Pulsars High Energy Astrophysics

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 interpulse ~P/10 pulse

Pulse profiles Average pulse profile very uniform Individual pulses/sub-pulses very different in shape, intensity and phase t average envelope Sub-pulses show high degree of polarization which changes throughout pulse envelope

Pulsar period stability Period extremely stable: 1 part in 10 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 ??? 12

Rotation of a neutron star Gravitational force > centrifugal force where and P is the period For structural stability:

Reducing: G = 6.67x10 m kg s ; P = 33x10 s => butso Crab -3

Substituting numbers for Crab then: so  > 1.3 x 10 kg m This is too high for a white dwarf (which has a density of ~ 10 kg m ), so it must be a neutron star. kg m

Pulsar energetics Pulsars slow down => lose rotational energy - can this account for observed emission? Rotational energy: so

Energetics - Crab pulsar Crab pulsar - M = 1 M  - P = seconds - R = 10 m = 0.8 x 10 kg m 4 kg m 2 382

and from observations: thus energy lost by the pulsar

This rate of energy loss is comparable to that inferred from the observed emission, for example in the keV range, the observed luminosity in the Crab Nebula is ~ 1.5 x 10 watts. Thus the pulsar can power the nebula. 30

Neutron Stars General parameters: - R ~ 10 km (10 m) -  ~ 10 kg m = 10 g cm - M ~ M  - surface gravity, g = GM/R 2 ~ 10 m s We are going to find magnetic induction, B, for a neutron star inner 12

Magnetic induction Magnetic flux, Radius collapses from 7 x 10 m to 10 m constant surface 8 4 RR Surface change gives R NS

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: B ~ 5 x 10 Tesla = 5 x 10 Gauss ns 711

Neutron star structure Neutron star segment solid core? crystallization of neutron matter 10 kg m 18-3 neutron liquid Superfluid neutrons, superconducting p+ and e- crust 1km 9km 10km Heavy nuclei (Fe) find a minimum energy when arranged in a crystalline lattice 2x10 kg m 4.3x10 kg m 10 kg m outerinner

Regions of NS Interior Main Components: (1) Crystalline solid crust (2) Neutron liquid interior - Boundary at  = kg/m 3 – 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  > kg/m 3 – 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 <  < kg/m 3. - 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/m 3. - 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 Evolved red dwarf secondary Accretion disk Roche point

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 ISM z = 0.35 Fe XXVI & Fe XXV (n = 2 – 3) and O VIII (n = 1 – 2) transitions with z = 0.35 Red plot shows: - source continuum - absorption features from circumstellar gas

X-ray absorption lines quiescence low-ionization circumstellar absorber redshifted, highly ionized gas z = 0.35 due to NS gravity suggests: M = 1.4 – 1.8 M  R = 9 – 12 km High T busts Fe XXVI (T > 1.2 keV) Low T bursts Fe XXV & O VIII (T < 1.2 keV)

EXO circumstellar material origin of X-ray bursts

Forces exerted on particles Particle distribution determined by - gravity - electromagnetism e-e- Newton Gravity Pulsar Magnetospheres

Magnetic force Newton This is a factor of 10 larger than the gravitational force and thus dominates the particle distribution. 13 R NS P NS

Neutron star magnetosphere Neutron star rotating in vacuum:  B Electric field induced immediately outside n.s. surface. Potential difference on scale of neutron star radius is:

Electron/proton expulsion  B protons Neutron star particle emission electrons 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 (  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- light cylinder, r Co-rotating plasma is on magnetic field lines that are closed inside light cylinder c Radius of light cylinder must satisfy:

A more realistic model... Radio Emission Radio Emission Velocity- of - Light Cylinder For r < r c, a charge-separated co- rotating 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 For pulses, magnetic and rotation axes cannot be co- aligned. Plasma distribution and magnetic field configuration complex for Neutron Star

A better picture Light cylinder Open magnetosphere Radio beam r=c/  B Closed magnetosphere Neutron star mass = 1.4 M  radius = 10 km B = 10 to 10 Tesla 49

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.  This is the case of a ‘dipole aerial’ – magnetic analogue of the varying electric dipole

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 Summed intensity of spontaneous radiation of individual particles exceeds does not exceed 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: ~10 8 Hz or 100MHz; ~3m

Crab flux density at Earth, F~10 watts m Hz Source radius, R~10km at distance D~1kpc then: Watts m Hz ster (1) Use Rayleigh-Jeans approximation to find T:

I = 10 watts m Hz ster From equation (1): 6 -2 this is much higher than a radio blackbody temperature! So -

Incoherent X-ray emission? In some pulsars, eg. Crab, there are also pulses at IR, optical, X-rays and  -rays. - Are these also coherent? Probably not – brightness temperature of X- rays is about K, equivalent to electron energies 10MeV, so consistent with incoherent emission. radio coherent IR, optical, X-rays,  -rays incoherent

Models of Coherent Emission high-B sets up large pd => high-E particles V B = Tesla R = 10 4 m e-e- e- e+ electron-positron pair cascade cascades results in bunches of particles which can radiate coherently in sheets

Emission processes in pulsars Important processes in magnetic fields : - cyclotron - synchrotron Curvature radiation => Radio emission Optical & X-ray emission in pulsars B High magnetic fields; electrons follow field lines very closely, pitch angle ~ 0 o =>

Curvature Radiation This is similar to synchrotron radiation. If v ~ c and  = radius of curvature, the radiation very similar to e - in circular orbit with: where is the gyrofrequency L e-e- ‘effective frequency’ of emission is given by:

Curvature vs Synchrotron Synchrotron Curvature B B

Spectrum of curvature radiation (c.r.) - similar to synchrotron radiation, For electrons: intensity from curvature radiation << cyclotron or synchrotron If radio emission produced this way, need coherence Flux 1/3 exp(- ) m

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

The better picture - again Light cylinder Open magnetosphere Radio beam r=c/  B Closed magnetosphere Neutron star mass = 1.4 solar masses radius = 10 km B = 10 to 10 Tesla 49

Light Cylinder Radiation sources close to surface of light cylinder Simplified case – rotation and magnetic axes orthogonal Outer gap region - Incoherent emission P P` Outer gap region - Incoherent emission X-ray and Optical beam Radio Beam Polar cap region - Coherent emission

Relativistic beaming may be caused by ~ c motion of source near light cylinder - radiation concentrated into beam width : Also effect due to time compression (2  ), so beam sweeps across observer in time: (the Lorentz factor) 2

In summary... Radio emission - coherent - curvature radiation at polar caps X-ray emission - incoherent - synchrotron radiation at light cylinder

Age of Pulsars Ratio (time) is known as ‘age’ of pulsar In reality, may be longer than the real age. Pulsar characteristic lifetime ~ 10 years Total no observable pulsars ~ 5 x

Pulsar Population To sustain this population then, 1 pulsar must form every 50 years. cf SN rate of 1 every years only 8 pulsars associated with visible SNRs (pulsar lifetime 1-10million years, SNRs thousand... so consistent) but not all SN may produce pulsars!!!

PULSARS END OF TOPIC