance
One way to denote the intrinsic luminosity of a star in the unit of magnitude
The Sun’s apparent magnitude is -26.7
The Sun absolute magnitude is +4.8

12. A star’s color depends on its surface temperature
Wien’s Law

14. Photometry, Filters and Color Ratios
Photometry measures the apparent brightness of a star
Standard filters, such as U (Ultraviolet), B (Blue) and V (Visual, yellow-green) filters,
Color ratios of a star are the ratios of brightness values obtained through different filters
These ratios are a good measure of the star’s surface temperature; this is an easy way to get temperature

15. Stellar Spectrum
E.g., Balmer lines: Hydrogen lines of transition from higher orbits to n=2 orbit; Hα (orbit 3 -> 2) at 656 nm

16. Classic Spectral Types
The spectral class and type of a star is directly related to its surface temperature: O stars are the hottest and M stars are the coolest

17. Classic Spectral Types
O B A F G K M
(Oh, Be A Fine Girl, Kiss Me!) (mnemonic)
Spectral type is directly related to temperature
From O to M, the temperature decreases
O type, the hottest, blue color, Temp ~ K
M type, the coolest, red color, Temp ~ 3000 K
Sub-classes, e.g. B0, B1…B9, A0, A1…A9
The Sun is a G2 type of star (temp K)

18. Luminosity, Radius, and Surface Temperature
Reminder: Stefan-Boltzmann law states that a blackbody radiates electromagnetic waves with a total energy flux F directly proportional to the fourth power of the Kelvin temperature T of the object:
F = T4

19. Luminosity, Radius, and Surface Temperature
A more luminous star could be due to
Larger size (in radius)
Higher Surface Temperature
Example: The first magnitude reddish star Betelgeuse is 60,000 time more luminous than the Sun and has a surface temperature of 3500 K, what is its radius (in unit of the solar radius)?
R = 670 Rs (radius of the Sun)
A Supergiant star

20. Finding Key Properties of Nearby Stars

21. Hertzsprung-Russell (H-R) diagrams reveal the patterns of stars
The H-R diagram is a graph plotting the absolute magnitudes of stars against their spectral types—or, equivalently, their luminosities against surface temperatures
There are patterns

22. Hertzsprung-Russell (H-R) diagram the patterns of stars
The size can be denoted
(dotted lines)
0.001 Rs To
1000 Rs

23. Hertzsprung-Russell (H-R) diagram the patterns of stars
Main Sequence: the band stretching diagonally from top-left (high luminosity and high surface temperature) to bottom-right (low luminosity and low surface temperature)
90% stars in this band
The Sun is one of main sequence stars
Hydrogen burning as energy source

24. Hertzsprung-Russell (H-R) diagram the patterns of stars
Main Sequence
Giants
upper- right side
Luminous (100 – 1000 Lsun)
Cool (3000 to 6000 K)
Large size (10 – 100 Rsun)
Supergiants
Most upper-right side
Luminous ( Lsun)
Huge (1000 Rsun)
White Dwarfs
Lower-middle
Dim (0.01 Ls)
Hot (10000 K)
Small (0.01 Rs)

25. A way to obtain the MASS of stars Binary Star System
Period: ~ 80 days

26. Binary Stars
Binary stars are two stars which are held in orbit around each other by their mutual gravitational attraction, are surprisingly common
Visual binaries: those that can be resolved into two distinct star images by a telescope
Each of the two stars in a binary system moves in an elliptical orbit about the center of mass of the system

27. Binary Stars
Each of the two stars in a binary system moves in an elliptical orbit about the center of mass of the system

28. Binary star systems: stellar masses
The masses can be computed from measurements of the orbital period and orbital size of the system
The mass ratio of M1 and M2 is inversely proportional to the distance of stars to the center of mass
This formula is a generalized format of Kepler’s 3rd law
When M1+M2 = 1 Msun, it reduces to
a3 = P2

29. Mass-Luminosity Relation for Main-Sequence Stars
The greater the mass of a main-sequence star, the greater its luminosity

30. Mass-Luminosity Relation for Main-Sequence Stars
Masses from 0.2 MΘ
to 60 MΘ
The greater the mass
The greater the luminosity
The greater the surface temperature
The greater the radius

31. Note: This is the end of the basics, which is from “Universe” by Freedman & Kaufmann
Feb. 11, 2009 (continued) 31

32. (2.1) Young Stellar Objects
Four stages of star formation
Form proto-star core within molecular cloud
Core grows from surrounding rotating disk
Bipolar flow along rotation axis
New star clears away the surrounding nebular material

33. (2.1) Young Stellar Objects
Energy source for a proto-star is gravitational potential energy.
The contract life is about 0.1% its potential nuclear life at the main sequence
Proto-stars are convective throughout, thus a new star is chemically homogeneous
Proto-star Evolution Track

34. (2.2) ZAMS
Zero-age main sequence star: a star just ignites the hydrogen fusion
In practice, “zero-age” means that the star has changed so little in radius, effective temperature and luminosity
Means a few thousand years for a massive star
Means 10 million years for the Sun
Means 1 billion years for the least massive stars

