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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:[email protected]
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)