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Pulsars High Energy Astrophysics [email protected] http://www.mssl.ucl.ac.uk/ 4. Pulsars: Pulsed emission; Rotation and energetics; Magnetic field; Neutron star structure; Magnetosphere and pulsar models; Radiation mechanisms; Age and population [3] 2 Introduction • Pulsars - isolated neutron stars Radiate energy via slowing down of rapid spinning motion (P usually ≤ 1sec, dP/dt > 0) • Neutron Stars – supported by degeneracy pressure; Fermi exclusion principle restricts position hence Heisenberg uncertainty principle allows large momentum/high pressure • Pulsating X-ray sources / X-ray pulsators - compact objects (generally neutron stars) in binary systems Accrete matter from normal star companion 3 (P ~ 10s, dP/dt < 0) Pulsars • Discovered through their pulsed radio emission • Averaging over many pulses we see: Period pulse (~P/10) interpulse 4 Pulse profiles • Average pulse profile very uniform • Individual pulses/sub-pulses very different in shape, intensity and phase t Sub-pulses show high degree of polarization which changes throughout pulse envelope average envelope 5 Pulsar period stability 12 • Period extremely stable: 1 part in 10 indicates some mechanical clock mechanism - this mechanism must be able to accommodate pulse-to-pulse variablity. • Pulsations of white dwarf ??? (but Crab pulsar period (P~1/30 sec) too short) • Rotation of neutron star ??? 6 Rotation of a neutron star For structural stability: Gravitational force > centrifugal force 2 where GMm mv 2 r r 2r and P is the period v P otherwise star would fly apart 7 Reducing: M GM 4 r => 3 2 2 2 4r PG r P 2 M but 4 3 r 3 G = 6.67x10 -11 so 3 3 2 PG -1 -2 m kg s -3 ; PCrab = 33x10 s 8 Substituting numbers for Crab pulsar then: 3 11 6 6.67 10 1100 10 kg m -3 so > 1.3 x 10 14 kg m -3 This is too high for a white dwarf (which has 9 a density of ~ 10 kg m-3 ), so it must be a neutron star. 9 Pulsar energetics • Pulsars slow down => lose rotational energy - can this account for observed emission? • Rotational energy: 1 2 I 4 2 I E I 2 2 2 2 P P 2 2 2 2 dE d 2 I 4 I dP so 2 3 dt dt P P dt 10 Energetics - Crab pulsar Crab pulsar - M ~ 1 M - P = 0.033 seconds 4 - R = 10 m 2 2 2 30 8 2 I MR 2 10 10 kg m 5 5 38 = 0.8 x 10 kg m 2 11 dE 4 0.8 1038 1 dP 10 watts and 2 dt 0.033 P dt 1 dP 3 10 watts P dt 42 from observations: 1 dP P dt ~ 10 11 1 s thus energy lost dE 31 3 10 watts by the pulsar dt 12 Rate of energy loss is greater than that inferred from the observed 2 - 20 keV emission, for which the observed luminosity in the Crab Nebula is 30 ~ 1.5 x 10 watts. Thus the pulsar can power the nebula. Characteristic age for magnetic dipole energy loss t = P/2 P• = 3.3.10-3/2 x 4.10-14 s ~ 1300 years Crab Nebula exploded in 1054 AD 13 Neutron Stars • General parameters: - R ~ 10 km (104 m) - inner ~ 1018 kg m-3 = 1015g cm-3 - M ~ 1.4 - 3.2 M 12 -2 2 - surface gravity, g = GM/R ~ 10 m s • We are going to find magnetic induction, B, for a neutron star. 14 Magnetic induction Magnetic flux, BdS constant surface RNS R 8 4 Radius collapses from 7 x 10 m to 10 m Surface change gives Bns 7 10 4 BSun 10 8 2 9 5 10 15 • The Sun has magnetic fields of several different spatial scales and strengths but its general polar field varies with solar cycle and is ≈ 0.01 Tesla. • Thus the field for the neutron star: 7 11 B ns ~ 5 x 10 Tesla = 5 x 10 Gauss • If the main energy loss from rotation is through magnetic dipole radiation then: B ~ 3.3 x 1015 • (P P) ½ Tesla or ~ 106 to 109 Tesla for most pulsars 16 Neutron star structure crust inner outer Neutron star segment neutron 1. liquid solid Superfluid core? neutrons, 2. superconducting p+ and e1km crystallization of neutron 9km matter 10km 1018 kg m -3 Heavy nuclei (Fe) find a minimum energy when arranged