The outer crust of non-accreeting neutron stars

1
The outer crust of non-accreting cold neutron
stars

astro-ph/0509325
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

2
The outer crust of non-accreting cold neutron
stars

Outline
Introduction The BPS Model Used Nuclear Models Results Summary and Outlook


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_at_GSI, TRIUMFs 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_at_GSI, TRIUMFs 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

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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 -gt 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
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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
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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
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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
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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 (?bmn) around ?4-51011g/cm3

Matthias Hempel Hirschegg, January 17, 2006
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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 N50 and N82
• again common nuclei at N82 124Mo , 122Zr,
  120Sr due to precise determination of dripline
  in this region
• medium super-heavy nucleus 180Xe

• last nucleus lying on the dripline with Z34-38,
  N82 (N84 for NL3) for all models

Matthias Hempel Hirschegg, January 17, 2006
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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
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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
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Results Sequences of all models

• magic numbers N50 and N82 almost always
  present
• good agreement around Z40 and N82 for all
  models
• compared to BPS 66Ni and 86Kr enter in, 76Fe
  never occurs

Matthias Hempel Hirschegg, January 17, 2006
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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 Z36 and
  N82
• 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
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