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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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Fuchs and Wolter, EPJA 30 (2006)
Symmetric matter
δ = 1
δ = 0Nuclear structure
Radioactive beams
HICs at low energies
Equation of state of nuclear matter
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
Yvonne Leifels - Rußbach 2017
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)
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
Equation of state of neutron matter
Yvonne Leifels - Rußbach 2017
K. Hebeler et al.,APJ 773 (2013)
NS = 1.97 Mʘ
NS = 2.4 Mʘ
Neutron star structure (F. Weber)
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
HICs: Characteristics
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
FOPI@GSI
HICs: Models
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
P. D
anie
lew
icz
et a
l.S
cien
ce 2
98, 1
592
(200
2)
HICs: Maximum densities reached
Yvonne Leifels - Rußbach 2017
higher incident energy → higher density
Bao-An Li, PRL 88, 192701 (2002)
EQUATION OF STATE OF NUCLEAR MATTER
Yvonne Leifels - Rußbach 2017
Equation of state of symmetric nuclear matter
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
Kaon production at low incident energies (
Kaon production is a density meter
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
Au+Au 1A GeV 3.5
Collective flows act as manometers
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
The equation of state of neutron and symmetric matter
Yvonne Leifels - Rußbach 2017
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
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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)
Yvonne Leifels - Rußbach 2017
Elliptic flow ratio of neutrons and charged particle
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
CONCLUSION AND OUTLOOK
Yvonne Leifels - Rußbach 2017
Conclusion
Yvonne Leifels - Rußbach 2017
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
Yvonne Leifels - Rußbach 2017
FAIR in 2025
Yvonne Leifels - Rußbach 2017
THANK YOU FOR YOUR ATTENTION