Page 1
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
Page 2
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?
Stefano Gandolfi (LANL) - [email protected] Neutron stars 2 / 30
Page 3
Nuclei and neutron stars
208Pb, ∼ 10−15m, 10−25 kg
neutron star,∼ 10 Km, 1030 kg (2 Msolar)
Stefano Gandolfi (LANL) - [email protected] Neutron stars 3 / 30
Page 4
Nuclei and neutron stars
208Pb, ∼ 10−15m, 10−25 kgneutron star,∼ 10 Km, 1030 kg (2 Msolar)
Stefano Gandolfi (LANL) - [email protected] Neutron stars 3 / 30
Page 5
Can we really describe nuclei and neutron stars starting from the sameforces???
Stefano Gandolfi (LANL) - [email protected] Neutron stars 4 / 30
Page 6
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)
Stefano Gandolfi (LANL) - [email protected] Neutron stars 5 / 30
Page 7
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)
Stefano Gandolfi (LANL) - [email protected] Neutron stars 5 / 30
Page 8
Neutron matter and neutron star structure
J. Lattimer
Stefano Gandolfi (LANL) - [email protected] Neutron stars 6 / 30
Page 9
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?
Stefano Gandolfi (LANL) - [email protected] Neutron stars 7 / 30
Page 10
Neutron matter and neutron star structure
The main constrain: maximum mass.
Demorest, et al., Nature 467, 1081 (2010)
Neutron star structure test the EOS!
Stefano Gandolfi (LANL) - [email protected] Neutron stars 8 / 30
Page 11
Neutron star matter
Neutron star radius sensitive to the EOS at nuclear densities.Maximum mass depends mostly to the composition.
Stefano Gandolfi (LANL) - [email protected] Neutron stars 9 / 30
Page 12
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!
Stefano Gandolfi (LANL) - [email protected] Neutron stars 10 / 30
Page 13
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...)
Stefano Gandolfi (LANL) - [email protected] Neutron stars 11 / 30
Page 14
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)
Stefano Gandolfi (LANL) - [email protected] Neutron stars 12 / 30
Page 15
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?
Stefano Gandolfi (LANL) - [email protected] Neutron stars 13 / 30
Page 16
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
Stefano Gandolfi (LANL) - [email protected] Neutron stars 14 / 30
Page 17
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
Stefano Gandolfi (LANL) - [email protected] Neutron stars 14 / 30
Page 18
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).
Stefano Gandolfi (LANL) - [email protected] Neutron stars 15 / 30
Page 19
Hypernuclei
In order to infer the hyperon-nucleon interactions, hypernuclei can becreated in experiments!
Stefano Gandolfi (LANL) - [email protected] Neutron stars 16 / 30
Page 20
Nuclei and hypernuclei
Few thousands of binding energies for normal nuclei are known.
Only few tens for hypernuclei.
Stefano Gandolfi (LANL) - [email protected] Neutron stars 17 / 30
Page 21
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.
Stefano Gandolfi (LANL) - [email protected] Neutron stars 18 / 30
Page 22
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.
Stefano Gandolfi (LANL) - [email protected] Neutron stars 19 / 30
Page 23
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
Stefano Gandolfi (LANL) - [email protected] Neutron stars 20 / 30
Page 24
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)!!!
Stefano Gandolfi (LANL) - [email protected] Neutron stars 21 / 30
Page 25
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
Stefano Gandolfi (LANL) - [email protected] Neutron stars 22 / 30
Page 26
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.
Stefano Gandolfi (LANL) - [email protected] Neutron stars 23 / 30
Page 27
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.
Stefano Gandolfi (LANL) - [email protected] Neutron stars 23 / 30
Page 28
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.
Stefano Gandolfi (LANL) - [email protected] Neutron stars 23 / 30
Page 29
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.
Stefano Gandolfi (LANL) - [email protected] Neutron stars 23 / 30
Page 30
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.
Stefano Gandolfi (LANL) - [email protected] Neutron stars 23 / 30
Page 31
Hyperons
Future, more ΛN experiments and/or Lattice QCD.Example: phase-shifts calculated with Lattice QCD.
Beane et al., Nuclear Physics A794, 62 (2007)
Stefano Gandolfi (LANL) - [email protected] Neutron stars 24 / 30
Page 32
Hyperons
Future, more ΛN experiments and/or Lattice QCD. Example: attempt toextract the potential with Lattice QCD:
HAL QCD collaboration.
Stefano Gandolfi (LANL) - [email protected] Neutron stars 25 / 30
Page 33
Stay tuned...
Remember, hyperons in dense matter is only onepossible scenario. Very active field...
Stefano Gandolfi (LANL) - [email protected] Neutron stars 26 / 30
Page 34
Summary of this lecture before the generalsummary:
Neutron star structure from the EOS
Maximum mass and radii
Hyperons and dense matter
Stefano Gandolfi (LANL) - [email protected] Neutron stars 27 / 30
Page 35
Summary of this lecture before the generalsummary:
Neutron star structure from the EOS
Maximum mass and radii
Hyperons and dense matter
Stefano Gandolfi (LANL) - [email protected] Neutron stars 27 / 30
Page 36
Summary of this lecture before the generalsummary:
Neutron star structure from the EOS
Maximum mass and radii
Hyperons and dense matter
Stefano Gandolfi (LANL) - [email protected] Neutron stars 27 / 30
Page 37
Summary of this lecture before the generalsummary:
Neutron star structure from the EOS
Maximum mass and radii
Hyperons and dense matter
Stefano Gandolfi (LANL) - [email protected] Neutron stars 27 / 30
Page 38
Wrap up...
Stefano Gandolfi (LANL) - [email protected] Neutron stars 28 / 30
Page 39
Last lesson...
The last but very important lesson.
Always acknowledge the funding agencies!!!
www.computingnuclei.org
Stefano Gandolfi (LANL) - [email protected] Neutron stars 29 / 30
Page 40
Last lesson...
The last but very important lesson.
Always acknowledge the funding agencies!!!
www.computingnuclei.org
Stefano Gandolfi (LANL) - [email protected] Neutron stars 29 / 30
Page 41
Stefano Gandolfi (LANL) - [email protected] Neutron stars 30 / 30