35. (2.2.1) Main Sequence Two kinds of nuclear fusion converting H to He
pp-chain
for stars less than 1.5 Msun
CNO cycle
For stars more than 1.5 Msun, Tc > 1.8 X 107 K
Fusion is much faster than PP-chain
C, N, O act as catalysts
Because of P=nKT=ρ/μ NAKT, number density decreases
Temperature must increase to maintain the pressure
Core must slowly contract and heat up
Faster energy generation, more luminous star

36. (2.2.2) Brown Dwarfs
Proto-stars which never get hot enough to fuse hydrogen to helium
The brown dwarf/main sequence cut is about Msun

37. Mass Cut versus star fate (also see Fig. 2.4)
(2.3) Post-main Sequence
< 0.05: No 2D fusion  “planet”
<0.085: No 1H Fusion  brown dwarf
=0.85: Hubble time scale
<1.50: PP chain, Helium flash, radiative core, He WD
<5.0: CNO cycle, no He flash, convective core, Carbon WD
<8.0: planetary nebula, O, Ne, Mg WD
<25: supernovae, neutron star
> 25: supernovae, black hole
Mass Cut versus star fate (also see Fig. 2.4)

38. Fig. 2.7. HR diagram of globular cluster M3
(2.3.1) Cluster HR Diagram
Stars in a cluster form at nearly the same time
“TOP” turnoff point can be used to determine the age of a cluster
SGB: sub-giant branch
RGB: red-giant branch
H-shell burning
Horizontal Branch
Helium core burning
AGB: Asymptotic Giant Branch
Helium shell burning
Variable stars caused RR Lyrae
by thermal instability
Fig HR diagram of globular cluster M3

39. Fig. 2.8: theoretical HR for clusters
(2.3.1) Cluster HR Diagram
Fig. 2.8: theoretical HR for clusters

40. (2.4) Red Giants The stage that hydrogen shell burning ignites
The shell burning adds helium ash into the core, causing the dormant core to contract
The shell burning causes the outer envelope to expand and thus cooling, producing red giants
The hydrogen shell burning occurs via the CNO cycle, the main source of N in the universe

41. Chap. 2 (continued)
Feb.18, 2009 41

42. (2.5) Helium Flash Core contracts, and density increases
Core becomes degenerate, that is the electron degeneracy pressure is larger than the gas thermal pressure
Degeneracy pressure is caused by the electron momentum associated with the Heisenberg uncertainty principle (ΔxΔp=ħ). It is also associated with Pauli-exclusive principle

43. (2.5) Helium Flash Star M < 0.4 Msun
core degenerate (ρ > 106 g cm-3)
but low temperature (< 107 K)
no further helium burning, produce helium white dwarf
Star M > 1.5 Msun
core not degenerate (ρ < 106 g cm-3)
but high temperature (> 108 K), ignite helium burning
Peaceful transition to helium burning
Star 0.4 Msun < M < 1.5 Msun
core degenerate (ρ < 106 g cm-3)
and high temperature (> 108 K)
helium flash: explosive helium burning

44. (2.5) Helium Flash
For a degenerate gas, the ignition of helium burning will heat the gas, but do not cause expand
The increased temperature makes the reaction go faster, which further heats the gas, which makes the reaction goes faster.
This cycle of explosive nuclear reaction continues until temperature is high enough so that thermal pressure exceeds degenerate pressure.
After helium flash, the core expands to a density about 103 g cm-3
It is mirrored by envelope contraction
Luminosity decreases, and effective temperature increases; the star heads to the left in the HR diagram

45. Density Evolution for model
(2.5) Helium Flash
Density Evolution for model
1 Msun, z=0.02

46. (2.5.1) Horizontal Branches (HB)
Giant stars with
Helium burning in the core
Through triple-α reaction
34He  12C and 12C (4He, γ)16O
Hydrogen burning in the surrounding shell through CNO cycle

47. (2.5.2) Asymptotic Giant Branches (AGB)
When helium core is exhausted, HB star becomes AGB
The C-O core contracts and heats up
Double shell burning
Helium burning in the shell surrounding the core
Hydrogen burning in the shell surrounding He shell

48. Fig. 2.14. Double Shell Burning
(2.5.2) AGB
Fig Double Shell Burning

49. (2.6) Later Phases, Initial Masses 6-10 Msun
During the Giant star phases, a star may lose a large fraction of mass through
Super wind
Pulsation
The blown-off envelope becomes planetary nebula (PN)
The residual core becomes a white dwarf
Composition: Carbon-oxygen
Mass: 0.55 – 1.3 Ms
Radius: 10-2 Rsun, or the size of the Earth
Energy source: residual heat of the atomic nuclei
Luminosity: 10-5 Lsun
Fading time: 1010 years

50. (2.6) Planetary Nebula
NGC 6543
IC 418

51. Fig. 2.15. Color-Magnitude HR diagram
(2.6.1) White Dwarfs
Fig Color-Magnitude HR diagram

52. Chap. 2 (to be continued) 52

53. End of Chap. 2
Note: 53