Core EoS developments in the NewCompStar...

Arnau Rios HuguetLecturer in Nuclear Theory

Department of PhysicsUniversity of Surrey

Core EoS developments in the NewCompStar era

Crab Pulsar

ⓒN

ASA NewCompStar Workshop, Catania, 7 November 2017

Summary

•Motivation

•Phenomenological models

•Ab initio developments

•Exotic phases •Hyperons

•Polarizations

•GW170817: EoS impact

2

Nuclear physics 2010s

3

τ1/2 > 1 Gy1 year < τ1/2 < 1 Gy1 day < τ1/2 < 1 year1 hour < τ1/2 < 1 day2 mins < τ1/2 < 1 hour3 s < τ1/2 < 2 mins0.1 s < τ1/2 < 3 sτ1/2 < 0.1 s

Segré chart

N

Z


3


Segré chart

N

ZUncharted territory, to

be explored at RIB facilities

Heavy Ion Research Facility Lanzhou

VECC Kolkata

Sao Paulo Pelletron


3


Segré chart

N

ZUncharted territory, to

be explored at RIB facilities

Segre chart time evolution

Isotope discovery rate ~30 /year

Thoenessen & Sherrill, Nature (Comments) 473, 25 (2011) Thoenessen, 2014 update, arXiv:1501.06761

https://people.nscl.msu.edu/~thoennes/isotopes/

•Nuclei comprise 99.9% of matter we see in the Universe & fuel stars •3 of 4 fundamental forces are relevant! •Nuclei exhibit all modern physics phenomena

Theoretical nuclear physics

5

Two philosophies

DOE/NSF Nuclear Science Advisory Committe, The Frontiers of Nuclear Science: A Long-Range Plan, 2007.


5

Two philosophies


•Phenomenological: nuclear properties from energy density functional

Phenomenological DFT charts

6

Erler, Birge, Kortelainen, Nazarewicz et al., Nature 486, 508 (2012)

6900± 500syst


7

Two philosophies



7

Two philosophies



•Ab initio: from QCD nucleon-nucleon force to nuclei?

Hagen, Ekstrom et al, Nature Physics 12 186 (2016)

Ab initio in 2016

8

Coupled cluster calculations of 48Ca

Equation of State: Pauli+interactions Mass-Radius relation

Jim Lattimer

Neutron matter & neutron stars

9

dp

dr“ ´G

c2pm ` 4⇡pr3qp✏ ` pqrpr ´ 2Gm{c2q

dm

dr“ 4⇡

c2✏r2

Tolman-Oppenheimer-Volkov equations

Equation of State: Pauli+interactions Mass-Radius relation

Jim Lattimer


9

dp

dr“ ´G


dm

dr“ 4⇡

c2✏r2


Nuclear quantity

Astro quantity


9

dp

dr“ ´G


dm

dr“ 4⇡

c2✏r2


3 X-ray bursts, 3 X-ray binaries & 1 isolated NS

Inferred EoS and M-R relation from observations

Steiner, Lattimer & Brown, ApJ 722, 33 (2010)

Summary

•Motivation




•Polarizations


10

EoS parameters

11

pp"q “?

" “ ⇢E

App⇢q “ ⇢2

BE{AB⇢

E

Ap⇢,�q “?

Astro observable

Nuclear physics observable

E

Ap⇢,�q “ E

Ap⇢0,�q

` 3⇢0BE{A

B⇢ˇˇ⇢0

ˆ⇢ ´ ⇢03⇢0

˙

` 9⇢202!

B2E{AB⇢2

ˇˇ⇢0

ˆ⇢ ´ ⇢03⇢0

˙2

` ¨ ¨ ¨

Taylor expansion

EoS parameters

11

pp"q “?

" “ ⇢E

App⇢q “ ⇢2

BE{AB⇢

E

Ap⇢,�q “?

Astro observable


E

Ap⇢,�q “ E

Ap⇢0, 0q ` 1

2!

B2E{AB�2

ˇˇ⇢0,�“0

�2

` 3⇢02!

B3E{AB�2B⇢

ˇˇ⇢0,�“0

�2

ˆ⇢ ´ ⇢03⇢0

˙

` 9⇢202!

"B2E{AB⇢2

ˇˇ⇢0,�“0

` 1

2!

