Presentation on theme: "High Energy Astrophysics"— Presentation transcript:
1High Energy Astrophysics PulsarsHigh Energy AstrophysicsEnrico Massaro notesReferences, -1. High Energy Astrophysics, Volume 2, Second Edition, Longair2. ‘Pulsar Astronomy’ by Lyne and Smith
2Pulsed emission;Rotation and energetics;Magnetic field;Neutron star structure;Magnetosphere and pulsar models;Radiation mechanisms;Age and population
3Introduction Period interpulse (~P/10) pulse Known radio pulsars appear to emit short pulses of radio radiation with pulse periods between 1.4 ms and 8.5 seconds (P usually ≤ 1sec, dP/dt > 0). Even though the word pulsar is a combination of "pulse" and "star," pulsars are not pulsating stars. Their radio emission is actually continuous but beamed, so any one observer sees a pulse of radiation each time the beam sweeps across his line-of-sight. Since the pulse periods equal the rotation periods of spinning neutron stars, they are quite stable.Periodinterpulse(~P/10)pulsePulsars (ie objects which emit radio pulses with very short periods) are isolated, highly magnetic neutron stars which radiate energy produced in the slowing down of their rapid spinning motion.Rotational period is generally less than 1 second and the period is increasing with time.Neutron stars are supported by degeneracy pressure because their internal densities are so high that classical gas formulae are inappropriate to describe conditions. The ‘pressure’ is a result of Heisenberg’s Uncertainty Principle and Fermi’s Exclusion Principle, which state that particles cannot occupy the same quantum state. The resultant mechanical momenta of the particles provides the pressure of the degenerate gas.Pulsating X-ray sources - X-ray pulsators, are compact objects (generally neutron stars) in binary systems which accrete matter from a normal star companion. The energy radiated is produced by accretion and modulated with the neutron star spin period. X-ray pulsator period generally tens of seconds, some with ~ few seconds. Their period is decreasing with time, ie. they are spinning up.X-ray pulsators are effectively binary pulsars.The magnetic axes of both pulsars and X-ray pulsators are not aligned with the rotation axis.See Smith, p12-13
4IntroductionRadio observations of pulsars have yielded a number of important results because:Neutron Stars – supported by degeneracy pressure; Fermi exclusion principle restricts position hence Heisenberg uncertainty principle allows large momentum/high pressure - are physics laboratories providing extreme conditions (deep gravitational potentials, densities exceeding nuclear densities, magnetic field strengths as high as B~ gauss) not available on Earth.Pulse periods can be measured with accuracies approaching 1 part in 1016, permitting exquisitely sensitive measurements of small quantities such as the power of gravitational radiation emitted by a binary pulsar system or the gravitational perturbations from planetary-mass objects orbiting a pulsar. Period increases quasi-regularly 10-20<dP/dt<10-12 s/s. However in some cases “glitches” are observed (abrupt decreasing of dP/dt).
5DiscoveryThe radical proposal that neutron stars exist was made with trepidation by Baade & Zwicky in 1934: "With all reserve we advance the view that a supernova represents the transition of an ordinary star into a new form of star, the neutron star, which would be the end point of stellar evolution. Such a star may possess a very small radius and an extremely high density." Pulsars provided the first evidence that neutron stars really do exist. They tell us about the strong nuclear force and the nuclear equation of state in new ranges of pressure and density, test general relativity and alternative theories of gravitation in both shallow and relativistically deep (GM/rc2>>0) potentials, and led to the discovery of the first extrasolar planets.Pulsars were discovered serendipidously in 1967 on chart-recorder records obtained during a low-frequency (=81 MHz) survey of extragalactic radio sources that scintillate in the interplanetary plasma, just as stars twinkle in the Earth's atmosphere.
6DiscoveryPulsar signals "had been recorded but not recognized" several years earlier with the 250-foot Jodrell Bank telescope. Most pulses seen by radio astronomers are just artificial interference from radar, electric cattle fences, etc., and short pulses from sources at astronomical distances imply unexpectedly high brightness temperatures T~1023–1030 K >>1012 K, the upper limit for incoherent electron-synchrotron radiation set by inverse-Compton scatteringbrightness temperature: Tb=Fc2/ k2, the temperature for which if F is given by the RJ formula (F~KT2) T=Tb.Cambridge University graduate student Jocelyn Bell noticed pulsars in her scintillation survey data because the pulses appeared earlier by about 4 minutes every solar day, so they appeared exactly once per sidereal day and thus came from outside the solar system.The sources and emission mechanism were originally unknown, and even intelligent transmissions by LGM ("little green men") were seriously suggested as explanations for pulsars.
