# Which is the coolest known neutron star

## Cores, stars, hyper cores Juergen Schaffnerâ € “Bielich - Institute for ...

**Cores**, **Stars**, **Hyper nuclei**

Jürgen Schaffner – Bielich

**Institute** for theoretical physics / astrophysics

Justus Liebig University, Giessen, July 11, 2006

- p.1

Nuclide map

- p.2

Formation of the heavy elements: supernova explosions

Animation of a supernova explosion (Chandra, NASA)

Suns with more than 8

Solar masses end in one

Supernova explosion

Supernova from AD 1054 was for

three weeks in broad daylight

visible (Crab Nebula)!

Supernovae emit several

a thousand times brighter than an entire one

Galaxy!

last closer supernova explosion

in the last 400 years: SN1987A

currently best "spot" in the universe for

the emergence of the elements in the r–

Process and in the νp process!

- p.3

Neutron stars and supernovae

arise in supernova explosions (star collapse, type II)

compact, massive objects: radius ≈ 10 km, masses 1 - 2M ⊙

extreme densities, multiple core density: ρ ≫ ρ 0 = 3 · 10 14 g / cm 3

- p.4

in the middle of the Crab Nebula: a pulsar, a rotating neutron star!

Masses of pulsars (Thorsett and Chakrabarty (1999))

more than 1700 pulsars known

best known mass:

M = (1.4411 ± 0.00035) M ⊙

(Hulse-Taylor pulsar)

extremely fast revolutions:

up to 716 Hz

(PSR J1748-2446ad)

News from pulsars with

White dwarfs:

(Nice, Splaver, Stairs (2005))

Massive pulsar J0751 + 1807:

M = 1.6 - 2.5M ⊙ (2σ)!

- p.5

Sounds of pulsars

PSR B0329 + 54: typical pulsar with a period of

0.7145519 s (1.4 pulses per second)

PSR B0833-45 (Vela Pulsar): in Vela Supernova remnant,

89 ms period (11 pulses per second)

PSR B0531 + 21 (Cancer pulsar): youngest known pulsar, im

Crab Nebula, period: 33 ms (30 pulses per second)

PSR J0437-4715: recently discovered pulsar, pulsates with a

Period of 5.7 ms (174 pulses per second)

PSR B1937 + 21: second fastest known pulsar with one

Period of 1.56 ms (642 pulses per second)

- p.6

Structure of a neutron star - the crust

ρ ≤ 10 4 g / cm 3:

the atmosphere

(Atoms)

ρ = 10 4 - 10 11 g / cm 3:

Shell or Outer Crust

(free e -, grid off **Cores**n)

ρ = 10 11 - 10 14 g / cm 3:

Inner crust

(Grid off **Cores**n,

free neutrons and e -)

- p.7

The crust of the neutron star

a grid out **Cores**n surrounded by free electrons

Wigner-Seitz cell, lattice structure is bcc

minimize E = E **Cores** + E grid + E e−

Loop over all particle-stable **Cores** (up to 14,000!)

use atomic mass table from Audi, Wapstra, Thibault (2003)

Extrapolation with different models

= ⇒ sequence of **Cores**n A Z as a function of density - p.8

Comparison with previous work

Baym, Pethick, Sutherland (1971): droplet model from 1966

Haensel, Zdunik, Dobaczewski (1989): Skyrme parametrization

SkP, spherical only **Cores**

Haensel and Pichon (1994): atomic mass table from 1992

plus droplet model

this work (Rüster, Hempel, JSB (2005)):

latest atomic mass table from 2003

Carrying out deformations for Skyrme model calculations

comparison with different skyrms for the first time

Parameter sets

first calculations with relativistic field theory

Models with entrainment of deformations

- p.9

Core models and mass tables

Finite Range Droplet Model: FRDM (Moeller, Nix, Myers, Swiatecki)

Skyrme parameterizations:

Extended Thomas-Fermi model plus BCS pair force: SkSC4,

SkSC18

Skyrme Hartree-Fock plus BCS pair strength: MSk7

Skyrme Hartree-Fock-Bogoliubov (HFB): SLy4, SkP, SkM *, BSk8

(Set SkSC4, SkSC1, MSk7, BSk8: S. Goriely, J. M. Pearson et al. (BRUSLIB))

(Set SLy4, SkP, SkM *: Dobaczewski, Stoitsov, Nazarewicz)

Relativistic parameterizations:

Relativistic middle field model: NL3, NL-Z2, TMA

Relativistic point coupling model: PCF1

Chiral Effective Lagrangian: Chiral

(2d calculations (deformations) for Set NL3: Lalazissis, Raman, Ring, and Set TMA: Geng,

