Short Gamma Ray Bursts The MRI print out on the launched jet Time - PowerPoint PPT Presentation

Kostas Sapountzis Center for Theoretical Physics – Polish Academy of Science Short Gamma Ray Bursts The MRI print out on the launched jet – Time Variability Warsaw 2018

Outline ● Short GRBs properties – The framework ● MRI Characteristics ● Initial configuration Useful quantities and simulation characteristics ● Results - Conclusion

Fishman G., Meegan C., 1995, AnRevAstronAstroph, 33 , 415 Kouveliotou et al 1993, ApJ, L, 413 , L101

The general SGRBs Framework Intensively transient phenomena, prompt emission in γ-rays, peak few 100 KeV Isotropic Energy up to 10 54 erg (less if collimated) Highly relativistic (compactness problem), γ>100. Low baryon loading, 10 -5 M O Lei et al, 2013, ApJ, 765 , 125 Two distinct phenomena (duration, hardness, location) Intense variability of the prompt radiation G. A. MacLachlan et al. 2013, MNRAS, 432 , 857 Two candidates of SGRB: BH-NS NS-NS (LIGO,VIRGO,FERMI) Abbott, B. P., et al. "Gravitational Waves and Gamma Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A." 2017, Phys. Rev. Lett. 119 , 161101 Berger E., Focus on the Electromagnetic Counterpart of the Neutron Star Binary Merger GW170817

The zoo of the sGRB progenitors Compact objects binaries outcome NS-NS ● Heavy NS dt =− 2 Ω 3 p m 0 2 Ι =( 2 / 5 ) M R p m = p m, 0 sin Ωt p M | 2 2 dt =− 2 | ¨ dE dΩ 3 I 3 3 c 3 c B = p m 0 2 r + sinθ ^ E = 1 / 2 I Ω ⃗ 3 ( 2 cosθ ^ θ ) 4 π r 3 M 15 G ( B ) 2 3 ( R ) ( 1.4 M ⨀ ) ( 1 ms ) 4 2 Ω 3 c 10 Km 10 M T τ sd = − dΩ / dt = 2 = 1.2 ⋅ 10 s 4 B 2 Ω 5 R ● supramassive NS Rigid Body Rotation (τ~τ sd ) ρ d ⃗ v d t =− ⃗ ∇ P − ρ ⃗ ∇ ρ ( ⃗ ∇ Φ x ' ) 3 x d 3 x' G ρ (⃗ ∬ d x ⃗ x )⃗ x − ⃗ |⃗ x ' | 3 x r , ∫ d ⋅⃗ x − ⃗ x − ⃗ x' ) (⃗ x' )(⃗ x ' ) d 2 ( x 2 ) = 1 1 3 x d 3 x' G ρ (⃗ 2 ∬ d x ) ρ ( ⃗ 2 2 − v x − ⃗ 3 |⃗ x' | 2 dt = 1 3 x ρ (⃗ 2 ∫ d x ) Φ (⃗ x )= W ∫ P ⃗ 3 x ∇⋅⃗ x d 2 1 d 3 x )− 2 ∫ ρv 3 x 2 ( ∫ ρ x 2 d 2 d 3 x = 3 Π 3 ∫ Pd 2 dt 2 I = 1 d 2 − 2 T 2 1 d I 2 dt 2 = 2 T + W + 3 Π P ∝ { ρ ⟩ ∝ { 5 / 3 5 / 3 / R 2 ρ Π = Μ ⟨ Μ 2 dt P → 2 ∝ J 2 T = 1 2 ∝ M R 2 Ω W ∝ G M 2 4 / 3 4 / 3 / R 2 I Ω ρ Μ 2 M R R

The zoo of the sGRB progenitors GM 2 M 4 / 3 GM 2 M 5 / 3 J J Ω c 0 =− α 3 + κ 3 2 + β 3 0 =− α 3 / 2 + κ 3 / 2 2 + β 3 / 2 ^ A : Ω = 1 + ^ 2 / ^ R R R 2 M R M R R 2 sin 2 r A Break up velocity ● HMNS Differential Rotation (winding of poloidal field → toroidal + Alfven waves → angular momentum redistribution) 2 ( B 0 ) ( R ) 1 / 2 ( 3 M ⨀ ) 1 / 2 12 G t A = R 10 20 Km M ∼ 10 s u A BH-NS Individual Object Magnetar Baumgarte T., Shapiro S., Shibata M., 2000, 528 , L29 The result depends on Members Initial State (mass, self-rotation, EOS, B) Details of the merging process ~7% (mass ejection, gravitational waves, ν)

