Neutron star Equa-ons of State: An ideal to aim towards

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1 Neutron star Equa-ons of State: An ideal to aim towards Astrophysical modeling generally requires EOS tables more extensive than tradi-onal pressure versus energy density: Chemical poten-als, density- deriva-ves of pressure, chemical poten-als Versus individual proton and neutron densi-es n p, n n (not just β- equilibrium) Effec-ve masses, superfluid gaps, transport proper-es Crust proper-es (composi-on, shear modulus) Consistently calculated, informed by state- of- the- art microscopic nuclear majer calcula-ons, explore symmetry energy varia-on Provided in a form useful for astrophysical codes (community effort) Not all or nothing any progress in way EOSs are prepared is valuable (e.g. see discussion in Lin, Andersson, Comer, PRD78, (2008) for the astrophysicist s perspec-ve) Nuclear astrophysics town mee-ng/aug /Texas A&M University W.G.Newton TAMU- Commerce

2 Over what mass range are we probing primarily proper-es of nucleonic majer? Target low mass stars for unambiguous signatures of nucleonic majer proper-es? What is the minimum mass nature produces? Neutron star masses M (M solar ) Nucleonic star R (km) How are low mass neutron stars born? e- capture SN scenario believed to produce many neutron stars over a -ght mass range at around 1.25M SUN Observa-onal evidence only circumstan-al (Type Ib/c Sne; proper-es of certain NS binary systems) Claim: 1D SN simula-ons are sufficient to model e- capture SN, and lijle mass loss, but no systema-c analysis yet performed If above holds, could place strong constraints on binding energy (thus EOS); Also a very important stellar evolu-onary scenario; influences NS ini-al mass func-on Hyperon, quark degrees of freedom appear Causality: R>2.9 (GM/c 2 ) 32 =5ρ 0 =4ρ 0 =3ρ 0 =2ρ E sym = 30.5 MeV (NN) 1.97(4) M solar 35.1 Gandolfi, Carlson, Reddy PRC85 (2012) 1.4 M solar

3 How thick is a neutron star crust? Crust thickness depends on crust- core transi-on pressure P cc P cc depends mainly on E sym (ρ 0 ), L(ρ 0 ), K sym (ρ 0 ) (alterna-vely E sym (ρ 0.1fm - 3 ), L(ρ 0.1fm - 3 )) Measurement of crust thickness gives constrains higher order terms in symmetry energy expansion (and vice versa!) Crust thickness probed by glitches, crust thermal relaxa-on -mescale, crust oscilla-ons Newton, Gearheart, Li, ApJS204 (2013) What does the crust- core transi-on look like? Pasta phases: How extensive? (depends on same symmetry energy quan--es as crust thickness) Can we perform reliable calcula-ons of their shear modulus, transport proper-es, entrainment parameters? Are they sensi-ve to the symmetry energy? Can we find unambiguous observa-onal signatures?

4 What does the crust- core transi-on look like? Calcula-ng pasta: the state of the art: Classical/quantum molecular dynamics, 3D(TD)HF How best to combine advantages of these techniques? (3DHF: quantum shell effects, band structure but small volume; C/QMD: larger volumes Mesophysics: how do pasta structures organize on larger scales; strong analogy with som condensed majer systems. Can we learn from som condensed majer techniques (lance Boltzmann )? Pais, Stone PRL 2012 Schneider, Horowitz, Hughto, Berry, PRC88 (2013)

5 How does the crust- core transi-on region influence neutron star dynamics? How do pasta layers influence: r- mode damping in the viscous boundary layer at crust- core interface? The frequencies of crust oscilla-ons? The coupling between crust and core oscilla-on modes? The evolu-on of the crustal magne-c field? Thermal relaxa-on of the crust? Haskell, Degenaar, Ho, MNRAS 424 (2012) Gearheart, Newton, Li, MNRAS418 (2011)

6 Effect of short- range correla-ons, tensor force, and the high- momentum tail Carbone et al, EPJA50 (2014) Subedi et al, Science 320 (2008) McGauley, Sargsian, arxiv: In asymmetric nuclear majer, large frac-on of protons occupy high momentum states due to SRCs Effect on proton superfluidity, ν- emission processes, transport proper-es Requires consistent microscopic calcula-ons at supra- satura-on densi-es