7DiscoveryAstronomers were used to slowly varying or pulsating emission from stars, but the natural period of a radially pulsating star depends on its mean density and is typically days, not seconds.
9Basic propertiesThere is a lower limit to the rotation period P of a gravitationally bound star, set by the requirement that the centrifugal acceleration at its equator not exceed the gravitational acceleration. If a star of mass M and radius R rotates with angular velocity =2/P
11Basic propertiesThe canonical neutron star has M~ 1.4MSun and R~ 10 km, depending on the equation-of-state of extremely dense matter composed of neutrons, quarks, etc. The extreme density and pressure turns most of the star into a neutron superfluid that is a superconductor up to temperatures T~109 K. Any star of significantly higher mass (M~3MSun in standard models) must collapse and become a black hole. The masses of several neutron stars have been measured with varying degrees of accuracy, and all turn out to be very close to 1.4MSun.
12White dwarf, neutron stars and black holes From the Salpeter IMF (number of stars formed each year per cubic Mpc with mass between M and M+dM):(M,M+dM)=2 10-12 M-2.35 dm98% of the stars will end forming a white dwarf, i.e. the total number of WD in a typical galaxy is ~1010Neutron stars will form if Mns>1.4MSun. They are thought to form form from the collapse of the core of stars with mass between 8 and 35 MSun. The total number of neutron stars in a typical galaxy is ~109.Black holes will form is MBH>3MSun. They are thought to form from the collapse of the core of stars with M>35 MSun. The total number of black holes in a typical galaxy is ~
13Basic propertiesThe Sun and many other stars are known to possess roughly dipolar magnetic fields. Stellar interiors are mostly ionized gas and hence good electrical conductors. Charged particles are constrained to move along magnetic field lines and, conversely, field lines are tied to the particle mass distribution. When the core of a star collapses from a size 1011 cm to 106 cm, its magnetic flux is conserved and the initial magnetic field strength is multiplied by 1010 , the factor by which the cross-sectional area a falls. An initial magnetic field strength of B~100 Gauss becomes B~ 1012 Gauss after collapse, so young neutron stars should have very strong dipolar fields.
14Magnetic induction Magnetic flux, constant Radius collapses from 7 x 10 m to 10 mconstantsurfaceRNSR84The integral of the magnetic field around the surface of the star must be a constant and the radius collapses from 7e8 m to 1e4m. Thus the ratio of the magnetic fields of the neutron star to the Sun is equivalent to the ratio of their radii squared… and this is approximately 5e9. So the magnetic field of a 1 solar mass neutron star is 5 billion times that of the Sun.Surface change gives
15Thus the field for the neutron star: The Sun has magnetic fields of several different spatial scales and strengths but its general polar field varies with solar cycle and is ≈ Tesla.Thus the field for the neutron star:B ~ 5 x 10 Tesla = 5 x GaussIf the main energy loss from rotation is through magnetic dipole radiation then:B ~ 3.3 x 1015 (P P) ½ Teslaor ~ 106 to 109 Tesla for most pulsars711nsIf we can assume that magnetic braking is responsible for the slowing-down of pulsars, then we can calculate the magnetic field strengths at the surface. From observed dP/dt, we find that magnetic field strengths of most pulsars typically lie in the range of to Tesla (but weaker for the millisecond pulsars, magnetic field B = 3e15 sqrt(P x dP/dt).•
16Pulsar energetics The traditional magnetic dipole model of a pulsar (Pacini 1966)Light cylinder (the cylinder centered on the pulsar and aligned with the rotation axis at whose radius the co-rotating speed equals the speed of light).RL=c/=(c/2)P=4.775109 cm
19Pulsar energeticsWhere P is the pulsar period. This electromagnetic radiation will appear at the very low frequency =1/P<1kHz, so low that it cannot be observed, or even propagate through the ionized ISM. The huge power radiated is responsible for pulsar slowdown as it extracts rotational kinetic energy from the neutron star. The absorbed radiation can also light up a surrounding nebula, the Crab nebula for example.
