1. Devil physics The baddest class on campus IB Physics

2. Tsokos Lesson E-5 Stellar evolution

3. IB Assessment Statements
Topic E-5, Stellar Processes and Stellar Evolution
Nucleosynthesis
E.5.1. Describe the conditions that initiate fusion in a star.
E.5.2. State the effect of a star’s mass on the end product of nuclear fusion.
E.5.3. Outline the changes that take place in nucleosynthesis when a star leaves the main sequence and becomes a red giant.

4. IB Assessment Statements
Topic E-5, Stellar Processes and Stellar Evolution
Evolutionary Paths of Stars and Stellar Processes
E.5.4. Apply the mass-luminosity relation.
E.5.5. Explain how the Chandrasekhar and Oppenheimer-Volkoff limits are used to predict the fate of stars of different masses.
E.5.6. Compare the fate of a red giant and a red supergiant.
E.5.7. Draw evolutionary paths of stars on an HR diagram.
E.5.8. Outline the characteristics of pulsars.

5. Objectives Describe how a star is formed
State the main sequences of nuclear reactions taking place in a star and say how the mass of the star determines which sequences actually take place
Describe the main stages in the evolution of a star and say how the mass plays a determining role

6. Objectives
Describe the end stages of stellar evolution and appreciate the significance of the Chandrasekhar limit
State the main properties of a black hole
State the main properties of pulsars
State the main characteristics of quasars
State the meaning of the term gravitational lensing

7. Nucleosynthesis
Interstellar space consists of gas and dust at a density of about kg/m2
One atom of hydrogen per cubic meter of space
74% hydrogen
25% helium
1% other

8. Nucleosynthesis
When the gravitational energy of a given mass exceeds the average kinetic energy of the thermal random motion of its molecules, the gas becomes unstable and tends to collapse
Jeans criterion

9. Nucleosynthesis
Stars form when relatively cool gas clouds (10 – 100 K) collapse under their own gravitation
When they contract, they heat up
Typical for the cloud to break up into smaller clouds and form several stars

10. Nucleosynthesis
When the collapsing gas is hot enough to produce visible light, the star is called a protostar

11. Nucleosynthesis
As the gas continues to compress, its temperature and pressure continue to increase
When the pressure in the core of the star equals the gravitational force, the star becomes fixed in shape

12. Nucleosynthesis
However, the combination of temperature (T = 106 to 107 K) and pressure in the core is so great that nuclear fusion (proton-proton cycle in E-2) reactions take place releasing large amounts of energy

13. Nucleosynthesis
The star maintains its shape so long as the number of fusion reactions creates enough heat and pressure to balance the gravitational force of contraction.

14. Mass – Luminosity Relation
The mass and age of a star will determine its luminosity
Applies to main sequence stars
α is between 3 and 4
Used to estimate the lifetime of a star on the main sequence
(Note that T = time, not temperature or period)

15. Mass – Luminosity Relation
Take α to be equal to 4
A star with one solar mass will spend 1010 years on the main sequence
A star with mass equal to 10 solar masses will spend 1/103 or times less than that

16. Mass – Luminosity Relation
Main sequence stars on the upper left of the HR diagram have very high luminosity and are thus very massive

17. Mass – Luminosity Relation
After a star has used 12% of its hydrogen (Schönberg – Chandrasekhar limit) its core will contract but its outside will expand substantially making it a very large star.
It then begins to leave the main sequence and move over to the red giant area

18. Mass – Luminosity Relation
Example Q3
We know the power output of our sun
We know the energy released per fusion reaction
We can determine the number of reactions per unit time to maintain this power
If we know the mass of the sun we can then find time to consume 12% of its hydrogen

19. Nuclear Reactions Beyond Main Sequence
When hydrogen in the core is depleted, fusion stops and the core contracts
Contraction heats up the core and that energy creates hydrogen fusion reactions on the surface of the core causing the outer layers to expand
The outer layers cool because of expansion
The star becomes bigger and cooler on the outside, but the core continues to heat up
This is a red giant

20. Mass and a Star’s Future
Low mass stars (less than 0.25 solar masses
No further nuclear reactions take place
Core stays a core of helium

21. Mass and a Star’s Future
Mass Between 0.25 and 4 solar masses
Temperature of the core reaches 108 K
Adequate for nuclear reactions involving helium to take place
No further reactions take place and the core consists of carbon and oxygen

22. Mass and a Star’s Future
Mass Between 0.25 and 4 solar masses

23. Mass and a Star’s Future
Mass Between 4 and 8 solar masses
Core temperature continues to rise
Nuclear reactions involving carbon and oxygen take place
Produces a core of oxygen, neon and magnesium

24. Mass and a Star’s Future
Mass Over 8 solar masses
The core of oxygen, neon and magnesium continues to contract reaching temperatures high enough for these elements to fuse and create heavier elements
In the outer layers, hydrogen continues to produce helium and helium produces carbon and oxygen
Processes continue with heavier elements settling in the core
Eventually, iron is produced – the heaviest element that can be produced through fusion

25. Mass and a Star’s Future
Mass Over 8 solar masses
The star ends its cycle of reactions with iron at its core, lighter elements surround it
The outer layers have expanded to a very large size
It is now a red supergiant

26. Mass and a Star’s Future
Mass Over 8 solar masses

27. Mass and a Star’s Future
Temperatures required for fusion reactions
Mass determines gravitational force which drives core temperature and pressure

