Transcript Pulsars (last updated 2005/6)

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 m v

2
r
r
2r
and P is the period
v
P
otherwise star would fly apart
7
Reducing:
M

GM 4 r
=>


3
2
2
2
4r
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
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 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


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
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

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 = (llo/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 ns
Gravity
31
18
Fgn s  me gns  9 10 10  10
12
Newton
25
Magnetic force
19
FB  evB  1.6 10

RNS

2 10 m
8
10 T
3
3310 s
4

5
 3 10 Newton
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
2rc
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
 310 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
2g
‘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 4g
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 4g
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