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Gravitational wave detection and numerical relativity

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Title: Gravitational wave detection and numerical relativity


1
Gravitational wave detection and numerical
relativity
  • ???
  • ???????????????
  • 2015-9-8
  • ??????????????????

2
Content
  • Gravitational wave, its detection and modeling
  • Introduction to NR and AMSS-NCKU code
  • Application to gravitational wave modeling
  • Summary and prospect

3
GR and its test
GR Newton Theory terms (v) terms (v2)
  • perihelion advance of mercury (1915, v
    )
  • Light bending (1919, v )
  • Gravitational redshift (1965, v )
  • Gravitational time delay (1968, v )
  • Indirect evidence of GW (1978, v )
  • Gravitational draging (2010, v )
  • GW detection (?, v1)

4
Einstein and GW
1915, general relativity 1916-2, based on
post-Newtonian approximation, claimed there are
no gravitational waves analogous to light
waves 1916-10, based on linear approximation
found monopole radiation. 1918, corrected it to
quadruple radiation 1936, showed that GW does
not exist
5
Theory of GW
1936-1962, debate 1962, Bondi convinced people
the existence of GW
6
Theory of GW
  • Bondis boundary condition is an essential
    assumption in his work
  • For Einsteins Eq including cosmological constant
  • Bondis original boundary condition
  • no GW any more Ashtekar, Bonga and Kesavan,
    CQG, 2015
  • New boundary condition
  • Similar GW behavior to Bondis original work
    He and Cao, IJMPD, 2015

The behavior of GW in different gravitational
theory is different So GW detection is possible
to test gravitational theory
7
Experiment of GW
1969, Weber claimed the detection of GW. But
people doubt it 1978, Hulse and Taylor
confirmed the quadruple energy balance,
implied the existence of GW 2015-2020, AdvLIGO
?
8
What is GW
geodesic deviation
Do not need linearization Do not need
perturbation
9
Importance of GW detection
  • This will be an unprecedented direct test of
    general relativity, especially in the highly
    dynamical and non-linear strong-field regime
  • Direct evidence for black holes, as well as give
    valuable information on stellar evolution theory
    and large scale structure formation and evolution
    in the universe
  • Information for neutron star and particle physics

10
Importance of GW detection
  • This will be an unprecedented direct test of
    general relativity, especially in the highly
    dynamical and non-linear strong-field regime
  • Direct evidence for black holes, as well as give
    valuable information on stellar evolution theory
    and large scale structure formation and evolution
    in the universe
  • Information for neutron star and particle
    physics

Gravitational Wave Astronomy
11
(No Transcript)
12
Can we detect this signal?
13
Data from detector
Theoretical wave form (strongly dynamical
spacetime, numerical method)
Data analysis Matched Filtering
14
Data analysis and template
15
Roughly speaking, a good source model can improve
the detection ability 10 to 100 times
16
Power of GW model
Improve SNR
RXJ1914.42456
17
Einsteins equation
  • Geometry respect metric diffeomorphism
    invariant
  • PDE respect second order hyperbolic partial
    differential equation (coordinate
    dependent)
  • Nonlinearity is nonlinear functions of
    metric depends on metric
    nonlinearly also
  • Complexity several thousands of terms

18
Exact solution
  • Although Exact Solutions of Einsteins Field
    Equations have near 700 pages, from 1915 till
    now, we have only two physically interesting
    solutions
  • Kerr solution single rotating star (vacuum).
  • Friedmann-Robertson-Walker cosmology homogenous
    isotropic universe.

19
Exact solution
  • Although Exact Solutions of Einsteins Field
    Equations have near 700 pages, from 1915 till
    now, we have only two physically interesting
    solutions
  • Kerr solution single rotating star (vacuum).
  • Friedmann-Robertson-Walker cosmology homogenous
    isotropic universe.

For real atrophysical systems no symetry at all
!!!
20
Approximate methods
  • Post-Newtonian method slowly varied spacetime
    (while strongly dynamical spacetime reduce
    gravitational wave)
  • Perturbation method spacetime known back
    ground small field as perturbation (known back
    ground means we almost know the solution already,
    linearity approximation)

21
Approximate methods
  • Post-Newtonian method slowly varied spacetime
    (while strongly dynamical spacetime reduce
    gravitational wave)
  • Perturbation method spacetime known back
    ground small field as perturbation (known back
    ground means we almost know the solution already,
    linearity approximation)

Weak GW cases
22
Numerical methods
Numbers and - /
23
Stability problem
  • Hahn and Lindquist, first BBH simulation (1964)
  • Smarr, Eppley, Choptuik,
  • P. Anninos, et al, first 3D BBH simulation, PRD
    52, 2059 (1995)
  • B. Brugmann, Int. J. Mod. Phys. D 8, 85 (1999),
    35 t.u.
  • S. Brandt et al, PRL 85, 5496 (2000), 50 t.u.