28. Evolutionary Paths and Stellar Processes
The path taken in the HR diagram and the ultimate fate of a star are dependent on mass

29. Evolutionary Paths and Stellar Processes

30. Evolutionary Paths and Stellar Processes
Star paths based on mass

31. Stars Under 8 Solar Masses
Energy from core contraction and fusion reactions in outer layers may force ejection of outer layers – planetary nebula
Causes a reduction in the mass of a star though it still continues to contract – white dwarf
Without fusion reactions in the outer layers, the star eventually cools to practically zero – black dwarf

32. Stars Under 8 Solar Masses
Electron pressure generated by Pauli Exclusion Principle (no two electrons can occupy the same quantum state) can stop star contraction only if the mass of the core is less than 1.4 solar masses – Chandrasekhar limit
Result is white dwarf
If core mass is greater than 1.4 solar masses, result is neutron star or black hole

33. Stars Under 8 Solar Masses
During transition from white to black dwarf, mass from other stars can be absorbed by the white dwarf
This mass heats up and emits light, increasing the star’s luminosity for a short period -- nova

34. Stars Over 8 Solar Masses
The photons produced by fusion reactions have enough energy to break iron nuclei in the core apart into protons and neutrons
Electrons are forced into protons turning them into neutrons (Pauli principle) and releasing neutrinos

35. Stars Over 8 Solar Masses
When the neutrons in the core are compressed to a certain point, they rebound to expand the core to a larger equilibrium size
This rebounding cause a shock wave that rips apart the outer layers – supernova
Core that remains is called a neutron star
Neutron pressure keeps star stable provided the mass is not more than 3 solar masses – Oppenheimer-Volkoff limit

36. Star Evolution

37. Star Evolution

38. Star Evolution – Ultimate Demise
If the mass of the core of a star is less than the Chandrasekhar limit of about 1.4 solar masses, the star will become a stable white dwarf in which electron pressure keeps the star from collapsing further.

39. Star Evolution – Ultimate Demise
If the core is more massive than the Chandrasekhar limit, the core will collapse further until electrons are driven into protons, turning them into neutrons. Neutron pressure now keeps the star from collapsing further and the star has become a neutron star.

40. Star Evolution – Ultimate Demise
If the core is substantially more massive than the Oppenheimer-Volkoff limit of about 2-3 solar masses, neutron pressure will not be enough to oppose the gravitational collapse and the star will become a black hole.

41. Black Holes (can you see it?)

42. Black Holes
If the mass of a collapsing star is greater than a few tens of solar masses, gravitational collapse is unstoppable
Reaches a density such that the escape velocity from the surface equals the speed of light, so nothing can escape (Hotel California – ‘You can check out any time you like, but you can never leave.’)
Light cannot escape.

43. Black Holes
We can calculate the radius that this occurs -- Gravitational Radius (Rg), Swarzchild Radius (Rs), or Event Radius

44. Evidence for Black Holes
Motion of nearby stars affected by its gravitational attraction
Watch for binary stars that emit X-rays where one star is invisible
Nine known of so far
Gas forced into black holes accelerate, become hot, then emit X-rays

45. Pulsars Neutron star with a magnetic field on the order of 108 T
May also rotate as well with periods from 30ms to 0.3s
Emit electromagnetic waves in the radio and X-ray ranges of the spectrum
Detected by radiotelescopes
Rotation causes radiation

46. Pulsars
Radiation is along a narrow cone around the axis of the magnetic field direction
As the star rotates, the axis of radiation precesses
Pulsing comes from passage of the axis

47. Quasars Stars exhibiting bookoo red-shifting
Corresponds to 95% of speed of light
Believed to be very active centers of very young galaxies
Theory is that they are powered by black holes

48. Gravitational Lensing
Radio signals from distant quasars are bent around a massive galaxy
Appear to be two different images
Provides information about the lensing body.

49. Σary Review Can you describe how a star is formed?
Can you state the main sequences of nuclear reactions taking place in a star and say how the mass of the star determines which sequences actually take place?
Can you describe the main stages in the evolution of a star and say how the mass plays a determining role?

50. Σary Review
Can you describe the end stages of stellar evolution and appreciate the significance of the Chandrasekhar limit?
Can you state the main properties of a black hole?
Can you state the main properties of pulsars?
Can you state the main characteristics of quasars?
Can you state the meaning of the term gravitational lensing?

51. IB Assessment Statements
Topic E-5, Stellar Processes and Stellar Evolution
Nucleosynthesis
E.5.1. Describe the conditions that initiate fusion in a star.
E.5.2. State the effect of a star’s mass on the end product of nuclear fusion.
E.5.3. Outline the changes that take place in nucleosynthesis when a star leaves the main sequence and becomes a red giant.

52. IB Assessment Statements
Topic E-5, Stellar Processes and Stellar Evolution
Evolutionary Paths of Stars and Stellar Processes
E.5.4. Apply the mass-luminosity relation.
E.5.5. Explain how the Chandrasekhar and Oppenheimer-Volkoff limits are used to predict the fate of stars of different masses.
E.5.6. Compare the fate of a red giant and a red supergiant.
E.5.7. Draw evolutionary paths of stars on an HR diagram.
E.5.8. Outline the characteristics of pulsars.

53. Questions?

54. Homework
#1-26 (6 Points)