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Neutron stars

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**1. **Neutron stars Death of a massive star
Core collapse & neutron star formation
Discovery of pulsars

**2. **I.7 : Core collapse in a massive star End of a massive star’s life (M>8Msun)
Center of star has fused all of the way to iron
Shells of other elements surround iron core
Only takes ~day to build up “dead” Chandrasekhar mass iron core
Core is held up by electron degeneracy pressure

**3. **Pop quiz… Why does fusion not proceed beyond iron?
A : Temperature never gets hot enough
B : Fusion of iron to heavier elements is too slow; so there is insufficient time to fuse beyond iron
C : Iron is the most tightly bound nucleus so its energetically unfavorable to fuse further
D : None of the above?

**4. **Once dead core exceeds 1.4Msun, electron degeneracy pressure cannot support it.
Core starts to collapse…
??109 kg/m3 - Density of core when collapse begins (onset of relativistic effects in electron motions)
??1010 kg/m3 - Fermi energy exceeds neutron-proton mass difference…
Inverse beta decay becomes energetically preferable to normal beta decay
Nuclei become very neutron rich… neutronization

**5. **??1014 kg/m3 - Individual nuclei are so neutron rich that they start to fall apart
Remaining nuclei surrounded by sea of free neutrons
This is called the neutron drip phase
??1016 kg/m3 - Neutron degeneracy pressure starts to become important
??1018 kg/m3 - Neutron degeneracy finally halts the collapse provided that M<3Msun
End up with a neutron star… typical mass of 1.4Msun with a radius of 10km

**6. **Remember White Dwarfs…
Where…

**7. **By analogy, neutron stars have (to a crude approximation)…
Where…
I.e., degenerate particles have mass mn, and ?=1

**8. **So, we can try to estimate radius of neutron star given what we know about white dwarfs
We know that
So we expect

**10. **Actually more complicated than white dwarf…
Have to use General Relativistic form of hydrostatic equilibrium equation
Neutrons don’t behave like an ideal degenerate gas… strong force interactions are crucial
There remain uncertainties about the “equation of state” of neutron stars

**11. **Question Consider a 1.4 solar mass neutron star. Neutron degeneracy pressure is responsible for supporting this star against gravity. But why is this star not subject to the same Chandrasekhar limit that affects White Dwarfs?

**13. **I.8 : Discovery of Pulsars

**14. **(Radio) Pulsars
First discovered by Bell and Hewish in 1967
Objects that emit very periodic pulses… periods range from 2ms to few seconds.
Process of elimination led people to believe that pulsars must be dues to rotating objects (only process that can be so stable)
But why need they be rotating neutron stars?

**15. **The observed spin rate of the object can be used to determine a minimum average density…
The minimum period (P) of a star is that for which the surface layers are “in orbit”…

**16. **
P=1s ? ??1?1011 kg/m3
P=10-1s ? ??1?1013 kg/m3
P=10-2s ? ??1?1015 kg/m3
So the measured periods imply neutron star densities!