nuclear structure iv: nuclear physics and neutron...

Nuclear structure IV:Nuclear physics and Neutron stars

Stefano Gandolfi

Los Alamos National Laboratory (LANL)

National Nuclear Physics Summer SchoolMassachusetts Institute of Technology (MIT)

July 18-29, 2016

Stefano Gandolfi (LANL) - [email protected] Neutron stars 1 / 30

Fundamental questions in nuclear physics

Nuclear astrophysics:

What’s the relation between nuclear physics and neutron stars?

What are the composition and properties of neutron stars?

How do supernovae explode?

How are heavy elements formed?


Nuclei and neutron stars

208Pb, ∼ 10−15m, 10−25 kg

neutron star,∼ 10 Km, 1030 kg (2 Msolar)


Nuclei and neutron stars

208Pb, ∼ 10−15m, 10−25 kgneutron star,∼ 10 Km, 1030 kg (2 Msolar)


Can we really describe nuclei and neutron stars starting from the sameforces???


Neutron matter and neutron star structure

TOV equations:

dP

dr= −G [m(r) + 4πr3P/c2][ε+ P/c2]

r [r − 2Gm(r)/c2],

dm(r)

dr= 4πεr2 ,

Boundary conditions: P(r = 0) = Pc and P(r = Rmax) = 0 (surface).An equation of state P(ρ) is needed.

Other useful quantities to know:

ε(ρ) = ρ [E (ρ) + mN)] energy density

P(ρ) = ρ2 ∂E∂ρ pressure

The total mass of the star is given by

M(R) =

∫ R

0

dr 4πr2ε(r)



J. Lattimer


Equation of state of neutron matter

Many many EOS of neutron matter exist! Just ”some”:

Ozel, Freire, arXiv (2016)

Which one(s) (if any) support neutron stars observations?



The main constrain: maximum mass.

Demorest, et al., Nature 467, 1081 (2010)

Neutron star structure test the EOS!


Neutron star matter

Neutron star radius sensitive to the EOS at nuclear densities.Maximum mass depends mostly to the composition.


Neutron star structure

8 9 10 11 12 13 14 15 16R (km)

0

0.5

1

1.5

2

2.5

3

M (

MO• )

Causality: R>2.9 (G

M/c2 )

ρ central=2ρ 0

ρ central=3ρ 0

error associated with Esym

35.1

33.7

32

Esym

= 30.5 MeV (NN)

1.4 MO•

1.97(4) MO•

Gandolfi, Carlson, Reddy, PRC (2012).

Accurate measurement of Esym put a constraint to the radius of neutronstars, OR observation of M and R would constrain Esym!


Neutron stars

0 2 4 6 8 10 12 14 16 180

0.5

1

1.5

2

2.5

R (km)

)M

(M

4U 1608-52

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0 2 4 6 8 10 12 14 16 180

0.5

1

1.5

2

2.5

R (km)

)M

(M

EXO 1745-248

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 2 4 6 8 10 12 14 16 180

0.5

1

1.5

2

2.5

R (km)

)M

(M

4U 1820-30

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

6 8 10 12 14 16 180.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

R (km)

)M

(M

M13

6 8 10 12 14 16 180.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-310×

R (km)

)M

(M

Cenω

6 8 10 12 14 16 180.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-310×

R (km)

)M

(M

X7

Steiner, Lattimer, Brown, ApJ (2010)

Neutron star observations can be used to ’measure’ the EOS andconstrain Esym and L. (Systematic uncertainties still under debate...)


Neutron star matter really matters!

8 9 10 11 12 13 14 15R (km)

0

0.5

1

1.5

2

2.5

M (

Mso

lar)

Esym

= 33.7 MeV

Esym

=32 MeV

Polytropes

Quark matter

Steiner, Gandolfi, PRL (2012), Gandolfi et al. EPJA (2014)


Fundamental questions in nuclear physics

What is the equation of state of dense matter?

What is the composition of neutron stars?

How do supernovae explode?

How are heavy elements formed?


