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Thomas Tauris MPIfR / AIfA Uni. Bonn
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1: Introduction
Degenerate Fermi Gases
Non-relativistic and extreme relativistic electron / (n,p,e-) gases
2: White Dwarfs
Structure, cooling models, observations
3: Neutron Stars
Structure and Equation-of-state
Radio Pulsars
Characteristics, observations, spin evolution, magnetars
4: Binary Evolution and Interactions
Accretion, X-ray Binaries, formation of millisecond pulsars
Black Holes
Observations, characteristics and spins
5: Testing Theories of Gravity Using Pulsars
Gravitational Waves
Sources and detection
Bonn, Summer 2017 Thomas Tauris - MPIfR / Bonn Uni. 2
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EoS for Baym-Bethe-Pethick (BBP) EoS
Stability of NSs
EoS for Nucleon-nucleon interactions
Muons, hyperons, -resonances, pion/kaon condensation
Superfluidity (glitches/cooling of NSs)
Bethe-Johnson (BJ) EoS
Quark (strange) stars / quark-novae
Summary of EoS above neutron drip
Structure of NSs Cross section
Soft vs Stiff EoS
Observational constraints on M and R
nuc
drip nuc
Bonn, Summer 2017
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Bonn, Summer 2017 4Thomas Tauris - MPIfR / Bonn Uni.
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Observational aspects of radio pulsars The radio pulsar population in the Milky Way
Pulse profiles / Scintillation / Dispersion measure
Emission properties
Spin evolution of pulsars in the PP-diagram The magnetic dipole model
Evolution with B-field decay
Evolution with gravitational wave emission
The braking index
True ages of radio pulsars
Magnetars Soft gamma-ray repeaters (SGRs) and Anomalous X-ray pulsars (AXPs)
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Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 6
B
Rotation axis Radio signal
Time
period
Perfect clock:
✓ P= seconds (PSR 1937+21) 0.001 557 806 448 872 75
A pulsar is a perfect physics laboratory:
✓ = 700 Hz (P=1,4 ms – 8 sec.)
✓ B = 10 G
✓ E = 10 L (F = 10 F )
✓ M = 1.4 M
✓ R = 10 km
13
rot145
Nuclear physics
Particle physics
Solid state physics
Atom physics
Plasma physics
Relativity
Giant atomic nucleus:
✓ A=10 baryons, = 2-10 core nuclear
57
✓ production of 10 (e, e ) per second
✓ TeV -rays
✓ e accelerated to 10 eV, =10 Volts
_
1616_
+
Magnetosphere:38
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Bonn, Summer 2017 Thomas Tauris - MPIfR / Bonn Uni.
The surface intensity of the radio emission, I using a Planck function demonstrates
that if the radio emission was caused by thermal black body radiation one would
obtain an extremely high brightness temperature (leading to absurdly large particle energies)
and therefore the radiation mechanism of a radio pulsar must be coherent
(Most models invoke curvature radiation or a maser mechanism).
3
2 /
23 2 1 1 1
24 29
2 1, 1.5
1
: 0.48 @ 436
(1 10 )
10 ( 10 )
h kT
hI I
c e
Crab f Jy MHz
Jansky erg cm s Hz st
kT eV T K
7
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~ 2400 radio pulsars
~ 50 X-ray pulsars
~ 300 neutron stars in X-ray binary systems
- Pulsars are concentrated in the Galactic plane in star forming regions (OB star progenitors)
- Large spread is caused by high velocities (kicks imparted to NS in supernova explosions)
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x (kpc)
y (
kp
c)Sun
Centre ofMilky Way
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Phase I @ 2023 Phase II @ 2030 Frequency range: 50 MHz to 14 GHz. • SKA-low array (50 – 350 MHz) (dipole antennas) • SKA-mid array (350 MHz – 14 GHz) (15 m. dish antennas) • SKA-survey array (350 MHz – 4 GHz) (a compact array of parabolic dishes)
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pulsar
Duty cycle: 1-5% for slow pulsars
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436, 660, 1420 MHz
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14
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15
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Solar system
emitted pulse observed pulse
16
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256 channels* 125 kHz
452 MHz
436 MHz(70 cm)
420 MHz distance 1/slope
LndlnDM e
L
e 0
DMcm
et
e
a
3
24
Bonn, Summer 2017 17Thomas Tauris - MPIfR / Bonn Uni.
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Bonn, Summer 2017 18Thomas Tauris - MPIfR / Bonn Uni.
111103 yrMdt
dM
• Most accurate method to determine a stellar wind
pulsar
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Bonn, Summer 2017 20Thomas Tauris - MPIfR / Bonn Uni.
Tauris et al. (2014)
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P
P
2
2
3||
3
2m
cEdipole
sin~|| 23BRm
NSrot IE
)/2(2
1 2 PIE NSrot
PPR
IcB
NS
NS 62
3
8
3
The magnetic-dipole model:
Active pulsar lifetime: 10-50 million yr
Millisecond pulsarsCharacteristic age
21
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2the deceleration law, is the braking index
3 pure dipole
5 pure gravitar (only spin-down by gravitational wave radiation)
nk n
n
n
2
3||
3
2m
cEdipole
sin~|| 23BRm 2 2 6
5
32
5gw
GE I
c
rot dipole plasma gwE I E E E
0
2 2 20 0 2
/
2 /
For example:
( )
1 2( ) 1 ln 1
2 2D
D
DD
D
t
t
B t B e
PP t P B e t
Pk
00
1
true age of pulsars: 1 , for , 3( 1) 2
nPP P
t P P nn P P P
( ) / 2
a b
a b
second derivative of magnetic moment
ellipticity (asymmetry rotation axis)
Bonn, Summer 2017 22Thomas Tauris - MPIfR / Bonn Uni.