25Emission mechanismThe neutron star is surrounded by a magnetosphere with free charges that produce intense electric currents. The neutron star is a spinning magnetic dipole, it acts as a unipolar generator. There are two main regions:The closed magnetosphere, defined as the region containing the closed field lines within the light cilinderThe open magnetosphere, the region where the field lines cannot close before RL and extend above this radius.If gravity is negligible, The total force acting on a charged particle is:
26Forces exerted on particles Pulsar MagnetospheresForces exerted on particlesParticle distribution determined by gravity electromagnetisme-Gravity1. Particle distribution around a neutron star is determined not only by gravity and temperature, but also by electromagnetic forces.2. Taking the example of the gravitational force on an electron, for a typical neutron star this is approx 1e-18 Newtons (on a proton, the gravitational force is 2e-15 Newtons).Newton
27Magnetic forceRNSNewtonPNS13This is a factor of larger than the gravitational force and thus dominates the particle distribution.
28Emission mechanismThe particles moves along the field lines and at the same time rotate with them. Charges in the magnetic equatorial region redistribute themselves by moving along closed field lines until they build up an electrostatic field large enough to cancel the magnetic force and give F=0 . The voltage induced is about 106 V in MKS units. However, the co-rotating field lines emerging from the polar caps cross the light cylinder (the cylinder centered on the pulsar and aligned with the rotation axis at whose radius the co-rotating speed equals the speed of light) and these field lines cannot close. Electrons in the polar cap are magnetically accelerated to very high energies along the open but curved field lines, where the acceleration resulting from the curvature causes them to emit curvature radiation that is strongly polarized in the plane of curvature. As the radio beam sweeps across the line-of-sight, the plane of polarization is observed to rotate by up to 180 degrees, a purely geometrical effect. High-energy photons produced by curvature radiation interact with the magnetic field and lower- energy photons to produce electron-positron pairs that radiate more high-energy photons. The final results of this cascade process are bunches of charged particles that emit at radio wavelengths.
29Magnetosphere Charge Distribution Rotation and magnetic polar axes shown co-alignedInduced E field removes charge from the surface so charge andcurrents must exist above the surface – the MagnetosphereLight cylinder is at the radial distance at which rotational velocity ofco-rotating particles equals velocity of lightOpen field lines pass through thelight cylinder and particles streamout along themFeet of the critical field lines are atthe same electric potential as theInterstellar MediumCritical field lines divide regions of+ ve and – ve current flows fromNeutron Star magnetosphere
30A more realistic model... For pulses, magnetic and rotation axes cannot be co- aligned.Plasma distribution and magnetic fieldconfiguration complex for Neutron StarRadioEmissionVelocity- of -Light CylinderFor r < rc, a charge-separated co-rotating magnetosphereParticles move only along field lines;closed field region exists within field-linesthat touch the velocity-of-light cylinderParticles on open field lines can flow out ofthe magnetosphereRadio emission confined to these open-fieldpolar cap regionsThe model presented on the previous slide assumes that the magnetic axis and rotation axis are co-aligned. However, this cannot be the case in this type of model if we are to be able to see pulsed radiation from a spinning neutron star. Such a misalignment implies that the plasma distribution and magnetic field configuration around a neutron star is much more complicate than this simple picture suggests.
31A better picture Radio beam r=c/w Open magnetosphere Light cylinder B Closed magnetosphereNeutron starmass = 1.4 Mradius = 10 kmB = 10 to 10 TeslaThis illustrates the model for a pulsar – where the axis of the neutron star’s magnetic field is offset from the rotation axis. The parameters shown are typical for a pulsar.49
32Curvature radiationThe extremely high brightness temperatures are explained by coherent radiation. The electrons do not radiate as independent charges e; instead bunches of N electrons in volumes whose dimensions are less than a wavelength emit in phase as charges Ne. Since Larmor's formula indicates that the power radiated by a charge q is proportional to q2, the radiation intensity can be N times brighter than incoherent radiation from the same total number N of electrons. Because the coherent volume is smaller at shorter wavelengths, most pulsars have extremely steep radio spectra. Typical (negative) pulsar spectral indices are ~1.7 (S-1.7 ), although some can be much steeper (>3) and a handful are almost flat (~0.5).
