R 1 Ma

pMf)

It is easy to see that these expressions are similar to those for the azimuthal components of gas velocity and magnetic field in the previous investigation of Zirakashvili et al. (1996) and in the theory of azimuthal symmetric MHD flows (Weber and Davis, 1969; Yeh, 1976; Sakurai, 1985). The only difference is the definition of the Alfvén Mach number. In Zirakashvili et al. (2001) it contains Bss instead of the square of the meridional regular magnetic field component. Eq.

3.15.7 shows that B^ is not reduced to the square of the azimuthal field component in Zirakashvili et al. (1996) but rather contains an additional term. Nevertheless, this term is inversely proportional to the square of the meridional velocity and hence quickly drops with height over the disk. Therefore at large heights above the disk B^ is given by

In the general case in which magnetic field components perpendicular to the surface S are present, Eq. 3.15.4 also describes the generation of a random magnetic field owed to differential rotation of neighboring surfaces. Nevertheless, all Bj components except determined by Eq. 3.15.5, 3.15.12 and 3.15.13 tend to zero as the wind accelerates. Hence expressions determined by Eq. 3.15.5, 3.15.11, 3.15.12 and 3.15.13 are valid in the general case for large heights above the disk. It is easy to picture the magnetic field geometry in the galactic halo (see Fig. 3.15.1).

Fig. 3.15.1. Flux-tube geometry characterized by the surface S which contains the wind stream lines. The flux-tubes of cross section A(s) have axial symmetry around z-axis. In the disk (z = 0) the gas rotates with angular velocity £2(r). Magnetic field disturbances, near isotropic in the galactic disk, become strongly elongated in the galactic halo. According to Zirakashvili et al. (2001).

Fig. 3.15.1. Flux-tube geometry characterized by the surface S which contains the wind stream lines. The flux-tubes of cross section A(s) have axial symmetry around z-axis. In the disk (z = 0) the gas rotates with angular velocity £2(r). Magnetic field disturbances, near isotropic in the galactic disk, become strongly elongated in the galactic halo. According to Zirakashvili et al. (2001).

From Fig. 3.15.1 can be seen that magnetic field lines are strongly elongated in one direction owing to wind acceleration and bend away from the meridional direction because of the rotation of the Galaxy. This picture is similar to the one obtained in our previous investigation for the regular magnetic field. The presence of the magnetic field gives some properties of an elastic body to the surface S, which can now resist to velocity shear. This feature allows magnetic connection and corresponding transport of angular momentum along this surface even for the zero regular magnetic field case.

3.15.4. Results of numerical calculations

Galactic wind numerical calculations were performed by Zirakashvili et al. (2001) for the same parameters of our Galaxy as described in Zirakashvili et al. (1996). They include the gravitational potential of Miyamoto and Nagai (1975) and take into account a dark matter halo of the Galaxy (Innanen, 1973). The geometry of the flow is prescribed. The surface S is chosen to have a hyperbolic form r2 z2

'o zo - ro where zo = 15 kpc is the galactic halo radius, and ro is that galacto-centric radius where the flux-tube under consideration originates. Energy conservation along the surface S was assumed (as in Zirakashvili et al., 1996):

— + JL-Qrum+ t \-0+ clc> a , ' = const, (3.15.15) 2 2 v p( -1) p(Yc -1)

where Yc and Yg are the adiabatic indices of CR and gas respectively. The values Yc = 1.2, and Yg = 16 were used. The only difference in comparison with the previous consideration of Zirakashvili et al. (1996) is the substitution of the z-

component of the regular magnetic field Bz by Bzz . These components coincide with the meridional component at small heights above the disk. Observations of the regular magnetic field in the galactic disk show a regular field of about 2 ^Gs which is parallel to the galactic disk (Rand and Kulkarni, 1989). This means that the vertical component of the regular field in the galactic halo is small and hardly exceeds 1 ^Gs. On the other hand, a random field of about 6^Gs exists in the disk.

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