thomas tauris bonn uni. / mpifrtauris/tauris_3.pdf · 2014. 1. 10. · fig. 8.4 (canuto 1975) the...
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Thomas Tauris Bonn Uni. / MPIfR
Heidelberg XXXI, Oct. 2013
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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
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Structure of WDs Basic characteristics Chandrasekhar mass and stability
EoS below neutron drip (Harrison-Wheeler / Baym-Pethick-Sutherland (BPS))
Neutron-rich nuclei Neutron drip Semi-empirical mass formula Including shell effects and lattice energy
Elementary treatment of WD cooling
Photon diffusion equation Luminosity, L (M,T) Residual ion thermal energy Cooling age Crystallization
Observations
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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)
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
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Neutron drip (nuclei, e-, n) 2 phase system
Fairly well-known EoS (e.g. BBP)
not well understood. Problems: nucleon-nucleon interactions
many-body problem
hyperons (nucleon-like strange baryons)
pion/kaon condensation
ultra-high densities:
no relativistic many-body Schrödinger equation is known
“meson clouds” around nucleons - quark-drip
(break-down of potential, no longer 2-body interactions)
neutron lattice?
11 34 10drip g cm
14 32.8 10drip nuc g cm
nuc
10 nuc
n n
n n n
n n
repulsion
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V(r)
The exchange of vector mesons (S=1)
induces repulsive NN forces, while the
exchange of scalar mesons (S=0)
induces attractive forces.
The two lowest mass vector mesons are:
(769 MeV), (783 MeV).
The intermediate-range attractive NN force is
caused by the (f0) meson (600 MeV), and
the long-range NN force by (140 MeV).
The Yukawa-like potential:
approximately describes the NN interactions.
(sum all pairs of NN interactions)
2
12
reV g
r
1
2V i j
i j
E V
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“Compressible liquid drop model”
Reid soft core: superposition of Yukawa-like potentials
Includes many-body interactions and improved Coulomb lattice effects
Minimizing the total energy density:
for constant n with respect to A
(baryon number density)
Nuclei must be stable against -decay (Z const.)
Free n-gas must be in equilibrium with neutrons inside nuclei:
Pressure balance between n-gas and nuclei:
( ) (1 ) ( )N N L n N N e en W W V n n
( 0, leaves the star)N Ne n p en p e
2
12
reV g
r
fraction of volume which is gas (1 )N N N nn A n V n n
G Nn n
G Nn nP P
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Fig. 8.1 + 8.2 (Bayn, Bethe & Pethick 1971).
4
3GTR
3( )g cm
no stable NS
For stability:
neutron drip
stable NS
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Fig. 9.2 + 9.3 (Baym & Pethick 1979).
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Fig.9.1 (c.f. Fig.6.2)
0c
dM
d
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Steiner, Lattimer & Brown (2012).
Note, deviation from 1/3R M
Lattimer (2009).
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• Muon contribution to EoS:
equilibrium:
Charge neutrality:
ee e n p e
p en n n
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2 14 3(106 MeV, 2.4 10 )e m c g cm
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Fig. 8.4 (Canuto 1975) The concentrations in a free hyperonic gas
as a function of total baryon density, n. Bednarik et al. (2011).
• Hyperons are nucleon-like strange baryons
(i.e. at least one s-quark, e.g.: )
0 ( ) 1116 MeVuds
0 0 3, , , , , ( , , , , , ) when 2 ( 10 )nucuus uds dds uss dss sss n fm
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• Baryons with only u- and d-quarks:
01232 MeV , , , ( , , , )n uuu uud udd ddd
0 0 0, , ,p p n n
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• have spin S=0 (bosons) and can form a Bose-Einstein condensate.
• Thus in their lowest energy state (z=0) they have no momentum and
therefore they do not contribute to the pressure P.
• Pion condensates therefore results in soft EoS
• Kaon condensates may form too
( 140 MeV > )n p e nucn p
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• A fermionic superfluid may form at low temperatures.
• Zero-viscosity due to Cooper pairs (BCS theory).
• Three types:
• Consequences: 1) Formation of vortices
2) Dynamical evolution: pulsar glitches
3) The cooling of NSs
4) The Meissner effect (B-flux tubes)
10
32
10
neutron superfluid - inner crust
neutron superfluid - core
proton superfluid - core
S
P
S
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The relaxation depends on the pinning/unpinning between core superfluid
vortices and the normal component of nuclei (lattices) in the inner crust,
transferring angular momentum.
/0 0( ) ( ) (1 )
tt t Q e Q
a t b
Vela
c nI I I
Weak coupling between
c: crust + charged particles
n: superfluid neutrons in core
(Two component model).
