1. The Death of a High Mass Star
Evolution of a star greater than about 4 solar masses post helium ignition
The star moves roughly horizontally across the Hertzprung-Russell diagram
Crossing the instability strip, becoming a Cepeid variable
Helium burning produces carbon and oxygen “ash”

2. Tracks of High Mass Stars
2,500
10-2 1
102
104
106
Luminosity (L¤)
40,000
20,000
10,000
5,000
Temperature (K)
Helium Ignition
3 M¤
5 M¤
9 M¤
15 M¤
End of core helium burning
Zero age
main sequence
Termination of core
hydrogen burning

3. Post-Helium Burning For stars above about 4 solar masses
the degenerate carbon-oxygen core can exceed the Chandrasekhar Limit
Degeneracy pressure can no longer support the core
Core collapse resumes
Pressures and densities become sufficient to burn carbon
core collapse temporarily halted

4. Post-Helium Burning Stars move back across the HR diagram
2,500
10-2 1
102
104
106
Luminosity (L¤)
40,000
20,000
10,000
5,000
Temperature (K)
Zero age
main sequence
Termination of core
hydrogen burning
3 M¤
5 M¤
9 M¤
15 M¤
Carbon/oxygen Ignition
Stars move back across the HR diagram
Neon “ash” accumulates in the core
core fusion stops again, a carbon shell continues to burn
The star becomes a Supergiant

5. Post-Helium Burning Note that:
At the cessation of each phase of core burning, the star moves to the red giant region
On ignition of a new source of core fuel, the star moves back across the HR diagram
The star eventually consists of a number of concentric shells at different stages of burning

6. Old High Mass Star Structure
Stars >8 solar masses can burn all the way to iron
Orbit of Jupiter
dia. ~ 1x Earth
High mass supergiant
dia. ~ 5 AU
L ~ 106 H He C Ne O Si Fe

7. Nearing the End Recall the rates at which fusion reactions proceed:
eg, for a 25 solar mass star

8. Nearing the End The star shown earlier is in its last day
What events occur next?
What is the timescale?
What are the consequences?

9. Core Collapse If a star fails to lose mass by other means...
e.g., via shell ejection as for low mass stars
…The iron core can reach the Chandrasekhar limit
The subsequent events lead to the destruction of the star

10. Core Collapse No nuclear processes can release energy from iron
Two mechanisms for absorbing energy:
Photodisintegration of nuclei
Electron capture by protons
As with the initial stages of star formation, there is now nothing to oppose free-fall under gravity

11. Core Collapse The free-fall collapse time of the core is very short
with a density of about 1012 kgm-3, the core can collapse in ~ 1ms
Temperature rises to ~5x109 K
g radiation sufficiently energetic to photodissociate 56Fe to He

12. Core Collapse g + 56Fe « 134He + 4n absorbs 124.4 MeV
About 75% dissociated

13. Core Collapse
As temperatures and densities rise, He nuclei can dissociate
g + 4He « 2p + 2n
All the fusion in the core is now undone
Total energy absorbed by a collapsing Chandrasekhar mass iron core ~ 1045 J
Equivalent to the energy output of the sun over 1010 years!

14. Core Collapse Densities continue to rise
The electron gas is definitely degenerate by this time
Recall from a workshop that the momentum of an electron at the fermi energy, Ef , is given by:

15. Core Collapse The energy of an electron at the Fermi Surface is:
If this energy becomes greater than 1.3 MeV, inverse b decay can occur:
e- + p ® n + ne
This becomes possible at densities ~1014 kgm-3

16. Core Collapse Neutrinos interact weakly with matter
Hence escape rapidly from the contracting core
For a core with the Chandrasekhar Mass, we have ~1057 electrons and protons
Hence the core loses ~1.6x1045 J
Neutrino pulse produced over a few seconds

17. Core Collapse
Core collapse is now only halted when the core reaches the density of atomic nuclei
~1017 kgm-3

18. A Supernova
The shockwave produced from the core bounce disrupts the outer layers of the star
The star’s luminosity leaps to ~108 solar luminosities
The gravitational energy released by the core collapse is ~1046 J
~2x1045 J absorbed by iron disintegration and inverse b decay
~1044 J in debris kinetic energy
~1042 J in optical energy in first year

19. A Supernova
Remainder of the energy contained within a hot, bloated remnant neutron star
Density ~ 1014 kgm-3, typical temp. ~1011 K
A dense plasma of neutrons, protons, other nuclei, electrons, photons and neutrinos
Essentially opaque to radiation
Remaining energy loss via neutrinos (mainly neutrino-antineutrino pair production)

20. Supernova Remnants Typically a rapidly expanding nebula is produced
e.g., the Crab Nebula, produced in a supernova explosion in 1054

