Simulation and Modeling of Gravitational Wave Sources
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The document discusses gravitational wave (GW) emission, elaborating on their weak nature and interaction with matter, as well as specific types of GW signals such as compact binary coalescence and bursts. It emphasizes the importance of simulation and modeling in detecting weak signals and estimating source parameters, along with challenges related to numerical relativity. The document also addresses various astrophysical phenomena and their implications in relation to gravitational waves and their detection.
![C.
D.
O-
@
COFI,
2015/12/05
9
GW
Signal
Types,
Simula&on
&
Modeling
NASA,
M.
Weiss
Vela
Coalescence
Signals
(Compact
Binary
Coalescence
[CBC])
(Ohme
2012)
• (Rela&vely)
simple
signal
morphology.
• Can
be
well
modeled
/
simulated;
ideal
for
matched
filtering.
• BH+BH
(BBH),
NS+NS,
NS+BH.
(J.
Blackman)](https://image.slidesharecdn.com/ottcofi20151205b-160226061749/85/Simulation-and-Modeling-of-Gravitational-Wave-Sources-9-320.jpg)
![C.
D.
O-
@
COFI,
2015/12/05
10
GW
Signal
Types,
Simula&on
&
Modeling
NASA,
M.
Weiss
Vela
Coalescence
Signals
(Compact
Binary
Coalescence
[CBC])
Bursts
• Complex
signal
morphology.
• Hard
or
impossible
to
model,
difficult
to
simulate.
• Chao&c
signal
components
(e.g.,
due
to
turbulence).
• Matched
filtering
generally
not
applicable.
(O-
2009)
Examples:
Core-‐collapse
supernovae
Postmerger
NS+NS](https://image.slidesharecdn.com/ottcofi20151205b-160226061749/85/Simulation-and-Modeling-of-Gravitational-Wave-Sources-10-320.jpg)
![C.
D.
O-
@
COFI,
2015/12/05
11
GW
Signal
Types,
Simula&on
&
Modeling
NASA,
M.
Weiss
Vela
Coalescence
Signals
(Compact
Binary
Coalescence
[CBC])
Bursts
Con0nuous
Waves
• Well
modeled,
highly
periodic
signals
due
to
small
deforma&ons
of
spinning
NSs.
(A.
Stuver)
(M.
Kramer)](https://image.slidesharecdn.com/ottcofi20151205b-160226061749/85/Simulation-and-Modeling-of-Gravitational-Wave-Sources-11-320.jpg)
![C.
D.
O-
@
COFI,
2015/12/05
12
GW
Signal
Types,
Simula&on
&
Modeling
NASA,
M.
Weiss
Vela
Coalescence
Signals
(Compact
Binary
Coalescence
[CBC])
Bursts
Con&nuous
Waves
• Cosmological:
Big
Bang,
infla&on
• Astrophysical:
superposi&on
of
cosmol.
popula&on
of
CBC/burst
events.
• Stochas&c
–
no
detailed
h(t)
predic&on
possible.
Stochas0c
Backgrounds](https://image.slidesharecdn.com/ottcofi20151205b-160226061749/85/Simulation-and-Modeling-of-Gravitational-Wave-Sources-12-320.jpg)
![C.
D.
O-
@
COFI,
2015/12/05
16
Numerical
Rela&vity
Simula&ons
NASA,
M.
Weiss
Vela
Proceedings
of
the
GR1
Conference
on
the
role
of
gravita&on
in
physics
University
of
North
Carolina,
Chapel
Hill
[January
18-‐23,
1957]
(via
P.
Laguna
&
D.
Shoemaker)
(K.
Thorne)
-‐>
It
took
un&l
2005
(Pretorius,
Campanelli+,
Baker+)
to
simulate
first
BBH
merger!](https://image.slidesharecdn.com/ottcofi20151205b-160226061749/85/Simulation-and-Modeling-of-Gravitational-Wave-Sources-16-320.jpg)
![Gamma-‐Ray
Bursts
C.
D.
O-
@
COFI,
2015/12/05
30
BATSE
LGRBs
SGRBs
• Two
general
groups
of
GRBs:
Long
and
Short
• Favored
model:
Beamed
Ultrarela&vis&c
ou}low
emi~ng
γ-‐rays.
[Reviews:
e.g.
Woosley
&
Bloom
‘06,
Piran
‘05,
Meszaros
’05]
NS-‐NS
/
NS-‐BH
merger
Massive
H/He-‐poor
Star
SGRB
LGRB
Simplis0c
Engine
Picture:
Energy
sources:
Gravita&onal
energy
(accre&on)
Black
Hole/NS
spin
energy.
Disk
Mass:
∼0.1
MSun
Disk
Mass:
∼1
MSun
Media0ng
Processes:
Neutrino
Pair
Annihila&on
Magnetohydrodynamics](https://image.slidesharecdn.com/ottcofi20151205b-160226061749/85/Simulation-and-Modeling-of-Gravitational-Wave-Sources-30-320.jpg)
![Core-‐Collapse
Supernova
Energe&cs
C.
D.
O-
@
COFI,
2015/12/05
37
• Collapse
to
a
neutron
star:
∼3
x
1053
erg
=
300
[B]ethe
gravita0onal
energy
(≈0.15
MSunc2).
-‐>
Any
explosion
mechanism
must
tap
this
reservoir.
• ∼1051
erg
=
1
B
kine&c
and
internal
energy
of
the
ejecta.
(Extreme
cases:
10
B;
“hypernova”)
• 99%
of
the
energy
is
radiated
in
neutrinos
on
O(10)s
-‐>
Strong
evidence
from
SN
1987A
neutrino
observa&ons.](https://image.slidesharecdn.com/ottcofi20151205b-160226061749/85/Simulation-and-Modeling-of-Gravitational-Wave-Sources-37-320.jpg)
![Gravita0onal-‐Waves
from
Core-‐Collapse
Supernovae
42
Reviews:
O-
09,
Kotake
11,
Fryer
&
New
11
Need:
accelerated
aspherical
(quadrupole)
mass-‐energy
mo&ons
Candidate
Emission
Processes:
v Turbulent
convec&on
&
shock
instability
(SASI)
v Rota&ng
collapse
&
bounce
v 3D
rota&onal
instabili&es
v Aspherical
mass-‐energy
ou}lows:
-‐>
aspherical
neutrino
emission
-‐>
aspherical
explosion
3
-150 -100 -50 0 50 100 150
x [km]
-150
-100
-50
0
50
100
150
z[km]
t = 10.00 ms
-30 -20 -10 0 10 20 30
x [km]
-30
-20
-10
0
10
20
30
z[km]
t = 68.88 ms
-30 -20 -10 0 10 20 30
x [km]
-30
-20
-10
0
10
20
30
z[km]
t = 69.39 ms
-30 -20 -10 0 10 20 30
x [km]
-30
-20
-10
0
10
20
30
z[km]
t = 84.00 ms
108 1010 1012 1014
log
108 1010 1012 1014
log
108 1010 1012 1014
log
109 1010 1011
log
FIG. 3: Snapshots of the meridional density distribution with
superposed velocity vectors in model u75rot1 taken at various
0 20 40 60 80 100 120 140
t tbounce [ms]
1
2
3
f[kHz]
u75rot2
3 2 1 0 1 2 3
log |D˜h+,e|2
400
200
0
200
Dh+,e[cm]
DhCCE
+,e u75rot1
DhCCE
+,e u75rot1.5
DhCCE
+,e u75rot2
1.6 0.8 0.0 0.8 1.6
t tBH [ms]
400
200
0
200
FIG. 4: Top: GW signals h+,e emitted by the rotating mod-
els as seen by an equatorial observer and rescaled by distance
C.
D.
O-
@
ERAU,
2015/11/30
GW
emission
weak
–
detectable
only
for
galac&c
CCSN](https://image.slidesharecdn.com/ottcofi20151205b-160226061749/85/Simulation-and-Modeling-of-Gravitational-Wave-Sources-42-320.jpg)
![GWs
from
Asymmetric
Neutrino
Emission
C.
D.
O-
@
CASS
UCSD
2009/11/18
49
[Epstein
1978,
Burrows
&
Hayes
1996,
Janka
&
Müller
1997,
Müller
et
al.
2004,
Dessart
et
al.
2006,
O-
2009]
• Any
accelerated
mass-‐energy
quadrupole
will
emit
GWs.
Asymmetric
neutrino
radia&on:
Asymmetric
neutrino
emission
in
core-‐collapse
SNe:
• Convec0on:
small-‐scale
varia&ons.
• Rapid
rota0on:
large-‐scale
asymmetry.
• Large-‐scale
asymmetries:
large-‐scale
asymmetry.
[O-
et
al.
2008]
GW
“Memory”
[Dessart
et
al.
2006,
O-
2008
Accre&on-‐Induced
Collapse
Large
h,
low
frequency](https://image.slidesharecdn.com/ottcofi20151205b-160226061749/85/Simulation-and-Modeling-of-Gravitational-Wave-Sources-49-320.jpg)
Simulation and Modeling of Gravitational Wave Sources
- 1. Chris&an D. O- TAPIR, California Ins&tute of Technology Simula&ng eXtreme Space&mes (SXS) Collabora&on Sherman Fairchild Founda0on Simula0on and Modeling of Gravita0onal Wave Sources
- 2. C. D. O- @ COFI, 2015/12/05 2 Gravita&onal Wave Emission • GWs (in GR!) are to lowest-‐order quadrupole waves. • Emi-ed by accelerated aspherical bulk mass-‐energy mo&ons. • “Slow-‐mo&on” “weak-‐field” quadrupole approxima&on: mass quadrupole moment dimensionless GW “strain” (displacement) G c4 ⇡ 10 49 s2 g 1 cm 1 First Numerical Es&mate: Ijk = Z ⇢xjxkd3 x d2 dt2 I ⇠ O(Mv2 ) h ⇠ 2G c4D Mv2 M = 1M D = 10 kpc v = 0.1c h ⇠ 10 19 M ⌘ ”aspherical mass” (adv. LIGO: ~4 x 10-‐24 @ 200 Hz)
- 3. C. D. O- @ COFI, 2015/12/05 3 GW Emission • GWs are very weak and interact weakly with ma-er. • No human-‐made sources (of detectable GWs): M = 1000 kgExample: ~⌦ R = 10 m ⌦ = 100 Hz D = 100 m (detector distance) h ⇠ 10 37-‐> GW strain amplitude: (adv. LIGO: ~4 x 10-‐24 @ 200 Hz)
- 4. C. D. O- @ COFI, 2015/12/05 4 GW Emission • GWs are very weak and interact weakly with ma-er. • No human-‐made sources. GW generator, TAPIR group, Caltech
- 7. C. D. O- @ COFI, 2015/12/05 7 NASA, M. Weiss Vela GW data stream + mock signal at SNR 10 mock GW signal Need signal predic&ons for: -‐> Detec&on of weak signals (matched filtering). -‐> Es&ma&on of source parameters & physics. -‐> Tests of General Rela&vity. Why Simula&on and Modeling?
- 8. 8 Simula0on vs. Modeling of GWs NASA, M. Weiss Vela Simula0on • From first principles. • Is self-‐consistent and depends on few free parameters. • Makes as few approxima&ons as possible. • Typically involves PDEs. • Extremely computa&onally expensive. Some&mes prohibi&vely expensive. • Yields reliable predic&ons (modulo systema&cs). Modeling • From phenomenological, approx. / perturba&ve model. • Depends on many free parameters. • Ohen tuned / calibrated based on simula&ons. • Typically involves ODEs. • Computa&onally inexpensive. • Yields predic&ons whose reliability must be tested with simula&ons. (both are needed) C. D. O- @ COFI, 2015/12/05
- 9. C. D. O- @ COFI, 2015/12/05 9 GW Signal Types, Simula&on & Modeling NASA, M. Weiss Vela Coalescence Signals (Compact Binary Coalescence [CBC]) (Ohme 2012) • (Rela&vely) simple signal morphology. • Can be well modeled / simulated; ideal for matched filtering. • BH+BH (BBH), NS+NS, NS+BH. (J. Blackman)
- 10. C. D. O- @ COFI, 2015/12/05 10 GW Signal Types, Simula&on & Modeling NASA, M. Weiss Vela Coalescence Signals (Compact Binary Coalescence [CBC]) Bursts • Complex signal morphology. • Hard or impossible to model, difficult to simulate. • Chao&c signal components (e.g., due to turbulence). • Matched filtering generally not applicable. (O- 2009) Examples: Core-‐collapse supernovae Postmerger NS+NS
