Neutron star properties from nuclear reactions...Neutron star properties from nuclear reactions Y. Leifels GSI Helmholtzzentrum für Schwerionenforschung GmbH Darmstadt Rußbach School

Neutron star properties from nuclearreactions

Y. LeifelsGSI Helmholtzzentrum für Schwerionenforschung GmbHDarmstadt

Rußbach School on Nuclear Astrophysics,

12-18 March 2017

Outline

Introduction Neutron stars and the equation of state of neutron matter

Heavy ion reactions and the equation of state of symmetric nuclear matter

The Link constraining the symmetry energy by laboratory experiments

Conclusion Outlook

Yvonne Leifels - Rußbach 2017

Phase diagram of QCD matter


Liquid gas coexistence

early universe at zero density and high temperature neutron star at small temperature and high density first order phase transition at high density

From nuclei to nuclear matter:Nuclear matter equation of state


E

AZN

pair3/1

2

c

2

sym3/2

surfvol EAZa

A)ZN(aAaAaE

Finite nuclei:

Infinite nuclear matter:

Symmetric matter δ=0

Neutron matter δ=1

0CT E),0T,(E),T,(E),T,(E thermal compressional

density dependentlocal potential:)(U

dUTAE )(1)0,(/

Esym

ρ (MeV/fm3)

The equation of state of neutron and symmetric matter


Esym

Neutron matter

Fuchs and Wolter, EPJA 30 (2006)

Symmetric matter

The nuclear matter equation of state (EOS) describes the relation between density, pressure, temperature, energy, and isospin asymmetry δ = (ρn–ρp)/ρ

2sym )(E)0,(A

E),(AE

Theoretical tools ab initio methods: use NN

interaction → solve many body problem

effective theories: parametrizing coupling constants → solve self-consistent mean field equations

Esym

Neutron matter


Symmetric matter

δ = 1

δ = 0Nuclear structure

Radioactive beams

HICs at low energies

Equation of state of nuclear matter


understanding heavy ion reactions: T= 5 MeV – 180 MeV..., ρ = 10-3 – 10...ρ0 mass: 6.540 · 10-24 kg size: 1.4 · 10-14 m life time: 3 -100 · 10-24 s

Equation of state of nuclear matter

understanding compact objects in astrophysics global properties of neutron stars: T = 0, ρ = 10-3 – 10ρ0 mass: 3 · 1030 kg radius: 1 · 104 m life time: essentially infinity

Yvonne Leifels - Rußbach 2017C

redi

t: D

anie

l Pric

e (U

/Exe

ter)

and

S

teph

an R

ossw

og(In

t. U

/Bre

men

)

NEUTRON STARS



Neutron stars

produced in core collapse supernovae

compact, massive objects: radius ≈ 10 km, mass 1-2 Mʘ

extreme densities, several times normal nuclear matter density ρ>>ρ0 = 2.5·1014g/cm3

in the middle of the CrabNebular: a fast rotatingneutron star

bulk matter in mechanical, thermal and beta equilibrium

Observing neutron stars (compilation from Özel and Freire)


nearly 2000 pulsars known of which 140 are binaries

average mass 1.44 Mʘ heaviest neutron stars

PSR J1614-2230 Mass: (1.97 0.04) M P. Demorest et al. 2010 Shapiro delay

PSR J0348+0432 Mass: (2.01 0.04) M J. Antoniadis et al. 2013 White dwarf spectroscopy

Neutron star mass – radius relation


P.B. Demorest et. al, doi:10.1038/nature09466J. M. Lattimer, M. Prakash, Astro.. J. 550, 426–442 (2001)

nucleons nucleons + exotic strangeness

solving the Tolman-Oppenheimer-Volkoff equation (describing neutron star in hydrostatic equilibrium) for specific equation of state

Schwarzschild limit (GR): R> 2GM = RS causality limit for EOS: R > 3GM mass limit from PSR J1614-2230 (red band): M=(1.97 0.04) M

X-Ray burster


Credit: Rob Hyns

binary systems of neutron starwith small mass star

normal companion feedingaccretion disk

close to the neutron star crustmaterial is heated and emittingX-Rays

outbursts of X-Rays due tounstable nuclear burning ofaccreted matter on NS surface

analysis of red-shifted X-Ray spectra to determine the radiusof the NS

Mass radius – constraints from X-Ray bursters and binaries


F. Ozel et al.http://arxiv.org/abs/1505.05155v1

J1614-2230 Demorest et al. 2010

J0348+0432Antoniadis et al. 2013

X-ray emission from binary accreting neutron stars normal companion feeding

accretion disk close to the neutron star

crust material is heatedand emitting X-Rays

neutron star radii R = 9 – 12 km

Future projects in X-ray astronomy:

Athena (ESA 2028)

