Stefan Rüster, Jürgen Schaffner-Bielich and Matthias HempelInstitut 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/0509325
Outline
IntroductionThe BPS Model
Used Nuclear ModelsResults
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 FAIR@GSI, TRIUMF’s ISAC-II or RIA project
many new theoretical nuclear models available
Motivation
Matthias HempelHirschegg, 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 FAIR@GSI, TRIUMF’s ISAC-II or RIA project
many new theoretical nuclear models available
Motivation
Matthias HempelHirschegg, 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
WN mass of the nuclei, binding energy B is the only input parameter
lattice energy WL
electron-screening effects -> deviations of e--distribution from uniformity
higher order corrections, not included in BPS
Matthias HempelHirschegg, 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 HempelHirschegg, 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, ne , nb, )
Matthias HempelHirschegg, 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 HempelHirschegg, 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 HempelHirschegg, January 17, 2006
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 HempelHirschegg, 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=mn) around =4-5¢1011g/cm3
Matthias HempelHirschegg, January 17, 2006
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 HempelHirschegg, January 17, 2006
Results – Sequences of selected models
without WSc and WEx
heaviest nuclei 180Xe appears only with screening
only small changes
Matthias HempelHirschegg, 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 HempelHirschegg, 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: 66Ni and 86Kr enter in, 76Fe never occurs
Matthias HempelHirschegg, 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 HempelHirschegg, 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 HempelHirschegg, January 17, 2006
Stefan Rüster, Jürgen Schaffner-Bielich and Matthias HempelInstitut 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/0509325