- 11. C. D. O- @ COFI, 2015/12/05 11 GW Signal Types, Simula&on & Modeling NASA, M. Weiss Vela Coalescence Signals (Compact Binary Coalescence [CBC]) Bursts Con0nuous Waves • Well modeled, highly periodic signals due to small deforma&ons of spinning NSs. (A. Stuver) (M. Kramer)
- 12. C. D. O- @ COFI, 2015/12/05 12 GW Signal Types, Simula&on & Modeling NASA, M. Weiss Vela Coalescence Signals (Compact Binary Coalescence [CBC]) Bursts Con&nuous Waves • Cosmological: Big Bang, infla&on • Astrophysical: superposi&on of cosmol. popula&on of CBC/burst events. • Stochas&c – no detailed h(t) predic&on possible. Stochas0c Backgrounds
- 13. C. D. O- @ COFI, 2015/12/05 13 Example 1: Coalescing BH+BH Pairs NASA, M. Weiss Vela Parameter space (J. Blackman) The Binary Black Hole Parameter Space Black hole masses m1, m2 Spin vectors ~1 and ~2, k~i k = k~Si k/m2 i < 1 Total mass M = m1 + m2 can be scaled out, leaving 7 parameters A moderately dense covering of the parameter space would require ⇠ 107 waveforms! Pure gravity! Gµ⌫ = 0 (K. Thorne) <-‐ this is why modeling is needed!
- 14. C. D. O- @ COFI, 2015/12/05 14 Binary Black Hole Coalescence NASA, M. Weiss Vela Ohme 2012 Strong field limit • Modeling: – Post-‐Newtonian (PN) approximants (expansion in v/c). Only inspiral. Fails in strong-‐field regime. – Effec&ve-‐one-‐body (EOB) and “Phenom”-‐type PN models: Fits of PN inspiral, merger, ringdown. Calibrated on NR simula&ons. – NR “surrogate models” via reduced-‐order modeling. • Simula&on: Numerical Rela&vity − direct integra&on of field eqns.
- 15. C. D. O- @ COFI, 2015/12/05 15 Binary Black Hole Coalescence NASA, M. Weiss Vela Buonanno & Sathyaprakash 14 Validity of methods Extreme Mass Ra&o (EMRI) mass ra&o strength of rela&vis&c dynamics/ gravity. c2 v2 ⇠
- 16. C. D. O- @ COFI, 2015/12/05 16 Numerical Rela&vity Simula&ons NASA, M. Weiss Vela Proceedings of the GR1 Conference on the role of gravita&on in physics University of North Carolina, Chapel Hill [January 18-‐23, 1957] (via P. Laguna & D. Shoemaker) (K. Thorne) -‐> It took un&l 2005 (Pretorius, Campanelli+, Baker+) to simulate first BBH merger!
- 17. Figure: C. Reisswig Folia0on of space0me 3-‐hypersurface • 12 first-‐order hyperbolic evolu&on equa&ons. • 4 ellip&c constraint equa&ons • 4 coordinate gauge degrees of freedom: α, βi. C. D. O- @ COFI, 2015/12/05 17 Numerical Rela0vity
- 18. C. D. O- @ COFI, 2015/12/05 18 Numerical Rela0vity Key issues • Ini&al condi&ons must sa&sfy Einstein equa&ons. • No unique way to formulate evolu&on equa&ons. • Gauge freedom – how choose gauge condi&ons? • Need combina&on of evolu&on equa&ons + gauges that yield to numerically stable simula&ons. BSSN Formula0on Generalized Harmonic Formula0on Nakamura+87, Shibata & Nakamura 95, Baumgarte & Shapiro 99 Friedrich 85, Pretorius 05, Lindblom+ 06 • Conformal-‐traceless reformula&on of Arnowi--‐Deser-‐Misner 59, York 79. • Addi&onal evolu&on equa&ons, condi&onally strongly hyperbolic. • Sensi&ve to gauge choice; good gauges known. • Most widely used evolu&on system today. • Choice of coordinates so that evolu&on equa&ons wave-‐equa&on like. Symmetric hyperbolic. • Sensi&ve to gauge choices, horizon boundary condi&ons. • Used primarily by Caltech/Cornell SXS code SpEC.