33Radiation Mechanisms in Pulsars Emission mechanismsTotal radiation intensitycoherentexceedsincoherentdoes not exceedRecall that TB = K for radio emission. It is still not well understood which physical mechanisms cause the actual pulsed emission in pulsars, although we have a nice model for the geometry and structure of pulsars.Therefore, in this section, we will be considering radiation mechanisms involving particles to investigate what is actually causing the pulses.1. Remember throughout that the outflow of particles results in an interaction with the magnetic field.2. In astrophysical conditions, emission mechanisms can be divided into coherent and incoherent, depending on whether or not the total radiation intensity can exceed the summed intensity of the spontaneous radiation of individual particles.3. Coherent light sources emit waves of the same frequency and the same phase, ie waves combine crest-to-crest with each other.4. Total amplitude of the summed wave is proportional to the number of sources5. Total intensity is proportional to the square of the number of sources.Summed intensity of spontaneous radiation of individual particles
34Incoherent emission - example For radiating particles in thermodynamicequilibrium i.e. thermal emission.Blackbody => max emissivitySo is pulsar emission thermal?Consider radio: n~108 Hz or 100MHz; l~3mWe will consider an example of incoherent emission, that of radiating particles in thermodynamical equilibrium, ie thermal emission. We know that blackbody radiation gives the maximum emissivity. So can pulsar emission be thermal?We will consider the radio emission from pulsars (1e8Hz; 100MHz; 3m) and use the Rayleigh-Jeans approximation on the long-wavelength side of the peak.
35(1) Use Rayleigh-Jeans approximation to find T: Watts m Hz ster -2-1-1-25-2-1Crab flux density at Earth, F~10 watts m HzSource radius, R~10km at distance D~1kpcthen:We are going to calculate the expected blackbody emission from a pulsar and compare this with the observed emission.Remember that since blackbody emission is the maximum emissivity that any (incoherent) source can have, if the observed emission is higher than the blackbody flux, then we know that the emission must be coherent.The temperature on the surface of a neutron star is about a million K and we want to know if the radio pulses are due to a coherent mechanism.Therefore we assume a blackbody spectrum so that the radio emission is on the long-wavelength side of the blackbody peak (which must be in X-rays).Then we are going to calculate the brightness temperature appropriate for the flux actually observed in the radio, and then see if this is a reasonable temperature.For the long-wavelength side of the radio peak, we use the Rayleigh-Jeans approximation for a blackbody (top equation).Then assuming a radius for the neutron star of 10km and a linear distance to the source of about 1kpc, the intensity at the surface of the neutron star (ie if it were a blackbody source) would be that given by equation (1).(1)
36this is much higher than a radio blackbody temperature! So -6-2-1-1In = 10 watts m Hz sterFrom equation (1):this is much higher than a radio blackbody temperature!Now we have the intensity at the surface of the neutron star, re-arranging (!) and inserting numerical values, we find that the temperature, if this were radiating like a blackbody, would be about 3e29K which is far, far too high to be a radio emission temperature.This corresponds to particle energies of kT~3e25 eV!! Since particles of such high energies are not observed, there cannot be incoherent radiation of this type in the radio band.Coherent emission can ‘raise’ the flux up to levels observed without the need for extremely high particle energies.
37Models of Coherent Emission high-B sets up large pd => high-E particlese-e-e+electron-positronpair cascadeB = 1.108TeslaR = 104 m1. The actual mechanism by which coherent radio emission is produced is not well understood.2. The enormous induced electric fields can drag electrons away from the neutron star surface accelerating the particles to a million times their rest mass energy (assuming a magnetic field of 1e8 Tesla, which sets up a potential difference between pole and equator of 1e18V).3. As they stream away they emit curvature radiation and the high energy photons produced interact with low energy photons to produce electron-positron pairs.4. These cascades produce bunches of particles, of dimension < a radio wavelength (~ 1 – 100 m), which can emit coherently in sheets.5. For N electrons in a bunch, radiation intensity is N2 times that of an individual charge.6. This model requires short rotation periods (about a second) and high magnetic fields (100 million Tesla) or the cascades cannot take place.7. Theory shows that B.P2 ≥ 107 Tesla/second is required to produce electron-positron cascades..1.1018Vcascades results in bunchesof particles which can radiatecoherently in sheets
38Emission processes in pulsars Important processes in magnetic fields : cyclotron synchrotronCurvature radiation => Radio emissionOptical & X-ray emission in pulsars=>In a strong magnetic field, the processes which are likely to be most important are cyclotron (for non-relativistic particles) and synchrotron (relativistic particles). These can produce the optical and X-ray emission of pulsars.Radio emission is produced by curvature radiation. This is caused by very high magnetic fields when the electrons follow field lines very closely, with a pitch angle close to zero. The field lines are generally curved so that the transverse acceleration produces radiation.BHigh magnetic fields; electrons follow field lines very closely, pitch angle ~ 0o
39Curvature vs Synchrotron Synchrotron CurvatureBB1. In synchrotron radiation, the pitch angle of the particle is relatively large and most of the synchrotron power comes from the shade region shown, ie an annular region.2. In curvature radiation where the magnetic field is unusually strong, particles follow the field lines very closely so that the pitch angle is very much smaller and most power is emitted over a much smaller radius.