in a crystalline lattice 2x1017 kg m -3 4.3x1014 kg m -3 109 kg m -3 17 Regions of NS Interior Main Components: (1) Crystalline solid crust (2) Neutron liquid interior - Boundary at = 2.1017 kg/m3 – density of nuclear matter Outer Crust: - Solid; matter similar to that found in white dwarfs - Heavy nuclei (mostly Fe) forming a Coulomb lattice embedded in a relativistic degenerate 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 and form neutrons) with free degenerate neutrons and degenerate relativistic electron gas. - For > 4.3.1014 kg/m3 – the neutron drip point, massive nuclei are unstable and release neutrons. - Neutron fluid pressure increases with 18 Regions of NS Interior (Cont.) 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 2.1017 < <1.1018 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 1.1018 kg/m3. - Its substance is not well known. - Could be a neutron solid, quark matter or neutrons squeezed to form a pion concentrate. 19 White Dwarfs and Neutron Stars • In both cases, zero temperature energy – the Fermi energy, supports the star and prevents further collapse • From exclusion principle, each allowed energy state can be occupied by no more than two particles of opposite spin • Electrons 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 pressure • Corresponding “classical” thermal KE would have T ~ 3.104 K and the related electron degeneracy pressure supports the star • For a high mass stellar collapse, inert Fe core gives way to a Neutron Star and neutron degeneracy pressure supports the star • NS has ~ 103 times smaller radius than WD so neutrons must occupy states of even higher Fermi energy (E ~ 1 MeV) and resulting 20 degeneracy pressure supports NS Low Mass X-ray Binary provides Observational Evidence of NS Structure Neutron star primary Accretion disk Roche point Evolved red dwarf secondary 21 Gravitationally Redshifted Neutron Star Absorption Lines • XMM-Newton found red-shifted X-ray absorption features • Cottam et al. (2002, Nature, 420, 51): - observed 28 X-ray bursts from EXO 0748-676 • Fe XXVI & Fe XXV z = 0.35 (n = 2 – 3) and O VIII (n = 1 – 2) transitions with z = 0.35 ISM z = 0.35 z = 0.35 ISM • Red plot shows: - source continuum - absorption features from circumstellar gas • Note: z = (llo/lo and l/lo = (1 – 2GM/c2r)-1/2 22 X-ray absorption lines quiescence low-ionization circumstellar absorber Low T bursts High T busts Fe XXV & O VIII Fe XXVI (T < 1.2 keV) (T > 1.2 keV) redshifted, highly ionized gas z = 0.35 due to NS gravity suggests: M = 1.4 – 1.8 M R = 9 – 12 km 23 EXO0748-676 origin of X-ray bursts circumstellar material 24 Pulsar Magnetospheres Forces exerted on particles Particle distribution determined by - gravity e- electromagnetism FB Fg n s Gravity Fgns me gns 9 10 31 10 10 12 18 Newton 25 Magnetic force FB evB 1.6 10 5 19 3 10 Newton RNS 2 10 m 8 10 T 3 33 10 s 4 PNS This is a factor of 1013 larger than the gravitational force and thus dominates the particle distribution. 26 Neutron star magnetosphere Neutron star rotating in vacuum: B Electric field induced immediately outside n.s. surface. E Bv 10 2 10 Vm 14 1 2 10 Vm 8 6 1 Potential difference on scale of neutron star radius is: ER 1018V 27 Electron/proton expulsion Neutron star particle emission B electrons protons Cosmic rays? 28 In reality... • Charged particles will distribute themselves around the star to neutralize the electric field. • => extensive magnetosphere forms • Induced electric field cancelled by static field arising from distributed charges or - E + 1/c (W x r) x B = 0 where E and B are electric and magnetic fields and W is the vector angular velocity of the neutron star 29 Magnetosphere Charge Distribution • Rotation and magnetic polar axes shown co-aligned • Induced E field removes charge from the