24
Numerical methods
GW detection will be earlier than Numerical
simulation of black hole collisions
Kip Thorne, In 2000
25
Brief history of Stability problem
  • J. Baker et al, PRL 87, 121103 (2001), 100 t.u.
  • B. Brugmann et al, PRL 92, 211101 (2004) 150 t.u.
  • F. Pretorius, PRL 95, 121101 (2005) M.
    Campanelli et al, PRL 96, 111101 (2006) J. Baker
    et al, PRL 96, 111102 (2006), stably!!
  • Penn State group, CQG 24, S33 (2007)
  • Jena group (Brugmann), PRD 76, 104015 (2007) PRD
    77, 024027 (2008)
  • AEI group, PRL 99, 041102 (2007)
  • Tokyo group, PRD 78, 064054 (2008)
  • Our group, PRD 78, 124011 (2008)

26
Reality, solvable
Numerical Relativity
Num tech, coding
Gauge, finite distance
Formalism problem (gauge)
27
Formalism problem
28
Different formalism admits different stability
Our modification is more stable Cao, Yo, and
Yu, PRD 78, 124011 (2008)
29
Different formalism admits different accuracy
new scheme
Our modification can reduce numerical noise Yo,
Lin and Cao, PRD 86, 064027 (2012)
Our modification can improve the spin accuracy
more than 7 times Yo, Cao, Lin and Pan, PRD 92,
024034 (2015)
30
Evolution PDE system of Einsteins equation
Einstein summation convention
Covariant derivative operator
Ricci tensor and trace free notation
Typically requiring ten of thousands floating
point operations per grid point !!!
31
Evolution PDE system of Einsteins equation
Einstein summation convention
Covariant derivative operator
Face to so massive computational request,
Solvable?
Ricci tensor and trace free notation
Typically requiring ten of thousands floating
point operations per grid point !!!
32
Parallized Mesh refinement
  • Several scales involved
  • black hole (1) ?
  • separation of black holes (10)
  • wave length of gravitational wave (50)
  • asymptotic region (1000-10000)
  • Computationally expensive on every grid point
    (less grid points, much more levels)

33
Mesh refinement
Take the advantage of spacetime symmetry
Example only, usually
12-16 levels 3x64x64x64
3x128x128x64
Cao, Yo, and Yu, 2007
Cao, Yo, and Yu, 2008
34
Boundary treatment
  • Real physical system, no boundary (non possible
    for numerics)
  • Compactify --- energy piles up
  • Artificial boundary (how to set BD condition)
  • Radiative boundary condition
  • Shibata and Nakamura PRD 95
  • Fortunately, it is STABLE!
  • but produce extra error!

35
Constraint preserving BD
Smooth BD required by theory
Hilditch, Bernuzzi, Thierfelder, Cao, Tichy and
Brugeman (2013)
Reduce phase error 10 times
36
NR code on the world
37
AMSS-NCKU code
  • 2006-2009, AMR infrastructure
  • 2007-2008, DAGH Einstein solver, work together
    with NCKU
  • 2009-2012, AMR infrastructure Einstein solver
    GW calculator other tools (independent)
  • 2013-2014, add GPU supporting, work with THU
  • In 2009, Jena NR group named our code AMSS-NCKU
  • In 2013, Einstein Toolkit leader gave us the
    pronunciation

38
AMSS-NCKU code
  • ??BSSN??
  • GPU??????
  • ???????

39
Parallel Scaling behavior
13x128x128x64, strong scaling test Cao, 2010
(MPI, OpenMP)
Weak scaling of Einstein Toolkit Lofflers talk,
2009
40
Test of AMSS-NCKU GPU code
The only GPU numerical relativity code to date
Titan top 1 super computer around the world (now
Tianhe 2) 1024x16 cores 1024 GPUs, Du
Zhihui, 2013
41
Structure of AMSS-NCKU GPU code
Two groups MPI processes, one for cpu and one for
gpu
MPI OpenMP CUDA
42
Application of AMSS-NCKU code
43
Horizon corresponds to black hole
44
BBH source model
EOB phenomenological model, Sun Baosan and Pan
Yi, 2013 NR AMSS-NCKU simulation result, Cao,
2013
45
Different GW behavior between GR and f(R)
BBH merge faster in f(R), More complicated GW
waveform show up in f(R)
Cao, Pablo, and Li, PRD 87 (2012) 104029
46
Summary and Prospect
  • GW detection is hard but important to science and
    theoretical model is criticaly important to the
    detection
  • AMSS-NCKU NR code has been well developed for GW
    source modeling
  • AMSS-NCKU code is portable to other astrophysical
    research including hydrodynamics and EM, which is
    needed by the GW source modeling of AdvLIGO
    (multi-messenger)
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