1. Chapter 20
Stellar Evolution

2. Important concepts Luminosity depending on temperature and radius.
Behavior of gases when they expand or contract.
Gravitational energy transformed into heat.
Nuclear fusion processes

3. The seven stages so far:

4. Stars Must Change Stars are constantly radiating energy.
The energy is replaced by nuclear fusion.
The energy available from fusion is very large, but finite.
Eventually the fusion sources change, then halt.
The star’s luminosity or temperature will change.

5. What was fighting gravity when the star was on the main sequence?

6. A star remains stable as long as it remains in hydrostatic equilibrium
Small increase in temperature results in
Increase in pressure , which results in
Expansion, which results in
Cooling, which results in
Recovering its equilibrium
and vice versa
Small decrease in temperature, results in
Decrease in pressure, which results in
Gravitational contraction, which leads to
Heating up
Recovering its equilibrium

7. Question 1 A star will spend most of its “shining” lifetime
1) as a protostar.
2) as a red giant.
3) as a main-sequence star.
4) as a white dwarf.
5) evolving from type O to type M.
A star will spend most of its “shining” lifetime
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8. Question 1 A star will spend most of its “shining” lifetime
1) as a protostar.
2) as a red giant.
3) as a main-sequence star.
4) as a white dwarf.
5) evolving from type O to type M.
In the main-sequence stage, hydrogen fuses to helium.
Pressure from light and heat pushing out balances gravitational pressure pushing inward.

9. Low-Mass Stars
The rates and types of fusion depend on the star’s mass.
Therefore all stars are unique.
Generally, stars with M < 3 M share many characteristics.
These are called low-mass stars.

10. Higher Mass = Shorter Lifetime
We can figure out main sequence lifetimes: (lifetime) = (energy available) / (rate energy used).
More mass = more fuel available.
Rate energy used = rate energy emitted (luminosity).
More massive stars have much higher luminosity.
They use their fuel up more quickly and leave the MS faster.

11. Main Sequence Lifetimes
Mass (M)
Luminosity (L)
Lifetime in billion years
17.5
52,500
0.01
2.0 14
1.1
1.0 10
0.67
0.15 53
0.21
0.011
290

12. Lifetime and Mass

13. The End of the Main Sequence
Main sequence (MS) stars fuse hydrogen to helium in their cores (creating heat and pressure).
This is the definition of the MS.
More massive stars have higher central temperatures, greater luminosity.
Eventually, much of the core H is converted to He.
The star will then expand and cool and become a subgiant.

14. Question 2 As stars evolve during their main-sequence lifetime
1) they gradually become cooler and dimmer (spectral type O to type M).
2) they gradually become hotter and brighter (spectral type M to type O).
3) they don’t change their spectral type.
As stars evolve during their main-sequence lifetime
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15. Question 2 As stars evolve during their main-sequence lifetime
1) they gradually become cooler and dimmer (spectral type O to type M). 2) they gradually become hotter and brighter (spectral type M to type O). 3) they don’t change their spectral type.
CLL: HR diagram and lifetime
A star’s main sequence characteristics of surface temperature and brightness are based on its mass.
Stars of different initial mass become different spectral types on the main sequence.

16. Stage 8, Subgiant branch: Composition changes
Hydrogen burns fastest at the center

17. What happens to the pressure as nuclear fusion runs out fuel?

18. Without pressure fighting gravity, what happens to the core?

19. As the fuel in the core is used up, the core contracts; when it is used up the core begins to collapse.
Figure Hydrogen- Shell Burning As a star’s core converts more and more of its hydrogen into helium, the hydrogen in the shell surrounding the nonburning helium “ash” burns ever more violently. By the time shown here (a little after stage 8 in Table 20.1), the core has shrunk to a few tens of thousands of kilometers in diameter, whereas the star’s photosphere is ten times the star’s original size.

20. What happens to core’s temperature as it collapses?
As gases compress, they heat up.
Gravitational kinetic energy is converted into kinetic energy (temperature) of the gas.

21. Where does that heat go, if it cannot be used to stimulate fusion?
Half of the heat increases the temperature.
The other half radiates away into the outer shell.

22. What happens to the envelope as it heats up?
Hydrogen begins to fuse outside the core and star expands.
What happens to the density of the star’s outer layer as it expands?
Density drops. Temperature remains same.
Figure Hydrogen- Shell Burning As a star’s core converts more and more of its hydrogen into helium, the hydrogen in the shell surrounding the nonburning helium “ash” burns ever more violently. By the time shown here (a little after stage 8 in Table 20.1), the core has shrunk to a few tens of thousands of kilometers in diameter, whereas the star’s photosphere is ten times the star’s original size.

