Moment of Inertia of Neutron Star Crust Calculations vs. Glitches Observations Joanna Porębska Jagiellonian University – prof. Marek Kutschera & Nuclear Physics Institute (Polish Academy of Sciences) - collaboration with dr Sebastian Kubis, Cracow Dense Matter in HIC and Astrophysics, Dubna,

General structure of NS core crust

Equations of Internal Structure 3) Equation of State (EoS) 1)Tolman-Oppenheimer-Volkoff (TOV), r Sch ~4km → GR 2) mass=f(r)

EoS… in more details only some analytical solutions energy density (APR model) energy per particle (nucleon) derivatives of E,ε masses

EoS… density & pressure density and pressure - full expressions leptons

Neutrality & β equilibrium β equilibrium electrical neutrality

Compressibility K  stability considerations V(n) - isoscalar potential E s (n) – symmetry energy corresponding to the interactions isovector channel

EoS again... two regimes APR - Akmal, Pandharipande & Ravenhall (npe  ) SLy - Skyrme, Lion SLyAPR low densityhigh density n limit 0.01 n cc 0.08 n sat 0.16 n max ~15 n sat n baryon density saturation of nuclear interactions

Calculations the fourh-order Runge-Kutta integration method (rk4) output: Moment of Inertia (Pethick, Ravenhall formulae) Results…

Glitches staff What are they…? Glitch - sudden spin-up of pulsar produced by angular momentum transfer from the superfluid component of the stellar interior to the normal crust What do they say about crust Moment of Inertia? … frequency jump spin-down rate jump

I crust from glitches I c - solid crust + tightly coupled rest (90% of all the star) I res - angular mom. reservoir A - pulsar activity parameter G - coupling parameter – minimum fraction of the star mom. of in. that stores angular momentum and imparts it to the crust in glitches Alpar ’93 >2.4%, Datta&Alpar ’93 >3.4% for 1.4M Θ

Conclusions.. Hybrid approach (calculative-observational) Verification/falsification Quite nice confirmation.. Still under construction Considerations.. to be continued

References M.Camenzind, Compact Objects in Astrophysics (WD, NS & BH) (Springer-Verlag, Berlin Heidelberg, 2007) N.K.Glendenning, Compact Stars: Nuclear Physics, Particle Physics and GR (Springer-Verlag, New York, 1997) P.Haensel, A.Y.Potekhin, D.G.Yakovlev, Neutron Stars 1: Equation of State and Structure (Springer, 2007) S.Kubis, Phys. Rev. C 76, (2007) C.P.Lorenz, D.G.Ravenhall, C.J.Pethick Phys. Rev. Lett. 70, 4 (1993) B.Link, R.I.Epstein, J.M.Lattimer, Phys. Rev. Lett. 83, 17 (1999) D.G.Ravenhall, C.J.Pethick, ApJ 424: (1994)

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