Equation of state and neutron starproperties constrained bynuclear physics and observationIngo Tews, with T. Krüger, K. Hebeler, and A. SchwenkNeutron Stars in Globular Clusters and Triples, December 16, 2013
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 1
Motivation
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 2
Main points
Chiral effective field theory: Epelbaum et al., PPNP (2006) and RMP (2009)
I Systematic basis for nuclear forcesI Based on Standard ModelI Naturally includes many-body forcesI Very successful in calculations of nuclei and nuclear matter
Ab-initio calculations using chiral EFT can be used to constrain equation of statein neutron-rich conditions
Neutron matter applications Krüger, IT, Hebeler, Schwenk, PRC (2013), PLB (2013)
I Symmetry energyI Neutron Star M-R relationI Chiral condensate
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 3
Chiral effective field theory for nuclear forces
Separation of scales:low momenta q � breakdown scale ΛB
Expand in powers of (q/ΛB)n
n=0: leading order (LO),n=2: next-to-leading order (NLO), ...
expansion parameter ≈ 1/3
Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Hammer, Kaiser, Machleidt, Meißner,...December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 4
Chiral effective field theory for nuclear forces
Systematic: can work to desiredaccuracy and obtain error estimates
Consistent: naturally includesmany-body forces
Recently: first complete N3LO neutronmatter calculationIT, Krüger, Hebeler, Schwenk, PRL 2013
In neutron matter:I simpler, only certain parts of the
many-body forces contributeI chiral 3- and 4-neutron forces are
predicted to N3LO
Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Hammer, Kaiser, Machleidt, Meißner,...December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 5
Chiral EFT for neutron matter
0 0.05 0.1 0.15
n [fm-3]
0
5
10
15
20
E/N
[M
eV
]
EM 500 MeVEGM 450/500 MeVEGM 450/700 MeV
Neutron matter energy per particle:
EN
(n0) = 14.1 − 21.0 MeV
Includes theoretical uncertainties:I Variation of coupling constantsI Includes uncertainties in
calculational scheme
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 6
Chiral EFT for neutron matter
0 0.05 0.1 0.15
n [fm-3]
0
5
10
15
20
E/N
[M
eV
]
EM 500 MeVEGM 450/500 MeVEGM 450/700 MeVNLO lattice (2009)
QMC (2010)
APR (1998)
GCR (2012)
Universal properties at low densitiesI agreement with
Quantum Monte Carlo andNLO lattice calculationsGezerlis, Carlson, PRC (2010)
Epelbaum et al., EPJ A (2009)
Good agreement with othercalculations at higher densities
I but in thoseno theoretical uncertaintiesAkmal et al., PRC (1998)
Gandolfi et al., PRC (2012)
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 6
Chiral EFT for neutron matter
0 0.05 0.1 0.15
n [fm-3]
0
5
10
15
20
E/N
[M
eV
]
this workLS 180LS 220
LS 375FSU2.1NL3TM1DD2SFHoSFHx
Chiral EFT constrainsneutron-matter energy per particle
Rules out manymodel equations of stateKrüger, IT, Hebeler, Schwenk, PRC (2013)
Lines from Hempel, Lattimer, G. Shen
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 7
Impact on Symmetry Energy
28 30 32 34 36
SV [MeV]
20
40
60
80
L [
MeV
]
Tamii et al. (2011)
Hebeler et al. (2010)
N3LO
(this work)
Kor
tela
inen
et al
. (20
10)
Neutron matter band puts constraintson symmetry energy and itsdensity dependenceHebeler et al., PRL (2010)
I SV = 28.9 − 34.9 MeVI L = 43.0 − 66.6 MeV
Good agreement withexperimental constraintsDipole polarizability - Tamii et al., PRL (2011)
Nuclear masses - Kortelainen et al., PRC (2010)
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 8
Impact on Neutron Stars
Equation of state for neutron star matter: extend results to small Ye,p
Hebeler et al., PRL (2010) and APJ (2013)
Agrees with standard crust EOSafter inclusion of many-body forces
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 9
Impact on Neutron Stars
Equation of state for neutron star matter: extend results to small Ye,p
Hebeler et al., PRL (2010) and APJ (2013)
Agrees with standard crust EOSafter inclusion of many-body forces
13.0 13.5 14.0
log 10 [g / cm3]
31
32
33
34
35
36
37
log
10P
[d
yn
e/c
m2]
1
2
3
with c i uncertainties
crust
crust EOS (BPS)
neutron star matter
12 231
Extend to higher densities usingpolytropic expansion
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 9
Impact on Neutron Stars
Heaviest neutron star: M = 2.01 ± 0.04M�
Demorest et al., Nature (2010), Antoniadis et al., Science (2013)
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 10
Impact on Neutron Stars
Constrain resulting EOS: causality and heaviest observed 1.97 M� neutron star
Chiral EFT interactions provide strong constraints for EOS
Rule out many model equations of state
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 11
Impact on Neutron Stars
8 10 12 14 16
Radius [km]
0
0.5
1
1.5
2
2.5
3
Mas
s [M
°.]
this workRG evolved
causa
lity
Radius for 1.4 M� neutron star:I R = 9.7 − 13.9 km
Maximum mass neutron star:I Mmax ≤ 3.05M� (14km)
Uncertainties from many-body forcesand polytropic expansion
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 12
Impact on Neutron Stars
If a 2.4 M� neutron star was observed:
Even stronger constraints on high-density equation of state
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 13
Impact on Neutron Stars
8 10 12 14 16Radius [km]
0
0.5
1
1.5
2
2.5
3
Mas
s [M
0.]
this work
causa
lity
Radius for 1.4 M� neutron star:I R = 11.5 − 13.9 km
Maximum mass neutron star:I Mmax ≤ 3.05M� (14km)
Uncertainties from many-body forcesand polytropic expansion
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 14
Chiral Condensate
0 0.05 0.1 0.15 0.2
n [fm-3]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
<q_
q>
n_____
<q_
q>
0
0 0.2 0.4 0.6 0.8 1 1.2
n [n0]
EGM 450/500 MeVEGM 450/700 MeVleading term σπN
Chiral condensate is order parameterfor phase transition to quark matter
In neutron matter:I interaction impede phase
transitionI phase transition to
quark matter unlikely
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 15
Summary
Chiral EFT constrains neutron matter equation of state:I Controlled theoretical uncertaintiesI Inclusion of many-body forces
Applications of neutron matter resultsI Symmetry energyI Neutron star M-R relationI Chiral condensate
Work with T. Krüger, K. Hebeler, and A. Schwenk
Thanks for your attention!
December 16, 2013 | Institut für Kernphysik | Theory Center | Ingo Tews | 16