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3-D simulations of Phase-transition-induced Collapse of Neutron Stars

3-D simulations of Phase-transition-induced Collapse of Neutron Stars. Kim, Hee Il & Lee, Hyung Mok (SNU) KPS meeting, Jeju, 10/18/2007. Phase transition to a Quark Star. Quark Star Stable  (strange) quark star Metastable  mixed phase quark star Observations

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3-D simulations of Phase-transition-induced Collapse of Neutron Stars

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  1. 3-D simulations of Phase-transition-induced Collapse of Neutron Stars Kim, Hee Il & Lee, Hyung Mok (SNU) KPS meeting, Jeju, 10/18/2007

  2. Phase transition to a Quark Star • Quark Star • Stable  (strange) quark star • Metastable  mixed phase quark star • Observations • Millisecond pulsar (XTE J1739-285, 1122 Hz, 2006) • Long duration supernova (SN2006gy): Quark nova after SN explosion • GRB… • Recent works • Lin, et al (2006): GWs, Newtonian Hydro • Yasutake, et al (2007): GWs during the core collapse, Newtonian-hydro

  3. Rotating Stars • Various instability modes  obs by GW etc. • Milisecond pulsars, Collapse to black holes, etc. • Equilibrium solution: hydrostatic solution • Initial data for the numerical works • Non-rotating case: trivial integration • Rotating star: differential eq. with undetermined boundary surface • How to??? • Many ideas after the seminal work of James (68)

  4. Hachisu’s self consistent field method (HSCF 86) • Newtonian star • Special_relativistic_Hydro+pseudo_Newtonian  JHKim’s poster • Integral representation instead of the differential eq.  define entalphy H and some constants • Iteration method ( r f  H with b.c. (H=0)  r ) • Parameters: axis ratio & central density • Solutions for almost all parameter ranges • New ring-like sequence (Dyson-Wong ring)

  5. Rotating equilibrium star for GR (Komatsu, Eriguchi, & Hachisu, KEH89) • Iteration: r  metrics  H with b.c. (H=0)  r • Parameters: axis ratio, maximum density, rotation parameter A • Perfect fluid e.m. tensor, Tab • Fluid four-velocity, ua • Proper velocity w.r.t zamo, v • angular velocity measured • from infinity,W • Hydrostatic eq is integrable if • j(W) is given by hands • H is entalphy

  6. GR Hydro simulations with Cactus/Carpet/Whisky • Cactus provides Einstein equation solvers • Carpet is a mesh-refinement driver for Cactus • Whisky is a GRHydro code based on Cactus • Oriented for 3-D simulations • Free softwares but partly unavailable

  7. Numerical schemes of Whisky • Flux conservative scheme Primitive: r, p, v, h, W  Conservative: D, S, t

  8. High Resolution Shock Capturing :HRSC Method of Lines (MoL) –PDE  ODE by integrating over a cell Should Calculate the flux at the cell boundaries!

  9. - Reconstruction - : to increase the order of accuracy • TVD (Total variation diminishing),Minmod (limiter) • PPM (Piecewise parabolic method) • ENO (Essentially Non-Oscillatory)

  10. - Flux calculation as a Riemann problem – Conservative system with Discontinuous initial data For linear eq. Shock • Nonlinear Solvers: • Roe solver • HLLE (Harten-Lax-van • Leer-Einfeldt) solver • Marquina solver Rarefaction

  11. Collapse of neutron stars induced by the phase transition • Not implemented yet • Nuclear matter  quark matter • ~ softened EOS • ~ instant change of polytropic EOS: stiff  soft • Expected results and Questions • weak transition  GW emission during the stabilization period • strong transition  BH formation in the end • Comparison with the Newtonian results ? • Especially non-axisymmetric instability ?

  12. Initial neutron star model & other numerical setup • Neutron star • Polytropic EOS: P=KrG & P=(G-1)re : r mass density, e specific internal energy density • r_center = 6x1014gcm-3 ~ 2 rnucleon • Axis ratio = 0.83  W = • G=2, K=100  90 • NR setup • Evolution: BSSN • Lapse: 1+log • Shift: static • Unigrid (PUGH) & Fixed Mesh Refinement (Carpet)

  13. Tests on Starbucks:max 10 cpus and 10 giga ram with 1gigabit ethernet Lapse Mass density

  14. Evolution of central mass density • Seems to be converging as the resolution increases • Showing the stabilization PUGH : 64x64x32 128x128x64 180x180x84 Carpet : With 3 levels 64x64x64 128x128x64

  15. Gravitational wave extraction: Q_even (l=2 & m=0) at 40M & 60M • GWs become stronger at larger distances ??? • too coarse to extract GWs • too close extraction points • Unfortunately, extraction code for Carpet is not available yet Unigrid 128x128x64 Unigrid 180x180x84

  16. Concluding Remarks • Softened EOS can make NSs collapse • It requires more expensive and elaborated studies to get meaningful numbers and results • Wave extraction • Detectability (# of events, …) • Microphysics (details of the transition, realistic EOSs, …) • Instabilities (non-axisymmetric modes)

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