It was found that the meridional initial wind velocity uo = 28.4 km/sec. The results of expected changes of the magnetic field H, temperature T, meridional u and azimuthal u0 components of the galactic wind velocity with distance from the disco-equator z up to z = 75 kpc are shown on the Fig. 3.14.1 (the critical points with smooth transition are located at 5.3 kpc - the slow magnetosonic, at 8.1 kpc -the AlfVénic, and at 30 kpc - the fast magnetosonic; it was found also that generated by Galaxy rotation azimuthal magnetic field falls as s-1).

Fig. 3.14.1. Expected distribution of magnetic field |h| , meridional u and azimuthal u^

galactic wind velocities and gas temperature T in the rotating Galaxy. According to Zirakashvili et al. (1993).

3.14.2. Solution for CR propagation in the rotating Galaxy

On the basis of the solution shown in Fig. 3.14.1 Ptuskin and Zirakashvili (1993) investigated CR propagation in the Galaxy governed by the diffusion-convection processes:

- B~l(BKf')' + (u + Va )'-B-1(B(u + ))')f = 2g(p)S{s), (3.14.7)

3 dp where f (p, s) is the CR distribution function and CR sources concentrated in disk are assumed to have a power law spectrum Q ^ p~Ys . The diffusion coefficient is determined by the expression k = K// cos2 a; K// = vrLH2 /(6n2kresW(kres)), (3.14.8)

where kres = 1/rL and rL is the Larmor radius. The growth rate of CR streaming instability for Alfven waves generation r. = -6n3e2Va (kresc2 j-1 Jdp(1 - p2reJp2 pK//fcosa, (3.14.9)

pres where pres = e|Hjckres . The non-saturated Landau damping of Alfven waves will be (according to Volk and Cesarsky, 1982; see also above, Section 3.5):


¡3 = 4ml/H2 . (3.14.11) The diffusion coefficient will be

K// = Ys(s -2) 31/2c3fflH-1H2E-1 (p/mc)s-3B(s)cosa, (3.14.12) 9n2 (Ys - 4)

where E is the particle's full energy. This model is in a good agreement with data on mean matter thickness < X > = 10(v/c) g/cm2 for pc/Ze < 5 GV and < X >

^ p-0'55 for pc/Ze > 5 GV, but predicts too large stellar anisotropy

which gives 5% at energy 1014 eV (measured amplitude is about 0.05 % at 1012—l014 eV and about 3% at 1017 eV). Ptuskin and Zirakashvili (1993) note that this discrepancy can be caused by peculiarities of local conditions near the sun that do not affect the energy spectrum and chemical composition, but are very important for the observed CR anisotropy.

3.15. On the transport of random magnetic fields by a galactic wind driven by CR; influence on CR propagation

3.15.1. Random magnetic fields in the galactic disc and its expanding to the dynamic halo

Zirakashvili et al. (2001) considered the transport of random magnetic fields by galactic wind driven by CR and their influence on CR propagation in the Galaxy. As was considered in previous Sections 3.11 and 3.12, the galactic wind driven by CR is a prominent example of the dynamical importance of energetic particle nonlinear effects in our Galaxy (Ipavich, 1975; Breitschwerdt et al., 1987, 1991; Zirakashvili et al., 1996). The main matter is that CR sources in the galactic disk generate energetic particles which can not freely escape from the Galaxy but rather generate Alfven waves through kinetic stream instability (see Section 3.3). In spite of strong nonlinear Landau damping (Livshits and Tsytovich, 1970; Lee and Volk, 1973; Kulsrud, 1978; Achterberg, 1981; Achterberg and Blandford, 1986; Fedorenko et al., 1990; Zirakashvili, 2000) such waves lead to an efficient coupling of thermal gas and energetic particles (Ptuskin et al., 1997) and CR drive galactic wind flow owing to their pressure gradient. In the simplest approximation one can assume that a frozen-in magnetic field is adverted from near the galactic disk region to the galactic halo. Such a field and its tension were taken into account by Zirakashvili et al. (1996) for calculations of the galactic wind flow. An idealized regular magnetic field configuration was considered. Zirakashvili et al. (2001) develop these ideas further and take into account the random magnetic field component that exists in the galactic disk and dynamically dominates over the regular component.

3.15.2. Basic equations described the transport of the random magnetic fields

According to Zirakashvili et al. (2001), magneto-hydrodynamic (MHD) turbulence is created in the galactic disk mainly by the numerous supernovae; it seems that turbulent diffusion and helicity really provide dynamo action in the disk of our Galaxy (Parker, 1992). Those effects can be less important in the galactic halo, especially if galactic wind flow exists. The approximation used by Zirakashvili et al. (2001) is that at heights of several hundred pc the magnetic inhomogeneities created in the upper part of the disk are picked up by the wind flow and transported into the galactic halo. They neglect turbulent magnetic diffusion and reconnection here. The magnetic field B is frozen into the galactic wind gas and evolves according to equation

It was assumed that gas velocity u and density p are non random quantities and are described by the steady state equations

p(uV)u = -v(pg + Pc)+ pVO - 4-([B x[Vx b] . (3.15.3)

Here Pg and Pc are the pressures of gas and CR respectively, O is the gravitational potential. Angular brackets mean averaging over volume. It is easy to see from Eq. 3.15.3 that dynamical effects of the magnetic field can be described if one knows the mean tensor By = ^¡B^. The equation for this tensor can be derived from Eq. 3.15.1:

^ = -ukVkBij - 2BijVhuh + BkjVku + BikVkuj . (3.15.4)

Then Zirakashvili et al. (2001) consider steady state solutions of Eq. 3.15.4 corresponding to the steady state Eq. 3.15.2 and Eq. 3.15.3. This is a development of previous results of Zirakashvili et al. (1996) (where the steady state Eq. 3.15.1 for the regular magnetic field was used) to the case including random magnetic fields.

3.15.3. The random magnetic field effects in the galactic wind flow with azimuthal symmetry

Assuming azimuthal symmetry of the galactic wind flow it is convenient to introduce the coordinate s in meridional direction and the azimuthal angle 0. The tensor components By should be written in terms of those coordinates. The gas velocity has the meridional and azimuthal components us and u^, respectively. For the sake of simplicity it was assumed that the magnetic field is tangent to the surface S along which the galactic wind streams. Therefore there are only three independent components: Bss, Bs^ and B^. Introducing the flux-tube cross-

section A(s) one can obtain:

r rBss

Bss B

Using the ^-component of Eq. (3.15.3) one finds angular momentum conservation along the surface S:


Here the quantities Q and C are constant along the surface S, and r is the distance from the axis of rotation. Expressions for u^ and Bs^ can be found using Eq.

3.15.6 and 3.15.7. They contain the denominator 1 -Ma , where a =V 4npu2s/Bss (3.15.9)

is the meridional Alfvén Mach number. Assuming acceleration of the wind flow from sub-AlfVénic to super-AlfVénic velocities one can find a relation between C and Q which leads to finite values of u^ and Bs^ :

were ra is the distance from the AlfVénic point Ma = 1 to the axis of rotation. As a result

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