Synergetic Growth of the Rayleigh-Taylor and Richtmyer-Meshkov Instabilities in the Relativistic Jet. Jin Matsumoto RIKEN

Transcription

1 Synergetic Growth of the Rayleigh-Taylor and Richtmyer-Meshkov Instabilities in the Relativistic Jet Jin Matsumoto RIKEN

2 Morphological Dichotomy of the Jet 3C 31 Cygnus A FR I (Fanaroff-Riley Class I) FR II (Fanaroff-Riley Class II) Morphology is one of the most fundamental property of the relativistic jet. A morphological dichotomy between FR I and FR II - A complex combination of several intrinsic and external factors Instabilities play an important role in the morphology and stability of the jet through the interaction between the jet and external medium.

3 Hybrid Morphology Radio Sources NGC 612 (5GHz) Morganti et al FR I FR II FR I type on one side and FR II type on the other side of AGN Properties of the ambient medium is responsible for the morphological dichotomy between FR I and FR II jet? similar jets (power, composition, Lorentz factor)

4 (a) Side View z1 z2 z3 Z many numerical works in order to investigate the un-shocked JM& Masada 13 propagation dynamics of ambient medium the relativistic jet shocked (e.g., Komissarov+97, ambient medium Marti+ 97, Aloy+ 00, Zhang+ 03,04, Mizuta+ 06, cocoon Perucho+ 08, Morsony+07, P3 Lazzati+ 09, Lopez- P2 Camara+ 13) Jet P1 reconfinement shock in the collimated jet (Norman et al. 1982; contact Sanders 1983) reconfinement discontinuity (CD) region radial oscillating motion and repeated excitation of the reconfinement region (e.g., (b) Top View Gomez+ 97, JM+ 12, Mizuta+ 14) (b1) Expansion Phase [z=z1] (b2) Contraction Phase (I) [z=z2] (b3) Contraction Phase (II) [z=z3] expanding CD contracting CD contracting CD bow shock P3 adiabatic cooling P2 P1 expanding shock contracting shock expanding shock [P1 < P2 < P3] [P1 < P2 < P3] [P2 < P3 < P1]

5 Motivation of Our Study jet interface radial inertia force reconfinement region < cross section of the jet Rayleigh-Taylor instability grows? To investigate the propagation dynamics and stability of the relativistic jet - using relativistic hydrodynamic simulations focus on the transverse structure of the jet 2D simulations: evolution of the cross section of the relativistic jet 3D simulation: propagation of the relativistic jet

6 Evolution of the cross-section of the relativistic jet

7 Time Evolution of Jet Cross Section The effective inertia is important. relativistically hot plasma: effective inertia: The effective inertia of the jet is lager than the external medium although the density of the jet is smaller than the external medium in our setting. jet cross section JM & Masada 2013 The amplitude of the corrugated jet interface grows as time passes. A finger-like structure is a typical outcome of the Rayleigh-Taylor instability.

8 Time Evolution of Jet Cross Section The effective inertia is important. relativistically hot plasma: effective inertia: The effective inertia of the jet is lager than the external medium although the density of the jet is smaller than the external medium in our setting. JM & Masada 2013 In addition to the growth of the Rayleigh-Taylor instability, the growth of the Richtmyer-Meshkov instability is also contributed to the finger like structures.

9 Richtmyer-Meshkov Instability (RMI) contact discontinuity 0 The Richtmyer-Meshkov instability is induced by impulsive acceleration due to shock passage. The perturbation amplitude grows linearly in time = k 0A v, A

10 Time Evolution of Jet Cross Section JM & Masada 2013 Richtmyer-Meshkov instability is secondary excited between the RTI fingers. Almost all finger-like structures in panel (f) have their origin in the RMI.

11 (a) Side View z1 z2 z3 Z many numerical works in order to investigate the un-shocked JM& Masada 13 propagation dynamics of ambient medium the relativistic jet shocked (e.g., Komissarov+97, ambient medium Marti+ 97, Aloy+ 00, Zhang+ 03,04, Mizuta+ 06, cocoon Perucho+ 08, Morsony+07, P3 Lazzati+ 09, Lopez- P2 Camara+ 13) Jet P1 reconfinement shock in the collimated jet (Norman et al. 1982; contact Sanders 1983) reconfinement discontinuity (CD) region radial oscillating motion and repeated excitation of the reconfinement region (e.g., (b) Top View Gomez+ 97, JM+ 12, Mizuta+ 14) (b1) Expansion Phase [z=z1] (b2) Contraction Phase (I) [z=z2] (b3) Contraction Phase (II) [z=z3] expanding CD contracting CD contracting CD bow shock P3 adiabatic cooling P2 P1 expanding shock contracting shock expanding shock [P1 < P2 < P3] [P1 < P2 < P3] [P2 < P3 < P1]

