Simulating Accreting Binary Black Holes€¦ · Zilhão (UB) Simulating Accreting Binary Black Holes IGWM2015, May 14 7 / 31. Outline 1 Introduction 2 Setup Approximate Black Hole

Simulating Accreting Binary Black Holes

Miguel Zilhão1,2 Scott Noble2,3 Manuela Campanelli2

Yosef Zlochower2

1Departament de Física Fonamental & Institut de Ciències del Cosmos,Universitat de Barcelona

2Center for Computational Relativity and GravitationRochester Institute of Technology

3University of Tulsa, Tulsa OK

May 14 2015, 5th Iberian Gravitational Wave Meeting

Zilhão (UB) Simulating Accreting Binary Black Holes IGWM2015, May 14 1 / 31

Contents

1 Introduction

2 SetupApproximate Black Hole Binary SpacetimeWarped coordinate transformation

3 PN order exploration

4 Final Remarks


Outline

1 Introduction



4 Final Remarks


Context

General Relativity + Magnetohydrodynamics (GRMHD):

quasarsgamma-ray burstsactive galactic nucleiaccretion disks


Binary Black Hole Accretion Disks

Circumbinary accretion disks shouldform around massive binary blackholes systemsUnderstanding circumbinary accretionflows is essential for identification ofbinary black holes



Gravitational Waves (GW) and light(EM) originate in different mech-anisms, independently constrainingmodelsEither GW or EM observations ofclose supermassive BH binarieswould be the first of its kind!Follow up observations can often bemade via coordinated alert systems



time-dependent gravity moves matter aroundgas is heated and becomes luminouslight emitted reaches observerwe can make predictions for this emitted light

Goalssimulate EM waves coming from these objectsfocusing on inspiral, merger, and ringdown phaseGW observations of these events in tandem with EM observationsexplore dynamics of high-energy plasma and strong field regimeof gravitymake predictions so that people now what to look for in the data


Outline

1 Introduction



4 Final Remarks


GRMHD

General Relativity + Magnetohydrodynamics (GRMHD):

Rµν −R2

gµν = 8π(T Hµν + T EM

µν

)T Hµν = ρhuµuν + Pgµν

T EMµν = FµλFνλ −

gµν4

F 2

where ρ, ε, P, uµ and h ≡ 1 + ε+ P/ρ are the fluid rest mass density,specific internal energy, gas pressure, 4-velocity, and specific enthalpy


Code

The Harm3d codeIdeal-MHD on curved spacetimes (does not evolve Einstein’s Equa-tions)Spacetime described through a vacuum post-Newtonian (PN) ap-proximation8 coupled nonlinear 1st-order hyperbolic PDEs ; 1 constraint eq.Finite Volume conservative scheme; Method of Lines with 2nd-order Runge-KuttaMesh refinement via coordinate transformation: Eqs. solved onuniform “numerical” coordinates related to “physical” coordinatesvia nonlinear algebraic expressionsParallelization via uniform domain decomposition; 1 subdomain perprocess


“Diagonal” gridding scheme

Radial cell extents are smallerat smaller radii in order to re-solve smaller scale features ofthe accretion flow there.More cells are concentratednear the plane of the disk andthe binary’s orbit.


Example: circumbinary disk

log10 of density integrated in θ (surface density)


Outline

1 Introduction



4 Final Remarks


Approximate global spacetime

Approximate, global spacetime for a non-spinning BBH system inquasi-circular trajectory, during inspiral regime.

(spinning case now under development)

Spacetime is divided into different zones, inside which differentapproximations are used to obtain approximate metrics.These approximate metrics are connected throughtime-dependent asymptotic matching, using transition functions.


Metric

Inner Zones (IZ): closeto BHs;Near Zone (NZ):“intermediate” region;Far Zone (FZ):gravitational waveregion;Buffer Zones (BZ):transition regions.


Zones

IZ is the region close to either BH where the metric can bedescribed by a perturbed Schwarzschild or Kerr solution.NZ is the region far away from either BH, but less than agravitational wave wavelength λ from the binary’s center of mass,such that the metric can be described by a PN expansion.FZ is the region outside a gravitational wave wavelength from thebinary’s center of mass, where the metric can be described by amultipolar post-Minkowskian (PM) expansion.Such subdivision of spacetime is only valid when the SMBHs aresufficiently well-separated and slowly-inspiraling, breaking downat separation of roughly 10M.Matching between IZ and NZ is exact to 1PN order, and onlyapproximate to 2PN order.

(work to improve this is under way)


Outline

1 Introduction



4 Final Remarks


Warped Cartesian coordinates

1Xmax − Xmin

∂X∂x

= 1 −ax1 τ̃(y , y1, δy3

)[τ̃ (x , x1, δx1)− 2δx1]

−ax2 τ̃(y , y2, δy4

)[τ̃ (x , x2, δx2)− 2δx2]

1Ymax − Ymin

∂Y∂y

= 1 −ay1 τ̃(x , x1, δx3)[τ̃(y , y1, δy1

)− 2δy1

]−ay2 τ̃(x , x1, δx4)

[τ̃(y , y2, δy2

)− 2δy2

]

0.0 0.2 0.4 0.6 0.8 1.0x

0.0

0.2

0.4

0.6

0.8

1.0


Example

3 2 1 0 1 2 3X

3

2

1

0

1

2

3

Y


Field loop evolution

Advected magnetic field loop

Bx , By =

{−Aloopy/rc , Aloopx/rc ; r < Rloop ,

0; r ≥ Rloop


Field loop evolution


Warped Spherical Coordinates

r(y) = Rin + (br − sar ) y + ar [sinh (s(y − yb)) + sinh (syb)]

ar ≡Rout − Rin − br

sinh (s(1 − yb)) + sinh (syb)− s

The meaning of the parameters is more readily gleaned when lookingat ∂r/∂y :

∂r∂y

= br + sar [cosh (s(y − yb))− 1]


Examples


Binary Warped Gridding scheme


Disk with black hole binary


Outline

1 Introduction



4 Final Remarks


a = 100


a = 40


a = 20


Outline

1 Introduction



4 Final Remarks


Final Remarks

We have tools to model single black hole accretion disksWe have tools to make observational predictions from thesesimulations;We are in the process of applying these tools to the binary case:

Implemented dynamic warped gridding scheme in the Harm3d codeThis construction is very general and in no way relies in MHD, orBH evolutions.Successfully passes “Field Loop” and “Bondi” tests

We have been evaluating how PN order affects gas dynamicsGoal: evolve circumbinary accretion disk around binary black hole


Documents

Simulating Accreting Binary Black Holes€¦ · Zilhão (UB) Simulating Accreting Binary Black Holes IGWM2015, May 14 7 / 31. Outline 1 Introduction 2 Setup Approximate Black Hole