Nuclear structure IV: Nuclear physics and Neutron stars

Nuclear structure IV: Nuclear physics and Neutron stars Stefano Gandolfi Los Alamos National Laboratory (LANL) National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016 Stefano Gandolfi (LANL) - stefano@lanl.gov 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? Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 2 / 30

Nuclei and neutron stars 208 Pb, 10 15 m, 10 25 kg Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 3 / 30

Nuclei and neutron stars 208 Pb, 10 15 m, 10 25 kg neutron star, 10 Km, 10 30 kg (2 M solar ) Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 3 / 30

Can we really describe nuclei and neutron stars starting from the same forces??? Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 4 / 30

Neutron matter and neutron star structure TOV equations: dp dr = G[m(r) + 4πr 3 P/c 2 ][ɛ + P/c 2 ] r[r 2Gm(r)/c 2, ] dm(r) dr = 4πɛr 2, Boundary conditions: P(r = 0) = P c and P(r = R max ) = 0 (surface). An equation of state P(ρ) is needed. Other useful quantities to know: ɛ(ρ) = ρ [E(ρ) + m N )] energy density P(ρ) = ρ 2 E ρ pressure The total mass of the star is given by M(R) = R 0 dr 4πr 2 ɛ(r) Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 5 / 30

Neutron matter and neutron star structure J. Lattimer Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 6 / 30

Equation of state of neutron matter Many many EOS of neutron matter exist! Just some : Özel, Freire, arxiv (2016) Which one(s) (if any) support neutron stars observations? Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 7 / 30

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) - stefano@lanl.gov Neutron stars 8 / 30

Neutron star matter Neutron star radius sensitive to the EOS at nuclear densities. Maximum mass depends mostly to the composition. Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 9 / 30

Neutron star structure M (M O ) 3 2.5 2 1.5 1 0.5 Causality: R>2.9 (GM/c 2 ) 32 error associated with E sym ρ central =3ρ 0 E sym = 30.5 MeV (NN) ρ central =2ρ 0 33.7 35.1 1.97(4) M O 1.4 M O 0 8 9 10 11 12 13 14 15 16 R (km) Gandolfi, Carlson, Reddy, PRC (2012). Accurate measurement of E sym put a constraint to the radius of neutron stars, OR observation of M and R would constrain E sym! Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 10 / 30

Neutron stars 2.5 4U 1608-52 0.0012 2.5 EXO 1745-248 0.0016 0.0014 2.5 4U 1820-30 0.0016 2 0.001 2 0.0012 2 0.0014 M (M ) 1.5 1 0.0008 0.0006 0.0004 M (M ) 1.5 1 0.001 0.0008 0.0006 M (M ) 1.5 1 0.0012 0.001 0.0008 0.0006 0.5 0.0002 0.5 0.0004 0.0002 0.5 0.0004 0.0002 0 0 2 4 6 8 10 12 14 16 18 R (km) 0 0 0 2 4 6 8 10 12 14 16 18 R (km) 0 0 0 2 4 6 8 10 12 14 16 18 R (km) 0 M (M ) 2.4 2.2 2 1.8 1.6 1.4 M13 0.0014 0.0012 0.001 0.0008 0.0006 M (M ) 2.4 2.2 2 1.8 1.6 1.4 ω Cen -3 10 0.8 0.7 0.6 0.5 0.4 0.3 M (M ) 2.4 2.2 2 1.8 1.6 1.4-3 10 0.45 0.4 0.35 0.3 0.25 0.2 0.15 1.2 0.0004 1.2 0.2 1.2 0.1 1 0.0002 1 0.1 1 X7 0.05 0.8 6 8 10 12 14 16 18 R (km) 0 0.8 6 8 10 12 14 16 18 R (km) 0 0.8 6 8 10 12 14 16 18 R (km) 0 Steiner, Lattimer, Brown, ApJ (2010) Neutron star observations can be used to measure the EOS and constrain E sym and L. (Systematic uncertainties still under debate...) Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 11 / 30

Neutron star matter really matters! 2.5 2 E sym = 33.7 MeV E sym =32 MeV Polytropes Quark matter M (M solar ) 1.5 1 0.5 0 8 9 10 11 12 13 14 15 R (km) Steiner, Gandolfi, PRL (2012), Gandolfi et al. EPJA (2014) Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 12 / 30

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) - stefano@lanl.gov Neutron stars 13 / 30

