Phase transition induced Phase transition induced collapse of Neutron starscollapse of Neutron stars

Kim, Hee IlKim, Hee IlAstronomy Program, SNUAstronomy Program, SNU13th Haengdang Symposium, 11/30/2007

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. helios

eismology Gravitational wave emission

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

G

p

42

2

Hachisu’s self consistent field method (HSCF 86)

Newtonian star Integral representation instead of the differential eq. d

efine 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)

Rotating equilibrium star for GR (Komatsu, Eriguchi, & Hachisu, KEH89)

Iteration: metrics with b.c. (H=0) Parameters: axis ratio, maximum density, rotation parameter A

22222222222 )(sin)( dtdredrdredteds • Perfect fluid e.m. tensor, Tab

• Fluid four-velocity, ua

• 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

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 spacetim

e structure even in weak field limit Low resolution due to the limited computational resources

SR + pseudo-Newtonian approach Modified Poisson equation:

iiTTG 0

0activeactive2 where4

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, Newt

onian-hydro

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 ?

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

Initial neutron star model & other numerical setup Neutron star

Polytropic EOS: P=K& P=(mass density, specific internal energy density

_center = 6x1014gcm-3 ~ 2 nucleon

Axis ratio = 0.83

NR setup Evolution: BSSN Lapse: 1+log Shift: static Unigrid (PUGH) & Fixed Mesh Refinement (Carpet)

Tests on Starbucks: max 10 cpus and 10 giga ram with 1gigabit ethernet

Lapse Mass density

Evolution of central mass density• Seems to be converging as the resolution increases• Showing the stabilization

PUGH :

64x64x32128x128x64180x180x84

Carpet : With 3 levels

64x64x64128x128x64

Density profileRho_center

Gravitational wave extraction: Q_even (l=2 & m=0) at 40M & 60M

Unigrid 128x128x64 Unigrid 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

Quadrupole momentji

ij xxDxdI 3

Gravitational Wave???

r

tItIh yyxx )'()'(

r

tIh xy )'(

2

r

tIh

r

tItIh xyyyxx )'(

2 )'()'(

Psi_4_Re : outgoing waves???

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 EOS

s, …) Instabilities (non-axisymmetric modes) BH formation?