23. The stages on the HR diagram
Core collapses
Shell expands
Hydrogen burning in the shell:
Star expands and becomes more luminous.
Nuclear fusion inside slows down.
Star expands and cools down.

24. Question
What inevitably forces a star like the Sun to evolve away from being a main-sequence star?
1) The core begins fusing iron.
2) The star uses up all of its supply of hydrogen.
3) The carbon detonation explodes it as a type I supernova.
4) Helium builds up in the core, while the hydrogen-burning shell expands.
5) The core loses all of its neutrinos, so all fusion ceases.
Answer: 4

25. What inevitably forces a star like the Sun to evolve away from being a main-sequence star?
1) The core begins fusing iron.
2) The star uses up all of its supply of hydrogen.
3) The carbon detonation explodes it as a type I supernova.
4) Helium builds up in the core, while the hydrogen-burning shell expands.
5) The core loses all of its neutrinos, so all fusion ceases.
When the Sun’s core becomes unstable and contracts, additional H fusion generates extra pressure, and the star will swell into a red giant.

26. Stage 9:Red Giants
Later, the star expands and its luminosity rises. The star becomes a red giant.
H fusion takes place in a shell around the core.
The core becomes more dense, and becomes electron degenerate.
This means pressure is not from moving atoms, but from a quantum mechanical effect: there’s a limit to how tightly electrons can be packed together (Pauli exclusion principle).

27. Why the Luminosity Increases
When the core shrinks, the pressure increases.
Nuclear fusion in the shell goes faster.
Faster nuclear reactions release more energy.
This energy leaves the star’s surface at a higher rate.

28. Red Giants

29. Stage 10:Helium fusion Temperatures 100,000,000K
Core is small, dense, electron degenerate.
Outer envelope is greatly expanded, cooler.
Fusion of He begins in the degenerate core.
Helium fuses to carbon via the triple-alpha process.
This starts suddenly in the helium flash.
Star shrinks and heats up.

30. Triple-Alpha Process

31. Temperature and helium fusion
The average kinetic energy in a gas of atoms is
The kinetic energy must supply the work
to push against the electrostatic forces
The electromagnetic force is proportional to the product of the charges Q1 and Q2.
Therefore T ~ Q1 x Q2

32. Stage 10: Helium Fusion fusion
Once the core temperature has risen to 100,000,000 K, the helium in the core starts to fuse, through a three-alpha process:
4He + 4He → 8Be + energy
8Be + 4He → 12C + energy
The 8Be nucleus is highly unstable and will decay in about 10–12 s unless an alpha particle fuses with it first. This is why high temperatures and densities are necessary.

33. The helium flash:
The pressure within the helium core is almost totally due to “electron degeneracy”—two electrons cannot be in the same quantum state, so the core cannot contract beyond a certain point.
This pressure is almost independent of temperature—when the helium starts fusing, the pressure cannot adjust and expand the gas, which would result in cooling.
For hours the temperature increases rapidly until final the normal pressure increases and expansion cools the star again.

34. Question
1) those heavier than iron, because of supernovae
2) iron, formed just before massive stars explode
3) odd-numbered nuclei, built with hydrogen fusion
4) even-numbered nuclei, built with helium fusion
What type of atomic nuclei heavier than helium are most common, and why?
Answer: 4

35. 1) those heavier than iron, because of supernovae
2) iron, formed just before massive stars explode
3) odd-numbered nuclei, built with hydrogen fusion
4) even-numbered nuclei, built with helium fusion
What type of atomic nuclei heavier than helium are most common, and why?
Helium nuclei have an atomic mass of 4; they act as building blocks in high-temperature fusion within supergiants.

36. The Horizontal Branch & the AGB
After the helium flash, the stars are on the horizontal branch of the H-R diagram.
At first, He  C in the core, H  He in a shell around the core.
Helium is then used up in the core.
He fusion in an inner shell and H fusion in an outer shell.
Star gets more luminous and cool, enters the asymptotic giant branch (AGB).

37. Question The “helium flash” occurs
1) when T-Tauri bipolar jets shoot out.
2) in the middle of the main sequence stage.
3) in the red giant stage.
4) during the formation of a neutron star.
5) in the planetary nebula stage.
The “helium flash” occurs
Answer: 3

38. The “helium flash” occurs
1) when T-Tauri bipolar jets shoot out.
2) in the middle of the main sequence stage.
3) in the red giant stage.
4) during the formation of a neutron star.
5) in the planetary nebula stage.
The “helium flash” occurs
When the collapsing core of a red giant reaches high enough temperatures and densities, helium can fuse into carbon quickly – a “helium flash”.