40n exp(-n) n Spectrum of curvature radiation (c.r.) - similar to synchrotron radiation,For electrons:intensity from curvature radiation << cyclotron or synchrotronIf radio emission produced this way, need coherenceFluxn1/3exp(-n)nnmThe spectrum of curvature radiation has the same form as that of synchrotron radiation, varying with the cube root of frequency at low frequencies and falling exponentially above the peak frequency.For likely values of the parameters, it turns out that the intensity produced by an electron by curvature radiation is much smaller than that radiated by the cyclotron or synchrotron processes. If radio emission is produced in this way, then coherence must play a big part and could solve the problem of energetics. Coherence may indicate that bunches of particles are travelling and emitting together.
41Incoherent X-ray emission? In some pulsars, eg. Crab, there are also pulses at IR, optical, X-rays and g-rays.- Are these also coherent?Probably not – brightness temperature of X-rays is about 1011 K, equivalent to electron energies 10MeV, so consistent with incoherent emission.So we have deduced that the emission which produces the radio pulses must be coherent to match observed flux levels. But what about in the X-rays?In fact IR, optical, X-ray and gamma-ray pulse emission can be attributed to an incoherent mechanism in a neutron star. Thus different mechanisms are at work in different wavelengths - coherent in the radio but incoherent in the optical and X-rays.However it is not well known whereabouts in the magnetosphere the processes which produce the higher energy pulses actually take place.radiocoherentIR, optical, X-rays, g-raysincoherent
42Beaming of pulsar radiation Beaming => radiation highly directionalTake into account- radio coherent, X-rays and Optical incoherent- location of radiation source depends on frequency- radiation is directed along the magnetic field lines- pulses only observed when beam points at EarthModel:- radio emission from magnetic poles- X-ray and optical emission from light cylinderFor periodic pulses to appear from a rotating neutron star, it is necessary that the radiation is highly directional.We also have to take into account the coherence of radio emission (at least) and possibly differences in the location of the source of radiation at different frequencies (eg radio and X-ray emission may not be emitted from the same regions).These pieces of observational evidence point towards the following structure for a pulsar:1. Radio pulses due to particles streaming away from the star at the magnetic poles. Supporting evidence from this model comes from radio beam widths and polarization of the emission. Another possibility is magnetic braking where waves are emitted from the polar caps.2. X-ray brightenings occuring at the light cylinder. The evidence for this theory is from the fact that high energy radiation is only observed from young pulsars with short periods. For example there are only 8 pulsars associated with supernova remnants out of over 500 known pulsars.3. The source of radiation is probably localized inside the light cylinder, rather close to the surface of the neutron star and this is for two reasons :Stability of the pulses indicates that there is little opportunity for the emission region to wander about its mean position: andHigh degree of directionality of the radiation suggests that it is produced in a region where the field lines are not greatly dispersed in direction and this is true near the surface.