EQUATION OF STATE OF NEUTRON MATTER


Equation of state of neutron matter


K. Hebeler et al.,APJ 773 (2013)

NS = 1.97 Mʘ

NS = 2.4 Mʘ

Neutron star structure (F. Weber)


low densities: lattice of neutrons (outer crust) higher densities: neutron fluid (inner crust, neutron matter) high densities: production of short-lived final states involving high-energetic

n’s in initial state very high densities: even pure quark matter predicted

HEAVY ION REACTIONS


HICs: Characteristics


below or close to Fermi Energy ~ 30 MeV/umean field dominating

>~100 MeV/unuclear collisions getting dominant

phase transition to quark gluon plasma

quark matter

280 MeV/u pion productionresonance matter

HICs: Characteristics


reaching high densities, several ρ0

thermal pressure and creation of particles

fast, transient state, several fm/c

non-equilibrium, dynamical system

different N/Z ratio access to properties by

models

compressionparticle creation

AuAu

thermal γ

p,n,d,t,α...Φ,Ξ,Ω

π,K,η

ρ→e±

expansionfreeze-out

resonance decays

Au+Au, 1 GeV/u

FOPI@GSI

FOPI detector at GSI


FOPI@GSI

HICs: Models


Statistical/thermalmodels

employing equilibrium concepts

Fluid dynamics analytical or quasi-analytical solutionsEOS is input quantity

idealized continuum description assuming local equilibrium

Microscopic transport two different approachesmean-field/NN potential as input quantity

elastic and inelastic cross sectionsin-Medium effects

off-shell particle propagation

Transport model predictions


P. D

anie

lew

icz

et a

l.S

cien

ce 2

98, 1

592

(200

2)

HICs: Maximum densities reached


higher incident energy → higher density

Bao-An Li, PRL 88, 192701 (2002)

EQUATION OF STATE OF NUCLEAR MATTER


Equation of state of symmetric nuclear matter


infinite symmetric nuclear matter N=Z ground state properties: ρ0 = 0.16 N/fm3 and E(ρ0) = -16 MeV

expansion in density:

compression modulus: = 231± 5 MeV from GMR

...)(18

E)0,(E 2020

0

2

22 )0,(/9

TAE

κ = 380 MeV

κ= 200 MeV

Consequences of different EOS


a “soft” equation of state yields more compression than a hard one a “hard” equation of state results in more pressure observables which are sensitive to either density or pressure

Density

PressureIQMD: C. Hartnack et al.

udd

udu

uds

su

ddu

np

n

K+

Λ

Kaon production is sensitive to density


Kaon production at low incident energies (

Kaon production is a density meter


Sturm et al,PRL (2001)

nuclear matter is compressed up to 2-3 ρ0 comparisons of experimental data with different model

predictions (!) favor a soft equation of state

from KAOS@GSI

Collective flows – The manometer


Elliptic flow v2

Side flow v1

R

vvddN )2cos(2)cos(21~ 21

0°0° 0° 180°0°-180° 0°

Discovery at BevalacH.A. Gustafsson, et al., Phys. Rev. Lett. 52 (1984) 1590.R.E. Renfordt, et al., Phys. Rev. Lett. 53 (1984) 763.

z

z

pEpEln

21Yrapidity:

side flow

elliptic flow

Determination of the impact parameter vector b


Modulus: number of particles ejected

correlated to impact parameter

Direction: momentum vectors of emitted

particles point - on the average -into the reaction plane

Side and elliptic flow in mid-central Au+Au collisions


Au+Au 1A GeV 3.5

Collective flows act as manometers


P. D

anie

lew

icz

et a

l.S

cien

ce 2

98, 1

592

(200

2)

side flow

elliptic flow

additional constraints needed on momentum dependence of NN potential and in-medium cross sections

newer data on elliptic flow in agreement with a soft EOS (SM)→ most available data and Kaon production is reasonably described by this model (input parameters constrained with experimental data)

Reisdorf et al,NPA 876 (2012)

Equation of state of symmetric matter


Kaon production is sensitive to density Collective flow of particles sensitive to pressure experimental data at intermediate energies suggest that the EOS for

symmetric nuclear matter at 2-3 ρ0 is soft: κ = 200-230 MeV

B. Lynch, Prog. Part. Nucl. Phys. 62, (2009) 427

SYMMETRY ENERGY


The equation of state of neutron and symmetric matter


Esym

Neutron matter


Symmetric matter

The nuclear matter equation of state (EOS) describes the relation between density, pressure, temperature, energy, and isospin asymmetry δ = (ρn–ρp)/ρ

2sym )(E)0,(A

E),(AE

pair3/1

2

c

2

sym

3/2surfvol

EAZa

A)ZN(a

AaAaE

Finite nuclei:

Bethe-Weizsäcker mass formula

δ = 1

δ = 0

Nuclear symmetry energy


Fuchs and Wolter,EPJA 30 (2006)

Soft

Super soft

Hard

0d

)(dE3L sym0

Slope parameter

Largely unconstrained at high densities → related to uncertainty of three-body and tensor forces at high density

....18

K3LE)(E

2

0

0sym

0

00,symsym

J. LattimerAnnu. Rev. Nucl. Part.Sci 2012, 62:485

J. Lattimer, M. Prakash, Phys. Rep. 621 (2016) 127

L (

MeV

)

S0 (MeV)

Experimental constraints to the Symmetry energy


Sensitive observables that are or will bemore extensively explored : masses: Isobaric Analog States (IAS) isospin diffusion between nuclei of

different N/Z in peripheral HIC Sn+Sn

neutron skins: scattering with electrons, anti-

protons excitation of nuclei: Pygmy

resonances, dipolpolarizability... neutron and proton transverse and

elliptical flow fragmentation of hot nucleiNuclear physics and astrophysics constraints white area experimentally allowed

overlap region

Experimental constraints to the Symmetry Energy


Observables below !!! and at saturation density

neutron stars at high densities

?

cluster/HIC Sn+Sn/ IAS: Horrowitz et al. JPhG 41 (2014)Brown: arXiv:1308.3664Zhang: PLB 726 (2013)

Symmetry energy at high densities


hard

softBao-An Li, PRL 88, 192701 (2002)δ

= (ρ

n–ρ p

)/ρ.