39. Stage 11: The AGB
Double shell burning

40. After the AGB
Electrons become degenerate again, stopping increase of temperature necessary to ignite massive carbon fusion.
The star expands, cools.
The outer layers are ejected into space.
The ejected material creates a planetary nebula.
The core shrinks and gets very hot, eventually to cool into a compact white dwarf.

41. The Death of a Low-Mass Star
This graphic shows the entire evolution of a Sun-like star.
Such stars never become hot enough for fusion past carbon to take place.
Figure G-Type Star Evolution Artist’s conception of the relative sizes and changing colors of a normal G-type star (such as our Sun) during its formative stages, on the main sequence, and while passing through the red-giant and white-dwarf stages. At maximum swelling, the red giant is approximately 70 times the size of its main-sequence parent; the core of the giant is about 1/15th the main-sequence size and would be barely discernible if this figure were drawn exactly to scale. The duration of time spent in the various stages—protostar, main-sequence star, red giant, and white dwarf—is roughly proportional to the lengths shown in this imaginary trek through space. The star’s brief stay on the horizontal and asymptotic-giant branches are not shown.

42. The Death of a Low-Mass Star
There is no more outward fusion pressure being generated in the core, which continues to contract.
The outer layers become unstable and are eventually ejected.
Red giant instability due to helium flashes
Figure Red-Giant Instability Buffeted by helium-shell flashes from within, and subject to the destabilizing influence of recombination, the outer layers of a red giant become unstable and enter into a series of growing pulsations. Eventually, the envelope is ejected and forms a planetary nebula.

43. Stage 12: Planetary Nebula Formation
UV radiation ionizes the inner parts of the cloud that was formed from ejected star materials.

44. Planetary Nebulae
Spirograph nebula: Dr. Raghvendra Sahai (JPL) and Dr. Arsen R. Hajian (USNO), NASA and The Hubble Heritage Team (STScI/AURA). Eskimo nebula: NASA/ A. Fruchter and the ERO team (STScI). NGC 6751: A. Hajian (USNO) et al., Hubble Heritage Team (STScI/AURA), NASA. Helix nebula: Anglo-Australian Telescope, photograph by David Malin. Cat's eye nebula: J.P. Harrington and K.J. Borkowski (University of Maryland), HST, NASA. M2-9: Bruce Balick (University of Washington), Vincent Icke (Leiden University, The Netherlands), Garrelt Mellema (Stockholm University), and NASA.

45. White Dwarfs They start hot and cool with time (important).
Not very luminous - small.
Masses 0.6 – 1.4 M, radius like Earth.
Core is mainly carbon and is degenerate.
Final state depends on how much mass is lost in the planetary nebula phase.
There is also mass lost in the red giant phase.
All low-mass stars become white dwarfs.

46. Summary
CLL: Death sequence, Low mass star

47. Review Stage 1 through 7: Formation of a protostar.
What allowed the protostar to contract without reaching equilibrium between pressure and gravity?
a) Increasing density
b) Decreasing pressure
c) Cooling through radiation

48. Low density star contracts as energy is radiated away preventing pressure to oppose contraction.

49. Stage 8: Subgiant branch
What is the reason that a star leaves the mainsequence?
a) Increase of pressure due to enhanced nuclear fusion inside the core.
b) Ceasing of hydrogen burning inside the core.
c) Hydrogen burning inside the shell

50. Hydrogen burning ceases inside the core

51. The HR diagram shows a decrease in Temperature and increase in size on the subgiant branch
What are the reasons for the increase in size?
a) Core collapses but shell expands due to hydrogen burning
b) Pressure inside core increases, star expands
c) Size doesn’t matter.