GW170817 – GRB 170817A Δt = ( 1.74 ± 0.5 ) s + 180 KeV E p = 158.1 − 33 46 erg E iso = ( 4.58 ± 0.19 ) 10 high spin prior restriction ( χ < 0.89 ) m 1 = ( 1.81 ± 0.45 ) M ⨀ m 2 = ( 1.11 ± 0.25 ) M ⨀ + 0.47 M ⨀ M tot = 2.82 − 0.09 low spin prior restriction ( χ < 0.05 ) m 1 = ( 1.48 ± 0.12 ) M ⨀ m 2 = ( 1.26 ± 0.10 ) M ⨀ + 0.04 M ⨀ M tot = 2.74 − 0.01 90% credible interval Granot et al 2017, ApJ, 850 , L24 Abbott et al 2017, ApJ, 848 , L13

The MagnetoRotational Instability (MRI) ● A purely HD Keplerian disk is stable, Rayleigh stability criterion ∂ 2 Ω )> 0 ⇒ stable 2 ( R Ω ∝ R − 3 / 2 ∂ R ● The MHD instability due to Balbus & Hawley, 1991 (Velikhov 1959, Chandrasekhar 1960) review. ● Mechanical analogy ● Characteristics 2 − 1 / 2 4 Ω | dΩ z ) λ max = 2 π ( v A dln R | √ ( 4 Ω 2 + κ 2 ) ω max = 1 2 | dΩ 2 2 + d Ω 2 + 2 (⃗ 2 ]+(⃗ 2 [(⃗ 4 − ω 2 [ κ dln R | k ⋅⃗ v A ) k ⋅⃗ v A ) k ⋅⃗ v A ) dlnR ]= 0 ω

The MagnetoRotational Instability (MRI) ● The GR in Kerr Gammie C., 2004, ApJ, 614 , 309 Novikov – Thorne (1973) B = 1 + a circular μ 3 / 2 μ = d x 2 x μ ν λ r d μ dx d x dτ ={ B / √ C, 0 , 0 , 1 / ( r 3 / 2 √ C ) }= u t { 1,0,0, Ω } u 2 =− Γ νλ C = 1 − 3 3 / 2 r + 2 ar dτ dτ dτ 2 D = 1 − 2 r + α Perturbations x 2 x μ d μ → x μ + ξ μ μ u λ ξ μ u ν ξ ν u σ − 2 Γ νλ λ 2 =−∂ σ Γ νλ 2 r dτ 4 ( ω 3 / 2 + 3 a 3 / 2 − 3 a 2 / r 2 2 / r 2 1 − 4 a / r 1 − 6 / r + 8 a / r 2 = 1 2 = 1 2 ) ( ω 2 ) = 0 2 − v 2 − k ξ ∝ e − iωt ω v k 3 3 C C r r Assume a spring: 1 ν Into the Lagrangian: L = 1 ν − 1 μ ˙ 2 g μν ˙ 2 h μν ξ μ ξ 2 h μ ν ξ μ ξ ν 2 γ x x 2 γ 2 x μ 2 ( γ C ) = 0 − iωt d μ u λ ξ μ u ν ξ ξ ∝ e 2 − 3 D ν u σ − 2 Γ νλ λ − γ 2 h ν μ ξ ν 2 ( κ 2 ) + γ 2 =−∂ σ Γ νλ 4 − ω 2 + 2 γ ω 3 dτ r 2 [ (⃗ C ] = 0 2 − 3 D 2 [ κ 2 ] +(⃗ 2 + 2 (⃗ 4 − ω ω k ⋅⃗ v A ) k ⋅⃗ v A ) k ⋅⃗ v A ) 3 r z ) 3 ( C ) 2 2 λ max = 2 π ( v A =− 1 1 D =− 9 2 D 2 2 f ( r ,α ) ω max, τ ω max ,t 16 Ω 16 C Ω r http://www.inp.demokritos.gr/~sbonano/RGTC/

The MagnetoRotational Instability (MRI) Real world (simulations) problems ● Nonlinear coupling of the instability modes: What’s the proper resolution to resolve MRI properly? θ φ = 2 π v A = 2 π v A θ φ Q MRI Q MRI θ φ Ω dx Ω dx Sanot et al. 2004 Hawley J. et al 2011 θ > 6 − 8 Q MRI ● In 3D the situation is even more complicate r ) mid ≤ 4 ( dx θ φ φ / dx Q MRI Q MRI > 200 ● Empirical tests with different resolutions Sanot et al. 2004, ApJ, 605 , 321 Hawley J. et al, 2011, 738 , 84

Simulation Set Up arXiv:1802.02786 ● The disrupted NS as a FM torus (hydro dynamic, steady state) See Fishbone L., Moncrief V., 1976, ApJ, 207 , 962 ● The magnetic field circular wire k = √ A 0 2 ) K ( k 2 )− 2 E ( k 2 ) ( 2 − k 4 R sinθ A φ = √ r 2 2 + R 2 + 2 r R sinθ 2 + R 2 + 2 r Rsinθ k r K,E the complete elliptic functions, R at P max of FM torus, A 0 controls the initial plasma- β ● The ISM density has the lowest value ● System in total not in balance

Simulation Set Up Weakly magn Medium magn Torus radii (r g ) A 0 T MRI ISM density Q MRI Model r in r max t g Harm units Harm units HD-Therm 50 60 1.6 · 10 -9 10 630 9 HD-Mag 50 60 8.6 · 10 -8 200 630 151 MD-Therm 20 25 1.0 · 10 -8 1.6 174 9 MD-Mag 20 25 3.9 · 10 -7 32 174 173 LD-Therm 10 12 4.0 · 10 -8 0.32 61 13 LD-Mag 10 12 2.5 · 10 -7 3.1 61 122

Quantities Connection with SR jet theory μ u ν + 1 μ = μ u ν κ b k u κ b k δ ν μ − b μ b ν Τ ν ρξu + b 2 b ⏟ ⏟ μ μ ( T m ) ν ( T em ) ν Magnetic acceleration beyond finite resolution region ξ : specific enthalpy r σ = ( T em ) t : magnetization parameter r ( T m ) t r T t μ = r : total plasma energy ρu SR Poynting σ = (Thermal+inertial) energy flux μ = Total energy flux mass flux Vlahakis N. & Konigl A. MNRAS, 2003, 596 , 1080 μ = γ ξ ( 1 + σ )

Simulation MD-Mag

Simulation MD-Mag HARM: Gammie C., McKinney J., Toth G, 2003, ApJ, 589 , 444. Noble S., Gammie C. , McKinney, J. C., Del Zanna L., 2006, ApJ, 641 , 626. Gudinov, HLL, Shock capturing, fixed Kerr space α= 0.9 Res: 1020 x 512 hslope: 0.3 Γ = 4/3

(40,200) Snapshots MD-Mag BZ Activity Point of MRI Resolution Ω F = F tθ F θ φ Ω H = α 2 ( 1 + √ 1 − a 2 ) (10,200) Yuang H., Zhang F., Lehner L., Phys. Rev. D, 91 , 124055

Analysis of the results MD

Analysis of the results LD

Analysis of the results HD MRI from shorter radii?

Conclusions ● A well formed jet, intense variable, highly magnetized and of lower density outflow is launched ● MRI is accurately reflected on the time variability of the ejected outflow using the μ ~ γ max quantity ● The MRI print out is more intense at the inner part of the flow ● The Blandford-Znajek BH mechanism is functioning effectively ● The precise characteristic of the initial torus, a new era?

Tia n k y o u f o r y o u r a t t e n t i o n Further Comments – Questions: Kostas Sapountzis ( kostas@cft.edu.pl ) Agnieszka Janiuk (agnes@cft.edu.pl)