Equation of state and neutron star properties constrained by nuclear ...

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


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


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



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)



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


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)


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



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



Heaviest neutron star: M = 2.01 ± 0.04M�

Demorest et al., Nature (2010), Antoniadis et al., Science (2013)



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



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



If a 2.4 M� neutron star was observed:

Even stronger constraints on high-density equation of state



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


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


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!


Equation of state and neutron star properties constrained by nuclear ...

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