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Pulsars High Energy Astrophysics

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Presentation on theme: "Pulsars High Energy Astrophysics"— Presentation transcript:

1 Pulsars High Energy Astrophysics

2 2 4.Pulsars: Pulsed emission; Rotation and energetics; Magnetic field; Neutron star structure; Magnetosphere and pulsar models; Radiation mechanisms; Age and population [3]

3 3 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 (P ~ 10s, dP/dt < 0)

4 4 Pulsars Discovered through their pulsed radio emission Averaging over many pulses we see: Period interpulse (~P/10)pulse

5 5 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

6 6 Pulsar period stability 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 ??? 12

7 7 Rotation of a neutron star Gravitational force > centrifugal force where and P is the period otherwise star would fly apart For structural stability:

8 8 Reducing: G = 6.67x10 m kg s ; P = 33x10 s => butso Crab -3

9 9 Substituting numbers for Crab pulsar 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

10 10 Pulsar energetics Pulsars slow down => lose rotational energy - can this account for observed emission? Rotational energy: so

11 11 Energetics - Crab pulsar Crab pulsar - M ~ 1 M - P = seconds - R = 10 m = 0.8 x 10 kg m 4 kg m 2 382

12 12 and from observations: thus energy lost by the pulsar

13 13 Rate of energy loss is greater than that inferred from the observed keV emission, for which the observed luminosity in the Crab Nebula is ~ 1.5 x 10 watts. Thus the pulsar can power the nebula. Characteristic age for magnetic dipole energy loss = P/2 P = /2 x s ~ 1300 years Crab Nebula exploded in 1054 AD 30

14 14 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

15 15 Magnetic induction Magnetic flux, Radius collapses from 7 x 10 m to 10 m constant surface 8 4 R Surface change gives R NS

16 16 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: B ~ 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 (P P) ½ Tesla or ~ 10 6 to 10 9 Tesla for most pulsars ns 711

17 17 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

18 18 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

19 19 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.

20 20 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 ~ 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 ~ 10 3 times smaller radius than WD so neutrons must occupy states of even higher Fermi energy (E ~ 1 MeV) and resulting degeneracy pressure supports NS

21 21 Low Mass X-ray Binary provides Observational Evidence of NS Structure Neutron star primary Evolved red dwarf secondary Accretion disk Roche point

22 22 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 Note: z = ( and = (1 – 2GM/c 2 r) -1/2

23 23 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)

24 24 EXO circumstellar material origin of X-ray bursts

25 25 Forces exerted on particles Particle distribution determined by - gravity - electromagnetism e-e- Newton Gravity Pulsar Magnetospheres

26 26 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

27 27 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:

28 28 Electron/proton expulsion B protons Neutron star particle emission electrons Cosmic rays?

29 29 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 where E and B are electric and magnetic fields and is the vector angular velocity of the neutron star

30 30 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

31 31 Pulsar models Here 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:

32 32 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

33 33 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

34 34 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

35 35 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.

36 36 Radiation Mechanisms in Pulsars Emission mechanisms Total radiation intensity Summed intensity of spontaneous radiation of individual particles exceeds does not exceed coherent incoherent

37 37 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

38 38 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:

39 39 I = 10 watts m Hz ster From equation (1): 6 -2 this is much higher than a radio blackbody temperature! So -

40 40 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

41 41 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

42 42 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 =>

43 43 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:

44 44 Curvature vs Synchrotron Synchrotron Curvature B B

45 45 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

46 46 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

47 47 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

48 48 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

49 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 Light Cylinder

50 50 Relativistic beaming may be caused by motion of source with v ~ c near the light cylinder - radiation concentrated into beam width Also effect due to time compression (2, so beam sweeps across observer in time: 2 – 3 needed to explain individual pulse widths (the Lorentz factor)

51 51 In summary... Radio emission - coherent - curvature radiation at polar caps X-ray emission - incoherent - synchrotron radiation at light cylinder

52 52 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

53 53 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!!!


55 55 Neutron star segment solid core? crystallization of neutron matter kg m -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

56 56 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

57 57 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

58 58 Pulsars Period interpulse (~P/10)pulse

59 59 Pulse profiles t average envelope

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