2.3. The physics of magnetic field amplification and evolution in spiral galaxies
2.3.1. The fundamental processes. The equations governing the evolution of magnetic field in non-viscous conducting plasma consist of Maxwell's equations, Ohm's law, the equation of continuity, and an equation of motion:
The electric and magnetic fields are E and B, respectively, is the mass density, j is the current density, is the conductivity, c is the net charge density, P the pressure, v the velocity, and is the gravitational potential. We note in passing that P includes the interstellar thermal gas and cosmic ray pressures, including that of the (sometimes ignored) relativistic protons and heavier nuclei. These particles may have 102 times the energy of the `visible' synchrotron-emitting relativistic electrons. The evolution of the magnetic field is described by solutions to the induction equation (cf Parker 1979), which can be derived from equations (2.1), (2.3) and (2.4)
where = c2 / 4 is the magnetic diffusivity. If the magnetic field is `frozen in', then = 0 (or = ), so that the term × ( × B) vanishes. Another relevant quantity is the magnetic Reynolds number,
where [B] and [v] are the typical variation scales for B and v, respectively. For most purposes in this review, the regime Rm >> 1 applies. In the absence of pressure and density perturbations, MHD waves will propagate with the Alfvén velocity which is given by
For a more complete discussion of physical processes in magnetoplasmas the reader is referred to Parker (1979), Zel'dovich et al (l983), Priest (1985), Asseo and Sol (1987) and references therein. It is important to note that equation (2.7) does not contain a source term for magnetic field. This underlines the need for theories to account for the source of magnetic fields - such as the Biermann battery mechanism, or a cosmological seed field (cf section 5). Thus a pre-existing 'seed' field is presupposed. The second important point is that even after a source, or seed field is identified, a generation process is required to sustain the fields against resistive and other decay processes - represented by the second term in equation (2.7).
The gravitationally-driven dynamics of disk galaxies naturally provide a large scale, ordered motion with a large energy density. The following section describes the 'conventional' galactic dynamo mechanism, which is based on concepts developed earlier for the Sun and Earth (Parker 1955, Steenbeck et al 1966, Steenbeck and Krause 1969, and others). It attempts to describe how ordered galactic motions can amplify, and at the same time produce ordered magnetic fields, which 'tap into' the larger source of gravitational energy in large spiral galaxies. It assumes that the initial fields were very much weaker than at the present epoch - an assumption which we shall later call into question. It also largely ignores the role of cosmic rays, an aspect which we also discuss later.
2.3.2. The conventional galactic dynamo in 'well-behaved' disk galaxies. Spiral disk galaxies possess gravitationally driven ordered motions, namely a 'solid body' (v r) rotation which, due to the galaxy's distributed mass, transforms into differential rotation at larger galactocentric radii. The latter may or may not be quasi-Keplerian (depending on the global distribution of mass), but in any case there is velocity shear (v / r). Superimposed on these global dynamics are streaming motions, possibly induced by density waves and/or magnetic fields (see below) and, for some galaxies, non-axisymmetric motions due to gravitational interactions with satellite or other nearby galaxies. Finally there are interstellar turbulent motions, typically a few km s-1. Typical (kinetic) energy densities due to global rotation, grav, are of order 3.3 × 10-10 erg cm-3, but these decrease significantly at large galactocentric radii. By contrast, energy densities of the synchrotron-emitting cosmic ray gas cr are of order 10-12 erg cm-3 and the interstellar magnetic energy density is m = ((B / 5µ G)2 × 10-12 erg cm-3. The energy density of the smaller-scale turbulent motions, t = 1/2 v2, is 0.6 × 10-12 erg cm-3. Of fundamental significance for the physics of large scale MHD processes in galaxies are the facts just illustrated, that grav dominates the others (except at large galactocentric radii), and that
We can further note that the V of density wave-induced streaming motions are of order 5-10 km s-1, so that grav 3 × 10-13 erg cm-3, is not much different from cr, m and t. Another important energy component to consider is that due to supernovae (or multiple supernovae within a small galactic region) and dense clusters of young stars, both of which can, temporarily and locally, deposit significant energy densities (in the form of cr, m and t) into the otherwise 'quiescent' interstellar disk. We shall call this component * . These basic energetic facts are key to the evolution of magnetic fields in galaxy disks.
