Dense Matter and Neutrinos. J. Carlson - LANL

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1 Dense Matter and Neutrinos J. Carlson - LANL Neutron Stars and QCD phase diagram Nuclear Interactions Quantum Monte Carlo Low-Density Equation of State High-Density Equation of State Neutron Star Matter (protons, hyperons, etc.) Mass/Radius relations and observations Neutrinos - neutron star cooling Future Collaborators: S. Gandolfi (LANL) A. Gezerlis (Guelph) D. Lonardoni (ANL) A. Lovato (ANL) S. Reddy (UW/INT)

2 1-2 Solar Masses ~12 km radius Neutron Stars Predicted by Baade and Zwicky 1 year after discovery of the neutron Outer Crust nuclei + electrons! Inner Crust nuclei + neutrons + electrons! Core neutrons+protons+electrons+ We will concentrate on the core: bulk of the star dominates the M/R curve important for neutrino cooling charge neutrality + small electron mass ~1% electrons, protons

3 QCD phase diagram (minimal) from FAIR, new facility in Darmstadt high density and cold very difficult to reach in experiments Color superconductor at very high density; important for neutron stars?

4 Neutron Star Mass/Radius Relations For many years only ~ solar mass neutron stars observed Recently several observed with ~ 2 solar masses! see Demorest, et al Nature 467: 281 (21) Transitions to superconducting quark matter Wide range of predictions for mass/radius relationship

5 Nuclear Interactions Up to ~2-3 x nuclear densities, matter can be described as a system of interacting nucleons phase shifts for NN scattering - simple model (AV8 ) compared to experiment δ (deg) S Argonne V8 SAID δ (deg) S1 Argonne V8 SAID δ (deg) -2 1 P1 Argonne V8 SAID E lab (MeV) 2 3 P E lab (MeV) -1 3 P1 Argonne V8 SAID E lab (MeV) 3 2 Argonne V8 SAID 3 P2 δ (deg) -2 Argonne V8 SAID δ (deg) δ (deg) 1 δ (deg) E lab (MeV) D1 Argonne V8 SAID E lab (MeV) δ (deg) E lab (MeV) Argonne V8 SAID 3 D E lab (MeV) Stefano Gandolfi (LANL) δ (deg) E lab (MeV) ε 1 Argonne V8 SAID E lab (MeV) At =, k F ' 33 MeV. At r=2 Two neutrons ρ : kf ~ have 2 Efm -1 CM ' 12 MeV, E LAB '24 MeV.! Argonne NN accurate up to (at least) 2-3. implies 2 nucleons at Fermi surface have ECM = 16 MeV; Elab ~ 32 MeV EOS of neutron matter, symmetry energy, and the e ect of hyperons to neutron star structure

6 Nuclear Interactions Very low densities dominated by 1 S interaction Very similar to cold atomic Fermi Gases H = X i p 2 i 2m + X i<j V (r ij ) Neutron-Neutron Scattering length ~ -18 fm π Ei.b (MeV) I I.5 I 1. r (fm) pion + 2-pion + short-range repulsion

7 Quantum Monte Carlo Methods H = X i p 2 i 2m + X i<j V ij +... V ij = X k V k ij(r ij ) O k ij O k ij = 1, i j, i r ij j r ij,l S ij [1, i j ] H = E = 2 A ( A Z) X i=1 (i)(r) 2 A = 7x1 19 amplitudes for 66 neutrons in 3A=198 dimensions

8 Quantum Monte Carlo (Auxiliary Field Diffusion Monte Carlo) =exp[ H ] T exp[ H ] exp[ V /2] exp[ T ]exp[ V /2] Kinetic Term is a diffusion process in 3A coordinates Spin-dependent potential terms rewritten as coupled to an auxiliary field which is sampled by Monte Carlo, giving rotations of spins (and isospins) exp[ V i j ] = X x=±1 exp[ V 1/2 1/2 i x] exp[ V 1/2 1/2 j x] The simulation is a branching random walk in 3A coordinates and A spins and isospins.

