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Stability of Expanding Jets Serguei Komissarov & Oliver Porth University of Leeds and Purdue University TexPoint fonts used in EMF. Read the TexPoint manual.

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Presentation on theme: "Stability of Expanding Jets Serguei Komissarov & Oliver Porth University of Leeds and Purdue University TexPoint fonts used in EMF. Read the TexPoint manual."— Presentation transcript:

1 Stability of Expanding Jets Serguei Komissarov & Oliver Porth University of Leeds and Purdue University TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA A A A A

2 Introduction AGN jets are remarkably stable compared to their terrestrial counterparts. They propagate over distances up to one billion(!) of initial jet radius; They exhibit substantial radial expansion. The radius of M87 jet increases by ~ one million times. Expansion is know to have a stabilising effect (e.g. Moll et al. 2008); They propagate through atmospheres with rapidly decreasing pressure (and density). We are out to check that: These are related. The stability is due to the loss of connectivity, caused by the rapid decline of external pressure.

3 Stability and Causality Only global instabilities can threaten the jet survival. For a global instability to develop, the jet has to be causally connected in the transverse direction. The condition is - Mach angle (for the fastest wave), - jet opening angle.

4 Stability and Causality Hot jets: Jets confined by external pressure, The jet expands freely – not causally connected – when Poynting-dominated relativistic jets: The same conclusion ! (Komissarov at al.,2009, Lyubarsky 2009) is a critical value.

5 Stability and Causality is a typical value for AGN. ( Begelman et al. 1984 ) Inner Edge of Radiation-Supported Accretion Disk: Radio Lobes: In coronas of ellipticals ( 100pc – 10kpc ), Expect closer to the core -> free expansion.

6 Steady-State Jets via 1D simulations One can use 1D time-dependent simulations to construct approximate 2D steady-state solutions. Example. 2D steady-state continuity equation: Suppose. Replace v 1 with c and x 1 with ct to obtain - 1D time-dependent continuity eq. Boundary conditions: Replace at the 2D jet boundary with at the 1D “jet” boundary.

7 Steady-State Jets via 1D simulations Test model: Axisymmetric Relativistic MHD jets The initial solution describes a 1D cylindrical jet in magnetostatic equilibrium (Komissarov 1999); purely azimuthal magnetic field. bb  p  Kink-unstable in uniform external medium O ’ Neil et al.(2012)

8 Steady-State Jets via 1D simulations Test model: Axisymmetric Relativistic MHD jets 

9 Expanding 3D Jets in a Periodic Box The approach: Introduce time-dependent external pressure, to study the role of expansion on stability of jets using the periodic box setup. To allow perturbations of the external gas we use the forcing approach: The same approach is used to control other parameters of the external gas. The value of  is such that for  the results are not strongly influenced by the forcing, which inhibits wave emitted by the jet.

10 Perturbation (kinks): z - distance along the jet, L z – box size (Mizuno et al., 2011) Expanding 3D Jets in a Periodic Box

11 Constant external pressure,  The jet is destroyed over the distance ~ 100 initial radii ( c=1 )

12 Expanding jet,  The jet propagates at least ten times further (1000 initial radii; end of simulations) It develops irregular “knotty” structure

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14 Jet energetics; 3D versus 1D (steady-state) At r < 500 R j,0, the 3D solution follows closely the steady-state one. At r > 500 R j,0 (the highly-nonlinear phase), wave losses and magnetic dissipation in the 3D model.

15 Preliminary conclusions Rapid decline of external pressure is the main factor behind the observed stability of astrophysical jets; Jets are expected to flare when entering flat sections of external atmospheres. Instability -> Dissipation -> Emission. Bulk acceleration is another likely outcome for highly magnetized relativistic jets.

16 This is still “work in progress”; Rapid decline of external pressure is identified as the main factor behind the observed stability of astrophysical jets; Jets are expected to flare when entering flat sections of external atmospheres. Instability -> Dissipation -> Emission. Bulk acceleration is another likely outcome for highly magnetized relativistic jets. The End Preliminary conclusions


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