Pulsars

1
Pulsars

• High Energy Astrophysics
• emp_at_mssl.ucl.ac.uk
• http//www.mssl.ucl.ac.uk/

2
Introduction

• Pulsars - isolated neutron stars
  - radiate energy via slowing down of rapid
  spinning motion (P usually lt 1sec, dP/dtgt0)
• Pulsating X-ray sources / X-ray pulsators
  compact objects (generally neutron stars) in
  binary systems. Accrete matter from normal star
  companion. (P 10s secs, dP/dtlt0)

3
Pulsars cont.

• Discovered in radio
• Averaging over many pulses we see

Period
pulse
P/10
interpulse
4

• Measuring pulse complicated by Doppler motion of
  Earth and frequency dispersion in pulse arrival
  times.
• Individual pulses
• av. very constant, individual pulses variable

5
Pulsar period stability
12

• 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 (P1/30 sec) too short).
• Rotation of neutron star???

6
Rotation of a neutron star

• Gravitational force gt centrifugal force
• where and P is the period

7

• Reducing
• G 6.67x10 m kg s P 33x10
  s

gt
but
so
-3
-11
3
-1
-2
Crab
8

• Substituting numbers for Crab then
• so r gt 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.

-3
kg m
14
-3
9
-3
9
Pulsar energetics

• Pulsars slow down gt lose rotational energy - can
  this account for observed emission?
• Rotational energy

so
10
Energetics - Crab pulsar

• Crab pulsar
  - M 1 solar mass
  - P 0.033 seconds
  - R 10 m
• 0.8 x 10 kg m

4
2
kg m
38
2
11

• and
• from observations
• thus energy lost
  by the pulsar

12

• This rate of energy loss is comparable to that
  inferred from the observed emission, for example
  in the 2-20keV range, the observed luminosity in
  the Crab Nebula is approx. 1.5 x 10
  watts.
• Thus the pulsar can power the nebula.

30
13
Irregularities in pulsar emission

• Short timescales - pulsar slow-down rate is
  remarkably uniform
• Longer timescales - irregularities apparent -
  in particular, glitches

A glitch is a discontinuous change of period
P
glitch
t
14
Glitches

• Glitches are caused by stresses and fractures in
  the external layers, the so-called crust of the
  neutron star.
• For example,
• is the observed value for the Crab pulsar.

15
Pulse profiles

• Average pulse profile very uniform
• Individual pulses/sub-pulses very different in
  shape, intensity and phase

Sub-pulses show high degree of polarization which
changes throughout pulse envelope
t
average envelope
16
Neutron Stars

• General parameters
  - R 10 km (10 m)
  - r 10 kg m 10
  g cm - M 0.2 - 3.2 solar
  masses - surface
  gravity 10 m s
• We are going to find magnetic induction, B, of a
  neutron star.

4
18
-3
15
-3
inner
-2
12
17
Magnetic induction

• Magnetic flux,
• Radius collapses from 7 x 10 m to 10 m

constant
surface
radius Sun
8
4
Surface change gives
18

• The general field of Sun is uncertain but should
  be 0.01 Tesla.
• Thus the field for the neutron star,
  B 5 x 10 Tesla 5 x 10 Gauss
• Next - how long does B last?

7
11
ns
ns
19
Decay time of magnetic field

• Decay time of
  magnetic field
• D - typical dimension over which field varies
  significantly (for n.s., D 3 x 10 m)
• s - conductivity

3000m
10km
Polar cap
3
20

• Thus,
• t (3 x 10 ) (10 ) (4p10 )
• 10 seconds 3 x 10 years
• But magnetic field Crab pulsar still intense
  after 1000 years gt interior must be
  superconducting (s and t both very large)
• Neutron stars very dense and zero-T energy
  supports star and prevents collapse.

3
10
-7
11
3
21
Neutron star structure
crust
Heavy nuclei (Fe) find a minimum energy when
arranged in a crystalline lattice

• Neutron star segment

neutron liquid
1.
solid core?
Superfluid neutrons, superconducting p and e-
2.
17
-3
2x10 kg m
1km
14
-3
crystallization of neutron matter
4.3x10 kg m
9km
9
-3
10 kg m
18
-3
10km
10 kg m
22

• 1. Between densities of 4.3 x 10 kg m and 2
  x10 kg m , the lowest energy state is reached
  when nuclei are embedded in an electron and
  neutron fluid.
• 2. Above 2x10 kg m , there is a continuous
  neutron fluid with electrons and protons as minor
  constituents.