- 19. C. D. O- @ COFI, 2015/12/05 19 • Spectral Einstein Code: SpEC Caltech-‐Cornell-‐CITA-‐Fullerton Simula&ng eXtreme Space&mes Collabora&on (SXS) • Generalized harmonic formula&on. • Explicit mul&-‐domain, mul&-‐frame pseudo-‐spectral methods. C++. • Severely scaling limited > 48 cores. 1 simula&on with 40 orbits: 3-‐6 months on 48 cores. • Proprietary (closed source). More info on h-p://www.black-‐holes.org Example Computa0onal Approach: SpEC
- 20. C. D. O- @ COFI, 2015/12/05 20 Pfeiffer/Scheel
- 21. C. D. O- @ COFI, 2015/12/05 21 BBH & Advanced LIGO/Virgo NASA, M. Weiss • BBH Source popula&on & parameters unknown! • Present EOB/Phenom models calibrated for moderate (mostly aligned) spins, mass ra&os m1/m2 ~ 1 – 1:10. • NR simula&ons needed for rest of parameter space (high spin, precession). (at 40 Mpc) (at 1 Gpc) (at 1 Gpc) (at 1 Gpc)
- 22. C. D. O- @ COFI, 2015/12/05 22 Complete Waveforms: Problems NASA, M. Weiss Vela • 7D parameter space – at least 107 simula&ons needed. • Many cycles in sensi&vity band: N ⇠ 4 2⇡ ⇥ 104 ✓ M M ◆ 5/3 O(100) for 5+5 M⦿ -‐> Impossible with numerical rela&vity simula&ons!
- 23. C. D. O- @ COFI, 2015/12/05 23 Complete Waveforms: Solu&ons NASA, M. Weiss Vela • Many cycles in sensi&vity band: N ⇠ 4 2⇡ ⇥ 104 ✓ M M ◆ 5/3 (~130 for 5+5 M⦿) Solu&on: “Hybridiza0on” Further problem: # of required NR cycles unknown; dependent on system parameters.
- 24. C. D. O- @ COFI, 2015/12/05 24 Complete Waveforms: Solu&ons NASA, M. Weiss Vela Solu&on: “Surrogate Model” via Reduced-‐Order Modeling • 7D parameter space – at least 107 simula&ons needed. (1) Intelligently & sparsely sample parameter space with O(1,000) numerical rela&vity simula&ons. (2) Interpolate between waveforms to obtain waveform for any set of BBH parameters. Basic Idea: Goal: Build model that is as good as NR and can be a subs&tute for NR simula&ons (surrogate).
- 25. Have N reduced basis waveforms (blue lines) Fit data at N empirical time nodes (red lines) using known data (black dots) Evaluate fits at arbitrary parameter(s) (cyan dots) Use empirical interpolant to uniquely determine new data (cyan line) C. D. O- @ COFI, 2015/12/05 25 Numerical Rela&vity Surrogate Models Vela (by Jonathan Blackman)
- 26. C. D. O- @ COFI, 2015/12/05 26 Numerical Rela&vity Surrogate Models NASA, M. Weiss Vela (by Jonathan Blackman, Blackman+15) 1D surrogate model (mass ra&o). Work on mul&-‐D surrogate models in progress.
- 27. C. D. O- @ COFI, 2015/12/05 27 Example 2: NSNS and BHNS Mergers NASA, M. Weiss Vela • Harder: must simulate also ma-er (and magne&c fields) -‐> (magneto)-‐hydrodynamics, neutrinos, nuclear EOS. • But: lower mass -‐> PN approx. valid for much/most(NSNS) of inspiral. M1 ~ M2 ~ 1.4 MSun -‐> galac&c NSNS binaries! MBH ~ 7-‐10 x MNS (Belczynski+’10) (but no BHNS systems known) credit: D. Tsang
- 28. C. D. O- @ COFI, 2015/12/05 28 NSNS in the Advanced Detector Band NASA, M. Weiss Vela • Poten&al to constrain nuclear equa&on of state.
