The outer crust of non-accreting cold neutron stars

1. The outer crust of non-accreting cold neutron stars astro-ph/0509325

2. The outer crust of non-accreting cold neutron stars Matthias Hempel The New Physics of Compact Stars

3. Motivation • 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 FAIR@GSI, TRIUMF’s ISAC-II or RIA project • many new theoretical nuclear models available grey: known masses dark-blue: recent measurements light-blue: accessible at FAIR Matthias Hempel Hirschegg, January 17, 2006

4. Motivation • 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 FAIR@GSI, TRIUMF’s ISAC-II or RIA project • many new theoretical nuclear models available grey: known masses dark-blue: recent measurements light-blue: accessible at FAIR green: present in outer crust Matthias Hempel Hirschegg, January 17, 2006

5. 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

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

7. 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

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

9. 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

10. 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

11. Results – Equation of State • up to ' 1010 g/cm3 sequences are identical and rely only on experimental data! • last common nucleus: 84Se • differences in BPS: 66Ni and 86Kr were not found • but: EoS shows no noticeable differences, almost model-independent Matthias Hempel Hirschegg, January 17, 2006

12. 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=mn) around =4-5¢1011g/cm3 Matthias Hempel Hirschegg, January 17, 2006

13. Results – Sequences of selected models • five selected most modern models, all including deformations • from 56Fe to a sequence of Nickel isotopes • isotone sequences at magic numbers N=50 and N=82 • again common nuclei at N=82: 124Mo , 122Zr, 120Sr; due to precise determination of dripline in this region • medium super-heavy nucleus 180Xe • 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

14. Results – Sequences of selected models • without WSc and WEx • heaviest nuclei 180Xe appears only with screening • only small changes Matthias Hempel Hirschegg, January 17, 2006

15. 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

16. 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: 66Ni and 86Kr enter in, 76Fe never occurs Matthias Hempel Hirschegg, January 17, 2006

17. 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

18. 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

19. The outer crust of non-accreting cold neutron stars astro-ph/0509325