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

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Computational General Relativistic Astrophysics
at Wash U What are we doing lately?
Nov., 2006 Numerical Relativity
Group Washington University
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We are having a good time.
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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 eqnsGR-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
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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
  Wans Talk
• Dont 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
  Taos Talk

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New Infrastructure Built
2. GR-AStro-2D For axisymmetric systems,
evolves one slice of 3D cartisian

Brandt et.al
i. Resolution and coverage 6003
6570x6570x5 ii.Extensive Validation and
convergence tests
---------------Ke Jian Jins talk
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What are we using GR-Astro-AMR GR-Astro-2D for?
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Physics Focus Prompt vs. Delayed Collapse

• NSNS coalescence 1.41.42.8 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 MltM_eq
• ----merged object at point of
  threshold collapses with critical phenomena

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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
  Jins talk

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

Solution Space
Position of threshold plane depends on EOS
Growth time of unstable mode 0.05ms
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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 (MgtM_eq)?
• ---effect of angular momentum?

spherical
Axisymmetric
?
With ang. momentum
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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 momentum0.87
  of critical Kerr
  
• ----------------Hui-Min
  Zhangs talk

Capture
Inspiral
Lgt0.87M2
Llt0.87M2
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What is the window of angular momentum in
realistic NS inspiral coalesence

• If less than 0.87M2, prompt collapse, no
  critical behavior
• If more than 0.87M2 (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
  Wolfmeyers talk (progress report)

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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 0.87M2, 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