B4E{AB⇢2�2

ˇˇ⇢0,�“0

�2

* ˆ⇢ ´ ⇢03⇢0

˙2

` ¨ ¨ ¨

Taylor expansion

EoS parameters

11

pp"q “?

" “ ⇢E

App⇢q “ ⇢2

BE{AB⇢

E

Ap⇢,�q “?

Astro observable


Taylor expansion

E

Ap⇢,�q “ E0 ` Esym�2

` L�2

ˆ⇢ ´ ⇢03⇢0

˙

` 1

2!

K0 ` Ksym�2

( ˆ⇢ ´ ⇢03⇢0

˙2

` ¨ ¨ ¨

What do we know?EoS parameters

12

E

Ap⇢,�q “ E0 ` Esym�2 ` L�2

ˆ⇢ ´ ⇢03⇢0

˙` 1

2!

K0 ` Ksym�2

( ˆ⇢ ´ ⇢03⇢0

˙2

` ¨ ¨ ¨

Quantity Experimental probe Value Decade

ρ0 (e,e’) elastic scattering 0.16 fm-3 ~1940s

E0 E/A nuclear systematics -16 MeV ~1970s

K0 GMR resonance in N~Z 240±20 MeV ~1980s

Esym IAS, Isospin Diffusion, 32±2 MeV 2000s

L n skins, Isospin Diffusion, IVMR 45±15 MeV 2010s

Kτ IVMR -550±100 MeV 2020s

Symmetry energy and slope

Lattimer & Lim, ApJ 771 51 (2013)

Model-independent EoS bounds

13

•Nuclear physics bounds exist

•Help constrain EoS

•Allowed region is small

24 26 28 30 32 34 36 38 40

S0 [MeV]

0

20

40

60

80

100

120

L[ M

eV]

Allowed

Excluded

Mas

ses

Sn neutron skin

Pbdip

olepo

lariza

bility

HIC

GDR

IAS+

�R

UGUG analytic

Unitary gas

Tews, Lattimer, Okinishi, Kolomeitsev, ApJ 848 105 (2017); arXiv:1611.07133

Model-independent EoS bounds

14

EUG “ 3

5⇠"F

⇠ « 0.37

Bertsch kFa " 1

Cold gas experiments show:

⇠ « 0.37 ´ 0.93pkFaq´1

What if ENM>EUG?

S0 “ L

6

«1 ` 2

ˆ2E0

UGL

˙3{2�´ E0

Margueron, Hoffmann Casalli, Gulminelli, arxiv:1708.06894; Chatterjee, Gulminelli, Raduta, Margueron, arXiv:1709.00189

See J. Margueron’s talk

Metamodelling the EoS

15

•Meta-modelling is used often in other fields •General nuclear physics knowledge explored •Insight gained on averages & correlations

https://arxiv.org/abs/1709.00189

Summary

•Motivation




•Polarizations


16

Complications

17

NN interaction is not unique ...but phase-shift equivalent!

0

30

60

90

δ [

deg

]

Nij

CDBonnAv18N3LONij93

0 50 100 150 200 250E [MeV]

0

60

120

180

δ [

deg

]

1S

0

3S

1

S. Aoki, et al. Comput. Sci. Dis. 1 015009 (2008)

Complications

17

NN interaction is not unique

•Non-uniqueness of nucleon forces ✘

...but phase-shift equivalent!

0

30

60

90

δ [

deg

]

Nij

CDBonnAv18N3LONij93

0 50 100 150 200 250E [MeV]

0

60

120

180

δ [

deg

]

1S

0

3S

1


Complications

17


Carlson et al., Phys. Rev. C 68 025802 (2003)

Strong short-range correlations

•Non-uniqueness of nucleon forces ✘•Short-range core needs many-body treatment ✘


Complications

17


•Non-uniqueness of nucleon forces ✘•Short-range core needs many-body treatment ✘•Three-body forces needed for saturation ✘

Saturation point of nuclear matter

Li, Lombardo, Schulze et al. PRC 74 047304 (2006)S. Aoki, et al. Comput. Sci. Dis. 1 015009 (2008)

Weinberg, Phys. Lett. B 251 288 (1990), NPB 363 3 (1991) Entem & Machleidt, PRC 68, 041001(R) (2003)

