Transcript Pulsars
Pulsars High Energy Astrophysics [email protected] http://www.mssl.ucl.ac.uk/ Introduction • Pulsars - isolated neutron stars Radiate energy via slowing down of rapid spinning motion (P usually ≤ 1sec, dP/dt > 0) • Pulsating X-ray sources / X-ray pulsators - compact objects (generally neutron stars) in binary systems Accrete matter from normal star companion (P ~ 10s, dP/dt < 0) Pulsars • Discovered through their pulsed radio emission • Averaging over many pulses we see: Period pulse ~P/10 interpulse 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 Pulsar period stability • Period extremely stable: 1 part in 10 12 indicates some mechanical clock mechanism - although this mechanism must be able to accommodate pulse variablity. • Pulsations of white dwarf ??? (but Crab pulsar period (P~1/30 sec) too short). • Rotation of neutron star ??? Rotation of a neutron star For structural stability: Gravitational force > centrifugal force 2 GMm m v 2 r r 2r where v and P is the period P Reducing: M GM 4 r => 3 2 2 2 4r P G 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 Substituting numbers for Crab 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 a density of ~ 10 9 kg m-3 ), so it must be a neutron star. 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 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 dE 4 0.8 10 1 dP 10 and watts 2 dt 0.033 P dt 38 1 dP 3 10 watts P dt 42 from observations: 1 dP P dt ~ 10 11 1 s thus energy lost dE 31 310 watts by the pulsar dt This rate of energy loss is comparable to that inferred from the observed emission, for example in the 2 - 20 keV range, the observed luminosity in the Crab Nebula is 30 ~ 1.5 x 10 watts. Thus the pulsar can power the nebula. Neutron Stars • General parameters: - R ~ 10 km (104 m) - inner ~ 1018 kg m-3 = 1015g cm-3 - M ~ 0.2 - 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. Magnetic induction Magnetic flux, BdS constant surface 8 RNS R 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 • The general field of Sun is uncertain and varies with the solar cycle but should be ≈ 0.01 Tesla. • Thus the field for the neutron star: 7 11 Bns ~ 5 x 10 Tesla = 5 x 10 Gauss 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 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 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. Low Mass X-ray Binary provides Observational Evidence of NS Structure Neutron star primary Accretion disk Roche point Evolved red dwarf secondary 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 z = 0.35 z = 0.35 • Red plot shows: - source continuum - absorption features from circumstellar gas ISM ISM 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 EXO0748-676 origin of X-ray bursts circumstellar material Pulsar Magnetospheres Forces exerted on particles Particle distribution determined by - gravity e- electromagnetism FB Fg ns Gravity 31 18 Fgn s me gns 9 10 10 10 12 Newton Magnetic force 19 FB evB 1.6 10 RNS 2 10 m 8 10 T 3 3310 s 4 5 3 10 Newton PNS This is a factor of 1013 larger than the gravitational force and thus dominates the particle distribution. 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 Potential difference on scale of neutron star radius is: ER 1018V 1 Electron/proton expulsion Neutron star particle emission B electrons protons Cosmic rays? 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 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 Pulsar models 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 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 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 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 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. Radiation Mechanisms in Pulsars Emission mechanisms Total radiation intensity exceeds does not exceed Summed intensity of spontaneous radiation of individual particles coherent incoherent 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 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) 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 this is much higher than a radio blackbody temperature! K 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 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 Emission processes in pulsars • Important processes in magnetic fields : - cyclotron Optical & X-ray => - synchrotron emission in pulsars • Curvature radiation => Radio emission B High magnetic fields; electrons follow field lines very closely, pitch angle ~ 0o 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 Curvature vs Synchrotron Synchrotron Curvature B B • 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 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 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 Light Cylinder • Radiation sources close to surface of 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 • 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 2 P 1 2 3 2g g 4g In summary... • Radio emission - coherent - curvature radiation at polar caps • X-ray emission - incoherent - synchrotron radiation at light cylinder Age of Pulsars . Ratio P / 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 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!!! PULSARS END OF TOPIC