21. Supernova Remnants The collapsed core remains as a neutron star
What are the properties of such objects?
Density?
Temperature?
Is there an upper limit to their mass?
How do they appear

22. Stellar Remnants White Dwarfs Neutron Stars
Originate from low mass stars
Mass less than the Chandrasekhar limit
Supported by the pressure of a degenerate electron gas
Neutron Stars
Originate from high mass stars
Mass may be greater than the Chandrasekhar Limit
Supported by nuclear forces

23. White Dwarfs Sirius B the first to be observed (1862)
Luminosities very low
~10-3 solar luminosities
Surface temperatures high
~30,000 K
Masses of the order of one solar mass
measured from orbital motions

24. White Dwarfs Implications:
High temperature and low luminosity imply low radius - comparable with the Earth
Mass comparable to the sun implies high density - typically 109 kgm-3
Electrons form a degenerate quantum gas

25. White Dwarfs Pressure arises from:
Pauli Exclusion Principle
Heisenberg’s Uncertainty Principle
Given an electron density of n with a mean momentum p and velocity v , the pressure is:

26. White Dwarfs A density n implies a mean spacing Dx = n-1/3
Hence, from Heisenberg, the momentum, p, will be: p ~ Dp ~ h/Dx = hn1/3
The mean velocity is then (m = mass of electron): v = p/m ~ (h/m)n1/3
The pressure is therefore approximately: P = 1/3 nvp ~ 1/3 ((h2/m)n5/3

27. White Dwarfs
If the electrons are non-relativistic, the pressure is given exactly by (Lecture 5 and Physics of Stars secn 2.2)
Using the density given earlier, this gives a typical pressure of 1016 atm.

28. White Dwarfs Mass-Radius Relationship
To estimate the mass-radius relationship, we require an estimate of the pressure required to support the star: R
Gravitational acceleration acting on column ~ GM/R 2
Mass of column ~ rR ~ M/R 2
Hence P ~ GM 2/R4
Weight of column of material = P
Unit area

29. White Dwarfs
Equating this pressure with that derived from degeneracy considerations we find:
Noting that n = r/mp and M ~ rR3 we obtain the proportionality:
Consequence: More massive white dwarfs are smaller!

30. White Dwarfs
As white dwarfs increase in mass, electrons are forced closer together
Hence, in accordance with Heisenberg, their momenta increase
Consequently, their speeds approach c and they become ultra-relativistic
The degeneracy pressure is now given by:

31. White Dwarfs
The pressure does not now rise fast enough to support the increase in gravity, and a maximum mass is achieved
The Chandrasekhar Mass, given by:
~1.4 solar masses

32. Neutron Stars
A stellar core exceeding this mass cannot form a white dwarf
Collapse continues until nuclear densities are reached
A neutron star is formed, supported by degeneracy pressure of neutrons
Again, R µ M-1/3
Typical radius ~ km

33. Neutron Stars Structure: Not well known
Physics of “neutron matter” not well established

34. Neutron Stars Other properties: High gravitational fields
Escape velocity ~ 50%c
High magnetic fields
Concentrated fields from original star
High rotation rate
Conservation of angular momentum
Typical rotational period for a new neutron star ~ 30ms

35. Neutron Stars
Pulsars
High magnetic fields lead to “beaming” of particles and radiation along magnetic poles
High spin rates lead to rapid “pulsing”

36. Neutron Stars

37. Neutron Stars Other manifestation:
Synchrotron radiation from supernova remnants, implying strong magnetic fields and a power source

38. Neutron Stars Spin rate slows with time Due to loss of energy
The Crab pulsar is slowing at about 3x10-8s per day
Energy loss consistent with that required to power the Crab Nebula

39. Neutron Stars Upper limit for mass
The properties of neutron star matter are not well known
Current estimates place the limit at about 2-3 solar masses
Find the mass (and hence the radius) at which the escape velocity = c
Certainly no more than 5
What happens to stellar cores above this limit?

40. Black Holes Neutron degeneracy can no longer support the star
collapse resumes, with nothing now to support it
Escape velocity exceeds c
light can no longer escape
sphere surrounding the collapsed star where the escape velocity = c is termed the Event Horizon

41. Black Holes Simple structure:
All mass in a singularity at infinite density
Radius of event horizon, the Schwarzschild radius, given by RSch = 2GM/c2

42. Black Holes Cannot be directly seen Indirect evidence
Strong x-ray source Cygnus X-1
“Flickers” on a timescale of 0.01s (hence small)
Identified with a B0 supergiant star, HDE
Radio outbursts also occur
Spectral shifts show this is a binary system with HDE having a mass of 30 solar masses and an invisible companion with mass 7 solar masses

43. Black Holes
Conclusion:
unseen companion is a black hole