Simulations of General Relativistic Hydrodynamics

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Simulations of General Relativistic Hydrodynamics

• Kim, Hee Il (SNU)
• The 20th NR meeting

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GR Hydro

• Fluid dynamics in a strong Gravitational field
• Astrophysics (mainly for NSs)
• Single star evolution supernova, instability
• Evolution of Binary Star
• NSNS, NSBH
• GRMHD GRB, Astrophysical Jets
• Cosmology
• Evolution of the universe
• Primoridial black holes Critical phenomena

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ShibataShapiro Group single star

• Axisymmetric collapse simulations of rotating
  massive stellar cores in full general relativity
  Numerical study for prompt black hole formation.
  Phys.Rev.D71084013,2004. e-Print
  astro-ph/0504567
• Constraining nuclear equations of state using
  gravitational waves from hypermassive neutron
  stars. Phys.Rev.Lett.94201101,2005. e-Print
  gr-qc/0504082
• Three-dimensional simulations of stellar core
  collapse in full general relativity
  Nonaxisymmetric dynamical instabilities.Phys.Rev.
  D71024014,2005. e-Print astro-ph/0412243
• Numerical evolution of secular bar-mode
  instability induced by the gravitational
  radiation reaction in rapidly rotating neutron
  stars. Phys.Rev.D70084022,2004. e-Print
  astro-ph/0408016
• New criterion for direct black hole formation in
  rapidly rotating stellar collapse.Published in
  Phys.Rev.D70084005,2004. e-Print gr-qc/0403036
  

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• Stability of rigidly rotating relativistic stars
  with soft equations of state against
  gravitational collapse. Astrophys.J.605350-359,2
  004. e-Print astro-ph/0403172
• Gravitational waves from axisymmetric rotating
  stellar core collapse to a neutron star in full
  general relativity.Phys.Rev.D69084024,2004.
  e-Print gr-qc/0402040
• Gravitational waves from axisymmetrically
  oscillating neutron stars in general relativistic
  simulations. Phys.Rev.D68104020,2003. e-Print
  astro-ph/0402184
• Collapse of rotating supramassive neutron stars
  to black holes Fully general relativistic
  simulations.Astrophys.J.595992,2003. e-Print
  astro-ph/0310020
• Dynamical bar-mode instability of differentially
  rotating stars Effects of equations of state and
  velocity profiles.Mon.Not.Roy.Astron.Soc.343619,
  2003. e-Print astro-ph/0304298

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• Axisymmetric general relativistic hydrodynamics
  Long term evolution of neutron stars and stellar
  collapse to neutron stars and black holes.
  Phys.Rev.D67024033,2003. e-Print
  gr-qc/0301103
• Collapse of a rotating supermassive star to a
  supermassive black hole Analytic determination
  of the black hole mass and spin.Astrophys.J.5779
  04-908,2002. e-Print astro-ph/0209251
• Dynamical instability of differentially rotating
  stars.Mon.Not.Roy.Astron.Soc.334L27,2002.
  e-Print gr-qc/0206002
• Collapse of a rotating supermassive star to a
  supermassive black hole Fully relativistic
  simulations.Astrophys.J.572L39-L44,2002.
  e-Print astro-ph/0205091

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ShibataShapiro NSNS

• The Final Fate of Binary Neutron Stars What
  Happens After the Merger? e-Print gr-qc/0701145
   Unknown
• Merger of binary neutron stars to a black hole
  disk mass, short gamma-ray bursts, and
  quasinormal mode ringing.Phys.Rev.D73064027,2006
  . e-Print astro-ph/0603145  Unknown
• Binary neutron stars in a waveless
  approximation.Phys.Rev.Lett.97171101,2006.
• Merger of binary neutron stars with realistic
  equations of state in full general
  relativity.Phys.Rev.D71084021,2005. e-Print
  gr-qc/0503119 
• Merger of binary neutron stars of unequal mass in
  full general relativity.Phys.Rev.D68084020,2003.
  e-Print gr-qc/0310030  Unknown TOPCITE 50
• Gravitational waves from the merger of binary
  neutron stars in a fully general relativistic
  simulation.Prog.Theor.Phys.107265,2002.
  e-Print gr-qc/0203037  Unknown TOPCITE 50

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Shibata BHNS

• Merger of black hole-neutron star binaries
  Nonspinning black hole case.Masaru Shibata
  (Tokyo U.) , Koji Uryu (Wisconsin U., Milwaukee)
  . Dec 2006. 5pp.Published in Phys.Rev.D74121503,
  2006.e-Print gr-qc/0612142  Unknown
• Merger of black hole-neutron star binaries in
  full general relativity.Masaru Shibata (Tokyo
  U.) , Koji Uryu (Wisconsin U., Milwaukee) . Nov
  2006. 14pp.Submitted to Class.Quant.Grav.

