Time‐dependent Magnetohydrodynamic Self‐similar Extragalactic Jets

Abstract

Extragalactic jets are visualized as dynamic erruptive events modelled by timedependent magnetohydrodynamic (MHD) equations. The jet structure comes through the temporally self-similar solutions in two-dimensional axisymmetric spherical geometry. The two-dimensional magnetic field is solved in the finite plasma pressure regime, or finite β regime, and it is described by an equation where plasma pressure plays the role of an eigenvalue. This allows a structure of magnetic lobes in space, among which the polar axis lobe is strongly peaked in intensity and collimated in angular spread comparing to the others. For this reason, the polar lobe overwhelmes the other lobes, and a jet structure arises in the polar direction naturally. Furthermore, within each magnetic lobe in space, there are small secondary regions with closed two-dimensional field lines embedded along this primary lobe. In these embedded magnetic toroids, plasma pressure and mass density are much higher accordingly. These are termed as secondary plasmoids. The magnetic field lines in these secondary plasmoids circle in alternating sequence such that adjacent plasmoids have opposite field lines. In particular, along the polar primary lobe, such periodic plasmoid structure happens to be compatible with radio observations where islands of high radio intensities are mapped.

A three-dimensional magnetohydrodynamic model of planetary nebula jets, knots, and filaments

“…Examples of knots can be found in the M2-9 Twin Jet Nebula, NGC 5307, and filaments in MyCn 18 Hourglass Nebula, NGC 6543 Cat's Eye Nebula, NGC 2392 Eskimo Nebula, M2-9 Twin Jet Nebula, NGC 6543. In a recent publication (Tsui & Serbeto 2007) of an axisymmetric two-dimensional model, extragalactic polar jets are described from the same self-organizational perspective through an eigenvalue equation with regular eigenfunctions. Jets are driven by plasma pressure to progressively collimate along the polar axis.…”

“…For the present case, we follow the same apporach but remove the axisymmetric assumption to seek three-dimensional self-similar solutions to model jets, knots, and filaments. Earlier works on temporally self-similar MHD with self-consistent evolution functions include one-dimensional (Osherovich et al 1993(Osherovich et al , 1995 and twodimensional (Tsui & Tavares 2005) cylindrical models of magnetic ropes in the solar-terrestrial environment, two-dimensional axisymmetric model of atmospheric ball lightning in spherical coordinates (Tsui 2006;Tsui et al 2006), active galactic nucleus jets in astrophysical plasmas (Tsui & Serbeto 2007), traditionally treated as a steady state accretion-ejection MHD transport phenomenon from the accretion disk to the polar axis (Blandford & Payne 1982;Pelletier & Pudritz 1992). As for three-dimensional self-similar MHD solutions, there is one earlier case of interplanetary solar magnetic ropes (Gibson & Low 1998), which is not appropriate for astrophysical applications.…”

Unique Solutions to Boundary Value Problems in the Cold Plasma Model

“…But the Cinquini-Cibrario equation is interesting in its own right, in connection with normal forms for second-order linear elliptic-hyperbolic equations [1]. Moreover, polar forms of the Cinquini-Cibrario equation arise in models of atmospheric and space plasmas-compare, for example, equation (9) of [5] and equation (19a) of [17] with section 3 of [2]. (Such plasmas are cold, but in a relative rather than absolute sense.)…”

Dynamics of rising magnetized cavities and ultrahigh energy cosmic ray acceleration in clusters of galaxies

“…We study the expansion of the cavity by applying a self‐similar solution. Substantial work has been done in self‐similarly expanding magnetic structures (Low 1982; Prendergast 2005; Tsui & Serbeto 2007; Gourgouliatos & Lynden‐Bell 2008; Gourgouliatos & Vlahakis 2010; Takahashi, Asano & Matsumoto 2011). Lyutikov & Gourgouliatos (2011) and Dalakishvili et al (2011) have found solutions of force‐free magnetic fields that expand in a self‐similar manner.…”