9 Equation of State (E/A) for neutrons and cold Fermi atoms Energy / Energy of Free fermions E / E FG k F [fm -1 ] Lee-Yang QMC s-wave QMC AV4 Cold Atoms k F a Density 1/3 atoms w/ effective range Neutrons Cold Atoms

10 Superfluidity (s-wave) Spin up, down densities in a trap ρ ρ radius =.45(5) JC and Reddy, PRL 27 analyzing MIT data Zweirlein 1 / E F ( k / k F ) 2 = 2 k 2 F 2m =.5 (3) (k min /k f ) 2 =.8(1) JC and Reddy, PRL 25

11 Superfluid Pairing Gap k F [fm -1 ] / E F BCS-atoms Neutron Matter Cold Atoms QMC Unitarity BCS-neutrons Solid lines: BCS mean-field theory Points w/ error bars: QMC k F a Gezerlis and Carlson, PRC 21, 212 Cold Atoms have highest superfluid gap / EF of any system; Neutrons have highest pairing gap / EF in nature.

12 Equation of State at Higher Densities: near nuclear saturation symmetric nuclear matter pure neutron matter Symmetry energy E = -16 MeV ρ =.16 fm -3 Nuclear saturation From experiments: E SNM ( )= 16MeV, =.16fm 3, E sym = E PNM ( ) + 16 The symmetry energy is accesible (indirectly) by experiment

13 At higher densities three-nucleon interactions start to become important π π π π π π π π π π + short-range correlations (spin/isospin independent). Calibrated to light nuclei Carlson, Pieper, Wiringa, many papers

14 Consider a wide range of three-nucleon forces that give the same symmetry energy and then see how they extrapolate to high density We consider di erent forms of three-neutron interaction by only requiring a particular value of E sym at saturation. 12 Energy per Neutron (MeV) E sym = 33.7 MeV different 3N di erent 3N: V 2 + V R V 2 + V µ R (several µ) V 2 + ṼR V 3 + V R Neutron Density (fm -3 )

15 Equations of state with a fixed symmetry energy Energy per Neutron (MeV) E sym = 35.1 MeV (AV8 +UIX) E sym = 33.7 MeV E sym = 32 MeV E sym = 3.5 MeV (AV8 ) Neutron Density (fm -3 ) Gandolfi, Carlson, Reddy, PRC (212) Gandolfi, Carlson, Reddy 212 Stefano Gandolfi (LANL) EOS of neutron matter, symmetry energy, and the e ect of hyperons to neutron

16 Strong Correlation between Symmetry Energy and its Derivative 7 65 AV8 +UIX L (MeV) E sym =32. MeV E sym =33.7 MeV 35 AV E sym (MeV) Gandolfi et al., EPJ (214) New chiral interaction models give very similar results

17 Fits to nuclear masses Lattimer and Lim, ApJ 213

18 Variety of Experimental Constraints

19 TOV equations: Equation of State to Mass / Radius dp dr = G[m(r)+4 r3 P/c 2 ][ + P/c 2 ] r[r 2Gm(r)/c 2 ], dm(r) dr =4 r 2, from Lattimer Tolman Oppenheimer Volkov equations: 1939 used free neutron gas to estimate upper bound of.7 solar masses see Silbar and Reddy: arxiv:nucl-th/3941 for an introduction

20 Neutron Star Mass/Radius: Calculations EOS used to solve the TOV equations. 3 M (M O ) Causality: R>2.9 (GM/c 2 ) 32 error associated with E sym ρ central =3ρ ρ central =2ρ (4) M O 1.4 M O E sym = 3.5 MeV (NN) R (km) Gandolfi, Carlson, Reddy, PRC (212).

