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

(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.

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

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 thanthe 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 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.

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

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

Neutron star - general parameters

Earth white dwarf neutron star

neutron star

surface gravity

escape velocity

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

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 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 .

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

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:

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

Neutron star magnetosphere (IV)

( Schematic illustration by D Page, University of Mexico)

Neutron star magnetosphere (V)

at the light cylinder

co-rotating plasmas areon the magnetic-fieldlines closed inside thelight cylinder

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

coherent

incoherent

yes

no

Does the totalradiation intensityexceed the sumintensity ofspontaneousradiation of individualemitting elements?

random phase

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:

Pulsar emission - coherent vs incoherent

Consider the radio emission from the Crab pulsar:

This gives an intensity

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.

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

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.

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

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 thansynchrotron radiation.It therefore require coherent process, if the pulsar radio emission is due tocurvature radiation.

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”.

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.

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 systemsBinary 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