- 29. Mul0-‐Physics, Mul0-‐Messenger Astrophysics 29 C. D. O- @ YKIS 2013, 2013/06/07 Nuclear Equa0on of State (EOS) Neutrinos/Neutrino Interac0ons Nuclear Reac0ons & Opaci0es Crust Physics & Superfluidity (SF) EOS Crust/SF hot EOS hot EOS Neutrinos Neutrinos Neutrinos hot EOS Neutrinos Nuclear Nuclear Nuclear hot EOS EM aherglow/ counterpart
- 30. Gamma-‐Ray Bursts C. D. O- @ COFI, 2015/12/05 30 BATSE LGRBs SGRBs • Two general groups of GRBs: Long and Short • Favored model: Beamed Ultrarela&vis&c ou}low emi~ng γ-‐rays. [Reviews: e.g. Woosley & Bloom ‘06, Piran ‘05, Meszaros ’05] NS-‐NS / NS-‐BH merger Massive H/He-‐poor Star SGRB LGRB Simplis0c Engine Picture: Energy sources: Gravita&onal energy (accre&on) Black Hole/NS spin energy. Disk Mass: ∼0.1 MSun Disk Mass: ∼1 MSun Media0ng Processes: Neutrino Pair Annihila&on Magnetohydrodynamics
- 31. C. D. O- @ COFI, 2015/12/05 31 NSNS Simula&ons: Outcomes NASA, M. Weiss Vela Sensi&vity to system mass, mass ra&o, and nuclear EOS.
- 32. C. D. O- @ HIPACC Summer School 2014, 2014/07/23 32 BHNS Merger Scenario Kyohei Kawaguchi
- 33. C. D. O- @ COFI, 2015/12/05 33 NSNS/NSBH Modeling and Simula&on NASA, M. Weiss Vela • NSNS: PN approxima&on valid through inspiral, mul&-‐physics NR+GR(M)HD simula&on for merger/postmerger evolu&on. • BHNS: PN approxima&on valid in inspiral if mass ra&o MBH/MNS small and BH spin small. But: most likely BH spin large, MBH/MNS > ~7:1. -‐> need long NR+GR(M)HD BHNS inspiral simula&ons. credit: D. Tsang
- 34. C. D. O- @ COFI, 2015/12/05 34 Example 3: Core-‐Collapse Supernovae NASA, M. Weiss Vela • Explosions of massive stars: Gravity bombs.
- 35. C. D. O- @ COFI, 2015/12/05 35 © Anglo-‐Australian Observatory Core-‐Collapse Supernovae: Supernova 1987A Large Magellanic Cloud Progenitor: BSG Sanduleak -‐69° 220a, ≈18 MSUN Explosions of Massive Stars 8M . M . 130M
- 36. Reminder: Core Collapse Basics C. D. O- @ COFI, 2015/12/05 36 Nuclear equa&on of state (EOS) s&ffens at nuclear density. Inner core (~0.5 MSun) -‐> protoneutron star core. Shock wave formed. Outer core accretes onto shock & protoneutron star with O(1) M⦿/s. -‐> Shock stalls at ~100 km, must be “revived” to drive explosion. Reviews: Bethe’90 Janka+’12
- 37. Core-‐Collapse Supernova Energe&cs C. D. O- @ COFI, 2015/12/05 37 • Collapse to a neutron star: ∼3 x 1053 erg = 300 [B]ethe gravita0onal energy (≈0.15 MSunc2). -‐> Any explosion mechanism must tap this reservoir. • ∼1051 erg = 1 B kine&c and internal energy of the ejecta. (Extreme cases: 10 B; “hypernova”) • 99% of the energy is radiated in neutrinos on O(10)s -‐> Strong evidence from SN 1987A neutrino observa&ons.
- 38. C. D. O- @ COFI, 2015/12/05 38 Example 3: Core-‐Collapse Supernovae NASA, M. Weiss Vela • Explosions of massive stars: Gravity bombs. • Mul&-‐dimensional, mul&-‐physics, mul0-‐scale problem. • What is the detailed explosion mechanism? • Sources of GW bursts -‐> GWs carry informa&on on mul&-‐D dynamics and explosion mechanism (O- 09). • Mul&-‐Messenger Astronomy -‐> neutrinos, GWs, photons!