An elegant theory for field amplification called the - dynamo was originally applied to solar magnetic fields (Steenbeck and Krause 1969), and was worked out in the 1960s for galactic magnetic fields by Stix (1975), White (1978), Parker (1966, 1971) and Vainstein and Ruzmaikin (1971). The theory makes use of what is called the mean field approximation (cf Krause and Rädler 1980) which is needed to accommodate the fact that we are dealing with averages over a range of correlation scales <li> and times <ti> of the velocity field, and fluctuations in the magnetic field <Bi>. Proof of the validity of the mean field approximation, although not trivial, has been worked out (Krause and Rädler 1980, Zel'dovich et al 1983; cf also van Kampen 1974, Knobloch 1978); it is, roughly speaking, an MHD analogue of statistical mechanical methods in the study of gases. However the validity of the mean-field solutions has been questioned by Kulsrud and Anderson (1992) who calculate that the build-up of fluctuation energy on small scales occurs before the mean field has a chance to be amplified (see section 2.3.5 below for a related discussion). This latter question should eventually be resolvable through ISM magnetic field measurements over the appropriate range of scales. The tentative result is that the magnetic fluctuation energy does not appear to increase at smaller scales. In fluid mechanics the energy density-wavenumber (k) distribution follows a Kolmogorov spectrum, whose logarithmic slope is -5/3 up to some maximum k, where viscosity effect take over and cause a small-scale (high k) cut-off. By contrast, in magnetohydrodynamic theory there appears to be no analogously definitive exponent which can confidently specify the variation of magnetic field strength with fluctuation scale. In a stratified, rotating and turbulent (or convective) section of the galaxy disk, the first induction action, which is due to the velocity shear, d / dr, causes an azimuthal field, B, if there is initially a radial field, Br, (Krause 1987). If we approximate the galaxy disk as a flattened, oblate spheroid of scale b along the rotation (z-) axis, and whose radial scale is a, we can, following Krause (1987), define an parameter
where r is the radial coordinate. We now consider an additional effect when turbulence is introduced into this stratified, magnetized layer: turbulent motion will be subject to the Coriolis force in this rotating system. Thus, for example, as a bubble of gas expands out of the plane, it will create an expanding `loop' which, due to its Bz component (see figure 4) will be twisted by the Coriolis force as it moves out of the plane; in the right-handed sense above the plane (if is directed upwards as in figure 4), and in the opposite sense below the plane, thus introducing an natural helicity to the outflowing magneto-plasma. This gives rise to the so-called -effect. Note that the moving Bz component will induce a current which is antiparallel to B (see also below).
Figure 4. Illustration of the -effect due to the Coriolis force in a rotating galaxy disk (after Krause 1987).
Another natural consequence of the -effect is the production of a poloidal magnetic field component. Because the energy density of the rotational motion is normally higher than t in a well behaved spiral galaxy, the repeated twisting and stretching effects can amplify the field in the disk. In mean-field electrodynamics, , related to the helicity, <v . ( . v)>, is defined as
where is the correlation time of the turbulent velocity field represented by vT. The characteristic -parameter (again following Krause 1987) is
We are now in a position to evaluate these parameters for the disk of a spiral galaxy, such as the Milky Way. The rotational shear, r d / dr (Oort's constant) near the Sun is -30 kpc km s-1, vT is 10 km s-1, a 15 kpc. The size of the turbulent elements, 100 pc. The lifetime of the turbulent elements, , the only non-measurable, can be reasonably estimated from / v 3 × 1014 s (= 107 yr). A key point is that, specifically due to the Coriolis force, the average <vT . ( × vT)< is non-zero, so that when we incorporate into the field regeneration equation (2.7), we see that the -term will affect the growth of the magnetic field. The helicity can be expressed as
(Krause 1987) where L( ) is the scale height, a value for which can be taken from Simard-Normandin and Kronberg's (1980) estimate of the magneto-ionic thickness of the Milky Way's disk in the vicinity of the Sun (section 2.2.3).