45Pulsar populationThe P-Pdot Diagram is useful for following the lives of pulsars, playing a role similar to the Hertzsprung-Russell diagram for ordinary stars. It encodes a tremendous amount of information about the pulsar population and its properties, as determined and estimated from two of the primary observables, P and Pdot Using those parameters, one can estimate the pulsar age, magnetic field strength B, and spin-down power dE/dt. (From the Handbook of Pulsar Astronomy, by Lorimer and Kramer)
46Pulsar populationPulsars are born in supernovae and appear in the upper left corner of the PP diagram. If B is conserved, they gradually move to the right and down, along lines of constant B and crossing lines of constant characteristic age.Pulsars with characteristic ages <105yr are often found in SNRs. Older pulsars are not, either because their SNRs have faded to invisibility or because the supernova explosions expelled the pulsars with enough speed that they have since escaped from their parent SNRs. The bulk of the pulsar population is older than 105 yr but much younger than the Galaxy (1010 yr). The observed distribution of pulsars in the PPdot diagram indicates that something changes as pulsars age. One possibility is that the magnetic fields of old pulsars decays on time scales 107 yr, causing pulsars to move straight down in the diagram until they fall below into the graveyard below the death line.
47Pulsar populationThe death line in the PPdot diagram corresponds to neutron stars with sufficiently low B and high P that the curvature radiation near the polar surface is no longer capable of generating particle cascades (Prad scales with B2 and P-4).Almost all short-period pulsars below the spin-up line near log[Pdot/P(sec)]~-16 are in binary systems, as evidenced by periodic (i.e. orbital) variations in their observed pulse periods. These recycled pulsars have been spun up by accreting mass and angular momentum from their companions, to the point that they emit radio pulses despite their relatively low magnetic field strengths B 108 G (the accretion causes a substantial reduction in the magnetic field strength). The magnetic fields of neutron stars funnel ionized accreting material onto the magnetic polar caps, which become so hot that they emit X-rays. As the neutron stars rotate, the polar caps appear and disappear from view, causing periodic fluctuations in X-ray flux; many are detectable as X-ray pulsars.
48Pulsar populationMillisecond pulsars (MSPs) with low-mass (M~0.1-1 MSun) white-dwarf companions typically have orbits with small eccentricities. Pulsars with extremely eccentric orbits usually have neutron-star companions, indicating that these companions also exploded as supernovae and nearly disrupted the binary system. Stellar interactions in globular clusters cause a much higher fraction of recycled pulsars per unit mass than in the Galactic disk. These interactions can result in very strange systems such as pulsar-main-sequence-star binaries and MSPs in highly eccentric orbits. In both cases, the original low-mass companion star that recycled the pulsar was ejected in an interaction and replaced by another star. (The eccentricity e of an elliptical orbit is defined as the ratio of the separation of the foci to the length of the major axis. It ranges between e for a circular orbit and e for a parabolic orbit.) A few millisecond pulsars are isolated. They were probably recycled via the standard scenario in binary systems, but the energetic millisecond pulsars eventually ablated their companions away.
49Neutron StarsGeneral parameters: R ~ 10 km (10 m) r ~ kg m = 10 g cm M ~ M- surface gravity, g = GM/R2 ~ 10 m sWe are going to find magnetic induction, B, for a neutron star.418-315-3inner12-2Neutron stars are supported by degeneracy pressure because their internal densities are so high that classical gas formulae are inappropriate to describe conditions.The ‘pressure’ is a result of Heisenberg’s Uncertainty Principle and Fermi’s Exclusion Principle, which state that particles cannot occupy the same quantum state. Particle positions are very tightly constrained so the resultant mechanical momenta of the particles provides the pressure of the degenerate gas.The surface gravity of a neutron star, g(ns) is given by the equationg(ns) = (GM)/R^2= (6.67e-11 x 2e30) / (1e8) m/s^2= 1e12 m / s^2We are going to find the value for the magnetic induction of a neutron star by thinking of the Sun contracting with its magnetic field to form a neutron star.