- 39. C. D. O- @ COFI, 2015/12/05 39 Magneto-‐Hydrodynamics Nuclear and Neutrino Physics General Rela&vity Boltzmann Transport Theory Dynamics of the stellar fluid. Nuclear EOS, nuclear reac&ons & ν interac&ons. Gravity Neutrino transport. Fully coupled! • Addi&onal Complica&on: Core-‐Collapse Supernovae are 3D – Rota&on, fluid instabili0es, magne0c fields, mul&-‐D stellar structure from convec&ve burning, etc. • Full problem: 3D space, 3D momentum space + &me Detailed CCSN Simula0ons: Ingredients
- 40. The 3D Fron0er – Petascale Compu0ng! C. D. O- @ COFI, 2015/12/05 40 • Modeling: only for photons (light curve, spectra). • Simula0on required for everything else. • Some early work: Fryer & Warren 02, 04 • Loads of new work since ~2010: Fernandez 10, Nordhaus+10, Takiwaki+11,13, Burrows+12, Murphy+13, Dolence+13, Hanke+12,13, Kuroda+12, O-+13, Couch 13, Takiwaki+13, Couch & O- 13, 15, Abdikamalov+15, Couch & O’Connor 14, Lentz+15, Melson+15ab, Cardall&Budiardja 15, Radice+15, Summa+15 O-+2013
- 41. 41 O-+2013 Caltech, full GR, parameterized neutrino hea&ng
- 42. Gravita0onal-‐Waves from Core-‐Collapse Supernovae 42 Reviews: O- 09, Kotake 11, Fryer & New 11 Need: accelerated aspherical (quadrupole) mass-‐energy mo&ons Candidate Emission Processes: v Turbulent convec&on & shock instability (SASI) v Rota&ng collapse & bounce v 3D rota&onal instabili&es v Aspherical mass-‐energy ou}lows: -‐> aspherical neutrino emission -‐> aspherical explosion 3 -150 -100 -50 0 50 100 150 x [km] -150 -100 -50 0 50 100 150 z[km] t = 10.00 ms -30 -20 -10 0 10 20 30 x [km] -30 -20 -10 0 10 20 30 z[km] t = 68.88 ms -30 -20 -10 0 10 20 30 x [km] -30 -20 -10 0 10 20 30 z[km] t = 69.39 ms -30 -20 -10 0 10 20 30 x [km] -30 -20 -10 0 10 20 30 z[km] t = 84.00 ms 108 1010 1012 1014 log 108 1010 1012 1014 log 108 1010 1012 1014 log 109 1010 1011 log FIG. 3: Snapshots of the meridional density distribution with superposed velocity vectors in model u75rot1 taken at various 0 20 40 60 80 100 120 140 t tbounce [ms] 1 2 3 f[kHz] u75rot2 3 2 1 0 1 2 3 log |D˜h+,e|2 400 200 0 200 Dh+,e[cm] DhCCE +,e u75rot1 DhCCE +,e u75rot1.5 DhCCE +,e u75rot2 1.6 0.8 0.0 0.8 1.6 t tBH [ms] 400 200 0 200 FIG. 4: Top: GW signals h+,e emitted by the rotating mod- els as seen by an equatorial observer and rescaled by distance C. D. O- @ ERAU, 2015/11/30 GW emission weak – detectable only for galac&c CCSN
- 43. GWs from Convec0on & Standing Accre0on Shock Instability 43 Recent work: Murphy+09, Kotake+09, 11, Yakunin+10, E. Müller+12, B.Müller+13 OTT, & BURROWS Vol. 707 he es 7) es, e- ng m 8) We Figure 2. Sample of GW strain (h+) times the distance, D, vs. time after Murphy+09 C. D. O- @ ERAU, 2015/11/30 GW burst! Murphy+09
- 44. Time-‐Frequency Analysis of GWs 44 Murphy, O-, Burrows 09, see also B. Müller+13 fp ⇠ !BV 2⇡ Peak emission traces buoyancy frequency at proto-‐NS edge. (buoyancy frequency) C. D. O- @ ERAU, 2015/11/30
- 45. GWs from Rota0ng Collapse & Bounce C. D. O- @ ERAU, 2015/11/30 45 Recent work: Dimmelmeier+08, Scheidegger+10, O-+12, Abdikamalov+14 • Axisymmetric: ONLY h+ • Simplest GW emission process: Rota0on + mass of inner core + gravity + s0ffening of nuclear EOS • Strong signals for rapid rota&on (-‐> millisecond proto-‐NS).
