Upper limits on the effect of
pasta on potential neutron star
observables
William Newton
Michael Gearheart, Josh Hooker, Bao-An Li
Crust composition and transition
densities according to the liquid
drop model
William Newton
Michael Gearheart, Josh Hooker, Bao-An Li
Introduction
• Liquid drop model: what and why?
• Range of crustal properties from uncertainties in symmetry
energy, low density pure neutron matter EoS, ‘residual’ model
effects
• Pasta, core transition densities
• Free neutron fraction
• (A,Z)
• Given liquid droplet model pasta predictions, is there any
prospect of setting interesting observational limits?
> Mountains
> Torsional oscillations
Compressible Liquid Drop Model (CLDM)
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6
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Compressible Liquid Drop Model (CLDM)
PROS:
• Physically transparent
• Easy and quick to calculate compositional quantities (A,Z,Xn...)
for use in macroscopic NS models
• Lots of CLDM crust models out there: which one to use?
CONS:
• Semi-classical, macroscopic; no shell effects
• WS approximation not good at the highest densities
of the inner crust.
• Exactly how wrong does CLDM get near the crust-core transition?
Compressible Liquid Drop Model (CLDM)
Uniform nuclear matter EoS
Surface energy
Nuclear Matter EoS
Nuclear Matter EoS
Nuclear Matter EoS
Nuclear Matter EoS
MSL
SCH2
Chen, Cai, Ko, Xu, Chen, Ming 2009
Nuclear Matter EoS
Data point: Warda, Vinas, Roca-Maza, Centelles 2009
L – Esym Correlation
Crust-core and spherical-pasta transition densities
Crust-core and spherical-pasta transition densities
Crust-core and spherical-pasta transition densities
Liquid drop crust-core transition
agrees well with stability analyses
Free neutron fraction
Free neutron fraction
Upper limits on the effect of
pasta on potential
observables
Pasta effects: mechanical
Crust shear modulus (Strohmayer et al 1991)
Pasta effects: mechanical
• Upper limit on the effect of pasta on mechanical
phenomena:
Set μpasta = 0
• Good approx. to take μ at deepest layer of crust;
I. ‘Solid pasta’ – μ at crust-core boundary
II. ‘Liquid pasta’ – μ at spherical-pasta
boundary
MOUNTAINS
Ushomirsky, Cutler, Bildsten MNRAS 319, 2000 CRUSTAL TORSIONAL MODES
Liquid drop inputs to shear modulus
Global crust and star properties (M = 1.4 MSUN)
Deformation from mountain on crust
Liquid pasta
Torsional crust oscillations
Conclusions
• Liquid drop model predicts a range for the transition densities and
composition; current nuclear data favours, e.g.:
• 0.11 < ncrust-core< 0.05 fm-3
• 0.07 < npasta < 0.05 fm-3
• Symmetry energy (magnitude and slope), dominates the uncertainty in
the range; correlated with constraints on low density PNM for a given
form of the nuclear matter EoS
• Large pasta layer favored by current nuclear data
• Estimates of the maximal effect of pasta on mechanical properties of
the crust suggest a significant contribution of the pasta layer to
observational phenomena such as SGR QPOs, potential GWs from
mountains
• Similar (though slightly larger) signature to crustal superfluid
• Relatively clean signature in maximum mountain size
OPEN ISSUES/FUTURE
• What is the shear modulus at the bottom of the inner crust?
• How do the liquid drop predictions compare with microscopic
calculations (e.g. 3DHF); can it be used as a guide?
• Pasta contribution to crustal moment of inertia and moment of inertia of
crustal superfluid neutrons (glitches); bubble cooling;
Surface Energy
Lattimer et al, Nucl. Phys A., 1985
Fits to data: σ0≈1.1 MeV fm-2
Fits to data and modeling:
and p ≈ 3
Curvature is also included: