Stability of Expanding Jets Serguei Komissarov Oliver Porth
Stability of Expanding Jets Serguei Komissarov & Oliver Porth University of Leeds and Purdue University
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 M 87 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.
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.
Stability and Causality Jets confined by external pressure, • Hot jets: 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.
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 ( 100 pc – 10 kpc ), Expect closer to the core -> free expansion.
Steady-State Jets via 1 D simulations One can use 1 D time-dependent simulations to construct approximate 2 D steady-state solutions. Example. 2 D steady-state continuity equation: Suppose . Replace v 1 with c and x 1 with ct to obtain - 1 D time-dependent continuity eq. Boundary conditions: Replace at the 2 D jet boundary with at the 1 D “jet” boundary.
Steady-State Jets via 1 D simulations Test model: Axisymmetric Relativistic MHD jets The initial solution describes a 1 D cylindrical jet in magnetostatic equilibrium (Komissarov 1999); purely azimuthal magnetic field. bf p G s Kink-unstable in uniform external medium O’Neil et al. (2012)
Steady-State Jets via 1 D simulations Test model: k= 0. 5 Axisymmetric Relativistic MHD jets k =1. 0 k=1. 5 k=2. 0
Expanding 3 D 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 m is such that for k=0 the results are not strongly influenced by the forcing, which inhibits wave emitted by the jet.
Expanding 3 D Jets in a Periodic Box Perturbation (kinks): z - distance along the jet, Lz – box size (Mizuno et al. , 2011)
Constant external pressure, k=0. The jet is destroyed over the distance ~ 100 initial radii (c=1)
Expanding jet, k=1. 0 The jet propagates at least ten times further (1000 initial radii; end of simulations) It develops irregular “knotty” structure
Jet energetics; 3 D versus 1 D (steady-state) At r < 500 Rj, 0 , the 3 D solution follows closely the steady-state one. At r > 500 Rj, 0 (the highly-nonlinear phase), wave losses and magnetic dissipation in the 3 D model.
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.
Preliminary conclusions • 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
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