Computational General Relativistic Astrophysics at Wash U: What are we doing lately?

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

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 finetuning initial data! ----------------Ke Jian Jin’s talk

9. Critical phenomena in general Solution Space near threshold plan Position depends on EOS 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(?)

10. Critical phenomena with a changing EOS Solution Space 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

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? spherical Axisymmetric ? With ang. momentum

12. Prompt Collapse with Angular Momentum Capture • 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 Inspiral L>0.87M^2 L<0.87M^2

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