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ShibataShapiro MHD

• Magnetorotational collapse of massive stellar
  cores to neutron stars Simulations in full
  general relativity.Phys.Rev.D74104026,2006.
  e-Print astro-ph/0610840  Unknown
• Collapse and black hole formation in magnetized,
  differentially rotating neutron stars.e-Print
  gr-qc/0610103  Unknown
• Evolution of magnetized, differentially rotating
  neutron stars Simulations in full general
  relativity.Phys.Rev.D73104015,2006. e-Print
  astro-ph/0605331  Unknown
• Magnetized hypermassive neutron star collapse a
  central engine for short gamma-ray
  bursts.Phys.Rev.Lett.96031102,2006. e-Print
  astro-ph/0511142  Unknown
• Collapse of magnetized hypermassive neutron stars
  in general relativity.Phys.Rev.Lett.96031101,200
  6. e-Print astro-ph/0510653
• Magnetohydrodynamics in full general relativity
  Formulation and tests.Phys.Rev.D72044014,2005.
  e-Print astro-ph/0507383  Unknown

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Cactus/Carpet/Whisky

• Luca Baiotti, Ian Hawke, Luciano Rezzolla, Erik
  Schnetter, Gravitational-Wave Emission from
  Rotating Gravitational Collapse in three
  Dimensions, Phys. Rev. Lett. 94, 131101 (2005),
  arXivgr-qc/0503016.
• Burkhard Zink, Nikolaos Stergioulas, Ian Hawke,
  Christian D. Ott, Erik Schnetter, Ewald Müller,
  Black hole formation through fragmentation of
  toroidal polytropes, Phys. Rev. Lett. 96, 161101
  (2006), arXivgr-qc/0501080.
• Frank Löffler, Luciano Rezzolla, Marcus Ansorg,
  Numerical evolutions of a black hole-neutron star
  system in full General Relativity, Phys. Rev.
  Lett. 97, 141101 (2006), arXivgr-qc/0606104.
• Christian D. Ott, Harald Dimmelmeier, Andreas
  Marek, Hans-Thomas Janka, Ian Hawke, Burkhard
  Zink, Erik Schnetter, 3D Collapse of Rotating
  Stellar Iron Cores in General Relativity with
  Microphysics, arXivastro-ph/0609819

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• Burkhard Zink etal, Non-axisymmetric instability
  and fragmentation of general relativistic
  quasi-toroidal stars, arXivastro-ph/0611601.
• Christian D. Ott etal, Rotating Collapse of
  Stellar Iron Cores in General Relativity,
  arXivastro-ph/0612638.
• Luca Baiotti, Ian Hawke, Luciano Rezzolla, On the
  gravitational radiation from the collapse of
  neutron stars to rotating black holes,
  arXivgr-qc/0701043.
• Bruno Giacomazzo, Luciano Rezzolla, WhiskyMHD a
  new numerical code for generial relativistic
  magnetohydrodynamics, arXivgr-qc/0701109.
• Burkhard Zink etal, Fragmentation of general
  relativistic quasi-toroidal polytropes,
  arXiv0704.0431 gr-qc.
• Where is NSNS???

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Numerical Implementation

• Flux conservative scheme

Primitive rho, p, v, h, W ? Conservative D, S,
tau
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Method of Lines (MoL) PDE ? ODE by integrating
over a cell
High Resolution Shock Capturing HRSC
Should Calculate the flux at the cell boundaries!
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- Reconstruction -
to increase the order of accuracy

• TVD (Total variation diminishing),Minmod
  (limiter)
• PPM (Piecewise parabolic method)
• ENO (Essentially Non-Oscillatory)

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- Flux calculation as a Riemann problem
Conservative system with Discontinuous initial
data ?
For linear eq.
Shock

• Nonlinear Solvers
• Roe solver
• HLLE (Harten-Lax-van
• Leer-Einfeldt) solver
• Marquina solver

