Download Neutron stars and pulsars

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
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
Pulsar - the discovery
Studying interplanetary scintillation,
Hewish & Bell found pulsations
in the recordings of the source
CP 1919.
(Top left) The first recording of the pulsar PSR 1919+21. (Bottom left) Fast chart recording showing individual
pulses (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.
Pulsar - the Crab pulsar
off
on
optical images of the crab nebula and the central pulsar
- supernova in 1054 AD
- pulse period of 33 ms
image of the Crab
pulsar obtained by
the Einstein X-ray
satellite
Pulsar phenomenology - the pulses
- the pulse duty cycle is usually about
- the pulse periods are extreme stable: stability reaching
Pulsar phenomenology - the light house model
- fast spinning magnetic star
- magnetic dipole axis not aligned
with the spinning axis
- beamed emission
Pulsar - structure stability (I)
In order to avoid flying apart, the gravitational force must be larger than
the centrifugal force of a rapidly spinning star.
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
density
and
, the
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.
Pulsar - energetic (I)
The kinetic energy of a spinning star is
Energy loss would lead to period change, implying
For the Crab pulsar
Suppose that
This gives
and
and
Pulsar - energetic (II)
The X-ray luminosity (at the 2 - 20 keV band) of the Crab nebula is
observed to be
.
Thus, the energy extracted from the rotation of the central star is
sufficient to power the Crab nebula.
The characteristic age of a pulsar (assuming that the energy loss is
due to magnetic dipole radiation) is given by
For the Crab pulsar,
, which gives
Neutron star - general parameters
neutron star
white dwarf
Earth
surface gravity
escape velocity
neutron star
Neutron star - internal structure (I)
superfluid neutrons,
and superconducting
protons and electrons
outer crust
inner crust
neutron fluid
interior
heavy nuclei (Fe) at
their minimum-energy
configurations in the
crystalline lattices.
neutron superfluid
core ?
atmosphere
1 km
crystallization of
nucleon matter ?
9 km
10 km
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.
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 ?
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
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
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
.
Neutron star - magnetic field (II)
If a spinning neutron star has a dipole magnetic field and the dipole
axis and spin axis are not aligned to each other, it will emit electromagnetic radiation.
As rotational energy is extracted, we can obtain an estimate of the
neutron-star magnetic field from the measurement of the rate of
change in the spin period.
For
and
we have
.
,
Neutron star magnetosphere (I)
Charge particles in the vicinity of a fast rotating magnetised neutron star
are subjected to gravitational force and electro-magnetic force.
electro-magnetic force
gravitational force
for parameters similar to the Crab pulsar’s
Neutron star magnetosphere (II)
rotating neutron star in vacuum
a strong electric field is induced by
the rotating magnetic dipole field:
B-field dipole axis
electric potential difference on
scale of neutron-star radius:
Neutron star magnetosphere (III)
open magnetosphere
B-field dipole axis
Such a large potential difference
could lead to the acceleration of
protons, electrons and other
charged particles.
However, the charged particle will
redistribute themselves around the
star, creating an electric field
which neutralise the induced field
due to the rotation of the neutronstar magnetic field.
closed magnetosphere
filled with charged
particles
This leads to the creation of an
extensive magnetosphere.
Neutron star magnetosphere (IV)
( Schematic illustration by D Page, University of Mexico)
Neutron star magnetosphere (V)
light cylinder
at the light cylinder
co-rotating plasmas are
on the magnetic-field
lines closed inside the
light cylinder
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
Pulsar emission - coherent vs incoherent
Does the total
radiation intensity
exceed the sum
intensity of
spontaneous
radiation of individual
emitting elements?
yes
random phase
coherent
no
incoherent
Pulsar emission - coherent vs incoherent
Examples 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:
Pulsar emission - coherent vs incoherent
Consider the radio emission from the Crab pulsar:
This gives an intensity
Pulsar emission - coherent vs incoherent
The corresponding brightness temperature is therefore
This temperature is too high to be the thermal temperature of the
emitting plasma.
The radio emission cannot be incoherent.
The Crab pulsar also emits optical/IR radiation and X-rays.
Question: Are the other emissions from the pulsar also incoherent?
Pulsar emission - coherent vs incoherent
The brightness temperature of the X-rays is about
, equivalent to
electron energies of
.
It is possible to produce these X-rays with an incoherent process.
Incoherent radiation:
radio emission
Coherent radiation:
optical/IR radiation, X-rays, gamma-rays
Pulsar emission - coherent emission sources
Electron-positron pair cascade
leads to particle bunching.
Bunched particles can radiate
coherently in sheets.
High magnetic field, together with fast spinning,
sets up a large electric potential difference, which
leads to the production of very high-energy
particles.
Pulsar emission mechanism
Pulsar environment: strong magnetic field, very energetic particles
Electrons travel along the field line
closely in high speeds, with very
small pitch angles.
Radiative processes in a magnetic field:
- cyclotron radiation
- synchrotron radiation
optical and X-ray pulsar emission
- curvature radiation
radio pulsar emission
Pulsar emission mechanism
synchrotron radiation
curvature radiation
effective frequency of curvature radiation
gyro-frequency
curvature radius
Pulsar emission mechanism
The spectrum of curvature radiation is similar to that of synchrotron radiation.
For electrons, incoherent curvature radiation is generally much weaker than
synchrotron radiation.
It therefore require coherent process, if the pulsar radio emission is due to
curvature radiation.
Pulsar - age and population
The characteristic age of a
pulsar is given by
Death line: it corresponds to
the critical voltage that neutron
star has to generate for the
polar-cap gap to break down
due to electron-positron
avalanche. The pulsar would
be “invisible”.
Pulsar - age and population
Horizontal:
The B field is more or
less constant.
Vertical:
The B field decays.
The evolution of pulsars
can be considered as
current flows in the B-P
plane.
The birth rate of pulsars is estimated to be 1 in 80 years.
The supernova rate is about 1 in 30 year.
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
Pulsars in binary systems
Binary system PSR 1913+16
- 2 neutron stars one pulsed, another not
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
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