To illustrate how a differentially rotating galaxy disk can amplify a pre-existing magnetic field, we re-write equation (2.7) now incorporating :
where and are taken as constants (up to this point). A typical galactic value for the magnetic diffusivity is 0.1 v, 1025 cm2 s-1 .
2.3.3. Solutions to the mean field dynamo regeneration equation in the linear regime. Solutions to (2.15) can be written in the form
where = - k2 ± k, k being the wavenumber (Zel'dovich et al 1983). |B| grows exponentially with time for non-zero helicity, positive or negative, and if the scales are sufficiently large (k < || ). Another consequence of equation (2.15) is that a mean electric field, hence a mean current, will be directed along the magnetic field (Moffatt 1978, Krause and Rädler 1980) as illustrated in figure 4. The mean field generation equation should be regarded as an approximation of a complex MHD problem in 3D , and there are several simplifying assumptions implicit in our summary discussion here. Our purpose here is limited to illustrating the fundamental physical processes, and to showing how the solutions indeed provide a first-order confirmation of the observed geometry of magnetic fields in disk galaxies, and possibly their present-day strengths. Later in sections 2.3.4 and 2.3.5, we shall cast doubt on whether the standard, mean field dynamo can actually work in many galaxies.
A requirement of (2.15) and (2.16) is that characteristic field growth times be longer than 5. Other restrictive statements we have made above must be modified under different (but still reasonable!) assumptions. For example, our statement above that connects the mean helicity with the parameter is subject to the assumption that the turbulence associated with is isotropic. In reality, because of stratification, gravity, and rotational motion in galaxy disks, is generally a tensor (cf Krause and Rädler 1980, 1986, Elstner et al (1992). As Zel'dovich et al (1983) point out, mean field generation, i.e. solutions of the form |B| et (Re > 0) are also possible if the turbulence is homogeneous and anisotropic. For the purpose of this review, this latter fact serves to underline the relative robustness (though not unchallenged) of the mean field solutions as they apply to disk galaxies. The reader is referred to Zel'dovich et al (1983) for a lucid physical treatment of kinematic turbulent dynamos, and their application to galactic magnetic fields.
To create an expected `model' field distribution, it is instructive to parameterize the and effects separately, and then establish, for typical disk galaxy conditions, which modes dominate in what part of the galaxy. The numerical values of the and parameters (2.1 1 and 2.13), from the observationally estimated values in (2.3.2) above are: C - 7000 (the minus sign from the negative d / d r), and C 50 / L. It is immediately evident that |C| / C >> 1, meaning that the dominant induction action for the amplification of the azimuthal (toroidal) field in the disk is differential rotation (cf Krause 1987). Another useful parameter is C1 = C C 10-5 for the Milky Way. The C-parameters are convenient for exploring the solutions for model galaxy disks, which were first obtained by Stix (1975). The general result for the - dynamo is illustrated in figure 5 : The azimuthal field distribution is shown on the right-hand side of this composite flat-ellipse model, and the left side illustrates that a poloidal component, which has a quadrupole geometry in 3D, is also produced by the - dynamo.
Figure 5. The 3D magnetic field configuration produced by the - dynamo in the Rat ellipsoid model of Stix (1975), and White (1978) (adapted from White 1978, showing the morphology of the mean-field solutions For the azimuthal (rh side) component, and a 2D slice of the quadrupolar poloidal component (lh side).
