thomas tauris bonn uni. / mpifrtauris/tauris_3.pdf · 2014. 1. 10. · fig. 8.4 (canuto 1975) the...

Thomas Tauris Bonn Uni. / MPIfR

Heidelberg XXXI, Oct. 2013

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

Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 2

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

Heidelberg XXXI, Oct.2013

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


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

Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR

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

Heidelberg XXXI, Oct.2013 6 Thomas Tauris - Bonn Uni. / MPIfR

“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


Fig. 8.1 + 8.2 (Bayn, Bethe & Pethick 1971).

4

3GTR

3( )g cm

no stable NS

For stability:

neutron drip

stable NS

Fig. 9.2 + 9.3 (Baym & Pethick 1979).

Fig.9.1 (c.f. Fig.6.2)

0c

dM

d

Steiner, Lattimer & Brown (2012).

Note, deviation from 1/3R M

Lattimer (2009).


• Muon contribution to EoS:

equilibrium:

Charge neutrality:

ee e n p e

p en n n


2 14 3(106 MeV, 2.4 10 )e m c g cm

//upload.wikimedia.org/wikipedia/commons/1/13/Muon_Decay.svg

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

http://en.wikipedia.org/wiki/File:Baryon_decuplet.svg

• Baryons with only u- and d-quarks:

01232 MeV , , , ( , , , )n uuu uud udd ddd

0 0 0, , ,p p n n


http://en.wikipedia.org/wiki/File:Baryon_decuplet.svg

• 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


• 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

Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR

http://images.iop.org/objects/ccr/cern/51/3/16/CCast1_03_11.jpg

http://images.iop.org/objects/ccr/cern/51/3/16/CCast1_03_11.jpg

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.


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.


neutrino cooling photon cooling

Yakolov & Pethick (2004)

Douchin & Haensel (2001)

Superfluidity affects the neutrino emission processes and the heat capacity.


Lattimer (2009)

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


Trümper et al. (2004).

Lattimer (2009)

Antoniadis et al. (2013)


• 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


Nice (2013)

Any PK measurement yields a line in the (m1,m2)-plane.

Hence, two PK parametres determines m1 and m2 uniquely.

• The double pulsar PSR J0737-3039

Kramer et al. (2006).


Lattimer (2013)

www.stellarcollapse.org/nsmasses

PSR J0348+0432 M=2.01 0.04

Antoniadis et al. (2013)

http://www.stellarcollapse.org/nsmasses

http://www.stellarcollapse.org/nsmasses

inner crust

outer crust

Surface (few cm)

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


• 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.

http://quarknova.ucalgary.ca/media/index.html

Alford & Reddy (2003)

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=iumtJJPmANO1-M&tbnid=LLPY3ALCxEsz5M:&ved=0CAUQjRw&url=http://www.universetoday.com/70111/astronomy-without-a-telescope-strange-stars/&ei=KsaIUYXRHKea1AWjsYHgCA&bvm=bv.45960087,d.bGE&psig=AFQjCNG70Is84D2uLnmznIqiEx8IweA4mg&ust=1368004508736970

Weber (2005)

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).

46 Thomas Tauris - Bonn Uni. / MPIfR Heidelberg XXXI, Oct.2013

1: Introduction



2: White Dwarfs


3: Neutron Stars


Radio Pulsars




Black Holes



Gravitational Waves



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)



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


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

~ 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)


x (kpc)

y (

kp

c)

Sun

Centre of Milky Way


pulsar

Duty cycle: 1-5% for slow pulsars


436, 660, 1420 MHz


Solar system

emitted pulse observed pulse

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


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

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)


Tauris & Konar (2001)

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


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


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


Another famous giant flare (burst) is the August 27, 1998 event

(most intense flux of gamma-ray ever detected)

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

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.

Kaspi et al. (2001), ApJ. 558, 253

PPR

IcB

NS

NS 62

3

8

3

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


1: Introduction



2: White Dwarfs


3: Neutron Stars


Radio Pulsars




Black Holes



Gravitational Waves



thomas tauris bonn uni. / mpifrtauris/tauris_3.pdf · 2014. 1. 10. · fig. 8.4 (canuto 1975) the...

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