52. Nuclear fusion in the shell goes faster.
Collapsing core produces heat (gravitational energy transformed into heat), that radiates into the shell surrounding the core. Hydrogen begins to fuse inside the shell and star expands.
Nuclear fusion in the shell goes faster.
Faster nuclear reactions release more energy.
This energy leaves the star’s surface at a higher rate.
Figure Hydrogen- Shell Burning As a star’s core converts more and more of its hydrogen into helium, the hydrogen in the shell surrounding the nonburning helium “ash” burns ever more violently. By the time shown here (a little after stage 8 in Table 20.1), the core has shrunk to a few tens of thousands of kilometers in diameter, whereas the star’s photosphere is ten times the star’s original size. 52

53. Stage 9: Red Giant What keeps the core from collapsing further?
a) Pressure regained due to increase in
heat.
b) Pauli’s principle.
c) Rudy’s principle

54. H-burning shell and electron degenerate core

55. Stage 10:Helium fusion What happens during stage 10?
a) Shell is burning helium into carbon,
core contracts.
b) Core is burning helium into carbon
and shell contracts.

56. The pressure within the helium core is almost totally due to electron degeneracy,
so the core cannot contract beyond a certain point.
This pressure is almost independent of temperature—when the helium starts fusing, the pressure cannot adjust.

57. Helium begins to fuse extremely rapidly; within hours the enormous energy output is over, and the star once again reaches equilibrium
Figure Horizontal Branch A large increase in luminosity occurs as a star ascends the red-giant branch, ending in the helium flash. The star then settles down into another equilibrium state at stage 10, on the horizontal branch.

58. Stage 11: Asymptotic Giant Branch
Why does the star again develop into a Red Giant?
a) Hydrogen burning in the outer shell and Helium burning in the inner shell.
b) Increased hydrogen burning in the core
c) Carbon burning in the core.

59. Back to the giant branch
As the helium in the core fuses to carbon, the core becomes hotter and hotter, and the helium burns faster and faster.
The star is now similar to its condition just as it left the Main Sequence, except now there are two shells:
Figure Helium-Shell Burning Within a few million years after the onset of helium burning (stage 9), carbon ash accumulates in the star’s inner core. Above this core, hydrogen and helium are still burning in concentric shells.

60. The star has become a red giant for the second time
Figure Reascending the Red-Giant Branch A carbon-core star reenters the giant region of the H–R diagram—this time on a track called the asymptotic-giant branch (stage 11)—for the same reason it evolved there the first time around: Lack of nuclear fusion at the center causes the core to contract and the overlying layers to expand.

61. The Death of a Low-Mass Star
This graphic shows the entire evolution of a Sun-like star.
Such stars never become hot enough for fusion past carbon to take place.
Figure G-Type Star Evolution Artist’s conception of the relative sizes and changing colors of a normal G-type star (such as our Sun) during its formative stages, on the main sequence, and while passing through the red-giant and white-dwarf stages. At maximum swelling, the red giant is approximately 70 times the size of its main-sequence parent; the core of the giant is about 1/15th the main-sequence size and would be barely discernible if this figure were drawn exactly to scale. The duration of time spent in the various stages—protostar, main-sequence star, red giant, and white dwarf—is roughly proportional to the lengths shown in this imaginary trek through space. The star’s brief stay on the horizontal and asymptotic-giant branches are not shown.

62. The outer layers become unstable and are eventually ejected.
There is no more outward fusion pressure being generated in the core, which continues to contract.
The outer layers become unstable and are eventually ejected.
Figure Red-Giant Instability Buffeted by helium-shell flashes from within, and subject to the destabilizing influence of recombination, the outer layers of a red giant become unstable and enter into a series of growing pulsations. Eventually, the envelope is ejected and forms a planetary nebula.

63. The ejected envelope expands into interstellar space, forming a planetary nebula.
Figure Ejected Envelope A planetary nebula is an extended region of glowing gas surrounding an intensely hot central star (marked with an arrow here). The small, dense star is the core of a former red giant. The gas is what remains of the giant’s envelope, now ejected into space. (a) Abell 39, some 2100 pc away, is a classic planetary nebula shedding a spherical shell of gas about 1.5 pc across. (b) The brightened appearance around the edge of Abell 39 is caused by the thinness of the shell of glowing gas around the central core. Very little gas exists along the line of sight between the observer and the central star (path A), so that part of the shell is invisible. Near the edge of the shell, however, more gas exists along the line of sight (paths B and C), so the observer sees a glowing ring. (c) Ring Nebula, perhaps the most famous of all planetary nebulae at 1500 pc away and 0.5 pc across, is too small and dim to be seen with the naked eye. Astronomers once thought its appearance could be explained in much the same way as that of Abell 39. However, it now seems that the Ring really is ring shaped! Researchers are still unsure as to why a spherical star should eject a ring of material during its final days. (AURA; NASA)

64. The star now has two parts:
A small, extremely dense carbon core
An envelope about the size of our solar system.
The envelope is called a planetary nebula, even though it has nothing to do with planets—early astronomers viewing the fuzzy envelope thought it resembled a planetary system.

