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 (     H with b.c. (H=0)   ) 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:    metrics    with b.c. (H=0)   Parameters: axis ratio, maximum density, rotation parameter A Perfect fluid e.m. tensor, T ab Fluid four-velocity, u a Proper velocity w.r.t zamo, v angular velocity measured from infinity,  Hydrostatic eq is integrable if j(  ) 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:

8. 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

9. 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 ?

10. 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

11. Initial neutron star model & other numerical setup Neutron star  Polytropic EOS: P=K   & P=(  mass density,  specific internal energy density   _center = 6x10 14 gcm -3 ~ 2  nucleon  Axis ratio = 0.83       NR setup  Evolution: BSSN  Lapse: 1+log  Shift: static  Unigrid (PUGH) & Fixed Mesh Refinement (Carpet)

12. Tests on Starbucks: max 10 cpus and 10 giga ram with 1gigabit ethernet LapseMass density

13. 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

14. Density profile Rho_center

15. Gravitational wave extraction: Q_even (l=2 & m=0) at 40M & 60M Unigrid 128x128x64Unigrid 180x180x84 GWs become stronger at larger distances ??? too coarse to extract GWs too close extraction points Unfortunately, extraction code for Carpet is not available yet

16. Quadrupole moment

17. Gravitational Wave???

18. Psi_4_Re : outgoing waves???

19. 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?