Nuclear Equation of State: Combining Neutron-Star Merger and Laboratory Constraints

Betty Tsang, NSCL/MSU

tsangm at msu.edu

DNP workshop, Oct 13-17 2019

Crystal City, Virginia

Outline:Part I : supra saturation densityPart II: sub saturation density

mailto:tsangm@msu.edu

Equation of State of Nuclei – Liquid drop ModelP

roto

nImage by Andy Sproles, ORNL 2/3

V SB a A a A 3/1)1(

A

ZZaC

A

ZAasym

2)2(

Hu

bb

le S

T

Neutron star is a

giant nucleus with

(~1057n + ~1056p)

Element Esym/B

16O 0%

208Pb 3.8%

132Sn 4.6%

NS 40-57%

Neutron

Symmetry Energy from nuclear structure and reaction dynamics P

roto

nImage by Andy Sproles, ORNL

2/3

V SB a A a A 3/1)1(

A

ZZaC

A

ZAasym

2)2(

Hu

bb

le

ST

Equation of State of infinite nuclear matter

E/A (,) = E/A (,0) + 2S()

Femto-nova explosion created by Heavy Ion collisions

= (n- p)/ (n+ p) = (N-Z)/A

...183

)(

2

0

0

0

0

sym

o

KLSS sym

B

symP

EL

B0

0

33

0

Neutron

pressure contours

density contours

Au+Au collisions E/A = 1 GeVHow to squeeze nuclear matter

Observable:Particle emission patterns Transverse & Squeeze-out flow

Transport models:Density Pressure

Science 298, 1592 (2002)

Determination of symmetric matter EOS from heavy-ion collisionsDanielewicz et al., Science 298,1592 (2002)

1

10

100

1 1.5 2 2.5 3 3.5 4 4.5 5

neutron matter

Akmalav14uvIINL3DDFermi GasExp.+Asy_softExp.+Asy_stiff

P (

MeV

/fm

3)

/0

1

10

100

1 1.5 2 2.5 3 3.5 4 4.5 5

symmetric matter

RMF:NL3Fermi gasBogutaAkmalK=210 MeVK=300 MeVexperiment

P (

MeV

/fm

3)

/0

Confirmed by GSI Fourpi results (2016)

EOS/LBL

Pre

ssu

re (

MeV

/fm

3 )

Two observables from the high pressure formed in the overlap region:

Nucleons are “squezedout” above and below the reaction plane.

Nucleons from residues are deflected sideways in the reaction plane

Transport Models

Prakash 1988

S()stiff=12.7×(ρ/ρ0)2/3+38×(ρ/ρ0)

2/(1+ρ/ρ0)

S()soft=12.7× (ρ/ρ0)2/3+19× (ρ/ρ0)

1/2

+ symmetry pressure

Equation of States from Astrophysics, Experiments and Theory

Steiner et al., APJL 765:L5 (2013)LIGO: PRL 121.161101(2018)

X-ray bursts binary

GW170817

Science 298, 1592 (2002)

Phys. Lett. B 795, 533 (2019)

https://arxiv.org/ct?url=https://dx.doi.org/10.1103/PhysRevLett.121.161101&v=6a102e11

S()stiff=K.E.+38×(ρ/ρ0)2/(1+ρ/ρ0)

S()soft=K.E.+19× (ρ/ρ0)1/2

Density Dependence of Symmetry Pressure

Psym=PPNM-PSNM

Symmetric nuclear matter: Science 298, 1592 (2002)

“Pure” neutron matter fromGW170817(2018)

Symmetry Pressure

PLB 795, 533 (2019)

1. Crust: /0

Skyrme Interactions – n effective mass

C.Y. Tsang & B.A. Brown, arXiv: 1908.11824

CSkP family

Does GW correlate with quality of Skyrmes?>50% are within GW constraintDutra: PRC85, 035201 (2012)11 conditionsBest 16 (CSkP) and 5 (red stars) are inside GW.

C.Y. TsangF. Fattoyev

Neutron star calculations using NP EoS (Skyrme interactions)

Phys. Lett. B 796, 10 (2019)

R6.26

R6.63

PLB 796, 10 (2019)

Which Density to explore ?

Tommy Tsang

What observable to measure?

Tommy Tsang

What observable to measure?

Pions decayed from D formed at early time and reflects the high density regionPredicted to be sensitive to symmetry energy

Double Ratios: 𝑂(132𝑆𝑛+124𝑆𝑛)

𝑂(108𝑆𝑛+112𝑆𝑛)Reduce systematics both in experiments and in theories

10

%

B.A. Li, PRC 71, 014608 (2005)

132𝑆𝑛 + 124𝑆𝑛E/A=400 MeV

D Branching Ratio

p p0 p

nn 5 1 0

pp 0 1 5

np or pn 1 4 1All numbers ÷ by 6

https://groups.nscl.msu.edu/hira/cosmic/SpiritTPC.html“Cosmic and Nuclear Collision VR” in Google Play Store

https://groups.nscl.msu.edu/hira/cosmic/SpiritTPC.html

https://groups.nscl.msu.edu/hira/cosmic/SpiritTPC.html“Cosmic and Nuclear Collision VR” in Google Play Store

https://groups.nscl.msu.edu/hira/cosmic/SpiritTPC.html“Cosmic and Nuclear Collision VR” in Google Play Store

https://groups.nscl.msu.edu/hira/cosmic/SpiritTPC.htmlhttps://groups.nscl.msu.edu/hira/cosmic/SpiritTPC.html