65. Planetary nebulae can have many shapes:
As the dead core of the star cools, the nebula continues to expand and dissipates into the surroundings.
Figure Planetary Nebulae (a) The Eskimo Nebula clearly shows several “bubbles” (or shells) of material being blown into space from this planetary nebula, which resides some 1500 pc away in the constellation Gemini. (b) The Cat’s Eye Nebula, about 1000 pc away and 0.1 pc across, is an example of a much more complex planetary nebula, possibly produced by a pair of binary stars (unresolved at center) that have both shed envelopes. (c) M2-9, some 600 pc away and 0.5 pc end-to-end, shows surprising twin lobes (or jets) of glowing gas emanating from a central, dying star and racing out at speeds of about 300 km/s. (AURA; NASA)

66. Stages 13 and 14: White and black dwarfs
Once the nebula has gone, the remaining core is extremely dense and extremely hot, but quite small.
It is luminous only due to its high temperature.
Figure White Dwarf on the H–R Diagram A star’s passage from the horizontal branch (stage 10) to the white-dwarf stage (stage 13) by way of the asymptotic-giant branch creates an evolutionary path that cuts across the entire H–R diagram.

67. The small star Sirius B is a white-dwarf companion of the much larger and brighter Sirius A:
Figure Sirius Binary System Sirius B (the speck of light to the right of the much larger and brighter star Sirius A) is a white dwarf star, a companion to Sirius A. The “spikes” on the image of Sirius A are not real; they are caused by the support struts of the telescope. (Palomar Observatory)

68. As the white dwarf cools, its size does not change significantly; it simply gets dimmer and dimmer, and finally ceases to glow.

69. This outline of stellar formation and extinction can be compared to observations of star clusters. Here a globular cluster:
Figure Globular Cluster H–R Diagram (a) The globular cluster M80, some 8 kpc away. (b) Combined H–R diagram, based on ground- and space-based observations, for several globular clusters similar in overall composition to M80. The various evolutionary stages predicted by theory and depicted schematically in Figure are clearly visible. Note also the blue stragglers—main-sequence stars that appear to have been “left behind” as other stars evolved into giants. They are probably the result of merging binary systems or actual collisions between stars of lower mass in this remarkably dense stellar system. (See also Figure ) (NASA; data courtesy W.E. Harris)

70. Evolution of Stars More Massive than the Sun
It can be seen from this H-R diagram that stars more massive than the Sun follow very different paths when leaving the Main Sequence
Figure High-Mass Evolutionary Tracks Evolutionary tracks for stars of 1, 4, and 10 solar masses (shown only up to helium ignition in the low-mass case). Stars with masses comparable to that of the Sun ascend the giant branch almost vertically, whereas higher-mass stars move roughly horizontally across the H–R diagram from the main sequence into the red-giant region. The most massive stars experience smooth transitions into each new burning stage. No helium flash occurs for stars more massive than about 2.5 solar masses. Some points are labeled with the element that has just started to fuse in the inner core.

71. High-mass stars, like all stars, leave the Main Sequence when there is no more hydrogen fuel in their cores.
The first few events are similar to those in lower-mass stars—first a hydrogen shell, then a core burning helium to carbon, surrounded by helium- and hydrogen-burning shells.

72. Stars with masses more than 2
Stars with masses more than 2.5 solar masses do not experience a helium flash—helium burning starts gradually.
A 4-solar-mass star makes no sharp moves on the H-R diagram—it moves smoothly back and forth.

73. The main difference between low and high mass star are fusion processes into heavier elements.
Why can high mass stars create conditions for fusion into heavier elements?
More mass means more gravitational energy can be transformed into heat as star contracts.

74. A star of more than 8 solar masses can fuse elements far beyond carbon in its core, leading to a very different fate.
Its path across the H-R diagram is essentially a straight line—it stays at just about the same luminosity as it cools off.
Eventually the star dies in a violent explosion called a supernova.

75. Massive Post-MS Evolution
So far, pretty similar to lower mass stars studied already, but
Now we feel the big difference: higher M means gravity can crush the C core until it reaches T > 7 x 108 K so
Carbon CAN ALSO FUSE
12C + 4He  16O + 
Some: 16O + 4He  20Ne + 
Also some: 12C + 12C  24Mg + 
This fuel produces less energy per mass so C is burnt quickly.
Loops in the H-R diagram.

