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Neutron stars and pulsars
- Pulsar phenomenology - Neutron star structure - Neutron star
magnetic field - Neutron star magnetosphere - Pulsar emission
mechanisms
- Pulsar emission region - Pulsar population and evolution -
Neutron star zoo and exotic phenomena
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Neutron star - a brief historical overview
Chandrasekhar (1931) - degenerated stars would collapse at
Baade & Zwicky (1934) - existence of neutron stars - their
formation in supernova explosion - compact, with radii
Oppenheimer & Volkoff (1939) - equation of state for nucleon
matter - neutron star parameters:
Pacini (1967) - electromagnetic waves from rotating neutron star
- a neutron star may power the Crab nebula
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Pulsar - the discovery
(Top left) The first recording of the pulsar PSR 1919+21.
(Bottom left) Fast chart recording showing individualpulses (period
of 1.337 s) of the pulsar. (From Lyne & Graham-Smith
(1990).)(Right) Jocelyn Bell and the antenna/telescope that
discovered the first pulsar.
Studying interplanetary scintillation, Hewish & Bell found
pulsations in the recordings of the source CP 1919.
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Pulsar - the Crab pulsar
- supernova in 1054 AD
- pulse period of 33 ms
optical images of the crab nebula and the central pulsar image
of the Crabpulsar obtained bythe Einstein X-raysatellite
off
on
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Pulsar phenomenology - the pulses
- the pulse duty cycle is usually about - the pulse periods are
extreme stable: stability reaching
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Pulsar phenomenology - the light house model
- fast spinning magnetic star - magnetic dipole axis not aligned
with the spinning axis - beamed emission
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Pulsar - structure stability (I)
In order to avoid flying apart, the gravitational force must be
larger thanthe centrifugal force of a rapidly spinning star.
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Pulsar - structure stability (II)For the Crab pulsar, the pulsar
period is 33 ms. If it is the spin period,then the density of the
star
For a white dwarf with and , thedensity
The density of the pulsar is too high, and so it cannot be a
white dwarf.The alternative is that it is a neutron star.
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Pulsar - energetic (I)The kinetic energy of a spinning star
is
Energy loss would lead to period change, implying
Suppose that and
For the Crab pulsar and
This gives
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Pulsar - energetic (II)The X-ray luminosity (at the 2 - 20 keV
band) of the Crab nebula isobserved to be .
Thus, the energy extracted from the rotation of the central star
issufficient to power the Crab nebula.
The characteristic age of a pulsar (assuming that the energy
loss isdue to magnetic dipole radiation) is given by
For the Crab pulsar, , which gives
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Neutron star - general parameters
Earth white dwarf neutron star
neutron star
surface gravity
escape velocity
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Neutron star - internal structure (I)
core ?
crystallization ofnucleon matter ?
neutron fluidinterior
superfluid neutrons,and superconductingprotons and electrons
inner crust
1 km
9 km10 km
heavy nuclei (Fe) attheir minimum-energyconfigurations in
thecrystalline lattices.
outer crust
neutron superfluid
atmosphere
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Neutron star - internal structure (II)
Main Components: (1) atmosphere (2) crystalline solid crust (3)
neutron liquid interior - boundary at r = 2.1017 kg/m3 (density of
nuclear matter)
Atmosphere:- very thin, with thickness
Outer crust:- solid; matter similar to that in white dwarfs-
heavy nuclei (mostly Fe) forming a Coulomb lattice embedded in a
relativistic degenerate electron gas- lattice is minimum energy
configuration for heavy nuclei.
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Neutron star - internal structure (III)
Inner crust:- lattice of neutron-rich nuclei (electrons
penetrate nuclei to combine with protons and form neutrons) with
free degenerate neutrons and degenerate relativistic electron gas-
for (the neutron drip point), massive nuclei become unstable and
release neutrons
Neutron fluid Interior:- for , neutron fluid – superfluid of
neutrons and superconducting protons and electrons- matter density-
enabling magnetic field maintenance- near inner crust, some neutron
fluid can penetrate into inner part of lattice and rotate at a
different rate – pulsar glitches ?
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Neutron star - internal structure (III)
Core:- extending out to and density of- its constituents
uncertain- could be a neutron solid, quark matter or neutrons
squeezed to form pion condensates
- QCD phase transitions occur when density increases- a neutron
could become a quark star or a hybrid star in this scenario
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Neutron star - neutron star or quark star?
- radius of a neutron or quark star dependent on the equation of
state of the nucleon/quark matter- phase transition changing the
energy content of the star
for and
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Neutron star - magnetic field (I)
flux conservation:
progenitor star compact star
Suppose that a star with and collapses into a neutron star, flux
conservation implies a neutron-star magnetic field .
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Neutron star - magnetic field (II)
If a spinning neutron star has a dipole magnetic field and the
dipoleaxis and spin axis are not aligned to each other, it will
emit electro-magnetic radiation.As rotational energy is extracted,
we can obtain an estimate of theneutron-star magnetic field from
the measurement of the rate ofchange in the spin period.