50Neutron star structure crustinnerouterHeavy nuclei (Fe) find a minimum energy when arranged in a crystalline latticeNeutron star segmentneutron liquid1.solid core?Superfluid neutrons, superconducting p+ and e-2.17-32x kg m1kmThe diagram shows a segment (ie a slice) through a neutron star.Main Components: Crystalline solid crust (1) and neutron liquid interior (2)Boundary at r = kg/m3 – the density of nuclear matterOuter Crust: Solid; matter similar to that found in white dwarfs, ie heavy nuclei (mostly Fe) forming a Coulomb lattice embedded in a relativistic degenerate gas of electrons. Lattice is min energy configuration for heavy nuclei.Inner Crust (1): Lattice of neutron-rich nuclei (electrons penetrate nuclei to combine with protons and form neutrons) with free degenerate neutrons and a degenerate relativistic electron gas. For r > kg/m3 – the neutron drip point, massive nuclei are unstable and release neutrons. Neutron fluid pressure increases as the density increases.Neutron Fluid Interior (2): For 1 km < r < 9 km, ‘neutron fluid’ – superfluid of neutrons and superconducting protons and electrons. Enables B field maintenance. Density is < r < kg/m3. Near inner crust, some neutron fluid can penetrate into inner part of lattice and rotate at a different rate – glitches?Core: Extends out to ~ 1 km and has a density of kg/m3. Its substance is not well known - it could be a neutron solid, quark matter or neutrons squeezed to form a pion concentrate.On the very surface of the neutron star, densities fall below 109 kg/m3 and matter consists of atomic polymers of 56Fe in the form of a close packed solid. The atoms become cylindrical, due to the effects of the strong magnetic fields.14-3crystallization of neutron matter4.3x kg m9km9-310 kg m18-310kmkg m
51Regions of NS Interior Main Components: (1) Crystalline solid crust (2) Neutron liquid interior- Boundary at r = kg/m3 – density of nuclear matterOuter Crust:Solid; matter similar to that found in white dwarfsHeavy nuclei (mostly Fe) forming a Coulomb lattice embedded in a relativisticdegenerate gas of electrons.- Lattice is minimum energy configuration for heavy nuclei.Inner Crust (1):Lattice of neutron-rich nuclei (electrons penetrate nuclei to combine with protons andform neutrons) with free degenerate neutrons and degenerate relativistic electron gas.For r > kg/m3 – the neutron drip point, massive nuclei are unstable andrelease neutrons.Neutron fluid pressure increases with r1.Zero temperature energy – the Fermi energy, supports the star and prevents further collapse. From Pauli principle, each allowed energy state can be occupied by no more than two electrons of opposite spin.2. For electrons, even at 0o K, occupy a range of states of different Fermi energy states. In a collapsed star, they occupy a small volume and have well known positions. Hence by the uncertainty principle, they have a large momentum and generate a high temperature – independent pressure. The corresponding “classical” thermal KE would be ~ K. These electrons are called degenerate and so electron degeneracy pressure supports the star which in this case is a White Dwarf.3. For collapse of high mass stars, the inert Fe core gives way to a neutron star where neutron degeneracy pressure supports the star against gravity and prevents further collapse. Since the available size is much smaller than for a WD, neutrons are forced to occupy states of even higher Fermi energy (E ~ 1 MeV) and so the resulting degeneracy pressure can support the neutron star.
52Regions of NS Interior (Cont.) Neutron Fluid Interior (2):For 1 km < r < 9 km, ‘neutron fluid’ – superfluid of neutrons and superconductingprotons and electrons.- Enables B field maintenance.- Density is < r < kg/m3.Near inner crust, some neutron fluid can penetrate into inner part of lattice androtate at a different rate – glitches?Core:- Extends out to ~ 1 km and has a density of kg/m3.- Its substance is not well known.- Could be a neutron solid, quark matter or neutrons squeezed to form a pionconcentrate.