76. Massive Post MS Evolution on H-R Diagram
Start here on 10/26

77. Evolution of Stars More Massive than the Sun

78. Mass Loss from Giant Stars
All stars lose mass via some form of stellar wind. The most massive stars have the strongest winds; O- and B-type stars can lose a tenth of their total mass this way in only a million years.
These stellar winds hollow out cavities in the interstellar medium surrounding giant stars.

79. The sequence below, of actual Hubble images, shows a very unstable red giant star as it emits a burst of light, illuminating the dust around it:

80. Observing Stellar Evolution in Star Clusters
The following series of H-R diagrams shows how stars of the same age, but different masses, appear as the whole cluster ages.
After 10 million years, the most massive stars have already left the Main Sequence, while many of the least massive have not even reached it yet.
Figure Cluster Evolution on the H–R Diagram The changing H–R diagram of a hypothetical star cluster. (a) Initially, stars on the upper main sequence are already burning steadily while the lower main sequence is still forming. (b) At 107 years, O-type stars have already left the main sequence (as indicated by the arrows), and a few red giants are visible.

81. After 1 billion years, the main-sequence turnoff is much clearer.
After 100 million years, a distinct main-sequence turnoff begins to develop. This shows the highest-mass stars that are still on the Main Sequence.
After 1 billion years, the main-sequence turnoff is much clearer.
Figure Cluster Evolution on the H–R Diagram The changing H–R diagram of a hypothetical star cluster. (c) By 108 years, stars of spectral type B have evolved off the main sequence. More red giants are visible, and the lower main sequence is almost fully formed. (d) At 109 years, the main sequence is cut off at about spectral type A. The subgiant and red-giant branches are just becoming evident, and the formation of the lower main sequence is complete. A few white dwarfs may be present.

82. After 10 billion years, a number of features are evident:
The red-giant, subgiant, asymptotic giant, and horizontal branches are all clearly populated.
Figure Cluster Evolution on the H–R Diagram The changing H–R diagram of a hypothetical star cluster. (e) At 1010 years, only stars less massive than the Sun still remain on the main sequence. The cluster’s subgiant, red-giant, horizontal, and asymptotic-giant branches are all discernible. Many white dwarfs have now formed.
White dwarfs, indicating that solar-mass stars are in their last phases, also appear.

83. This double cluster, h and chi Persei, must be quite young—its H-R diagram is that of a newborn cluster. Its age cannot be more than about 10 million years.
Figure Newborn Cluster H–R Diagram (a) The “double cluster” h and chi Persei, two open clusters that apparently formed at the same time, possibly even orbiting one another. (b) The H–R diagram of the pair indicates that the stars are very young—probably only about 10 million years old. Even so, the most massive stars have already left the main sequence. (AURA)

84. The Hyades cluster, shown here, is also rather young; its main-sequence turnoff indicates an age of about 600 million years.
Figure Young Cluster H–R Diagram (a) The Hyades cluster, a relatively young group of stars visible to the naked eye, is found 46 pc away in the constellation Taurus. (b) The H–R diagram for this cluster is cut off at about spectral type A, implying an age of about 600 million years. A few massive stars have already become white dwarfs. (AURA)

85. Something odd with Algol
Algol is a 3.8-solar mass main sequence star of spectral type B8
with a red sub-giant binary companion of 0.8-solar mass in a nearly circular orbit.
Both are assumed to have formed at the same time.
What’s odd about this?
The larger star should have evolved faster than the smaller, that is already on the subgiant branch.

86. Each star has its zone of influence, called Roche lobe
Inside a star’s Roche lobe, its gravitational pull dominates the effects of rotational motion of the binary system and the gravitational pull of the companion star.
Any matter inside the RL belongs to the star and cannot flow away.
Outside the RL, matter can flow to either star.
The Lagragian point is where the gravitation pull from both stars balance.

87. Binary Star Evolution Most stars are in binary or multiple systems
If the binary is close enough, evolution is affected
More massive stars still can be on MS while less massive has evolved off (like Algol)
Only possible if there is mass transfer through Lagrangian point (L1) between Roche lobes

88. Binary Evolution Depends on Separation
Depending on orbital size and evolutionary stages, different scenarios are possible
Detached, evolve separately
Semi-detached, one fills Roche lobe, dumping on other
Contact or common-envelope, both overflow: single star with two fusion cores

89. Binary Evolution: Algol Type
Start detached
More massive leaves MS, blows up and overflows Roche lobe, dumping mass into less massive star.
Now 2nd star is more massive but still on MS