Stefan Rüster, Jürgen Schaffner-Bielich and Matthias Hempel Institut für theoretische Physik J. W. Goethe-Universität, Frankfurt International Workshop on Astrophysics and Nuclear Structure, Hirschegg, Austria, January 17, 2006 The outer crust of non-accreting cold neutron stars astro-ph/

Outline Introduction The BPS Model Used Nuclear Models Results Summary and Outlook Matthias Hempel The New Physics of Compact Stars The outer crust of non-accreting cold neutron stars

results rely on (unknown) masses of neutron-rich isotopes new experimental data of Audi, Wapstra and Thibault (2003): binding energies of over 2000 precisely measured nuclei nuclei present in the crust in reach to be measured by TRIUMF’s ISAC-II or RIA project many new theoretical nuclear models available Motivation Matthias Hempel Hirschegg, January 17, 2006 grey: known masses dark-blue: recent measurements light-blue: accessible at FAIR

results rely on (unknown) masses of neutron-rich isotopes new experimental data of Audi, Wapstra and Thibault (2003): binding energies of over 2000 precisely measured nuclei nuclei present in the crust in reach to be measured by TRIUMF’s ISAC-II or RIA project many new theoretical nuclear models available Motivation Matthias Hempel Hirschegg, January 17, 2006 grey: known masses dark-blue: recent measurements light-blue: accessible at FAIR green: present in outer crust

Motivation despite negligible mass and small radius (» 300 m) the properties of the crust are important for observations: heat transport electrical resistivity important for evolution of magnetic field low density EoS of special importance for low mass neutron stars

The BPS Model nuclei arranged in a bcc lattice within a free e - -gas the total energy density is given by W N mass of the nuclei, binding energy B is the only input parameter lattice energy W L electron-screening effects -> deviations of e - - distribution from uniformity higher order corrections, not included in BPS Matthias Hempel Hirschegg, January 17, 2006

The BPS Model Fermi-Dirac statistics influences the electrostatic interaction between the electrons: pressure P is given by groundstate for given pressure P: minimal  b for variation over A and Z Matthias Hempel Hirschegg, January 17, 2006

The BPS Model at transition of different equilibrium nuclei (A, Z) ! (A’, Z’) P and  b are equal, but density jump (  e, n e, n b,  ) Matthias Hempel Hirschegg, January 17, 2006

Used Nuclear Models - Overview all models contain data for A, Z and binding energy B mass tables taken from webpages of BRUSLIB and Dobaczewski, private communication or generated inhouse all Skyrme based mass tables take into account effects from deformations for spherical relativistic models calculations with and without pairing deformations included for NL3 and TMA (G.A. Lalazissis, L.S. Geng) if available, experimental data is used (besides BPS) Matthias Hempel Hirschegg, January 17, 2006

Used Nuclear Models – Neutron Driplines strong shell effects for relativistic, (non-deformed) spherical calculations pairing smoothes the dripline by smearing of energy levels deformations give an almost linear raise and larger Z good agreement of deformed calculations Matthias Hempel Hirschegg, January 17, 2006

Results – Equation of State up to  ' g/cm 3 sequences are identical and rely only on experimental data! last common nucleus: 84 Se differences in BPS: 66 Ni and 86 Kr were not found but: EoS shows no noticeable differences, almost model-independent Matthias Hempel Hirschegg, January 17, 2006

Results – Equation of State models separate from each other at high mass density about 10% maximum deviation jumps in the mass density as predicted neutron drip (  b =m n ) around  =4- 5¢10 11 g/cm 3 Matthias Hempel Hirschegg, January 17, 2006

Results – Sequences of selected models five selected most modern models, all including deformations from 56 Fe to a sequence of Nickel isotopes isotone sequences at magic numbers N=50 and N=82 again common nuclei at N=82: 124 Mo, 122 Zr, 120 Sr; due to precise determination of dripline in this region medium super-heavy nucleus 180 Xe last nucleus lying on the dripline with Z=34-38, N=82 (N=84 for NL3) for all models Matthias Hempel Hirschegg, January 17, 2006

Results – Sequences of selected models without W Sc and W Ex heaviest nuclei 180 Xe appears only with screening only small changes Matthias Hempel Hirschegg, January 17, 2006

Results – Sequences of selected models without lattice (lattice melts at finite T): smaller A and Z isotope sequences still same endpoint-region lattice important for sequence! Matthias Hempel Hirschegg, January 17, 2006

Results – Sequences of all models magic numbers N=50 and N=82 almost always present good agreement around Z=40 and N=82 for all models compared to BPS: 66 Ni and 86 Kr enter in, 76 Fe never occurs Matthias Hempel Hirschegg, January 17, 2006

Summary calculation of the outer crust using the extend BPS model and state-of-the-art experimental and theoretical mass tables first investigation for such an enlarged set of nuclear models, including relativistic ones and effects of deformation deformations: dripline rises steeper and almost linear EoS is almost not affected by small differences in the sequence the sequence follows the magic neutron numbers 50 and 82 until the dripline is reached final nucleus pinned down to be around Z=36 and N=82 one medium super-heavy element Matthias Hempel Hirschegg, January 17, 2006

Outlook modelling of the inner crust new approach: BPS method of the outer crust in coexistence with relativistic mean-field neutron-gas extension to finite temperature: suitable for neutron star mergers and core- collapse supernovae Matthias Hempel Hirschegg, January 17, 2006

Stefan Rüster, Jürgen Schaffner-Bielich and Matthias Hempel Institut für theoretische Physik J. W. Goethe-Universität, Frankfurt International Workshop on Astrophysics and Nuclear Structure, Hirschegg, Austria, January 17, 2006 The outer crust of non-accreting cold neutron stars astro-ph/