Characteristic age
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00
0
11
( ) 1 1nP
P t P n tP
Bonn, Summer 2017 23Thomas Tauris - MPIfR / Bonn Uni.
2 2
22 n nPPk n P P const
P
(cf. Lazarus et al. (2014) for evolutionary tracks)
0 0Given ( , , , ) we can calculate ( ) and ( ) :P P n const t P t P t
1: 1B const P
P
: 1const P P
2 3death line: / 3B P P P
6/7 4/3spin-up line: 4 / 3eqP B P P
0
0
2( )
( )
nP t
P t PP
Slope in the ( , ) diagram: 2P P n
log P
log P
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Tauris & Konar (2001)
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B-field decay in neutron stars, via crustal ohmic dissipation
and diffusion, and its dependence on input physics.
PPR
IcB
NS
NS 62
3
8
3
2
1
4
B cv B B
t
25
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A magnetar is a type of neutron star with an extremely
high B-field, the decay of which powers the high-
energy emission of anomalous X-ray pulsars (AXPs)
and soft gamma-ray repeaters (SGRs).
Duncan & Thompson & (1992) developed the theory to explain these objects.
Support for this extreme B-field picture comes from:
1) Location in P-Pdot diagram
2) Cannot be radio pulsars b/c
3) Cannot be X-ray binaries b/c absence of Doppler modulation in timing data
4) Cannot be neutron stars accreting from a fall-back disk b/c of detection of flares
5) Bursts can be explained by magnetic giant flares
Magnetars are detected both as persistent (quiescent) sources and burst sources.
There are currently 26 known magnetars: 13 SGRs and 13 AXPs
according to McGill SGR/AXP online catalogue:
http://www.physics.mcgill.ca/~pulsar/magnetar/main.html
with various burst, transient and persistent properties
X rotL E
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Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 28
The famous March 5, 1979 event
(the largest burst of gamma-rays ever detected)
Notice, the 8.0 sec cycle (spin period of NS).
16 additional small bursts seen between 1979-1983
and since then no burst have been detected.
The source was located in an LMC SN remnant
28
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Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 29
Another famous giant flare (burst) is the August 27, 1998 event
(most intense flux of gamma-ray ever detected)
29
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Robert C. Duncan, University of Texas at Austin
A magnetic twist gives rise to
X-ray emissions from a magnetar.
Twisted B-fields support excess currents in the magnetosphere.
Detection of resonant cyclotron scattering reveals the B-field strengths.
2 140.63 1 2 / ( /10 ) keVproton
cyclotronE GM c R B G
30
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Robert C. Duncan, University of Texas at Austin
Giant flares – a fireball model
Huge tension builds up in the crust from magnetic stress
- when released this energy produces a giant flare.
A trapped fireball (orange zone) on the surface of a neutron
star (brown). The fireball, containing positrons ( e+ ),
electrons ( e- ), and high-energy photons (γ), is confined by
the magnetic field (dark, arched lines). It loses energy by
emitting hard X-ray photons (orange squiggley arrows)
from its surface. The fireball also contains a trace of heavy
particles (protons and ions) which were blown off the
surface of the star. These heavy particles settle down
along field lines as the fireball loses energy and shrinks.
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Kaspi et al. (2001), ApJ. 558, 253
314
2 6
33.9 10
8
NSdipole
NS
c IB PP G
R
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Bonn, Summer 2017 34Thomas Tauris - MPIfR / Bonn Uni.
Magnetars are born with rapid spin
which creates extremely high B-fields
due to convection < 10 sec.
XDINs also have high B-fields.
Radio pulsars are born with moderate
B-fields (RRATs is a subpopulation).
CCOs (”anti-magnetars”) are born with
weak B-fields.
Maybe these neutron star populations
are connected with their evolution
(cf. some radio pulsars have very small
brakning indices and evolve upward
in the PPdot-diagram).
Espinoza et al. (2011), ApJ, 741, L13
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Observational aspects of radio pulsars The radio pulsar population in the Milky Way
Pulse profiles / Scintillation / Dispersion measure
Emission properties
Spin evolution of pulsars in the PP-diagram The magnetic dipole model
Evolution with B-field decay
Evolution with gravitational wave emission
The braking index
True ages of radio pulsars
Magnetars Soft gamma-ray repeaters (SGRs) and Anomalous X-ray pulsars (AXPs)
Bonn, Summer 2017 35Thomas Tauris - MPIfR / Bonn Uni.
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1: Introduction
Degenerate Fermi Gases
Non-relativistic and extreme relativistic electron / (n,p,e-) gases
2: White Dwarfs
Structure, cooling models, observations
3: Neutron Stars
Structure and Equation-of-state
Radio Pulsars
Characteristics, observations, spin evolution, magnetars
4: Binary Evolution and Interactions
Accretion, X-ray Binaries, formation of millisecond pulsars
Black Holes
Observations, characteristics and spins
5: Testing Theories of Gravity Using Pulsars
Gravitational Waves
Sources and detection
Bonn, Summer 2017 Thomas Tauris - MPIfR / Bonn Uni. 36
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Shapiro & Teukolsky (1983), Wiley-Interscience
Curriculum
- Chapter 10: p.267290.
Exercises: # 5, 6, 12, 14
- Monday May 29, 12:30-13:45
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Shapiro & Teukolsky (1983), Wiley-Interscience
Curriculum
- Chapter 8: p.(188-197), (220-240)
- Chapter 9: p.241-253, 253-258.
Exercises: # 5, 6, 12, 14
- Monday May 29, 12:30-13:45
Lecture: Monday May 22: 12:30-13-45
(Spin and B-field Evolution of Neutron Stars Radio Pulsars)
Bonn, Summer 2017 38Thomas Tauris - MPIfR / Uni. Bonn