Symmetry energy influences n/p content of the dense zone less/more neutron rich if symmetry energy is hard/soft needs observables which are testing ρn and ρp Methods compare systems with different isospin content 132Sn+124Sn ↔ 112Sn+112Sn study isospin partners n/p, t/3He, π-/π+, K+/K0

Elliptic flow of neutrons and protons


Elliptic flow v2 of n/p UrQMD (Q. Li et al.) predicts:

neutron flow much larger

neutron, proton flow equal

Towards model invariance:tested stability with different models:

observation is robust various microscopic models tested independent on input parameters

M.D. Cozma et al., arXiv:1305.5417P. Russotto et al., PLB 267 (2010) Y. Wang et al.,PRC 89, 044603 (2014)

“hard” Esym(ρ)

“soft” Esym(ρ) -v2

-v2

UrQMD: Qingfeng Li et al.Data. W. Reisdorf et al.

ASY – EOS Experiment

n/charged particles

impact parameter reaction planereaction planebackground

charged particles

background measurements for neutrons (shadow bars)

400A MeV Au+Au, 96Zr+Zr, 96Ru+Ru at GSI

TOF-Wall: 96 plasticbars

CHIMERA: 352CsJ(Tl), 16 siliconpad detectors

μ-Ball: 50 CsJ(Tl)


Elliptic flow ratio of neutrons and charged particle


parametrization for SE used in the UrQMD model: Esym = Esympot+Esymkin = 22MeV·(ρ/ρ0)

γ+12MeV·(ρ/ρ0)2/3

systematic errors corrected: γ = 0.72 ± 0.19 slope parameter: L = 72 ± 13 MeV, Esym(ρ0) = 34 MeV slope parameter: L = 63 ± 11 MeV, Esym(ρ0) = 31 MeV

P. R

usso

tto e

t al.,

PR

C (2

017)

Characteristic density regime


deducing density at which the difference between neutron and charged particle (p, H, all charged particles) flow is originating by using transport models

slope of Esym(ρ) constrained in this density regime!

Resulting symmetry energy


equation of state of symmetric nuclear matter symmetry energy

can be constrained by the systematic study of comparison of the flow of neutrons and charged particles

P. Russotto et al., PLB 267 (2010) P. Russotto et al., PRC (2017)

A. LeFevre et al., NPA (2016)

symmetry energy influences n/p ratio → nn, np, pp collisions

hard SE

inconsistent with results from neutron and proton flow

models are inconclusivesoft ↔ hard ↔ no dependence on SE

medium pion optical potential, self energies,

different for π- and π+ production via ∆ resonances, potential s- vs p-wave production

hard SE

It is not always that simple: Pion production


hard

soft

Au+Au, b < 2.5 fm

Data: W. Reisdorf et al., NPA 781 (2007)Calculations: Z. Xiao et al, PRL 102, (2009)

)(Y)(Y

pn

,

,0

The trick: changing the isospin of the colliding system


compare π- production in 132Sn+124Sn and 108Sn+112Sn different in-medium properties for pions not relevant no Coulomb effects experiment just done at Riken from the SPIRIT collaboration

B. Z

hang

et a

l., P

RC

(201

7)

Measuring pion production with radioactive beams

SAMURAI TPC

RAONSPIRIT TPCin SAMURAI Magnet

Charged particles and neutronsin HICs upto 400 AMeV Rectangular TPC With 12000 pads in x-z direction Active target option Inside a magnet (→ charged pions) Neutron detector


CONCLUSION AND OUTLOOK


Conclusion


Kaon and charged particle flow give consistent constraints on the symmetric part of the EOS soft κ = 200-230 MeV models „benchmarked“

extend to higher energies planned models predict observables of heavy ion

collisions give constraints to the nuclear symmetry energy at high densities

at the moment only very few measurements have been done n/p/charged particle flow in Au+Au

done Pion production just measured

robust observables model invariant ratios double ratios

Close collaboration between experiments and theory important Esym(ρ0) (MeV)

L (

MeV

)

J. Lattimer, M. Prakash, Phys. Rep. 621 (2016) 127

OUTLOOK


FAIR in 2025


THANK YOU FOR YOUR ATTENTION

Neutron star properties from nuclear reactions...Neutron star properties from nuclear reactions Y. Leifels GSI Helmholtzzentrum für Schwerionenforschung GmbH Darmstadt Rußbach School

Documents