Tews, Schwenk et al., PRL 110, 032504 (2013) Epelbaum, Frebs & Meissner, PRL 115, 122301 (2015)

NN forces from EFTs of QCD

Chiral perturbation theory•π and N as dof

•Systematic expansion

•2N at N3LO - LECs from πN, NN

•3N at N2LO - 2 more LECs

•(Often further renormalized)

18

OˆQ

⇤

˙

⇤ „ 1 GeV

ci

ci

π

ci

Perturbative calculations

19

Advantages •Symmetric, asymmetric & polarised •Local & non-local forces •3NF can be incorporated •Systematic expansion

Disadvantages •Induced 3NF ignored •Convergence?

λ=4 [fm-1]

0 1 2 3 4 5

k [fm-1]

0

1

2

3

4

5

k’ [fm

-1]

-2.5-2-1.5-1-0.5 0 0.5 1

λ=2 [fm-1]

0 1 2 3 4 5

k [fm-1]

-2.5-2-1.5-1-0.5 0 0.5 1

λ=1.5 [fm-1]

0 1 2 3 4 5

k [fm-1]

-2.5-2-1.5-1-0.5 0 0.5 1

λ=1 [fm-1]

0 1 2 3 4 5

k [fm-1]

-2.5-2-1.5-1-0.5 0 0.5 1

SRG evolution for 1S0 NN force

dHs

ds“ rrTrel, Hss, Hss ô � “ s´1{4

λ=4 [fm-1]

0 1 2 3 4 5

k [fm-1]

0

1

2

3

4

5

k’ [fm

-1]

-2.5-2-1.5-1-0.5 0 0.5 1

λ=2 [fm-1]

0 1 2 3 4 5

k [fm-1]

-2.5-2-1.5-1-0.5 0 0.5 1

λ=1.5 [fm-1]

0 1 2 3 4 5

k [fm-1]

-2.5-2-1.5-1-0.5 0 0.5 1

λ=1 [fm-1]

0 1 2 3 4 5

k [fm-1]

-2.5-2-1.5-1-0.5 0 0.5 1 +refit on 3-body &

4-body sector

+perturbative many-body calculations

Drischler, Hebeler & Schwenk, arXiv:1710.08220 Drischler, Hebeler & Schwenk, arXiv:1510.0672


20

Darmstadt


Holt et al

Wellenhofer, JW Holt, et al PRC 89 064009 (2014) arXiv:1404.2136


21

•No renormalisation of NN force

•Perturbative calculations, analytical where they can

Coraggio, JW Holt et al., PRC 89 044321 (2014) arXiv:1402.0965

Brueckner-Hartree-Fock•Diagrammatic approach based on Bethe-Goldstone expansion

•Infinite resummation of diagrams

22

Advantages •Symmetric, asymmetric & polarised •Local & non-local forces •3NF can be incorporated •Systematic expansion

Gp!q “ V ` VQ

! ´ ✏ ´ ✏1 ` i⌘Gp!q

Upkq “

ÿ

|~k1|†kF

x

~k~k1|Gp! “ ✏k ` ✏k1

q|

~k~k1yA

✏k “ ~2k22m⌧

` RerUpkqs

E

Ap⇢,�q “ 1

A

ÿ

⌧

ÿ

|~k|†kF⌧

ˆ~2k22m⌧

` 1

2RerU⌧ p~kqs

˙

Disadvantages •Missing diagrams? •Thermodynamical consistency

Hu, Zhang, Epelbaum, Meißner & Meng PRC 96 034307 (2017) arxiv:1612.05433

BHF & N4LO chiral forces

23

•Same error propagation as NN force

NLON2LON3LON4LO

0

10

20

30

40

0.1 0.2 0.3 0.4

(E/A

) PN

M [M

eV]

� [fm-3]

R = 0.9 fm

0

10

20

30

40

0.1 0.2 0.3 0.4

(E/A

) PN

M [M

eV]

� [fm-3]

0

10

20

30

40

0.1 0.2 0.3 0.4

(E/A

) PN

M [M

eV]

� [fm-3]

R = 1.0 fm

0

10

20

30

40

0.1 0.2 0.3 0.4

(E/A

) PN

M [M

eV]