The B solution shown in figure 5 is axisymmetric with respect to the galaxy's rotation axis, and it has reflection symmetry about the equatorial plane. Other solution modes are possible, and testable against observations, especially those of the Faraday RM distribution. Other eigensolutions of the regeneration equation can also produce field geometries which are antisymmetric about the equator (cf Krause 1987), and other azimuthal modes. In particular, the azimuth dependence of B is modulated by eim where m = 0 and m = 1 give axisymmetric and bisymmetric field distributions, respectively, as illustrated in figure 3. Two nearby galaxies (M81 and M51) appear to have an m = 1 mode azimuthal field distribution (cf Krause et al 1989, Tosa and Fujimoto 1978, Horellou et a1 1990 and figure 3(c)), while some other others, e.g. NGC 6946, appear consistent with an m = 0 mode for the global field, at least at low angular resolution. This is indeed the solution mode for the mean-field - dynamo with the highest growth rate, for the linear regime and with no distortions from axisymmetry (cf also Elstner et al 1992 for relevant numerical simulations). We note, however, that B-field maps from the radio data with the highest linear resolution (in kpc) suggest that reality may not be as simple as just indicated (section 2.2.2). A final judgement on the morphology of magnetic orientation and sign should await higher resolution images. So far, the highest resolution comes from the optical B-images but, as noted earlier, they are insensitive to the field sign.
Stimulated by the apparent existence of a dominant m = 1 mode in at least some galaxies (see section 2.2.2 above), several workers have explored the appropriate model parameter space for stable bisymmetric disk field solutions to the dynamo equations. Fujimoto and Sawa (1987, 1990) and Chiba and Tosa (1990) have produced numerical simulations showing this to be favored for thick magneto-ionic disk layers (zm 0.5 kpc) and larger turbulent velocities which persist away from the disk. Solutions exist which give a quasi-rigid rotation, BSS, which is close to that for spiral density wave pattern, DW. This makes it possible, even likely, for a resonant coupling to be set up between the two phenomena (Fujimoto and Sawa 1990, Tosa and Chiba 1990, Chiba and Tosa 1990). We recall (section 2.3.2) that the energy associated with the density wave-driven velocity perturbations is comparable to that in the magnetic field perturbations. Such an effect has at least two interesting implications for galaxy evolution: (i) large scale bisymmetric field amplification could, in the right circumstances, be enhanced by density wave patterns and vice versa, and (ii) the diffusion times of density waves, 109 yr (Toomre 1969), might be substantially modified, in particular, lengthened by magnetic reinforcement (see below).
Moss and Tuominen (1990) investigate solutions for 'thick disk' models in the non-linear regime (caused by an '-quenching' mechanism - see also Brandenburg et al 1989). They conclude that long term oscillations are possible between solution modes, in which bisymmetric and axisymmetric field geometries alternate over a galaxy's lifetime. They also find that the final mode, whether stationary or oscillatory, could depend on the initial conditions. The possibility of such non-linear, 'transient' phenomena has emerged largely as the result of increasing experience with non-linear galactic dynamo models. In particular Brandenburg et al (1992) and Poezd et al (1993), suggest that non-axisymmetric field patterns, including large scale field reversals in galaxy disks, are possibly transient phenomena, rather than stable solutions. This possibility, at least for the time being, complicates the interpretation of the early magnetic history of galaxies. Unlike with the Sun, we are not permitted the luxury of observing the time evolution of large scale galactic magnetic features!
An ingenious scenario to explain stable, non-axisymmetric fields has been proposed by Mestel and Subramanian (1991). They consider the two-arm spiral - the type most clearly observed to have a bisymmetric field pattern - which has been traditionally believed to be density wave-driven. They make the physically plausible assumption that the parameter is azimuth-dependent, and that it follows the spiral pattern imposed by the density wave. They obtain rapidly growing bisymmetric fields which corotate with the spiral pattern, in approximate agreement with the results of Fujimoto and Sawa (1990). Further, Mestel and Subramanian (1991) invoke independent arguments (Nakano 1984, Campbell and Mestel 1987) that a stronger field will bias the stellar mass spectrum, favoring the formation of more massive stars. The associated expanding H II regions/supernova remnants and planetary nebulae will then increase the turbulence, and hence quite likely the helicity (through interaction with the galactic rotation). This, in turn would further enhance the non-axisymmetric -distribution which is capable of reinforcing the dynamo which produced the bisymmetric field. This is a new idea, in which the field acts as a type of `catalyst', which increases energy input into the interstellar turbulence. If true, Mestel and Subramanian's mechanism would make it much more natural for the spiral structure to be at least partially magnetically influenced with the currently estimated field strengths, in contrast to previous thinking in this subject (see e.g. Binney and Tremaine 1987).