For and ,
we have .
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Neutron star magnetosphere (I)
Charge particles in the vicinity of a fast rotating magnetised
neutron starare subjected to gravitational force and
electro-magnetic force.
gravitational force
electro-magnetic force
for parameters similar to the Crab pulsar’s
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Neutron star magnetosphere (II)
rotating neutron star in vacuum
a strong electric field is induced bythe rotating magnetic
dipole field:
B-field dipole axis
electric potential difference onscale of neutron-star
radius:
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Neutron star magnetosphere (III)
B-field dipole axisSuch a large potential differencecould lead
to the acceleration ofprotons, electrons and othercharged
particles.
However, the charged particle willredistribute themselves around
thestar, creating an electric fieldwhich neutralise the induced
fielddue to the rotation of the neutron-star magnetic field.
closed magnetosphere filled with charged particles
This leads to the creation of anextensive magnetosphere.
open magnetosphere
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Neutron star magnetosphere (IV)
( Schematic illustration by D Page, University of Mexico)
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Neutron star magnetosphere (V)
at the light cylinder
co-rotating plasmas areon the magnetic-fieldlines closed inside
thelight cylinder
light cylinder
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Neutron star magnetosphere (VI)
- induced electric field lifting charges from the stellar
surface - charge and currents above the surface in the
magnetosphere
- open field lines passing through the light cylinder and
particles streaming out along them- footpoints of the critical
field lines at the same electric potential as the interstellar
medium- critical field lines dividing the regions of positive and
negative current flows from the neutron-star magnetosphere
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Pulsar emission - coherent vs incoherent
coherent
incoherent
yes
no
Does the totalradiation intensityexceed the sumintensity
ofspontaneousradiation of individualemitting elements?
random phase
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Pulsar emission - coherent vs incoherentExamples of incoherent
emission:
(1) radiating particles in thermal equilibrium - thermal
emission (2) black-body radiation (maximum intensity) (3) ……
Question: Is radio emission from pulsars coherent or
incoherent?
First, we define the brightness temperature of an intensity:
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Pulsar emission - coherent vs incoherent
Consider the radio emission from the Crab pulsar:
This gives an intensity
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Pulsar emission - coherent vs incoherentThe corresponding
brightness temperature is therefore
This temperature is too high to be the thermal temperature of
theemitting plasma.The radio emission cannot be incoherent.
Question: Are the other emissions from the pulsar also
incoherent?
The Crab pulsar also emits optical/IR radiation and X-rays.
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The brightness temperature of the X-rays is about , equivalent
toelectron energies of .
It is possible to produce these X-rays with an incoherent
process.
Pulsar emission - coherent vs incoherent
Incoherent radiation: radio emission Coherent radiation:
optical/IR radiation, X-rays, gamma-rays
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Pulsar emission - coherent emission sources
Electron-positron pair cascadeleads to particle bunching.
Bunched particles can radiatecoherently in sheets.
High magnetic field, together with fast spinning,sets up a large
electric potential difference, whichleads to the production of very
high-energyparticles.
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Pulsar emission mechanism
Radiative processes in a magnetic field:
- cyclotron radiation - synchrotron radiation
- curvature radiation
Pulsar environment: strong magnetic field, very energetic
particles
Electrons travel along the field lineclosely in high speeds,
with verysmall pitch angles.
optical and X-ray pulsar emission
radio pulsar emission
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Pulsar emission mechanism
synchrotron radiation curvature radiation
effective frequency of curvature radiation
gyro-frequency
curvature radius
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Pulsar emission mechanism
The spectrum of curvature radiation is similar to that of
synchrotron radiation.
For electrons, incoherent curvature radiation is generally much
weaker thansynchrotron radiation.It therefore require coherent
process, if the pulsar radio emission is due tocurvature
radiation.
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Pulsar - age and population
The characteristic age of apulsar is given by
Death line: it corresponds tothe critical voltage that
neutronstar has to generate for thepolar-cap gap to break downdue
to electron-positronavalanche. The pulsar wouldbe “invisible”.
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Pulsar - age and population
Horizontal:The B field is more orless constant.
Vertical:The B field decays.
The evolution of pulsarscan be considered ascurrent flows in the
B-Pplane.
The birth rate of pulsars is estimated to be 1 in 80 years.The
supernova rate is about 1 in 30 year.
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Pulsar - age and population
ms-pulsars: - periods of milliseconds - weak B field
“Original spin” or “born again”?
current view of their origin: - resurrected old pulsars -
pulsars in binary systems - spun up by accretion
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Pulsars in binary systemsBinary system PSR 1913+16- 2 neutron
stars one pulsed, another not
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Pulsars in binary systems
Be X-ray binaries:
- Be star + neutron star - very eccentric orbit - burst of
emission at periastron - quiescent at apastron
A0538-66
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Pulsars in binary systems
black widow pulsars - the pulsar wind blasting onto the
companion star - the companion star is eventually evaporated,
leaving a planetary mass object