Neutron stars

D. Page

Atmosphere: atomic andplasma physics

Crust: physics of superfluids(neutrons, vortex), solid statephysics (nuclei)

Inner crust: deformed nuclei,pasta phase

Outer core: nuclear matter

Inner core: hyperons? quarkmatter? π or K condensates?...?

Let’s discuss only one possible scenario: hyperons


High density neutron matter

If chemical potential large enough (ρ ∼ 2− 3ρ0), heavier particles form,i.e. Λ, Σ, ...

For example: it might be energetically convenient to change aneutron(ddu) into a Λ(uds).


Hypernuclei

In order to infer the hyperon-nucleon interactions, hypernuclei can becreated in experiments!


Nuclei and hypernuclei

Few thousands of binding energies for normal nuclei are known.

Only few tens for hypernuclei.


Hypernuclei and hypermatter:

H = HN +~2

2mΛ

A∑i=1

∇2i +

∑i<j

vΛNij +

∑i<j<k

V ΛNNijk

Λ-binding energy calculated as the difference between the system withand without Λ.


Λ hypernuclei

vΛN and V ΛNN(I) are phenomenological (Usmani).

B R [M

eV]

A-2/3

RN

RNN (I)

RNN (II)

0.0

10.0

20.0

30.0

40.0

50.0

60.0

0.0 0.1 0.2 0.3 0.4 0.5

A

0.0

15.0

30.0

45.0

60.0

0 20 40 60 80

Lonardoni, Pederiva, Gandolfi, PRC (2013) and PRC (2014).

V ΛNN (II) is a new form where the parameters have been fine tuned.

As expected, the role of ΛNN is crucial for saturation.


Hyper-neutron matter

Neutrons and Λ particles:

ρ = ρn + ρΛ , x =ρΛ

ρ

EHNM(ρ, x) =[EPNM((1−x)ρ)+mn

](1−x)+

[EPΛM(xρ)+mΛ

]x+f (ρ, x)

where EPΛM is the non-interacting energy (no vΛΛ interaction),

EPNM(ρ) = a

(ρ

ρ0

)α+ b

(ρ

ρ0

)βand

f (ρ, x) = c1x(1− x)ρ

ρ0+ c2

x(1− x)2ρ2

ρ20


Λ-neutron matter

EOS obtained by solving for µΛ(ρ, x) = µn(ρ, x)

E [M

eV]

l [fm-3]

PNM

RN

RN + RNN (I)

0

20

40

60

80

100

120

140

0.0 0.1 0.2 0.3 0.4 0.5 0.6pa

rticl

e fra

ctio

n

l [fm-3]

n

R R

0.2 0.3 0.4 0.5 0.6

10-2

10-1

100

Lonardoni, Lovato, Pederiva, Gandolfi, PRL (2015)

No hyperons up to ρ = 0.5 fm−3 using ΛNN (II)!!!


Λ-neutron matter

M [M

0]

R [km]

PNM

RN

RN + RNN (I)

RN + RNN (II)

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

11 12 13 14 15

PSR J1614-2230

PSR J0348+0432

Lonardoni, Lovato, Pederiva, Gandolfi, PRL (2015)

Drastic role played by ΛNN. Calculations can be compatible with neutronstar observations.

Note: no vΛΛ, no protons, and no other hyperons included


Hyperons

Understanding hyperon-nucleon interactions is crucial, but very fewexperimental data available:

∼ 4500 NN scattering data available, ∼ 30 ΛN

few thousands of binding energies for nuclei known. Only few tensfor hypernuclei.


Hyperons

Future, more ΛN experiments and/or Lattice QCD.Example: phase-shifts calculated with Lattice QCD.

Beane et al., Nuclear Physics A794, 62 (2007)


Hyperons

Future, more ΛN experiments and/or Lattice QCD. Example: attempt toextract the potential with Lattice QCD:

HAL QCD collaboration.


Stay tuned...

Remember, hyperons in dense matter is only onepossible scenario. Very active field...


Summary of this lecture before the generalsummary:

Neutron star structure from the EOS

Maximum mass and radii

Hyperons and dense matter


Wrap up...


Last lesson...

The last but very important lesson.

Always acknowledge the funding agencies!!!

www.computingnuclei.org


nuclear structure iv: nuclear physics and neutron...

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