surface so charge and currents must exist above the surface – the Magnetosphere • Light cylinder is at the radial distance at which rotational velocity of co-rotating particles equals velocity of light • Open field lines pass through the light cylinder and particles stream out along them • Feet of the critical field lines are at the same electric potential as the Interstellar Medium • Critical field lines divide regions of + ve and – ve current flows from Neutron Star magnetosphere 30 Pulsar models Here magnetic and rotation axes co-aligned: e- Co-rotating plasma is on magnetic field lines that are closed inside light cylinder Radius of light cylinder must satisfy: light cylinder, rc 2rc c P 31 A more realistic model... • For pulses, magnetic and rotation axes cannot be co- aligned. • Plasma distribution and magnetic field configuration complex for Neutron Star • For r < rc, a charge-separated corotating magnetosphere • Particles move only along field lines; closed field region exists within field-lines that touch the velocity-of-light cylinder • Particles on open field lines can flow out of the magnetosphere • Radio emission confined to these open-field polar cap regions Radio Emission Radio Emission Velocity- of Light Cylinder 32 Radio beam Open magnetosphere B A better picture r=c/ Light cylinder Closed magnetosphere Neutron star mass = 1.4 M radius = 10 km B = 10 4 to 109 Tesla 33 The dipole aerial Even if a plasma is absent, a spinning neutron star will radiate – and loose energy, if the magnetic and rotation axes do not coincide. a This is the case of a ‘dipole aerial’ – magnetic analogue of the varying electric dipole dE 4 6 2 2 R B sin a dt 34 Quick revision of pulsar structure 1. Pulsar can be thought of as a non-aligned rotating magnet. 2. Electromagnetic forces dominate over gravitational in magnetosphere. 3. Field lines which extend beyond the light cylinder are open. 4. Particles escape along open field lines, accelerated by strong electric fields. 35 Radiation Mechanisms in Pulsars Emission mechanisms Total radiation intensity exceeds does not exceed Summed intensity of spontaneous radiation of individual particles coherent incoherent 36 Incoherent emission - example For radiating particles in thermodynamic equilibrium i.e. thermal emission. Blackbody => max emissivity So is pulsar emission thermal? Consider radio: n~108 Hz or 100MHz; l~3m 37 Use Rayleigh-Jeans approximation to find T: 2kTn I n 2 c 2 Watts m -2 Hz -1ster -1 -25 -2 -1 Crab flux density at Earth, F~10 watts m Hz Source radius, R~10km at distance D~1kpc then: D 10 3 10 F I F 2 2 4 W 10 R 2 25 19 2 (1) 38 So 6 In = 10 watts m -2 Hz -1 ster -1 From equation (1): I n c 10 3 10 T K 2 23 8 2kn 2 1.4 10 10 2 310 K 29 6 8 2 2 K this is much higher than a radio blackbody temperature! 39 Incoherent 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 Xrays is about 1011 K, equivalent to electron energies 10MeV, so consistent with incoherent emission. radio coherent IR, optical, X-rays, g-rays incoherent 40 Models of Coherent Emission high-B sets up large pd => high-E particles e- ee+ electron-positron pair cascade B = 1.108Tesla R = 104 m 1.1018V cascades results in bunches of particles which can radiate coherently in sheets 41 Emission processes in pulsars • Important processes in magnetic fields : - cyclotron Optical & X-ray => - synchrotron emission in pulsars • Curvature radiation => B Radio emission High magnetic fields; electrons follow field lines very closely, pitch angle ~ 0o 42 Curvature Radiation • This is similar to synchrotron radiation. If ve- ~ c and = radius of curvature, the radiation very similar to e- in circular orbit with: c where nL is the L gyrofrequency 2g ‘effective frequency’ of emission is given by: m Lg 3 43 Curvature vs Synchrotron Synchrotron