ns-ns and bh-ns merger simulations lecture...

NS-NS and BH-NS Merger Simulations

Lecture 3

Yuk Tung Liu (廖育棟廖育棟廖育棟廖育棟))))

July 26-30, 2010

Asia Pacific Center for Theoretical Physics, Pohang (Korea)

2010 International School on Numerical Relativity

and Gravitational Waves

Outline of Lecture 3

History and BHNS parameters

Simulation results

Gravitational Waves

BH + Disk Remnants & SGRB

Future Directions

History

Newtonian/Pazynsky-Wiita Simulations

Lee & Kluzniak (1999); Lee (2000—2001)

Janka, Eberl, Ruffert, & Fryer (1999)

Rosswog, Speith & Wynn (2004); Rosswog (2005)

Ruffert & Janka (2009)

Conformal Flat Gravity

Faber et al (2006)

Full GR Simulations

Loffler, Rezzolla & Ansorg (head on collision; 2006)

Shibata & collaborators (Kyoto)

Shapiro & collaborators (Illinois)

Duez & collaborators (Cornell/Caltech/WSU/CITA)

Chawla et al (LSU/BYU/LIU/Perimeter)

BSNS Parameters

BH mass MBH: 2—1010 M⊙

BH spin

NS Mass or Compaction (MNS or C=GMNS/RNSc2)

MNS: 1 ~ 2 M⊙

NS spin (probably not important)

EOS ignorance (cold & hot)

Population Synthesis Result

Belczynski, Taam, Rantsiou & van der Sluys, Astrophys. J. 682 (2008) 474

aspin,init = 0.55

MNS / MBH

Fates of BHNS Merger

Newtonian analysis: Tidal disruption occurs at binary separation d with

2/3 1

3 2~ ~

,

NSBHNS

NS BH

NSBH

NS NS

MM dR q C

d R M

MMq C

M R

− −⇒

= =

ISCO

NS swallowed by BH

No disk

Tidal Disruption

Part of NS swallowed by BH

Disk? Outflow?

d t rISCO → tidal disruption

Tidal disruption likely to occur for• small q

• small C

• large BH spin (aligned with Lorb)

More careful analysis

, non-spinning BH

Taniguchi, Baumgarte, Faber & Shapiro, PRD 77 (2008) 044003



Simulation results

Gravitational Waves


Future Directions

Effect of Initial Separation

0.06235.41A-SSep

0.04417.17A-MSep

0.03338.81A

MΩΩΩΩD0

/ MCaseq=3

aBH / MBH=0

Γ=2 EOS

CNS=0.145

Etienne, Liu, Shapiro & Baumgarte, PRD 79 (2009) 044024

Convergence Test

Resolution in the innermost refinement box:

M/41.5 (LR), M/47.9 (MR), M/64.8 (HR)

Constraint violations ~10-2

δE=(Mi - Mf - EGW)/Mi ~ 10-4

δJ=(Ji - Jf - JGW)/Ji ~ 10-2

q=3

aBH / MBH=0.75

Γ=2 EOS

CNS=0.145

Initial sep. D0=5.5M


Effect of Mass Ratio on Disk Mass


Shibata, Kyutoku, Yamamoto & Taniguchi,

PRD 79 (2009) 044030

Discrepancy in q=3!

• accuracy degrades as matter crosses AMR

refinement boundaries → angular momentum

spuriously lost (2% Illinois, 5% Kyoto, ~1% Cornell?)

• need to perform more accuracy simulations

Foucart, Duez, Kidder & Teukolsky, arXiv:1007.4203

Γ=2 EOS, CNS=0.145, non-spinning BH

Effect of NS Compaction on Disk Mass

Shibata, Kyutoku, Yamamoto & Taniguchi, PRD 79 (2009) 044030

Γ=2 EOS, non-spinning BH

Effect of BH Spin on Disk Mass


Γ=2 EOS, CNS=0.145, q=1

15%

4%


Movie: a/M=0.75 case

Credit: S. Shapiro & UIUC REU team

(http://research.physics.illinois.edu/CTA/IRG/movies.html)

Movie: Effect of BH Spin

Credit: S. Shapiro & UIUC REU team

(http://research.physics.illinois.edu/CTA/IRG/movies.html)

