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Upper limits on the effect of pasta on potential neutron star observables William Newton Michael Gearheart, Josh Hooker, Bao-An Li

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Crust composition and transition densities according to the liquid drop model William Newton Michael Gearheart, Josh Hooker, Bao-An Li

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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

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Compressible Liquid Drop Model (CLDM)

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PROS: Physically transparent Easy and quick to calculate compositional quantities (A,Z,X n...) 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)

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Uniform nuclear matter EoS Surface energy Compressible Liquid Drop Model (CLDM)

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Nuclear Matter EoS

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SCH2 MSL Chen, Cai, Ko, Xu, Chen, Ming 2009

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Nuclear Matter EoS Data point: Warda, Vinas, Roca-Maza, Centelles 2009

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L – E sym Correlation

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Crust-core and spherical-pasta transition densities

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Liquid drop crust-core transition agrees well with stability analyses

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Free neutron fraction

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Upper limits on the effect of pasta on potential observables

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Pasta effects: mechanical Crust shear modulus (Strohmayer et al 1991)

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Upper limit on the effect of pasta on mechanical phenomena: Set μ pasta = 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

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Liquid drop inputs to shear modulus

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Global crust and star properties (M = 1.4 M SUN )

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Liquid pasta Deformation from mountain on crust

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Torsional crust oscillations

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Conclusions Liquid drop model predicts a range for the transition densities and composition; current nuclear data favours, e.g.: 0.11 < n crust-core < 0.05 fm < n pasta < 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;

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Surface Energy Fits to data: σ 0 ≈1.1 MeV fm -2 Fits to data and modeling: and p ≈ 3 Curvature is also included: Lattimer et al, Nucl. Phys A., 1985

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