1. Computational General Relativistic Astrophysics at Wash U: What are we doing lately? Nov., 2006 Numerical Relativity Group Washington University

2. We are having a good time….

3. Computational Infrastructure Built Lately Two new versions of GR-Astro: 1. GR-Astro-AMR With GR-Astro-AMR, i. We solve full set of Einstein eqns+GR-Hydro eqns.+realistic EOS. ii. AMR: covering a large region to get waveforms & covering the neutron stars with high resolutions. Coarse grid coverage Fine grid coverage

4. Validation of GR-Astro-AMR Tons of validation and convergence tests: i. Comparisons with the unigrid code for different systems ii. Convergence tests of 3 different kinds: a. increasing resolutions at all levels b. convergence with respect to adding levels c. comparing results with unigrid at each levels ------------to be described in Mew-Bing Wan’s Talk Don’t you dare to ask for convergence tests when you review papers from this group… Comparison of capability of code to others’ ------------to be described in Jian Tao’s Talk

5. 2. GR-AStro-2D: For axisymmetric systems, evolves one slice of 3D cartisian i. Resolution and coverage: 600^3 = 6570x6570x5 ii.Extensive Validation and convergence tests ---------------Ke Jian Jin’s talk New Infrastructure Built Brandt et.al

6. What are we using GR-Astro-AMR & GR-Astro-2D for?

7. Physics Focus: Prompt vs. Delayed Collapse NS+NS coalescence: 1.4+1.4=2.8 sure collapse Question is: When? ---prompt collapse: collapse in free falling time ~10 M^(1/2)~0.1ms ---delayed collapse: collapse after cooling/angular momentum transport time scale ~seconds or more. Gravitational wave signals can be very different from the two kinds of collapse. The No-Prompt-Collapse Conjecture---no prompt collapse in head-on collisions. Conjecture disproved. interesting results: ----merged objects can promptly collapse with M<M_eq ----merged object at point of threshold collapses with critical phenomena

8. Critical phenomena at the threshold of Prompt Collapses Collapse of an axisymmetric object (extending studies to non- spherical) Described by an EOS common in modeling NSs (more realistic) ---- We found: 1. An “universal” critical index ~10.8, 2. Growth time of unstable mode ~0.05ms 3. Critical phenomena observed by changing EOS, without fine tuning initial data! ----------------Ke Jian Jin’s talk

9. Critical phenomena in general NS fixed point A state in this layer will be attracted to the critical pt, showing critical behavior, but it is only a thin layer…need fine tuning to see(?) Position depends on EOS Solution Space near threshold plan

10. Critical phenomena with a changing EOS The study shows: Changing EOS slowly, the picture is still valid. Changing EOS, the threshold plane swipes through the solution space. A state originally not in the thin layer will later be in, and move towards the critical point. Implications: ---May not need to fine tune the initial data before seeing critical behavior ---the window of critical behavior depends on the timescales of change of EOS (1 s) and growth of the critical unstable mode (0.05ms)…..window can be wide. Position of threshold plane depends on EOS Growth time of unstable mode ~0.05ms Solution Space

11. Critical phenomena in nature? Interesting Questions: Will a proto-NS formed in supernova show critical behavior when cooling down in a timescale of seconds and collapse (SN 1987a)? What is the structure of the solution space near the threshold plane? ---limit cycle ---spherical critical solution? ---spherical unstable mode? ---periodic vs. static (M>M_eq)? ---effect of angular momentum? Axisymmetric spherical With ang. momentum ?

12. Prompt Collapse with Angular Momentum Dividing line between prompt and delayed collapse for NS coalescence in ---inspiral ---capture with an impact parameter In both cases: threshold of angular momentum~0.87 of critical Kerr ----------------Hui-Min Zhang’s talk L>0.87M^2 L<0.87M^2 Inspiral Capture

13. What is the window of angular momentum in realistic NS inspiral coalesence If less than ~0.87M^2, prompt collapse, no critical behavior If more than ~0.87M^2 (strictly CFQE irrotational ~0.94), will it be in the window that the threshold plane can swipe through and induce critical behavior, when the merged object (hypermassive NS) cools and loses angular momentum? Need to construct reliable initial data with far enough separation, in order to begin numerical evolution. How far is enough? -----------Randy Wolfmeyer’s talk (progress report)

14. Summary Message 1: Critical collapse might be observable in nature, through the softening of EOS. ---Could a substantial portion of inspiral coalescences lead to critical collapses? Message 2: The threshold of angular momentum for prompt gravitational collapse for NS coalescence is at ~0.87M^2, for both inspiral and capture (with polytropic EOS). ---Where is this 0.87 coming from? Message 3: We are having a good time at Wash U, with fun toys to play with (GR-Astro-AMR & GR-Astro-2D). ----as will be described in the following 5 talks by Wan, Tao, Zhang, Wolfmeyer and Jin