14
-3
17
-3
17
-3
23
Observational evidence
From Gravitationally-redshifted absorption lines
in the X-ray burst spectra of a neutron star,
Cottam et al., 2002, Nature (in press)
http//xxx.lanl.gov/ftp/astro-ph/papers/0211/0
211126.pdf
Investigating the low-mass X-ray binary
EXO0748-676 Neutron star primary accreting matter
from an evolved red dwarf secondary star via
Roche Lobe overflow through an accretion
disc. 335ksec observation with XMM-Newton in 2000
http//sci.esa.int/home/xmm-ne
wton/index.cfm
24
Low mass X-ray binary
Neutron star primary
Evolved red dwarf secondary
Roche point
Accretion disk
25
Outbursts
Total exposure time 335,000 sec in XMM-Newton
RGS 28 X-ray bursts, typically lasting 100
sec X-ray count rate in quiescence 0.5
cts/sec Burst count rate typically 9 ct/sec
26
X-ray absorption lines
hot bursts (gt1.2keV)
cold bursts (lt1.2keV)
quiescence
low-ionization circumstellar absorber
redshifted, highly ionized gas
z 0.35 M 1.4-1.8
solar masses R 9-12 km
27
EXO0748-676
origin of X-ray bursts
circumstellar material
28
Pulsar Magnetosphere

• First, defining scale height

The pressure difference supports the element of
atmosphere
h
h
29

• The pressure difference is given by
• where r is the density
• But
• thus and

(where m is the mass of constituent particles)
30
Formula for scale height

• Integrating
• gt pressure falls off exponentially with height
  in atmosphere with uniform temperature.

has the dimensions of distance and is called the
scale height.
31
Neutron star scale height

• For a neutron star,
  g 10 m s
  T 1 million K
• thus h 0.01m
• Thus the atmosphere of a neutron star is only the
  order of 10cm!

12
-2
0
32
Forces exerted on particles

• Particle distribution determined by
  gravity
  temperature
  electromagnetism

e-
Gravity
Newton
33
Magnetic force
Newton
13
This is a factor of 10 larger than the
gravitational force and thus dominates the
particle distribution.
34
Neutron star magnetosphere

• Neutron star rotating in vacuum

Electric field induced immediately outside n.s.
surface.
w
B
pd on scale of neutron star radius
35
Electron/proton expulsion

• Neutron star particle emission

w
B
electrons
Cosmic rays
protons
36
In reality...

• In reality, the charged particles will distribute
  themselves around the star to neutralize the
  electric field.
• gt extensive magnetosphere forms

37
Pulsar models

• Magnetic and rotation axes co-aligned

e-
Co-rotating plasma, mag field lines are closed
inside light cylinder
Radius of light cylinder must satisfy
p
light cylinder, R
L
38
A more realistic model...

• Note that if radiation pulses are to be
  predicted, magnetic axis and rotation axis cannot
  be co-aligned.
• gt plasma distribution and magnetic field
  configuration around a neutron star is much more
  complicated.

39
A better picture
Radio beam
rc/w
Open magnetosphere
Light cylinder
B
Closed magnetosphere
Neutron star mass 1.4 solar masses radius 10
km B 10 to 10 Tesla
4
9
40
The dipole aerial

• Even if a plasma is absent, a spinning neutron
  star will radiate if the magnetic and rotation
  axes do not coincide.

This is the case of a dipole aerial
a
41
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.