- 46. C. D. O- @ ERAU, 2015/11/30 46 Simple signal features: Axisymmetric rota&ng collapse Permits es&ma&on of core angular momentum. Can (almost) be used for matched filtering! GWs from Rota0ng Collapse & Bounce Recent work: Dimmelmeier+08, Scheidegger+10, O-+12, Abdikamalov+14
- 47. C. D. O- @ ERAU, 2015/11/30 47 3D Rota&onal Instabili&es Simula&on: C. D. O-, Visualiza&on: R. Kaehler
- 48. C. D. O- @ GW2010, UMN, 2010/10/15 48 Polar Observer + Polar Observer x Equatorial Observer x Equatorial Observer + O-+07
- 49. GWs from Asymmetric Neutrino Emission C. D. O- @ CASS UCSD 2009/11/18 49 [Epstein 1978, Burrows & Hayes 1996, Janka & Müller 1997, Müller et al. 2004, Dessart et al. 2006, O- 2009] • Any accelerated mass-‐energy quadrupole will emit GWs. Asymmetric neutrino radia&on: Asymmetric neutrino emission in core-‐collapse SNe: • Convec0on: small-‐scale varia&ons. • Rapid rota0on: large-‐scale asymmetry. • Large-‐scale asymmetries: large-‐scale asymmetry. [O- et al. 2008] GW “Memory” [Dessart et al. 2006, O- 2008 Accre&on-‐Induced Collapse Large h, low frequency
- 50. The Einstein Toolkit Project C. D. O- @ COFI, 2015/12/05 50 Mösta+14 Löffler+12 h-p://einsteintoolkit.org
- 51. The Einstein Toolkit C. D. O- @ COFI, 2015/12/05 51 Mösta+14 Löffler+12 • Collec&on of open-‐source sohware components for the simula&on and analysis of general-‐rela&vis&c astrophysical systems. h-p://einsteintoolkit.org
- 52. The Einstein Toolkit C. D. O- @ COFI, 2015/12/05 52 Mösta+14 Löffler+12 • Collec&on of open-‐source sohware components for the simula&on and analysis of general-‐rela&vis&c astrophysical systems. • Supported by NSF via collabora&ve grant to Georgia Tech, LSU, RIT, and Caltech. • ~110 users, 53 groups; ~10 ac&ve maintainers. • Goals: h-p://einsteintoolkit.org - Reproducibility. - Build a community codebase for numerical rela&vity and computa&onal rela&vis&c astrophysics. - Enable new science by lowering technological hurdles for researchers with new ideas. Enable code verifica&on/valida&on, physics benchmarking, regression tes&ng. - Make it easy for users to take advantage of new technologies. - Provide cyberinfrastructure tools for code and data management.
- 53. The Einstein Toolkit C. D. O- @ COFI, 2015/12/05 53 Mösta+14 Löffler+12 • Cactus (framework), Carpet (adap&ve mesh refinement) • GRHydro – GRMHD solver • McLachlan – BSSN/Z4c space&me solver (code auto-‐generated based on Mathema&ca script, GPU-‐enabled) • Ini&al data solvers / importers • Analysis tools (wave extrac&on, horizon finders, etc.) • Visualiza&on via VisIt (h-p://visit.llnl.gov) Available Components: • Regular releases of stable code versions. Most recent: “Somerville” release, November 2015 • Support via mailing list and weekly open conference calls. • Working examples for BH mergers, NS mergers, isolated NSs, rota&ng, magne&zed core collapse.
- 54. The Dawn of Gravita0onal Wave Astronomy Stay Tuned… LIGO-‐G1501322v1 D. Reitze Betelgeuse, D~200 pc