Upper limits on the effect of pasta on potential neutron

star observablesWilliam Newton

Michael Gearheart, Josh Hooker, Bao-An Li

Crust composition and transition densities according

to the liquid drop modelWilliam Newton

Michael Gearheart, Josh Hooker, Bao-An Li

Introduction

• Liquid drop model: what and why?• Range of crustal properties from uncertainties in symmetryenergy, low density pure neutron matter EoS, ‘residual’ modeleffects• Pasta, core transition densities• Free neutron fraction• (A,Z)

• Given liquid droplet model pasta predictions, is there anyprospect of setting interesting observational limits?

> Mountains> Torsional oscillations

Compressible Liquid Drop Model (CLDM)

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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 densitiesof 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

Compressible Liquid Drop Model (CLDM)

Nuclear Matter EoS

Nuclear Matter EoS

Nuclear Matter EoS

Nuclear Matter EoS

SCH2

MSL

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)

• Upper limit on the effect of pasta on mechanicalphenomena:

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

CRUSTAL TORSIONAL MODES

Pasta effects: mechanical

Ushomirsky, Cutler, Bildsten MNRAS 319, 2000

Liquid drop inputs to shear modulus

Global crust and star properties (M = 1.4 MSUN)

Liquid pasta

Deformation from mountain on crust

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 sizeOPEN 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

Fits to data: σ0≈1.1 MeV fm-2

Fits to data and modeling:

and p ≈ 3

Curvature is also included:

Lattimer et al, Nucl. Phys A., 1985