42
Radiation mechanisms in pulsars

• Emission mechanisms

Total radiation intensity
coherent
exceeds
incoherent
does not exceed
Summed intensity of spontaneous radiation of
individual particles
43
Incoherent emission - example

• eg. Radiating particles in thermodynamical
  equilibrium ie thermal emission.
• blackbody gt max emissivity
• So is pulsar emission thermal?
• consider radio n10 Hz 100MHz 3m

8
44
Use Rayleigh-Jean approximation to find T
Watts m Hz ster
-2
-1
-1
-25
-2
-1

• Flux density at Earth, F10 watts m Hz
• Source radius, R10km at distance D1kpc
• then

(1)
45
6

• 10 watts m Hz ster
• From equation (1)

-2
-1
-1
this is much higher than a radio blackbody
temperature
46
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 X-rays
  is about 100 billion K, equivalent to electron
  energies 10MeV, so consistent with incoherent
  emission.

radio coherent
IR, optical, X-rays, g-rays incoherent
47
Models of Coherent Emission

• high-B sets up large pd gt high-E particles

e-
e-
p
electron-positron pair cascade
B1e8Tesla
1e16V
cascades results in bunches of particles which
can radiate coherently in sheets
48
Emission processes in pulsars

• Important processes in magnetic fields
  - cyclotron
  - synchrotron
• Curvature radiation gt radio emission
  

Optical X-ray emission in pulsars
B
V. high mag fields e- follow field lines very
closely, pitch angle 0
49
Curvature Radiation

• This is similar to synchrotron radiation.
  If v c and r radius of curvature, radiation
  v. similar to e- in circular orbit with

e-
where n is the gyrofrequency
L
effective frequency of emission is given by
50
Curvature vs Synchrotron

• Synchrotron Curvature

B
B
51

• Spectrum of curvature radiation
  - similar to synchrotron radiation,
• e- intensity c.r. ltlt cyclotron or synchrotron gt
  radio produced this way, need coherence

Flux
n
1/3
-n
e
n
n
m
52
X-rays from curvature radiation?
18

• At frequency 10 Hz
  luminosity 10 J/s
  requires g 10
  and no. particles
  radiating nV 10 - 10 depending on density.
• This is too many for such energetic particles gt
  X-rays emitted by normal synchrotron

29
5
40
41
53
Beaming of pulsar radiation

• Beaming gt radiation highly directional
• Take into account
  - radio coherent, X-rays incoherent
  
  - location radiation source dep on frequency
• Model
  - radio from magnetic poles
  - X-rays
  from light cylinder

54
A better picture
Radio beam
rc/w
Open magnetosphere
Light cylinder
B
Closed magnetosphere
Neutron star mass 1.4 solar masses radius 10
km B 10 to 10 Tesla
4
9
55
Magnetic poles

• Radiation source localized near mag poles.

(simple, axisymmetric case)
b
Rad source localized near poles, narrow beam
produced along mag field. Polar caps defined by
field lines tangential to light cylinder.
light cylinder
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Important observed properties

• Pulses observed only when beam points at Earth.
• Rad source probably localized within light
  cylinder close to neutron star surface
  - no wandering and directionality
• Problem ALL radiation mechanisms at different
  frequencies (coherent or not) must have same
  orientation along magnetic field.

57
Origin of subpulses

• subpulses

Brightening on boundaries between closed and open
lines may produce subpulses
boundary
co-rotating plasma
58
Light Cylinder

• Radiation source close to surface of light
  cylinder.

P
P
simplified case
59
Light cylinder realistic but complex!

• Top view

rc/w
B
aligned w and B
Cross-section
torus
aligned w and B
60
What we see?
61

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

(the Lorentz factor)
2
62
Long Period Pulsars

• Not generally seen in optical or X-rays -
  is this emission produced at light cylinder?

power radiated by synchrotron
For dipole magnetic field
Also
63

• So if particles of the necessary energy E exist
  in all pulsars and emission occurs at R , we
  expect
  - radiated power
• and thus long period pulsars are weak emitters.

L
64
In summary...

• Radio emission
  - coherent
  - curvature radiation at
  polar caps
• X-ray emission
  - incoherent
  - synchrotron radiation
  at light cylinder

65
Magnetic energy nebula

• Neutron star slows down
  gt energy sufficient to feed nebula
• What about the magnetic energy?

Consider energy released at light cylinder. Area
4pR
2R
L
R
L
2
L
66

• Magnetic field at R is stretched out to vc.
• Magnetic energy density
• Mag energy crossing light cylinder per sec

L
But for mag dipole
so
67

• Substituting values for the Crab pulsar
• like rotational energy release, this is also
  comparable to observed emission from Crab Nebula

68
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 10

7
4
69
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!!!