Curvature B B 44 • Spectrum of curvature radiation (c.r.) - similar to synchrotron radiation, Flux n 1/3 exp(-n) n nm • For electrons: intensity from curvature radiation << cyclotron or synchrotron • If radio emission produced this way, need coherence 45 Beaming of pulsar radiation • Beaming => radiation highly directional • Take 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 Earth • Model: - radio emission from magnetic poles - X-ray and optical emission from light cylinder 46 Observational Evidence for Pulsar Emission Sites • Radio pulses come from particles streaming away from the NS in the magnetic polar regions: – Radio beam widths – Polarized radio emission – Intensity variability • Optical and X-ray brightening occurs at the light cylinder – Radiation at higher energies only observed from young pulsars with short periods – Only eight pulsar-SNR associations from more than 500 known pulsars • Optical and X-radiation source located inside the light cylinder – Pulse stability shows radiation comes from a region where emission position does not vary – High directionality suggests that emission is from a region where field lines are not dispersed in direction i.e. last closed field lines near light cylinder – Regions near cylinder have low particle density so particles are accelerated to high energies between collisions 47 Radio beam Open magnetosphere B The better picture - again r=c/ Light cylinder Closed magnetosphere Neutron star mass = 1.4 solar masses radius = 10 km B = 10 4 to 109 Tesla 48 Light Cylinder • Radiation sources close to surface of light cylinder Light Cylinder P X-ray and Optical beam Outer gap region - Incoherent emission P` Outer gap region - Incoherent emission Radio Beam Polar cap region - Coherent emission • Simplified case – rotation and magnetic axes orthogonal 49 • Relativistic beaming may be caused by motion of source with v ~ c near the light cylinder - radiation concentrated into beam width g , 1 g 1 1 2 (the Lorentz factor) • Also effect due to time compression (2g2, so beam sweeps across observer in time: P t 2 P 1 2 3 2g g 4g g ~ 2 – 3 needed to explain individual pulse widths 50 In summary... • Radio emission - coherent - curvature radiation at polar caps • X-ray emission - incoherent - synchrotron radiation at light cylinder 51 Age of Pulsars .• Ratio P / 2 P (time) is known as ‘age’ of pulsar In reality, may be longer than the real age. Pulsar characteristic lifetime ~ 107 years Total no observable pulsars ~ 5 x 10 4 52 Pulsar Population • To sustain this population then, 1 pulsar must form every 50 years. • cf SN rate of 1 every 50-100 years • only 8 pulsars associated with visible SNRs (pulsar lifetime 1-10million years, SNRs 10-100 thousand... so consistent) • but not all SN may produce pulsars!!! 53 PULSARS END OF TOPIC 54 crust inner Neutron star segment outer Heavy nuclei (Fe) find a minimum energy when arranged in a crystalline lattice neutron liquid solid core? Superfluid neutrons, superconducting p+ and e17 -3 2x10 kg m 1km 4.3x10 14 kg m-3 crystallization of neutron matter 1018 kg m-3 9km 10 9 kg m -3 10km 55 • Relativistic beaming may be caused by ~ c motion of source near light cylinder radiation concentrated into beam width : g , 1 g 1 1 2 (the Lorentz factor) • Also effect due to time compression (2g 2 ), so beam sweeps across observer in time: P t 2 P 1 2 3 2g g 4g 56 Pulsar Model • Radio emission from magnetic poles – Radio pulses due to particles streaming away from the neutron star in polar regions along open field lines – Observed radio beam widths and polarized emission support this model • X-ray and optical emission from light cylinder – Radiation only seen from young short period pulsars 57 Pulsars Period pulse (~P/10) interpulse 58 Pulse profiles t average envelope 59