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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 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