- p.10

QCD and chiral symmetry

Concept: help construct the effective Lagrangian of nuclear power

Symmetries of the QCD

QCD with N f = 3 massless quarks is invariant under

SU (3) L × SU (3) R chiral symmetry:

left-handed quark: q L = 1 (1 - γ 2 5) q

right-handed quark: q R = 1 (1 + γ 2 5) q

Explicit breaking of the chiral symmetry by finite

Quark masses:

m u = 1.5 - 4.5 MeV, m d = 5.0 - 8.5 MeV,

m s = 80 - 155 MeV (PDG 2004)

thus: m u, d ≪ m s ≪ M N ≈ 1 GeV

- p.11

QCD and Chiral Symmetry II

Spontaneous breaking of the chiral symmetry

non-vanishing vacuum expectation values:

Gell-Mann-Oaks-Renner relation:

m 2 πfπ 2 = - 1 2 (m u + m d) 〈0 | ūu + ¯dd | 0〉

= ⇒ 〈0 | ¯qq | 0〉 ≈ - (250 MeV) 3

QCD summation rule for Charmonium:

〈0 | G µν G µν | 0〉 ≈ (330 MeV) 4

generate the masses of the hadrons!

- p.12

Chiral effective Lagrangian

(Papazoglou, Zschiesche, JSB, Schramm, Stöcker, Greiner, PRC 59, 411 (1999))

invariant under SU (3) L × SU (3) R chiral symmetry

with scalars + pseudoscalars, vector + axial

Meson nonet

with baryon octet (and baryon decuplet)

with explicit and spontaneous symmetry breaking

Fit on hadron masses, **Cores** and **Hyper nuclei**

(∼ 10 parameters)

good description of hadron masses, nuclear matter, **Cores**n and

**Hyper nuclei**n

- p.13

Core sequence to the edge of core stability (Hempel, Rüster, JSB 2005)

10 30

10 29

10 28

66

Ni

86

Kr

84

Se

10 27

P in dyne / cm 2

10 26

10 25

10 24

10 23

10 22

10 21

10 20

10 19

56

Fe

62

Ni

64

Ni

10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12

in g / cm 3

BPS

NL3p

PCF1np

BSk8

SLy4

NL3def

TMA

outer crust starts with iron (56 Fe) up to ρ ≈ 10 7 g / cm 3

continue with nickel isotopes (Z = 28), then Kr, Se, Ge, Zn (N = 50)

= ⇒ magic numbers, shell closures!

Sequence initially independent of the parameter set (data!)

The equation of state is (almost) independent of the parameter set! - p.14

Core sequence for Skyrme models (Hempel, Rüster, JSB 2005)

adapted to the properties of selected **Cores**n and to

Equation of state for nuclear matter (SLy4: also for neutron matter)

Sequence of neutron rich **Cores** shows pronounced lines!

new shell closures on the verge of core stability?

- p.15

Core sequence and edge of core stability (Hempel, Rüster, JSB 2005)

48

44

40

Z

36

84

Se

82

Ge

80

Zn

32

28

SLy4

BSk8

24

NL3def

TMA

FRDM

20

10 10 2 5 10 11 2 5 10 12

in g / cm 3

Selection of the most modern mass tables (with deformations)

Same initial sequence: Se, Ge, Zn (data!)

The sequence remains within a narrow range of the atomic number Z

**Cores** become unstable and neutrons escape by ρ ≈ 5 · 10 11 g / cm 3

- p.16

**Cores** in the neutron star crust (Hempel, Rüster, JSB 2005)

Nuclear sequence along N = 50, N = 82, nuclear charges from Z = 46 - 34

general end point of the sequence at N = 82 and Z = 36 (!)

very similar edge of the core stability at N = 82 (!)

Update of the classic work of Baym, Pethick, Sutherland!

- p.17

X-ray speed camera

accretive

Neutron star:

X-ray speed camera (x-ray

burster)

Explosion on the

Surface of the

Neutron star

redshifted

Spectral lines visible!

(Cottam, Paerels, Mendez (2002))

Discovery of exotic **Cores**

technically possible!

