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Phase transition induced collapse of Neutron stars

Phase transition induced collapse of Neutron stars. Kim, Hee Il Astronomy Program, SNU 13th Haengdang Symposium, 11/30/2007. Neutron star collapse. Howto? Find a (initial) equilibrium star Perturb the equilbrium star Follow the evolution  Various instability modes

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Phase transition induced collapse of Neutron stars

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  1. Phase transition induced collapse of Neutron stars Kim, Hee Il Astronomy Program, SNU 13th Haengdang Symposium, 11/30/2007

  2. Neutron star collapse Howto? • Find a (initial) equilibrium star • Perturb the equilbrium star • Follow the evolution  Various instability modes • Showing the inner structure of a star, e.g. helioseismology • Gravitational wave emission

  3. Equilibrium Star • Stars are stable in most of their lifetime • = Hydrostatic solution • = initial data for evolution • Non-rotating star • 1D problem. Trivial to Integrate • Rotating star • 2D elliptic Differential eqs. • Unknow boundary surface

  4. Hachisu’s self consistent field method (HSCF 86) • Newtonian star • 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. HSCF in Special Relativistic regime • Why needs SR? • Newtonian approach breaks down • If the motion is relativistic, e.g. rapid rotation • If the equation of state is relativistic, e.g. quark matter • Full GR is too expensive • If the gravitiy is very weak, we don’t want to know the spacetime structure even in weak field limit • Low resolution due to the limited computational resources • SR + pseudo-Newtonian approach • Modified Poisson equation:

  7. 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

  8. 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 ?

  9. 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

  10. 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)

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

  12. 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

  13. Density profile Rho_center

  14. 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

  15. Quadrupole moment

  16. Gravitational Wave???

  17. Psi_4_Re : outgoing waves???

  18. Concluding Remarks • 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) • BH formation?

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