Moment of inertia
Problem: the two-component is too simplified and does not
explain data (healing parameter Q and relaxation time differ
for different glitches from the same pulsar)
A glitch is quickly (minutes)
communicated to the charged
particles via the B-field, but
very slowly (months) to the
superfluid neutrons.
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NS cooling depends on:
• EoS
• Neutrino emission
• Superfluidity
• Magnetic fields
• Light elements on surface
In highly degenerate matter a bystander particle
must be present to absorb momentum
Direct URCA: ( >2 )
nuc
e
e
e e
n p e
p e n
n n
Modified URCA:
e
e
e e
n n n p e
p e n
n n n n
Also neutrino emission due to Cooper pairing and bremsstrahlung.
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neutrino cooling photon cooling
Yakolov & Pethick (2004)
Douchin & Haensel (2001)
Superfluidity affects the neutrino emission processes and the heat capacity.
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Lattimer (2009)
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NS radii can be determined for a few young NSs
(the magificent seven) by fitting blackbody spectra:
Correction for the gravitational redshift:
In practice more difficult because of the unknown spectral hardening
(atmospheric corrections), and uncertainties in distance estimates.
2 4
2
4
44
LL R T F
d
FR d
T
2
2
1 2
1 2
R GMR T T
c RGM
c R
The apparent (observed) radius is larger than the true radius
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Trümper et al. (2004).
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Lattimer (2009)
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Antoniadis et al. (2013)
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• Shapiro delay measurements of binary radio pulsars.
• Measurements of other post-Keplerian parameters:
• Dual-line spectroscopy (measurements of WD spectra
Dopplershift, besides from radio pulsar timing).
, , ,bP e
Earth
Shapiro delay
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Nice (2013)
Any PK measurement yields a line in the (m1,m2)-plane.
Hence, two PK parametres determines m1 and m2 uniquely.
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• The double pulsar PSR J0737-3039
Kramer et al. (2006).
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Lattimer (2013)
www.stellarcollapse.org/nsmasses
PSR J0348+0432 M=2.01 0.04
Antoniadis et al. (2013)
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inner crust
outer crust
Surface (few cm)
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A ”soft” equation of state has an average system energy
which is attractive at nuclear densities. (e.g. a Reid potential).
A ”stiff” equation of state has a repulsive component at higher densities. For a given mass, M:
soft stiff
max
max
soft EoS: is small ( is small) is small, is large ( is small)
stiff EoS: is large ( is large) is large, is small ( is large)
P=K
c
c
P R M
P R M
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• MIT bagmodel • degenerate Fermi sea of massless quarkes
• energy density B
• important physics parameters: B, ms, s
(bag constant, mass of strange quark, strong interaction coupling constant)
• EoS:
• M(R) (quark stars with larger masses have larger radii)
• Difficult to confirm observationally (sub-ms pulsar: )
• Hybrid stars are very popular: quark core + normal matter
• Quark-novae represent the transition from a normal NS to hybrid star
1( 4 )
3P B
0.6P ms
See Weber (2005) Prog.Part.Nucl.Phys.54:193-288,
for a modern review.
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Weber (2005)
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A quark-nova is the violent explosion resulting from the conversion of
a neutron star to a quark star (Oyued, Dey & Dey, A&A 390 L39-42, 2002).
When a neutron star spins down, it may convert to a quark star through
a process known as quark deconfinement.
Direct evidence for quark-novae is lacking; however, recent observations
of supernovae SN 2006gy, SN 2005gj and SN 2005ap have been suggested
may point to their existence (Leahy & Ouyed, MNRAS 387, 1193, 2008).
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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
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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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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
rot 14 5
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
_
16 16 _
+
Magnetosphere: 38
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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
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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 of Milky Way
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pulsar
Duty cycle: 1-5% for slow pulsars
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436, 660, 1420 MHz
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57
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Solar system
emitted pulse observed pulse
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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
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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 pulsars Characteristic age
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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
0
1
true age of pulsars: 1( 1)
nPP
tn P P
( ) / 2
a b
a b
second derivative of magnetic moment
ellipticity (asymmetry rotation axis)
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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
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Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 68
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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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
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Another famous giant flare (burst) is the August 27, 1998 event
(most intense flux of gamma-ray ever detected)
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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 of 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
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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
PPR
IcB
NS
NS 62
3
8
3
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NS EoS above neutron drip Baym-Bethe-Pethick (BBP) EoS
Stability of NSs, exotic particles, quark stars
Exotic particles
Structure of NSs Cross section, soft vs.stiff EoS, observational constraints
Radio pulsars Observational properties
The magnetic dipole model
Spin evolution of pulsars in the PP-diagram
True ages
Magnetars
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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
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