Initial conditions resulting from mergers, or earlier tidal encounters clearly would violate the assumption of initial axisymmetry inherent in the models discussed above, and have thus far not been explored in detail (see also section 5.5.1). The general conclusion from the above is that departures from axisymmetry, which are strongly indicated in some galaxies, can be reproduced as either transient or permanent solutions to the mean field - dynamo regeneration equations. Lesch (1993) has emphasized the importance of the intrastellar gas, in contrast to the stellar component, in the excitation of non-axisymmetric instabilities in galaxies. His numerical model calculations produce significantly shorter field amplification times when the dynamo action is driven by non-axisymmetric features (e.g. strong bars, and some tidal interaction effects), than for an axisymmetric dynamo.
A further important point emphasized by Krause and Meinel (1988) is that, as long as C, (equation (2.13)) exceeds the critical value for field growth, the relative sizes of the linear growth rates may be unimportant in deciding what the final field configurations will be. Saturation effects, and non-linear effects due to back-reactions can erase a galaxy's memory of the relative growth rates of different field amplification modes.
2.3.4. The dynamo effect for inner galactic rotation zones (the 2-dynamo). In the nuclear regions, the magnetic field should have a poloidal geometry according to the standard dynamo model (cf figure 5). Unfortunately it is difficult to observationally isolate the morphology of the magnetic fields in and above the d / d r 0 zone from the disks onto which they are normally seen projected.
In the inner galactic zones, which are interior to most of the galaxy's mass, and is independent of galactocentric radius (d / d r 0), the parameter C is much smaller than in the outer galaxy disk. Hence the conditions for the amplification of disk fields no longer apply. However, the current generated by the helicity (-effect) just outside where d / d r becomes non-zero, generates a poloidal field component. In addition, because the inner rotating and conducting gas has some helicity ( 0), it causes a poloidal current, which reinforces the toroidal magnetic field. In turn, this toroidal magnetic field drives a toroidal current, which reinforces the poloidal magnetic field (cf Krause 1987). This is the 2 dynamo effect, which (a) stabilizes and/or amplifies the poloidal field component (Bz) in the inner (d / d r 0) region of the galaxy, and (b) provides a natural coupling to the predominantly azimuthal field in the outer, d / d r < 0 disk, which is due to the - dynamo described earlier. All of this assumes the absence of large scale outflow winds from the inner galactic zones.
2.3.5. The current state of comprehensive (disk + halo) dynamo-generated field morphologies in 'normal' spiral galaxies. A more complete model of a dynamo-regenerated magnetic field must include the halo, for which Sokoloff and Shukurov (1990) have proposed a mean-field dynamo model. In their model, the dynamo field growth times are of the order of, or greater than a typical galaxy's lifetime, so that some memory of the hypothesized primordial field could be discernible, given detailed observations of Faraday rotation in the halo. Unfortunately the latter are difficult to obtain, even in a 2D projection for a galaxy see11 edge-on. This is partly because of the loss of the third geometrical dimension in a system where axisymmetry cannot be assumed, and indeed may contain a quadrupolar mode (cf figure 5). Additionally, as emphasized by Sukumar and Allen (1991) in their study of NGC 891 and NGC 4565, significant Faraday dispersion effects at decimeter s - just where the polarized synchrotron radiation is most readily detectable - `erases' information about the magnetic field geometry at the rear parts of the halo, which is difficult, if not impossible to reconstruct. Theoretical modeling has been extended to combined halo + disk numerical simulation model calculations by Brandenburg et al (1992), in which the halo possesses strong turbulent diffusivity, and an halo 10 × disk. Initial axisymmetry is preserved throughout in their calculations, and galactic winds are assumed to be small ( 50 km s-1, so that the field is not advected away into the IGM and thereby `spoiling' the dynamo effect (see, however, below). The results of these, and the recent simulations of Elstner et al (1992) show that even with these simplifying assumptions, quite complex galactic field structures can emerge from the numerical solutions. Brandenburg et a1 (1993) have more recently extended their numerical models, concentrating on halos, and introducing galactic winds and departures from isotropy in . They have succeeded in obtaining solutions which give broad agreement with the 2D halo field maps of NGC 891 (which has a weak wind), and NGC 4631 (figure 7) which has a stronger wind and a striking, quasi-radial halo magnetic field geometry.