53White Dwarfs and Neutron Stars In both cases, zero temperature energy – the Fermi energy, supports the star and prevents further collapseFrom exclusion principle, each allowed energy state can be occupied by no more than two particles of opposite spinElectrons in a White Dwarf occupy a small volume and have very well defined positions – hence from uncertainty principle, they have large momentum/energy and generate a high pressure or electron degeneracy pressureCorresponding “classical” thermal KE would have T ~ K and the related electron degeneracy pressure supports the starFor a high mass stellar collapse, inert Fe core gives way to a Neutron Star and neutron degeneracy pressure supports the starNS has ~ 103 times smaller radius than WD so neutrons must occupy states of even higher Fermi energy (E ~ 1 MeV) and resulting degeneracy pressure supports NS
54Low Mass X-ray Binary provides Observational Evidence of NS Structure Neutron star primaryEvolved red dwarf secondaryRoche pointAccretion disk
55Gravitationally Redshifted Neutron Star Absorption Lines XMM-Newton found red-shifted X-ray absorption featuresCottam et al. (2002, Nature, 420, 51):- observed 28 X-ray bursts from EXOISMz = 0.35Fe XXVI & Fe XXV(n = 2 – 3) and O VIII(n = 1 – 2) transitionswith z = 0.35Red plot shows:- source continuum- absorption featuresfrom circumstellar gas1. If a photon starts out with wavelength lo at a radial distance r from a spherical gravitating mass M, then it will be red-shifted to a wavelength l wherez = (l-lo)/lo and l/lo = (1 – 2GM/c2r)-1/2. This is a General Relativistic formula.2. To avoid the lines being broadened by differential gravitational redshifting if they come from a region that is extended in radius, we need the source to be localised in a shell whose thickness is << r.3. This is certainly true for a neutron star where the surface layer where these lines are produced is extremely thin. Scale– height of a neutron star atmosphere is approx 10 cm!Note: z = (l-lo)/lo and l/lo = (1 – 2GM/c2r)-1/2
56X-ray absorption lines Low T burstsFe XXV & O VIII(T < 1.2 keV)High T bustsFe XXVI(T > 1.2 keV)quiescencelow-ionizationcircumstellarabsorberredshifted, highly ionized gasz = 0.35 due to NSgravity suggests:M = 1.4 – 1.8 MR = 9 – 12 kmFor a neutron star with these parameters, the structure is consistent with being made up mostly of “normal” neutron star matter.More exotic matter, such as strange quark matter or kaon condensates are unlikely, because, for this radius, the mass would have to be much lower (less than 1.1 solar masses) which is uncomfortably close to the lower limit for the formation of a neutron star.3. The implied birth mass for this star is near the average for non-accreting stars, and, assuming accretion for about a billion years (remember that this is the primary component of an accreting binary system), its mass agrees with those estimated for other accreting neutron stars.
58Observational Evidence for Pulsar Emission Sites Radio pulses come from particles streaming away from the NS in the magnetic polar regions:Radio beam widthsPolarized radio emissionIntensity variabilityOptical and X-ray brightening occurs at the light cylinderRadiation at higher energies only observed from young pulsars with short periodsOnly eight pulsar-SNR associations from more than 500 known pulsarsOptical and X-radiation source located inside the light cylinderPulse stability shows radiation comes from a region where emission position does not varyHigh directionality suggests that emission is from a region where field lines are not dispersed in direction i.e. last closed field lines near light cylinderRegions near cylinder have low particle density so particles are accelerated to high energies between collisions
59In summary...Radio emission coherent curvature radiation at polar capsX-ray emission incoherent synchrotron radiation at light cylinderTo summarize:The radio emission from pulsars is probably by coherent curvature radiation from the polar capsThe X-ray emission is probably due to incoherent synchrotron radiation at the light cylinder.
60Pulsar PopulationTo sustain this population then, 1 pulsar must form every 50 years.cf SN rate of 1 every yearsonly 8 pulsars associated with visible SNRs (pulsar lifetime 1-10million years, SNRs thousand... so consistent)but not all SN may produce pulsars!!!1. To sustain a population of 200,000 pulsars currently observed, 1 pulsar must form every 50 years (characteristic lifetime / no. pulsars).This is consistent with the estimated rate of 1 SN every 100 years in the Galaxy. Moreover only 8 pulsars have been associated with visible SNRs (eg. Crab, Vela and PSR ) out of more than 500 pulsars. This is entirely consistent with the difference in lifetimes of typical pulsars and SNRs.Note however that not all SN may produce pulsars… we need another origin for the production of pulsars, eg accretion induced collapse.
61Light Cylinder Radiation sources close to surface of light cylinder P Outer gap region- Incoherent emissionX-ray andOptical beamRadioBeamPolar cap region- Coherent emissionLight CylinderOuter gap region- Incoherent emissionThe source of the pulsar radiation at high energies may be close to the surface of the light cylinder. We will consider a simplified case, illustrated above, which shows the equatorial field pattern of a rotating dipole where the rotation axis is perpendicular to the dipole moment.P is on the tangent to the observer and P` is the point where an open field line crosses the light cylinder. Both points are possible locations of emission given the likely presence of high energy electrons around a pulsar.Gaps of low particle density exist between the last closed field line and the light cylinder. Particles can be accelerated to very high energies.The restricted range in longitudes where this occurs (about 10degrees) when the magnetic axis is offset from the rotation axis causes radiation pulses to be observed and matches the observed pulse widths of pulsars.Simplified case – rotation and magnetic axesorthogonal