Compare Neutron Star Inspiral and Premature Collapse

1. Compare Neutron Star Inspiral and Premature Collapse Jian Tao ( jtao@wugrav.wustl.edu ) Washington University Gravity Group MWRM-16 Nov 18th, 2006

2. Introduction • Our numerical implementations • Neutron star inspiral simulations and some comparisons to other groups’ results • Premature collapse problem • Conclusions and future plans

3. GR-Astro-AMR implementation • 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 • Computer Science Side • High level programming abstraction with Cactus • Adaptive grid hierarchy implementation withGrACE • Interconnection between Cactus and GrACE with PAGH

4. 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

5. Neutron star inspiral (II) Zoomed into the central region

6. Neutron star inspiral (III) • Geodesic separation • Different touching time means different phase of gravitational waves

7. Inspiral analysis (Rest Mass) • Rest mass • Baryon number shouldn’t be changed • Rest mass should stay the same

8. Inspiral analysis (Rest Mass) • Rest Mass • HRSC scheme helps to conserve the rest mass

9. Inspiral analysis (Constraints) • Constraints • Ham_Max and abs(Ham_Min) (left) • Convergence test for evolution (right)

10. Compare conserved quantities • ADM Mass • Small computational boundaries contribute to the conservation of ADM mass by retaining gravitational waves 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)

11. Compare conserved quantities • Angular Momentum • Higher resolution better conservation • Oscillations might come from initial data 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)

12. 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

13. 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 ?

14. Decompression Effetc • Numerical result • Proper radius of the isolated stars as R (same for both) • Geodesic distance between two stars as the binary separation

15. 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