� [fm-3]

-35

-30

-25

-20

-15

-10

-5

0

0.1 0.2 0.3 0.4 0.5 0.6

(E/A

) SN

M [M

eV]

� [fm-3]

R = 0.9 fm

-35

-30

-25

-20

-15

-10

-5

0

0.1 0.2 0.3 0.4 0.5 0.6

(E/A

) SN

M [M

eV]

� [fm-3]

-35

-30

-25

-20

-15

-10

-5

0

0.1 0.2 0.3 0.4 0.5 0.6

(E/A

) SN

M [M

eV]

� [fm-3]

R = 1.0 fm

-35

-30

-25

-20

-15

-10

-5

0

0.1 0.2 0.3 0.4 0.5 0.6

(E/A

) SN

M [M

eV]

� [fm-3] 20

25

30

35

40

45

Q0 Q2 Q3 Q4 Q5 Exp

asy

mm

[M

eV

]

R = 0.9 fm

30

40

50

60

70

Q0 Q2 Q3 Q4 Q5 Exp

L [

Me

V]

R = 0.9 fm

20

25

30

35

40

45

Q0 Q2 Q3 Q4 Q5 Exp

asy

mm

[M

eV

]

R = 1.0 fm

30

40

50

60

70

Q0 Q2 Q3 Q4 Q5 Exp

L [

Me

V]

R = 1.0 fm

Song, Baldo et al., PRL 81 1584 (1998) Lu, Li, Chen, Baldo & Schulze, PRC 96 044309 (2017)

BHF hole line expansion

24

•Updated calculations at the 3-hole-line level

Symmetric nuclear matter EoS

Logoteta, Bombaci, Kievsky PRC 94 064001 (2016); arxiv:1609.00649 See D. Logoteta Talk

Chiral forces with Δs

25

0 0.1 0.2 0.3 0.4

ρ[fm-3

]

0

20

40

60

80

100

E/A

[M

eV]

N3LO∆+N2LO∆1N3LO+N2LO(500)

N3LO+N2LO(450)

N3LO∆N3LO(500)

N3LO(450)

0 0.1 0.2 0.3 0.4

ρ [fm-3

]

-30

-20

-10

0

10

20

30

(a)

(b)

•BHF with Δ-full 2N & 3NF works

•Good saturation & isospin dependence

In-medium interaction Ladder self-energy

Dyson equationpp & hh Pauli blocking

Spectral function

One-body properties Momentum distributionThermodynamics & EoS

Transport

Self-consistent Green’s functions

•Diagrammatic approach for many-body propagators

•Infinite resummation of diagrams

•Off-shell energy dependence

•Spectral function

26

Advantages •Symmetric, asymmetric & polarised •Local & non-local forces •3NF can be incorporated •Thermodynamical consistency •Finite temperature

Disadvantages •Missing diagrams? •T=0 instability (but Gorkov!)

Ladder approximation with 3BF

27

Effective interactions

Carbone et al., PRC 88 054326 (2013) A. Carbone, PhD Thesis (2014)

Self-energy

In-medium T-matrix

= +

1

12

Self-energy

Two-body interaction

In-medium T-matrix

= +

Dyson equation

1

2

GII

Theoretical uncertainties: Chiral expansion

Carbone, Polls & Rios, PRC 88 044302 (2014)

Symmetric matter

28

LECscD=-1.11cE=-0.66K0~60 MeV

0 0.08 0.16 0.24 0.32

Density, ρ [fm-3

]

-20

-10

0

10

20

En

erg

y/n

ucl

eon

, E

/A [

MeV

]

N3LON2LON3LO+N2LO ddN2LO+N2LO dd

T=5 MeVSCGF

•3NF result is still underbound •Small difference in infinite matter for N3LO & N2LO... •In contrast to finite nuclei!