21 Observations - still controversial U EXO U M (M ) M (M ) M (M ) R (km) R (km) R (km) M (M ) M R (km) M (M ) ω Cen R (km) 1 Steiner, Lattimer, Brown, ApJ (21) constraints from individual stars M (M ) X R (km) Neutron star observations can be used to measure the EOS and R (km) constrain E sym and L. observations from 3 X-ray bursars plus 3 low-mass X-ray binaries Stefano Gandolfi (LANL) M (M ) constraints EOS of neutron matter, symmetry energy, and the e ect of hyperons to neutron star structure r ph =R M (M ) r ph >>R R (km) Mass radius constraints subject to assumptions M (M ) r ph =R R (km) M (M ) r ph >>R R (km) Fig. 9. The upper panels give the probability distributions forthemassversusradiuscurvesimpliedby the data, and the solid (dotted) contour lines show the 2-σ (1-σ) contours implied by the data. The lower panes summarize the 2-σ probability distributions for the 6 objects considered in the analysis. The left

22 Comparison of theory and observations E sym = 33.7 MeV E sym =32 MeV Polytropes Quark matter M (M solar ) R (km) 32 < E sym < 34 MeV, 43 < L < 52 MeV Steiner, Gandolfi, PRL (212).

23 What about other particles? protons Quadratic dependence of E versus n/p imablance Asymmetric nuclear matter E(, x) =E SNM ( )+E (2) sym( )(1 2x) energy per nucleon (MeV) 1-1 (2,66) (2,54) (2,38) (14,66) (14,54) (14,38) (38,66) original Finite size corrected (54,66) (38,54) x = N p /(N p +N n ) Gandolfi, Lovato, Carlson, Schmidt, arxiv: proton fraction also important for neutrino processes

24 What about other particles? hyperons, Hyperons are bound in nuclei by ~ 3 MeV. What happens in dense matter? B [MeV] NN (I) N A 1. NN (II) A -2/3 Lonardoni, Pederiva, SG, PRC (213) and PRC (214).

25 Hyperons in Neutron Matter 14 E [MeV] n [fm -3 ] particle fraction PNM N + NN (I) N [fm -3 ] Lonardoni, Lovato, Gandolfi, Pederiva, arxiv: (214) No hyperons for NN (II) up to =.5 fm 3! Best model gives no hyperons up to 3-4 x saturation density Stefano Gandolfi (LANL) EOS of neutron matter, symmetry energy, and the e ect of hyperons to neutron st

26 Neutrinos in neutron stars and proto-neutron stars Yakovlev 24

27 Neutron Star Cooling Introduction Sensitive to: Equation of state Neutrino Emission Superfluidity Magnetic Fields Surface Direct Urva: Lattimer, Pethick, Prakash, Haensel (1991) n p e νe n! p + e + e p + e! n + e modified Urca works throughout the core n + N! p + e + N + e much slower threshold associated with Fermi surfaces limit this to ρ > 2 ρ Requires ~ 15% proton fraction to satisfy energy and momentum conservation

28 Superfluidity suppresses familiar neutrino processes creates new process: production through Cooper pairing 3P2-3F2 pairing particularly important but not well constrained 3x1 8 K ~.26 MeV typical s-wave pairing gaps ~ 1 MeV angle average 3P2 ~.1 MeV log(nuclear saturation density in g/cm 3 ) ~ 14.4 Yakovlev, et al, 24 also see Gezerlis, Pethick, Schwenk arxiv:

29 Neutron and Proto-Neutron Star Cooling Neutron star cooling depends upon Equation of State Neutrino Emission and Propagation Neutron (and proton) Superfluidity +! Supernovae neutrino emission also depends upon weak response of matter interesting regime at low densities (.1 ρ) and moderate temperatures (non-degenerate matter)! Rapid progress in theory and observations

30 Summary/ Outlook Rapid progress in our understanding of cold dense matter! Excellent connections to Theory of strongly-correlated matter Experiments in cold atom physics Astrophysical observations Future measurements of gravitational waves Supernovae physics and neutrino physics