Compare Neutron Star Inspiral and Premature Collapse

Jian Tao ( jtao@wugrav.wustl.edu )

Washington University Gravity Group

MWRM-16 Nov 18th, 2006

Introduction

Our numerical implementations Neutron star inspiral simulations and

some comparisons to other groups’ results

Premature collapse problem Conclusions and future plans

GR-Astro-AMR implementation

Computer Science Side High level programming abstraction with Cactus Adaptive grid hierarchy implementation with GrACE Interconnection between Cactus and GrACE with PAGH

Physics Side Initializing with unigrid code or by

interpolating

existing data sets Evolving with GR-Astro-AMR (HRSC code) Analyzing with AMR and unigrid analysis

code

Neutron star inspiral (I) Initial data (CFQE Spectral Data)

Binary Polytropic EOS EOS K=123.84 Gamma=2 Separation d : 39.5 km Omega : 2220.05 rad/s Baryon mass S1 : 1.625 M_sol Baryon mass S2 : 1.625 M_sol ADM mass : 2.995 M_sol Total ang mom: 8.53 M_sol^2

(K. Taniguchi, E. Gourgoulhon,Physical Review D 68, 124025, 2003)

Isolated Star Baryon mass : 1.625 M_sol ADM mass : 1.515 M_sol Proper radius : 11.99 M_sol

Neutron star inspiral (II)

Zoomed into the central region

Neutron star inspiral (III) Geodesic separation

Different touching time means different phase of gravitational waves

Inspiral analysis (Rest Mass) Rest mass

Baryon number shouldn’t be changed Rest mass should stay the same

Inspiral analysis (Rest Mass) Rest Mass

HRSC scheme helps to conserve the rest mass

Inspiral analysis (Constraints) Constraints

Ham_Max and abs(Ham_Min) (left) Convergence test for evolution (right)

Compare conserved quantities

dxyz = 0.46 M_s L=148 M_s(633,633,317) 240 GB memory

(Masaru Shibata, Keisuke Taniguchi & Koji Uryu, 2003)Less than 2.4GB memory

(GR-Astro-AMR results)

ADM Mass Small computational boundaries contribute to the

conservation of ADM mass by retaining gravitational waves

Compare conserved quantities

dxyz = 0.46 M_s L=148 M_s(633,633,317) 240 GB memory

(Masaru Shibata, Keisuke Taniguchi & Koji Uryu, 2003)

Less than 2.4GB memory(GR-Astro-AMR results)

Angular Momentum Higher resolution better conservation Oscillations might come from initial data

Premature Collapse Problem (I)

A Brief History J. Wilson and G. Mathews reported so called “neutron star

crushing effect” in 1995 Many papers published to disprove the crushing effect E. Flannagan pointed out an error in their formulation in

1999 J. Wilson and G. Mathews still found destabilization effect,

though small, in their simulations even after they fixed the error found by Flannagan

Mark Miller investigated the problem with fully dynamical general relativistic simulation in 2005

Premature Collapse Problem (II)

Theoretical analysis (E. Flannagan, 1998)

post-Newtonian matched asymptotic expansion works when R/r is small

Simulations carried out by Mark Miller start with corotational binary system

Question : what if R/r is big ? How about irrotational binaries ?

Decompression Effetc Numerical result

Proper radius of the isolated stars as R (same for both) Geodesic distance between two stars as the binary

separation

Summary and future works Summary

GR-Astro-AMR code is applied to study neutron star inspirals and compared to a similar uni-grid similation by other groups

Investigated premature collapse problem with full general relativistic simulations

Future plans Investigate other possible sources of errors Try and implement 4th order finite difference operators Look into non-CFQE initial data