Transcript JDiener_SKA09II

Ferromagnetism in neutron matter
...and how it could apply to neutron stars
JPW Diener1 , FG Scholtz1,2, HB Geyer1, GC Hillhouse3
1 Institute
of Theoretical Physics, Stellenbosch University
2 National Institute for Theoretical Physics, Stellenbosch
3 New York Institute of Technology, Nanjing, China
Introduction
 We are investigating pulsar/neutron star
matter.
• One of the densest states of matter.
 Aiming to better understand the magnetic
field of these stars.
 Pulsars are made up (in part at least) of
nuclear matter.
 We are investigating the spontaneous
magnetisation of neutron matter.
Ferromagnetism
Unmagnetised matter
(Ferro)magnetised matter
 Ferromagnetism is a property of any system
that can undergo a phase transition from an
unmagnetised to a magnetised state.
Neutrons
 Neutrons are neutral particles,
Neutron with the
magnetic dipole moment
 with spin ±½.
 Dipole moment reacts to a external magnetic
field.
 Aligned dipole moments induce a magnetic
field.
 Spontaneous magnetisation will occur if a
stable, lower energy (magnetic) configuration
is available.
Relativity
 Relativistic description of ferromagnetism.
 Relativity: Albert Einstein’s most famous
equation:
E = mc 2
 More general form: E 2 = p2c 2 + m2c 4
 Considering plane waves solution and natural
2
2
2
units (ћ = c = 1)
E = k +m
 Non-relativistic energy-momentum
2
relationship:
k
E=
2m
Neutron matter dispersion relationship
Magnetic neutron matter
 Including the magnetic field in a relativistic
fashion, the energy-momentum relationship is
2
modified: 2
E = kz 2 + k2 + m2 ± bz


 For zero momentum:
E =  m ± bz 
 (External) magnetic field introduces a specific
direction, breaking spherical symmetry.
Neutron matter dispersion relationship (2)
Magnetised vs unmagnetised system
Ferromagnetic state
 External magnetic field makes a lower energy
state available.
 If lower energy state is favoured, a magnetic
field is induced.
 Ferromagnetic state would be stable if the
induced magnetic field is equal to the external
field.
Conclusions and way forward
 Have shown that lower energy state exists.
 Strength of induced magnetic field as function
of density still unknown.
• To be calculated.
 Compare to experimental known properties of
the neutron to determine accuracy.
 If there is agreement, then we would be able
to predict at what densities a ferromagnetic
phase would present itself.
Acknowledgements
This research is support by the
 SA SKA project,
and,
 Stellenbosch University.