Rarefaction
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Whisky 3D GRHydro Code for the EU
Network (mainly copied from http//www.whiskycode.
org)
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sonnim_at_bucks EUHydro pwd /home/sonnim/Cactus/ar
rangements/EUHydro sonnim_at_bucks EUHydro
ls ADMConstraints EOS_Polytrope WhiskyQuad
Whisky_IVP Whisky_Steer Auxilliary
Einstein Whisky_Analysis
Whisky_Init_Data Whisky_TOVSolver CVS
Hydra Whisky_DriftCorrect
Whisky_MeudonData Whisky_TOVSolverC CactusEinstei
n Whisky Whisky_Dust
Whisky_RNSID sonnim_at_bucks EUHydro
EUHydro ? Whisky in May, 2007
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• Whisky
• Provides the hydro variables and the evolution
  routines.
• 2. Calculates stress energy terms for a spacetime
  evolution routine.
• The basic routines all seem to work fine. We have
  good results and convergence for shock tubes, TOV
  stars (Cowling approximation and dynamic),
  rotating polytropes, the migration test and the
  forced collapse of an unstable TOV star. Some
  testing may still be required for any new run,
  but it seems solid.
• Whisky_Init_Data
• Provides some simple initial data, such as shock
  tubes (just simple cases right now) and TOV
  stars. Shock tubes work fine. TOV routines
  require LSODA and are largely untested currently
  we're using RNSID or the separate TOVSolver
  thorns.

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Whisky_RNSID Provides initial data for hydro and
spacetime variables for a single neutron star.
Currently used for the TOV tests as well. As
this is just an interface to the standard RNSID
code I think we can say this has been well
tested, with one exception you can't have a
point exactly on the origin at the moment.
Whisky_TOVSolver Provides initial data for
hydro and spacetime variables for a TOV star.
Works fine but doesn't do boosted solutions or
include support for the static conformal factor
as yet. Will provide up to 10 TOV stars "glued"
together in various ways along with various
perturbations. To make these configurations a
solution of the field equations you must use the
IVP solver.
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Whisky_IVP Given an initial guess for a solution
of Einstein's equations with matter this thorn
uses BAM to solve the York-Lichnerowicz initial
value problem. Normally used for perturbations of
solutions generated by RNSID or TOV_Solver.
Works ok for NS problems. Note that using BAM is
always a bit tricksy. EOS_Base Allows the
registration of multiple equations of state which
can be chosen between at run time. Works fine.
Is also used by GRAstro_Hydro. EOS_Ideal_Fluid
An implementation of the ideal gas EOS to use
with EOS_Base. Works fine. Is also used by
GRAstro_Hydro. EOS_Polytrope An implementation
of a polytropic EOS that uses EOS_Base. This is
a fudge, as EOS_Base isn't really designed for a
polytropic EOS. However it works and provides all
that we require with the minimum of code
rewriting. Stupid choice of name, though.
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ADMBase Provides spacetime variables and some
other utility routines. This is the standard
Cactus thorn from CactusEinstein. For our
purposes it just provides the spacetime
variables. ADMCoupling Couples the fluid /
spacetime variables (it's a Cactus thing and
doesn't do anything interesting) StaticConformal
Provides the static conformal factor. As we
currently have no initial data that uses a
conformal factor, this is just used for
compatibility. BSSN_MoL Evolves the spacetime
using the BSSN formulation of Einstein's
equations. This is essentially the standard
spacetime evolver used for black hole runs at
AEI, tweaked to use MoL. Is pretty constantly
tested. In the long term will be merged back into
the standard ADM_BSSN. ADMConstraints The
standard thorn from CactusEinstein. MoL
Generalized time integration.
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LORENE Binary Initial data (Meudon Data)
LORENE (Langage Objet pour la RElativité
NumériquE)LORENE is a set of C classes to
solve various problems arising in numerical
relativity, and more generally in computational
astrophysics. It provides tools to solve partial
differential equations by means of multi-domain
spectral methods.

• Initial Data
• Single rotating star
• NSNS
• BHBH
• BHNS
• Magnetized Star
• Superfluid Star
• Non conformally flat

• Lorene developers
• Gourgoulhon,
• Grandclement,
• Taniguchi,
• Marck (died)
• Novak,
• Bonazzola,

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Initial data of NSNS

• Quasi-equil. Conformally Flat Condition
• Oohara Nakamura (late 80, 97)
• Wilson Mathews (95,96) CFC
• Baumgarte etal., (97,98) corrotating binary
• Teukolsky(98) Shibata (98) potential flow
  irrotational binary
• Meudon group using Lorene (99,01)
• Elliptic equations for Lapse, Shift, Conformal
  factor velocity potential

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Lapse Shift
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Baryon density Velocity
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Etc
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Lorene Cactus(Whisky) using Whisky_MeudonData
I did it! BUT
OTL
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Concluding Remarks

• GRHydro simulations
• Diverse research topics
• Seem to be robust but incomplete yet
• We can touch some limited topics
• Whisky, Lorene
• Probably exchaustive expensive
• We have to do anyway
• GRHydro is not that far away
• Made in KCNR !!!