Neutron stars D. Page Atmosphere: atomic and plasma physics Crust: physics of superfluids (neutrons, vortex), solid state physics (nuclei) Inner crust: deformed nuclei, pasta phase Outer core: nuclear matter Inner core: hyperons? quark matter? π or K condensates?...? Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 14 / 30

Neutron stars D. Page Let s discuss only one possible scenario: hyperons Atmosphere: atomic and plasma physics Crust: physics of superfluids (neutrons, vortex), solid state physics (nuclei) Inner crust: deformed nuclei, pasta phase Outer core: nuclear matter Inner core: hyperons? quark matter? π or K condensates?...? Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 14 / 30

High density neutron matter If chemical potential large enough (ρ 2 3ρ 0 ), heavier particles form, i.e. Λ, Σ,... For example: it might be energetically convenient to change a neutron(ddu) into a Λ(uds). Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 15 / 30

Hypernuclei In order to infer the hyperon-nucleon interactions, hypernuclei can be created in experiments! Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 16 / 30

Nuclei and hypernuclei Few thousands of binding energies for normal nuclei are known. Only few tens for hypernuclei. Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 17 / 30

Hypernuclei and hypermatter: 2 H = H N + 2m Λ A i=1 2 i + i<j v ΛN ij + i<j<k V ΛNN ijk Λ-binding energy calculated as the difference between the system with and without Λ. Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 18 / 30

Λ hypernuclei v ΛN and V ΛNN (I) are phenomenological (Usmani). B [MeV] 60.0 50.0 40.0 30.0 20.0 NN (I) N 60.0 45.0 30.0 15.0 0.0 0 20 40 60 80 A 10.0 NN (II) 0.0 0.0 0.1 0.2 0.3 0.4 0.5 A -2/3 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) - stefano@lanl.gov Neutron stars 19 / 30

Hyper-neutron matter Neutrons and Λ particles: E HNM (ρ, x) = ρ = ρ n + ρ Λ, x = ρ Λ ρ ] ] [E PNM ((1 x)ρ)+m n (1 x)+ [E PΛM (xρ)+m Λ x +f (ρ, x) where E PΛM is the non-interacting energy (no v ΛΛ interaction), ( ) α ( ) β ρ ρ E PNM (ρ) = a + b ρ 0 ρ 0 and f (ρ, x) = c 1 x(1 x)ρ ρ 0 + c 2 x(1 x) 2 ρ 2 ρ 2 0 Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 20 / 30

Λ-neutron matter EOS obtained by solving for µ Λ (ρ, x) = µ n (ρ, x) E [MeV] 140 120 100 80 60 40 n 0.2 0.3 0.4 0.5 0.6 [fm -3 ] 10 0 10-1 10-2 particle fraction PNM N + NN (I) N 20 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 [fm -3 ] Lonardoni, Lovato, Pederiva, Gandolfi, PRL (2015) No hyperons up to ρ = 0.5 fm 3 using ΛNN (II)!!! Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 21 / 30

Λ-neutron matter 2.8 2.4 PNM 2.0 PSR J0348+0432 M [M 0 ] 1.6 1.2 N + NN (II) N + NN (I) PSR J1614-2230 0.8 0.4 N 0.0 11 12 13 14 15 R [km] Lonardoni, Lovato, Pederiva, Gandolfi, PRL (2015) Drastic role played by ΛNN. Calculations can be compatible with neutron star observations. Note: no v ΛΛ, no protons, and no other hyperons included Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 22 / 30

Hyperons Understanding hyperon-nucleon interactions is crucial, but very few experimental data available: 4500 NN scattering data available, 30 ΛN few thousands of binding energies for nuclei known. Only few tens for hypernuclei. Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 23 / 30

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) - stefano@lanl.gov Neutron stars 24 / 30

Hyperons Future, more ΛN experiments and/or Lattice QCD. Example: attempt to extract the potential with Lattice QCD: HAL QCD collaboration. Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 25 / 30

Stay tuned... Remember, hyperons in dense matter is only one possible scenario. Very active field... Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 26 / 30

Summary of this lecture before the general summary: Neutron star structure from the EOS Maximum mass and radii Hyperons and dense matter Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 27 / 30

Wrap up... Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 28 / 30

Last lesson... The last but very important lesson. Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 29 / 30

Last lesson... The last but very important lesson. Always acknowledge the funding agencies!!! www.computingnuclei.org Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 29 / 30

Stefano Gandolfi (LANL) - stefano@lanl.gov Neutron stars 30 / 30