- p.18

Structure of a neutron star - the nucleus

hyperon

star

quark − hybrid

star

s u

p

e

r

c

O

N + e

N + e + n

n, p, e, µ

n d

u

c

t

i

neutron star with

pion condensate

absolutely stable

strange quark

matter

µ

u, d, s

quarks

n, p, e, µ

n

G

p

traditional neutron star

n superfluid

u d s

Σ, Λ, Ξ, ∆

H

K -

π -

r o

t

no s

crust

Fe

10 6 g / cm 3

10 11 g / cm 3

10 14 g / cm 3

m s

strange star

R ~ 10 km

nucleon star

M ~ 1.4 M

- p.19

Neutron star matter for a free gas

Hadron p, n Σ - Λ others

appears at: ≪ n 0 4n 0 8n 0> 20n 0

Particles with a strange quark (Σ, Λ hyperons)

occur in dense neutron star matter!

But the corresponding equation of state gives one

Maximum mass of only

M max ≈ 0.7M ⊙ < 1.44m="">

= ⇒ Effects of the strong interaction are essential

to describe neutron stars!

- p.20

First hypercore measurement

**Hyper nuclei**: bonded

**Cores** with hyperons

1953: first

Hyperkernel measurement of

Danysz and Pniewski out

an emulsion experiment

in the cosmic

Cosmic radiation

Double star event: first

Star from the hypercore

Production, the second out

the hypercore decay

- p.21

Hypernuclear Spectroscopy

Production with (strange)

Kaon rays

Structures in the spectrum of

expiring pions

= ⇒ one-particle energies

of **Hyper nuclei**s!

first surprise: tiny

Spin-orbit splittings

in 12

Λ C! - p.22

One-particle levels in 17th

Λ O

Hyperon potential

(dotted line) is

less than that

Nucleon potential

(solid line)

Coulomb potential:

dash-dotted line

Spin-orbit splitting for

Hyperon is much smaller

than for nucleons

(JS, diploma thesis (1991))

- p.23

Λ One-particle energies

30

209

Pb

Binding Energy (MeV)

25

20

15

10

5

0

-5

89

Y

51 Exp.

Va 40 S RMF

Ca 28Si

16 13 12

O C C

s

G

H

f

d

p

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

A -2/3

(Rufa, JS, Maruhn, Stöcker, Greiner, Reinhard (1990))

measured in reactions (π +, K +)

Fit on single-particle energies: U Λ = −27 MeV for A → ∞

- p.24

GSI's HypHI program

Exploring the whole hypernuclide map for light systems!

Determination of the edges of the core stabilities

Stabilize hyperons **Cores**, 8 Be is unbound, but 9 ΛBe is bound! - p.25

ΛΛ **Hyper nuclei**

two Λs bound in one core, produced by Ξ - capture

10

1963 Danysz et al .: ΛΛ Be → 9 ΛBe + p + π−

6

1966 Prowse: ΛΛ He → 5 ΛHe + p + π−

1991 Aoki et al .:

13

ΛΛ B → 13 Λ C + π−

6

2001 E373 (KEK): ΛΛ He → 5 ΛHe + p + π−

2001 E906 (BNL):

4

ΛΛ H → 4 Λ He + π− (≈ 400 events!)

= ⇒ Double hypercore program of the PANDA collaboration, GSI!

- p.26

Summary of the hypercore systems

NΛ: attractive → Λ-**Hyper nuclei** from A = 3 - 209

U Λ = −30 MeV with n = n 0

NΣ:

4

Σ He hypercore bound by isospin forces

Σ - atoms: potential is repulsive

NΞ: attractive → 7 Ξ hypercore events

U Ξ = −28 MeV with n = n 0

quasi-free production of Ξ: U Ξ = −18 MeV

ΛΛ: attractive → 5 ΛΛ hypercore measurements

Y Y: Y = Λ, Σ, Ξ, otherwise unknown!

= ⇒ HYP2006 in Mainz, 9.-13. October! Hyperkernel programs: KEK, JLab,

Daphne, J-PARC, and PANDA, HYPHI @FAIR !!! - p.27

Neutron star matter and hyperons

Hyperons appear at n ≈ 2n 0!

non-relativistic potential model (Balberg and Gal, 1997)

Quark-meson coupling model (Pal et al., 1999)

Relativistic field theoretical model (Glendenning, 1985;

Knorren, Prakash, Ellis, 1995; JS and Mishustin, 1996)

Relativistic Hartree – Fock (Huber, Weber, Weigel, Schaab,

1998)

Brueckner – Hartree – Fock (Baldo, Burgio, Schulze, 2000; Vidana

et al., 2000)

Chiral effective Lagrangians (Hanauske et al., 2000)

density-dependent hadron field theory (Hofmann, Keil, Lenske,

2001)