Effect of BH Spin Orientation

Γ=2 EOS, CNS=0.145, a/M = 0.5


Disk mass does not change

significantly for i < 40º

Population synthesis:

Most BHNS system: i < 90º

~half of BHNS with i < 40º

16º80º

16º60º

7º40º

4º20º

0º0º

idiskiBH

Movie: Tilted BH Spin

Credit: http://www.black-holes.org/explore2.html

Precession of Disk

Different precession rate at different radii

Fragile et al [Astrophys. J. 691 (2009) 482]: should precess at

a constant rate as a solid body after ~4s

Timescale much longer than expected lifetime of BHNS disk

remnant (~100ms)

Effects of NS EOS

Simulations with Γ=2, Γ=2.75 and Shen EOS

Need to evolve electron fraction Ye in Shen EOS

Two limiting cases:

- weak interaction timescale p merger timescale, set s=0

- weak interaction timescale ` merger timescale, enforce β-equilibrium:

Duez et al, Class. Quantum Grav. 27 (2010) 114104

( ) ( )

: set by weak interaction and neutrino radiation

i

t e i eg Y g Y v s

s

ρ ρ∂ − + ∂ − =

n p eµ µ µ= +

Effects of NS EOS: Results

For a fixed NS compaction, disk mass, GW

waveforms are insensitive to NS EOS.

Higher compaction, lower disk mass.

Similar density and temperature in disk

Different disk composition between Shen-

Adv and Shen- β EOS (more electron-rich

in Shen-β EOS)

Larger tidal tail for stiff EOSs

No outflow in all GR simulations

Magnetized BHNS Simulation

Chawla et al, arXiv:1006.2839



Simulation results

Gravitational Waves


Future Directions

Gravitational Radiation

aBH = 0MBH / MNS = 3

rex = 30M – 80M Initial MΩ = 0.033

Solid lines: h+ , dash lines: h×


Γ=2 EOS, CNS=0.145

GW Power Spectrum

Γ=2 EOS, CNS=0.145, non-spinning BH


Duez et al, Class. Quantum Grav. 27 (2010) 114104

Γ=2 EOS, non-spinning BH

Shibata et al, PRD 79 (2009) 044030



Simulation results

Gravitational Waves


Future Directions

BH + Disk RemnantNSNS BHNS

Rezzolla et al, Class. Quantum Grav. 27 (2010)114105 Etienne, Liu, Shapiro & Baumgarte, PRD 79 (2009) 044024

Temperature Estimate (for Hybrid EOS)

Hybrid EOS: P(ρ , ε )= Pcold(ρ )+(Γth-1)ρ εth , ε = εcold + εth

Initially, P = Pcold

Estimate temperature by (c.f. Popham, Woosley, & Fryer 1999)

Post-merger disks: ρ ~ 1011– 1012 g cm-3 , T ~ 1010—1011K (kT ~ 1– 10 Mev)

cold cold

1P dε

ρ

= −

∫

4

th

3

2 n

kT aTf

mε

ρ= + f depends on # of species (γ, e±, υi , υi)

_

Hyperaccreting BH & SGRB

Possible SGRB central engine if Mdisk t 0.01M⊙ ,

Neutrino Dominated Advection Flow (NDAF)

– Popham, Woosley, & Fryer 99, Chen & Beloborodov 06

– Di Matteo, Perna, & Narayan 02, Setiawan, Ruffert, & Janka 06

– Lee, Ramirez-Ruiz, and Page 04, Shibata, Sekiguchi, & Takahashi 07

May produce a total γ-ray energy E ~ 1047—1050 erg from υυ annihilation

Angular frequency Ω decreases with increasing radius →MRI →MHD

turbulence → ultra-relativistic jets?

1

acc, 1 10 s 0.01 0.1 sM M τ−− −⊙

ɺ ∼ ∼

_



Simulation results

Gravitational Waves


Future Directions

Future Directions

More simulations

Longer inspiral orbits (better matching to PN waveform)

More accurate initial data (lower eccentricity, less spurious GW)

More accurate simulations

Cover more parameters: masses, spins, NS EOSs

Long term evolution of merged remnants (HMNS, BH+disk)

Magnetic fields

Neutrino transport

Improve Software

Better AMR technique

Implicit scheme?

ns-ns and bh-ns merger simulations lecture...

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