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

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 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

11. 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

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 4 th order finite difference operators  Look into non-CFQE initial data