12 Synergetic Growth of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities Im! = = 0.001% perturbation in the pressure s gk ( 2 h 0 ) jet ( 2 h 0 ) co ( 2 h) jet +( 2 h) co r vφ ave/c JM+ in prep D RTI & RMI exp(0.12t) t g = r jet 2 osci k = 2 = 1 4 = r jet /40 = 40

13 3D Local Simulation for the Jet Since the jet is overpressured initially, at the early evolutional stage the jet starts to expand. Finger-like structure emerges at the jet-external medium interface primally due to the RTI. In 3D case, you can also find the growth of the oscillation-induced RTI and RMI at the jet interface. RMI fingers are excited secondary between the RTI fingers. log ρ 0.5 During the radial oscillating motion of the jet, the two types of finger structures are amplified and repeatedly excited at the jet interface, and finally deform the transverse structure of the jet. unit in time:

14 Synergetic Growth of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities vφ ave/c D RTI & RMI 2D RTI & RMI exp(0.12t) The transverse structure of the jet is dramatically deformed by a synergetic growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities once the jet-external medium interface is corrugated in the case with the pressure-mismatched jet. t

15 Onset Condition for the RTI forward shock contact discontinuity reverse shock jet head dispersion relation! = i s gk 2 j jh 0 j 2 j jh j + 2 c c h 0 c c 2 c h c h 0 = P 0 c 2 estimation of the inertia cocoon jet: cocoon: 2 j j h 0 j 2 j P j 2 c c h 0 c P c jet is confined by cocoon P j P c jet 2 j j h 0 j 2 c c h 0 c > 0 contact discontinuity reconfinement shock The onset condition for the Rayleigh-Taylor instability is expected to be always satisfied in the jet-cocoon system.

16 3D jet propagation through the ambient medium

17 Numerical Setting: 3D Toy Model r [pc] jet 150 outflow boundary a c 2 =1 P a /P j =0.1 outflow boundary 300 z [pc] cylindrical coordinate relativistic jet (z-direction) ideal gas numerical scheme: HLLC (Mignone & Bodo 05) uniform grid: r = z =0.1, =2 /160

18 Jet Models two key parameters 2 j - the effective inertia ratio of the jet to the ambient medium: j,a = jh j a Neglecting the multi-dimensional effect, the propagation velocity of the jet head through a cold ambient medium can be evaluated by the balancing the momentum flux of the jet and the ambient medium in the frame of the jet head (Marti+ 97, Mizuta+ 04): v h = p j,a 1+ p j,a v j - dimension less specific enthalpy of the jet: h j

19 Result: Density The amplitude of the corrugated jet interface grows due to the oscillation-induced Rayleigh- Taylor and Richtmyer-Meshkov instabilities. Only the jet component is shown. Since the relativistic jet is continuously injected into the calculation domain, standing reconfinement shocks are formed.

20 Distribution of the Modified Effective Inertia 2 h 0 As predicted analytically, the effective inertia of the jet becomes larger than the cocoon envelope for all the models.

21 3D Rendering of the Tracer passive tracer: f f =1 f =0 : jet material : ambient ( f)+r ( fv) The oscillation-induced Rayleigh- Taylor instability is responsible for the distortion of the cross section at z = 30. Finger-like structures appeared in the cross-section at z = 65 and 90 are outcome of both the Rayleigh- Taylor and Richtmyer-Meshkov instabilities.

22 Inherent Property of Relativistic Jet initial evolution - radial expansion (hot models) - radial contraction (cold models) After initial stage, the cold jet also follows the same evolution path as the hot jet and thus excites the Rayleigh-Taylor and Richtmyer- Meshkov instabilities. Although the relativistic jet shows a rich variety of the propagation dynamics depending on its launching condition, the oscillation-induced Rayleigh-Taylor instability and secondary Richtmyer-Meshkov instability grow commonly at the jet interface and then induce a lot of finger-like structures.

23 Summary forward shock contact discontinuity reverse shock jet head Rayleigh-Taylor instability grows at the relativistic jet interface regardless of the launching condition of the jet when the jet is confined by the cocoon. cocoon jet contact discontinuity pure hydro confined jet unstable for the Rayleigh-Taylor instability reconfinement shock Any stabilization effect is necessary for FR II.