Electromagnetic counterparts to gravitationalwaves from binary black hole mergers

Fan ZhangBeijing Normal UniversityWest Virginia University

@2nd LeCosPA SymposiumDec 14, 2015

Multimessenger astronomy

I Gain much more information about the physics of the sources.I More convincing claims of first GW detection.I Verify progenitors to EM observations like kilonova.

Figure: As of 2010, mostly robotic wide-field optical telescopes, from MartinHenry KITPC talk.

GW trigger

EM Trigger:I Better sky localization for GW.I Streamline GW searches by reducing

number of free parameters.

GW Trigger:I GW observation is all-sky.I Can use GW signal to forewarn EM

observatories about impendingevents.

I On GW side: need low-latencypipeline – SPIIR as candidate.

I On EM side: need to understand whatto look for.

Figure: The antenna pattern for laserinterferometers. Left and rightcorrespond to the two GWpolarizations

EM counterpart from BNS and NS-BH mergers

I Most current workconcentrate on counterpartsto BNS or BH-NS mergers:e.g. sGRB.

1. Centrifugally supporteddisk rapidly accreting ontoBH for < 1s⇒ collimatedjet (sGRB)

2. Jet + circumburst mediuminteraction⇒ non-thermalafterglow for daysweeks.

3. Radioactive decay of heavyelements synthesized inthe ejecta⇒ kilonova for afew days.

Figure: Metzger and Berger (1108.6056)

EM counterparts from BBH

I What about BBH? Addforce-free electromagneticfield.

I Counterpart seen insimulations.

1. Early pre-merger: mostlycollimated dual-jets.

2. Near-merger: largeisotropic radiation seen.

3. Post-merger: settle downto collimated single jet.

I But what are the detailedmechanisms driving theradiation? Figure: Palenzuela et al Science V329, 927

(2010).

Intro to FFE

I Idealized approximation to magnetosphere of neutron stars andblack holes, containing (B dominated) EM field and tenuous plasma.

I The B field:Inherited for neutron star.Accretion disk or ion-supported torus for black hole.

I The Plasma: ∼ strong B field⇒ E field when compact object present⇒ accelerate stray charged particles⇒ emit photon above mass of e− and e+ pair⇒ pair production and sequence repeats (cascade )⇒ e− and e+ short out E along B⇒ ∃ gaps to replenish lost plasma (”dynamical equilibrium”).

Intro to FFE

I e− over-charged naked singularities, i.e. large EM charge, smallmass⇒ plasma is tenuous⇒ plasma inertia negligible⇒ cannot experience any force, motion decided by this condition⇒ no need for separate EOM for plasma, plasma simply becomesnonlinear modification to Maxwell’s equations.

I The force-free condition fixes the current, and the Maxwell eqns arethen

(∂t − Lβ)E =NKE + ∇ × (NB)−E × B

B2 N∇ · E

−NBB2 (B · ∇ × B − E · ∇ × E

−2KijE iB j + 2KE · B),

(∂t − Lβ)B =NKB − ∇ × (NE) .

Spacetime approach to FFE

Gralla & Jacobson arXiv:1401.6159I ∃ scalars φ1 and φ2 (Euler potentials), s.t.

F = dφ1 ∧ dφ2

I Force-free equations now

dφi ∧ d ∗ F = 0, i = 1, 2

metric only comes in through the Hodge dual.I Symmetry restricts form of F . Stationary and axisymmetric case:

φ1 = ψ(r , θ), φ2 = ψ2(r , θ) + φ − ΩF (ψ)t

ψ is the magnetic flux. ψ2 essentially total current. ΩF angularvelocity of B field lines.

BBH stages

Two types of plasma wavesI Alfven waves: propagate along magnetic

field lines, with group velocity = speed oflight.

I Fast magnetosonic waves: propagatemore like vacuum electromagnetic waves— more isotropic.

I Constitute the collimated and isotropiccomponents in the pre- and post-mergerstages, respectively. Figure: Schematic of the

gravitation-driven radiation.

BBH pre-merger

I Isotropic: dynamical spacetime⇒ Local EMenergy density of magnetized plasma deviatesfrom equilibrium⇒ Inhomogeneity propagateout as plasma waves.

I Collimated: kinetic-motion induced radiation.

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Lfastisotropic

LAlf

Lmcollimated

-4.4 -4.2 -4.0 -3.8 -3.6

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Figure: Analytical vs numerical results. arXiv:1508.02119

BBH post-mergerI Perturbation of monopole and uniform BG B +

Single BH. arXiv:406.4602 and 1503.06788

I Collimated: Blandford-Znajek process —travelling/Alfven modes as energy couriers?(see below)

I Isotropic (ringdown): magnetosphere QNMsas trapped/fast-magnetosonic modes. Cancompute their frequencies.

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-0.6 -0.4 -0.2 0.0 0.2 0.4-0.010

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ReH∆ΩaL

ImH∆

Ωa

L

l=1

l=2

l=3

Figure: Same asvacuum EMQNM freq whena = 0, δω/a fortrapped modesas black dots, forvacuum QNM asred circles.

Figure: The trappedand travelling modesfor monopole BG.

Figure: Exampletrajectory for eikonaltravelling wave packetin uniform B BG.

Future: better understanding of jets

I Final single jet: BZ solution is only for slow spin monopole orpoloidal BG, what of high spin? uniform BG?

I Early dual jets: analytical description of kinetic-motion jets?

I Efforts run into non-uniqueness: allowance for current enlarge spaceof possible solutions:

I Given an ΩF choice, often has a current that makes it happen (relatedby horizon BC), even with fixed BC at infinity (nonlinear eqns, nouniqueness?).

I Choose ΩF to satisfy additional symmetry etc to narrow down search.E.g. self-similar solution in NHEK (PRD 90, 124009, much more inLupsasca, Rodriguez, Strominger, arXiv:1406.4133, arXiv:1412.4124).

I Or get family of solutions “indexed” by ΩF . E.g. jet solutions of Gralla &Jacobson arXiv:1503.03848 (translationally symmetric) andarXiv:1503.06788 (axisymmetrically symmetric).

Importance of current sheet dynamics

I However, numerical simulations showdifferent ID leads to same finalsolution. Stability as selectioncriteria?

I No modal instability at the linear level.

I Instead, current sheet (non-FFE)dynamics may be the deciding factor.EOM for current sheet lacking?

I Thank you!

0 0.5 1 1.5 2ρ/ρEH

0

0.2

0.4

ΩF/ΩH

P1, t=0M

P1, t=40M

P1, t=80M

P1, t=120M

P2, t=0M

P2, t=40M

P2, t=80M

P2, t=120M

A1, t=120M

Figure: Evolution of ΩF for differentinitial data.