SETUP Primary Beam Target Ebeam/A sys evt(M) 2016124Xe

108Sn 112Sn 269 0.09 8 4/30-5/4

112Sn 124Sn 270 0.15 5 5/4-5/6

238Ｕ132Sn 124Sn 269 0.22 9 5/25-5/29

124Sn 112Sn 270 0.15 5 5/30-6/1

Z=1,2,3 100, 200 0.6 6/1

https://groups.nscl.msu.edu/hira/cosmic/SpiritTPC.html“Cosmic and Nuclear Collision VR” in Google Play Store

Shane, NIMA 784, 517; Barney, to be publishedTangwancharoen, NIMA 852,44, Lasko, NIMA 856, 92, Isobe, NIMA 899, 43, Jhang, JKPS 69, 144,

https://groups.nscl.msu.edu/hira/cosmic/SpiritTPC.html

Beam pipe

Types of events (top views: x vs. z)

, Slide 17

Target• Reaction upstream: before target

• Reaction on target: good eventActive Veto

• Reaction with gas inside TPC:

Active target events;

x(m

m)

z(mm)

Analysis challengesLarge amount of data (270 Tb)Tracking problems near target & WallElectronic saturation & Dynamic range from pions to Li (Estee, NIM) Space charge effect (C.Y. Tsang, NIM)Quality of track reconstruction, etc.

Analysis group @ MSU

Lynch Jhang Wang Barney Estee Tsang

Reference TQC1(T) TQC2(L) TQC2(T) b selectionAngular

selection.

Beamselection

Y(π

+) 1

32Sn+

124Sn

Inject π- MC Track

Efficiency Determination

Different analysis conditions

Efficiency corrected

Estee, tsang & Wang

0.5

0.6

0.7

0.8

0.9

(Arb

. Un

its)

Analysis of mirror systems – systematic errors

π-/π+ ratio shows symmetric in forward and backward rapidity

regions as expected.

Beam Target Ebeam/A sys108Sn 112Sn 269 0.09112Sn 124Sn 270 0.15132Sn 124Sn 269 0.22124Sn 112Sn 270 0.15

Jon Barney, PhD thesis, 2019

112Sn 124Sn

(Arb

. Un

its)

Note: Please do not quote any unpublished TPC data or transport calculation results.

Experimental ResultsLynch Jhang Wang

Barney Estee Tsang

Double Ratios: 𝑂(132𝑆𝑛 + 124𝑆𝑛)

𝑂(108𝑆𝑛 + 112𝑆𝑛)

Observable:

pion emission

Transverse &

Squeeze-out flow

Transport models:

Density & Pressure

for symmetric &

pure n-matter

Model

Assumptions

Mean Fields—

EoS

NN Collision

m*

…

Role of Transport modelsYong Jia Wang

Comparison to analytical limits ~4%Ono et al., PRC (in press)

BU

U-V

M

IBU

U

IQM

D_B

NU

LQM

D_I

MP

JAM

JQM

D

pB

UU

RV

UU

SMA

SH

TuQ

MD

4%

Code Evaluation Project III – controlled box simulationsw/o mean field and Pauli Blocking

Y(p)/

Y(p)

HIC transport code predictions

Variations between codes (+15%) > effect of symmetry energy (~5%)

Y(p

- /p

+ )1

32

+1

24

/Y(p

- /p

+)1

08

+11

2

Code 6Code 5Code 4Code 2 Code 3Code 1

Zuhai, 27-28, Sept, 2019

Pre-NuSym2019 meeting

Transport Models Evaluation Project Meetings

More work on model development and searching for more sensitive observables

Experiment measurements include: pions & charge particles, yields, spectra, flow

Crust-Core Transition

Lynch

and

Tsang, arX

iv:18

05

.107

57 5

.10

75

7 &

20

19

Crust core determination: Ducoin et al., PRC, 83 (2011) 045810.

Summary and OutlookAt low density, experimental data yields the density dependence of the symmetry

energy and allows extraction of the crust-core transition density and pressure.

New HIC experiments with Bayesian analysis will allow extraction of both the density and momentum dependence of isovector mean mean field potentials.

At supra-saturation density, connect & combine Nuclear Physics experimental EoS results to the neutron star merger results to extract improved EoSs for asymmetric matter and density dependence of symmetry energy.

Improvement can come from heavy ion reaction in the density range of ~20:

New experimental results from SpRIT & new experimental programs in FRIB & upgrade!

Improve the predictive power of transport theories.

• Continue the code evaluation project which is making significant progress.

NP (experiment and theory) should make connections to LIGO community and vice versa e.g. Use NP EoS as priors for GW analysis?

Needs collaborations and young scientists to join (especially PD and students)(tsangm AT msu.edu)