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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 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) 5 6 7 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: