Transcript Neutron Stars

Neutron Stars
Aree Witoelar
What is a neutron star?
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A collapsed core of
a massive star
Composed entirely
from neutron
Incredibly high
density
Creation of a neutron star
Fusion from H to Fe
in the core of stars
 No more fuel -> core
reaches tremendous
density and explodes
(Supernova)
 Inverse ß–decay
takes place:
p  e   n  ve
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56

Fe

26
e
26
 56n  26ve
Properties
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Mass = 1.3-1.5 Msun
(3.1030 kg)
Radius = 10 km
Density = 1014g/cc
Magnetic field =
1012 Gauss
Interior
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Increasing pressure
inwards creates
‘Pasta’ layers
Nuclear Physics of Neutron Stars
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Neutron stars are like giant neutron supernuclei
Testing models of Nuclei-Nuclei Interaction on
neutron stars
Estimating Neutron Star radius:
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Binding Energy
Fermi Gas model
Nuclei-Nuclei Interaction (first principles)
Binding Energy
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Binding energy for a nucleus
A
Z XN
BE ( A, Z )  av A  as A2 / 3  ac Z ( Z  1) A1 / 3

3 G 2 1 / 3
 a A ( A  2Z ) A  0 
M A
5 r0

2
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1
Assumptions for a huge ‘neutron nucleus’:
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No Coulomb energy
Neglect pairing energy
Neglect surface term with respect to volume term
Binding Energy (2)
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Simplified Binding energy
3 G 2 1/ 3
BE ( A, Z )  av A  a A A 
M A
5 r0
Bound state exist if binding energy is positive
Filling the constants, the result is
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A = 5 x 1055
R = 4.3 km
M = 0.045 solar mass
Same order of magnitude as observations
Fermi Gas model
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Treat neutron stars as degenerate Fermi gases (of
neutrons) held by gravity
Assume
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Constant density: average pressure
No nucleon-nucleon interaction
Number of possible states
4p 2 dp
dn 
V
3
( 2 )
Integrate to Fermi momentum pF
 9N 
pF  

 4 
1/ 3

R
Fermi Gas model (2)
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Calculate <Ekin/N> from Fermi momentum and
<Epot /N> from gravitational energy
Minimize total of kinetic and potential energy
 (9 / 4) 2 / 3
R
GM n3 N 1 / 3
The results are
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R = 12 km
 = 0.25 nucleons/fm3 (nucleus = 0.17 nucleons/fm3 )
Close to experimental values: gravitational pressure
compensated by Fermi pressure and nucleon-nucleon
repulsion
Nucleon-Nucleon Interaction
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Nuclear force is an interaction between colourless
nucleons with range of the same order of magnitude
as the nucleon diameter
It is not possible to extract n-n potential directly from
structure of nucleus
Different models with different parameterization
General form of n-n potential
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Quantities to determine interaction
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Separation of nucleons x
Relative momenta p
Total orbital angular momentum L
Relative orientation of spins s1 and s2
Potential is scalar
Symmetric under exchange of the two nuclei
central
spin-spin
Tensor
spin-orbit
-meson theory
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Nucleons are surrounded by field of massive (virtual)
particles called -mesons (pions)
Pion could be absorbed by another nucleon in its
lifetime
Momentum transfer -> akin to force (but attractive)
Direct analogy of EM force but photons have no
mass, pion have mass of 140 MeV/c2 -> finite range
Heisenberg uncertainty principle
E.t ~ 
t ~ 4.6 x1024 sec
range ~ v.t  1.4 fm
Covalent and Meson exchange
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Covalent bonds
(direct q-exchange)
are suppressed by
color restriction
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Meson exchange:
color-neutral q q
Yukawa potential:

V  g
e
mc
r
h
r
Equation of State
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The relations
between the density
and temperature to
its pressure and
internal energy,
specific heats, etc.
Pure neutron matter
is unbound
Many-Body Theory
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Hamiltonian:
1 2
H  
i   vij
i 2m
i j

 vijk  
i j k
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Four-body and higher
order interaction are
neglected
Neutron Star Radius
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Different models have different parameterizations of vijR
Summary
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Neutron stars are interesting!
Nuclear Physics: Approximate Neutron Star radius
with Binding Energy, Fermi Gas model, or NucleonNucleon interaction
Nucleon-Nucleon interaction is caused by meson
exchange (virtual particles)
Different n-n models predict different radii of neutron
stars