Equation of state of symmetric matter

Neutron matter

29

•Uncertainty band from unknown ChPT LECs + cutoff + MBPT •Finite temperature available too

Drischler, Carbone, Hebeler, Schwenk PRC 94 054307 (2016)

Neutron matter

30

•Mass-Radius relation from SCGF calculations •Cut-off variation (N3LO) and/or SRG evolution

0

0.5

1

1.5

2

2.5

3

8 10 12 14 16

Mass,M(SolarMasses)

Radius, R (km)

N3LO+3BFSLy

0

0.5

1

1.5

2

2.5

3

8 10 12 14 16

GR

P <∞

Causality

Neutron matter

30

•Mass-Radius relation from SCGF calculations •Cut-off variation (N3LO) and/or SRG evolution

Hebeler, Lattimer, Pethick, Schwenk ApJ 773 11 (2013)

0

0.5

1

1.5

2

2.5

3

8 10 12 14 16

Mass,M(SolarMasses)

Radius, R (km)

N3LO+3BFSLy

0

0.5

1

1.5

2

2.5

3

8 10 12 14 16

GR

P <∞

Causality

Ekstrom, Jansen, Hagen et al. PRC 91 051301(R) (2015); arXiv:1502.04682

Coupled cluster calculations

31

Ekstrom, Jansen, Hagen et al. PRC 91 051301(R) (2015); arXiv:1502.04682

Monte Carlo simulations•Energy minimisation via

imaginary time evolution

32

Advantages •Exact (up to sign problem?) •Symmetric (mostly) •Applied to nuclei •3NF can be incorporated

Disadvantages •Local interactions (mostly) •Access to energy only

BB⌧ | i “ ´H | i

| 0i “ lim⌧Ñ8

e´pH´E0q⌧ | i

•AFDMC made calculations possible in infinite PNM & SNM

•(Normally semi-)local interactionsCarslon et al. RMP 87 1067 (2015)

Tews, Gandolfi, Gezerlis & Schwenk PRC 93 024305 (2014)

Monte Carlo

33

Gezerlis, Tews, Epelbaum, Gandolfi et al. PRL 111 032501 (2013)

Benchmark calculations

34

Baldo, Rios, Vidana et al., PRC 86 064001 (2012)

10 MeV

T=0 EoS for neutron matter : many-body

5 MeV

Gandolfi, Gezerlis, Carlson, Annu. Rev. Nucl. Part. Sci. 65, 303 (2015)

5 MeV

Summary

•Motivation




•Polarizations


35

Vidana, Logoteta et al, EPL 94 11002 (2011)

Hyperon puzzle

36

Lonardoni, Lovato et al, PRL 114 092301 (2015)

AFDMC with local interactionsBHF with 3NFs

Exotic phases: spin saturation

37

Krueger, Hebeler, Schwenk PLB 744 18 (2015) arXiv:1408.4168

0.05 0.1 0.15

n [fm-3]

0

5

10

15

20

25

30

35

40

45

50

55

60

65

E/N

[M

eV]

0 1.44 1.81 2.07

kF [fm-1]

EGM 450/500 MeVEGM 450/700 MeVEM 500 MeVfree Fermi gas

0 0.05 0.1 0.15

0

0.05

(E - EFG) / EFG

Polarized neutron matter EoS Polarized neutron matter EoS

Sammarruca, Machleidt, Kaiser PRC 92 054327 (2015) arXiv:1505.04836

Vidana, Polls & Durant PRC 94 054006 (2016) arXiv:1609.03005

Summary

•Motivation




•Polarizations


38

LIGO/VIRGO, PRL 119 161101 (2017)

GW170817

39

Qij “ ´⇤✏ij

⇤pMq

LIGO/VIRGO, PRL 119 161101 (2017)

GW170817

40

Margalit & Metzger, arXiv:1710.05938

GW170817: maximum mass?•Kilonova aftermath & rotational energy

41

M † 2.2Md

Rezzolla, Most & Weih, arXiv:1711.00314

M † p2.16 ˘ 0.03qMd

Ruiz, Shapiro & Tsokaros, arXiv:1711.0047

•Ejected mass & rotation

•Magnetohydro GR simulations

M † 2.16Md

Shibata et al, arXiv:1710.07579

•Numerical relativity simulations

M † p2.15 ´ 2.25qMd


Mass measurements

42

Demorest et al., Nature 467, 1081 (2011)

Future perspectives

43

•Several advances in EoS during NewCompstar

•Uncertainty exploration is now routine

•Interplay between hamiltonian & many-body?

•Next decade: observations

•NICER

•Binary inspirals: GWs and others

•SKA

Core EoS developments in the NewCompStar...

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