Astrophysical Constraints on the Nuclear Equation of State Evgeni Kolomeitsev Matej Bel University, Banska Bystrica

Neutron Star Zoo >1400 neutron stars in isolated rotation-powered pulsars ~ 30 millisecond pulsars >100 neutron stars in accretion-powered X-ray binaries ~ 50 x-ray pulsar intense X-ray bursters (thermonuclear flashes) short gamma-ray bursts neutron star -- neutron star, neutron star -- black-hole mergers soft gamma-ray repeaters – magnetars (super-strong magnetic fields)

Measuring pulsar mass m2 m1 Pulsar mass can be measured only in binary systems direction of observation m1 m2 Newton gravity 5 Keplerian orbital parameters: orbital period, semi-major axis length,excentricity, … Orbital period P; projected semi-major axis x; eccentricity e; longitude and the time of periastron passage w,T0 Do not determine individual masses of stars and the orbital inclination. Einstein gravity 5 potentially measurable post-Keplerian parameters: orbit precession, Shapiro delay, gravitational redshift, …. Measuremnt of any 2 post-Keplerian parameters allows to determine the mass of each star.

White dwarf -- neutron star binaries Lattimer ARNPS62 (2012) For 28 pulsars of this type the masses are measured

Measuring pulsar mass X-ray binaries 14 masses are measured Low mass Lattimer ARNPS62 (2012)

Measuring pulsar mass Double neutron star binaries 1974 PSR B1913+16 Hulse-Taylor pulsar First precise test of Einstein gravitation theory 2003 J0737-3039 first double pulsar system Pulsar A: P(A)=22.7 ms, M(A)=1.338 Msol Pulsar B: P(B)=2.77 ms, M(A)=1.249±0.001 Msol Orbiting period 2.5 hours [Nature 426, 531 (2003), Science 303, 1153 (2004)]

Double neutron star binaries

Pulsar J1614-2230 Highest well-known mass of NS Measured Shapiro delay with high precision Time signal is getting delayed when passing near massive object. Highest well-known mass of NS there are heavier, but far less precisely measured candidates) P.Demorest et al., Nature 467, 1081-1083 (2010)

Cross section of a neutron star crust Nuclei and electrons Neutron-rich nuclei and electrons Nuclei, electrons and neutrons outer core inner core neutrons, protons, electrons, muons Exotics: hyperons, meson-condensates, quark matter ~10 km

Crust Nucleus melting density growth Pasta structure interplay of Coulomb energy and surface tension Negele & Vautherin (1973) saturation density Mcrust ~0.1Msol Rcrust~102—103 m

relativistic corrections Equilibrium condition for a shell in a non-rotating neutron star Newton’s Law INPUT: equation of state (EoS) boundary conditions: OUTPUT: neutron star density profile, radius R and mass M relativistic corrections

HHJ EoS limitting mass nlim=0.1n0 nlim~10-5 n0 stable unstable uncertainty in R~103 m

Ab inito calculations of the EoS starting from NN potential auxiliary field diffusion Monte Carlo technique [Gandolfi et al PRC 79, 054005 (2009)] variational chain-summation methods (Urbana) matters is superluminal at higher densities [Akmal, Pandharipande, Ravenhall PRC58(98)1804] non-relativistic EoS!

Lagrangian equations of motion

field Ansatz RMF model with density dependent coupling see talk K. Petrik

strong dependence on m*N (pure) Walecka model U(s)=0 modified Walecka U(s)=as3+bs4 maximal mass of NS PSR J1614-2230 weak dependence on K ! strong dependence on m*N Hardest EoS among RMF models

Relativistic Mean Field Models Nuclear EoS: Examples Relativistic Mean Field Models T. Gaitanos, M. Di Toro, S. Typel, V. Baran, C. Fuchs, V. Greco, H.H. Wolter NLr, NLrd scalar-field dependent couplings [Nucl. Phys. A 732, 24 (2004)] KVR, KVOR E.E. Kolomeitsev, D.N.Voskresensky reduction of hadron masses in dense medium is included [Nucl. Phys. A 759, 373 (2005)] density dependent couplings DD, D3C, DD-F S. Typel [Phys. Rev. C 71, 064301 (2005) ] Dirac- Bruekner-Hartree-Fock DBHF E.N.E. van Dalen, C. Fuchs, A. Faessler

within empirical range similar isospin diffusion in HIC atomic nuclei ab initio Urbana Argonne small large within empirical range similar isospin diffusion in HIC 62 MeV < L < 107 MeV B.A. Li, A.W. Steiner nucl-th/0511064 similar surface in atomic nuclei spin-orbit splitting RMF Models single nucleon spectra

- Boltzmann kinetic equation - Mean-field potential fitted to directed & elliptic flow [Danielewicz, Lacey, Lynch, Science 298, 1592 (2002)]

mass, size, dynamics of SN explosion integral quantity equation of state of dense matter phase transitions changed in degrees of freedom We want to learn about properties of microscopic excitations in dense matter How to study response function of the NS? How to look inside the NS?

Measuring pulsar temperature Measuring pulsar age for non-accreting systems period increases with time power-law spin-down 1) age of the associated SNR 2) pulsar speed and position w.r. to the geometric center of the associated SNR debris of supernova explosion; accreted “nuclear trash” Crab : 1054 AD Cassiopeia A: 1680 AD Tycho’s SN: 1572 AD 3) historical events

Neutron star cooling data Given: EoS Cooling scenario [neutrino production] Mass of NS Cooling curve

neutron star is transparent for neutrino CV - specific heat, L - luminosity emissivity each leg on a Fermi surface / T neutrino phase space ´ neutrino energy

standard: modified Urca exotic: direct Urca starts at some critical density, i.e. in stars with M>MDUcrit

EoS should produce a large DU threshold in NS matter ! DU process schould be „exotics“ (if DU starts it is dificult to stop it) [Blaschke, Grigorian, Voskresensky A&A 424 (2004) 979] EoS should produce a large DU threshold in NS matter ! [EEK, Voskresensky NPA759 (2005) 373]

no muons: relativistic limit ( ):

The universal “DU curve” “DU curve” for the symmetry energy 30MeV<J<35MeV Low density expansion Analysis of 36 RMF models gives [Dong, et al PRC85, 034308 (2012)]

Nuclear matter equations of state can be constraint at high densities using the neutron star phenomenology and a flow data analysis of heavy-ion collisions The EoS should be stiff enough to support massive neutron star The threshold for direct Urca reactions should high