- p.28

Composition in the neutron star

Ξ - appears before n = 3n 0

- p.29

Baryon fraction

10 0

GM1

p

10 −1

10 −2

10 −3

e

µ

Λ Ξ - n

Ξ 0

U Σ

= + 30 MeV

U Ξ

= −18 MeV

10 −4

0.0 0.3 0.6 0.9 1.2 1.5

Density (fm −3)

repulsive potential for Σ hyperons

Σ-hyperons are no longer represented in dense matter

Phase transition to hypermatter

Baryon fraction

10 0

10 −1

10 −2

10 −3

p

e

µ

Λ

Ξ

−

n

Ξ 0 GM1 (0.7)

Σ +

10 −4

0.0 0.3 0.6 0.9 1.2 1.5

Density (fm −3)

First order phase transition!

mixed phase over a wide range of densities

Hyperons (Λ, Ξ 0, Ξ -) appear at the beginning of the mixed phase

- p.30

Hypercompact neutron stars

new stable solution in the

Mass-radius relationship!

Neutron Star Twins:

M hyp ∼ M n but R hyp < r="">

self-tied compact

**Stars** for high attraction

with R = 7 - 8 km

(JSB, Hanauske, Stöcker, Greiner, PRL (2002))

- p.31

Third family of compacts **Stars**n

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¢

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¥¦¤

§¨©

¥¦¤

§¨©

¦ ¥

© ¤

¨

©

¥

¤

¥¦ ¤

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(Schertler, Greiner, JSB, Thoma (2000))

third solution of the TOV equations besides white dwarfs and

Neutron stars! Solution is stable!

generates even more compact ones **Stars** as neutron stars

is possible for every phase transition of the first order

- p.32

Summary:

neutron rich **Cores** in the crust of

Neutron stars

magic bowl closures determine the

Core sequence to the edge of core stability

Nuclear sequence determined only by nuclear masses

= ⇒ FRS @ GSI!

Hyperons occur at twice the nuclear density, only

Λ and Ξ hyperons are present

Occurrence of the hyperons determined by

Hyperon potentials

= ⇒ HypHI, PANDA @ GSI!

- p.33

outlook

Crust of neutron stars and neutron rich **Cores**:

parametric studies of isospin terms in the effective Lagrangian

Extension to the inner crust (with free neutrons)

Neutron separation energies = ⇒ r process

hot stellar matter:

Equation of state for supernovae and neutron star collisions

Distribution of **Cores** (not only for a representative core!)

= ⇒ Influence on dynamic processes in the r-process

Proto-neutron stars, neutrino-wind modeling

= ⇒ νp process

Development of a new chiral model:

calibrated linear sigma model (VMD)

Parity model for baryons

- p.34

Thanks to:

my astronuclear physics group:

Dipl.-Phys. Stefan Rüster

Dipl.-Phys. Mirjam Wietoska

Matthias Hempel

Irina SAGES

and the working group nuclear physics in astrophysics:

ITP: Dipl.-Phys. Thomas Cornelius, Dipl.-Phys. Uwe Heintzmann,

Dr. Lu Guo, Prof. Joachim Maruhn

FIAS: Khin Nyan Linn (M. Sc.), Dr. Thomas Bürvenich,

Prof. Igor Mishustin

CSC: Prof. Stefan Schramm

- p.35

Isolated neutron star RX J1856 (Drake et al. (2002))

next known neutron star

perfect cavity spectrum, no lines!

for ideal emitters: T = 60 eV and R ∞ = 4 - 8 km!

= ⇒ Neutron stars are cold and compact! - p.36

Core sequence for Skyrme models II (Hempel, Rüster, JSB 2005)

Skyrme parameterizations adapted to the binding energies of about

1000 **Cores**n (BRUSLIB database)

Approximation method: Extended Thomas – Fermi model (SkSC4),

Hartree jib plus BCS pair strength (MSk7) and full

Skyrme-Hartree-Fock-Bogoliubov invoice (BSk8)

Core sequence along N = 50 and N = 82: magic numbers (shell closures)

- p.37

Composition of neutron star matter

Baryon fraction

10 0

n

GM1

p

10 −1

10 −2

10 −3

e

µ

Λ Ξ -

Ξ 0

Σ 0 Σ + U Σ

= −30 MeV

U Ξ

= −28 MeV

10 −4

Σ -

0.0 0.3 0.6 0.9 1.2 1.5

Density (fm −3)

attractive potential for Σ and Ξ hyperons

Σ - appears first at n = 2n 0 in front of the Λ

= ⇒ a neutron star is a gigantic hyper nucleus!

- p.38

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