Parker (1992) has pointed out that, although the observation-based estimates of the physical parameters in section 2.3.2 give mean field solutions which appear to agree with observations, one key parameter, the turbulent diffusivity , needs careful physical justification (cf also Rosner and DeLuca 1989). Standard dynamo theory, as reviewed above, prescribes random kinematic swirling and mixing in order to explain the turbulent eddy diffusion, t 1025 cm2 s-1 (Parker 1955, 1970, 1979, Steenbeck et al 1966, Vainstein and Zel'dovich 1972). This model is based on both global and local kinematics, and assumes that the field is mixed and filamented down to scales of order 0.1 au. This smallest size is roughly the mixing scale which is required in order that molecular resistivity can provide the required dissipation of large scale fields in 108 yr; i.e. that required to provide a large enough value of so that the field regeneration according to equation (2.15) will actually work. As Parker (1992) has emphasized, there is no known way, with <B> as strong as several µG and |B| ( <B>) fluctuating on a scale of 100 pc, that the tension in such a strong <B> would permit the free swirling and mixing of magnetic flux which is needed to explain an eddy diffusion corresponding to t 1025 cm2 s-1. Such swirling and mixing are what is required to make large scale fields dissipate in 108 yr. Also, such turbulent mixing down to these small scales (a scenario favored by Kulsrud arid Anderson 1992) would imply the generation of much stronger small scale fields - for which there is no observational evidence. Observational indications of fluctuations with 1011 cm have been found by Lee and Jokipii (1976) but they are probably small amplitude, linear Alfvén waves which are unable to reduce galactic Joule dissipation rates down to the 108 yr required to make the conventional galactic - dynamo work (cf Parker 1992). Similar doubts about the effectiveness of the diffusivity term in the standard dynamo theory have been raised by Knobloch and Rosner (1981), and Rosner and DeLuca (1989), who emphasized, among other things, the likelihood of the galactic dynamo operating significantly out of the thin galactic disk. Numerical simulations of thick disk dynamos have meanwhile been undertaken by Moss and Tuominen (cf section 2.3.3 above), and others.
Does the - dynamo, despite some observational support, therefore not work? Or is there something missing? What the conventional literature on the mean-field - dynamo does not examine is the detailed spatial and temporal nature of the (relativistic) cosmic ray gas, provided by supernovae and pulsars, and the non-relativistic hot gas (105 -107 K) from active sites of star formation, i.e. large H II complexes and associations of O and B stars. It also ignores the recently verified existence of organized outflow from such sites - especially in the nuclear region. Such complexes can inject an additional energy density CR + * (the latter due to ionizing radiation and non-relativistic hot gas from young star complexes) which is 10-11 erg cm-3 over 100 pc or more. This can be an order of magnitude larger than the other energy densities in (2.10). Furthermore, symmetric outflow would destroy the symmetry of field sense above and below the plane which was illustrated in figure 5. Also, over a few × 108 yr, several of these transient (* 197 yr) `events' will occur at random over a galaxy's disk, and their effect will be to disrupt any long term monotonic mean-field dynamo build-up of a large scale field.
A related point is that the combination of the supernovae and O and B stars can produce `galactic fountains' (Shapiro and Field 1976, Bregman 1980, Cox 1981, Edgar and Chevalier 1986 and Kahn 1981), and more generally, galactic winds (cf Holzer and Axford 1970, Mathews and Baker 1971, Bardeen and Berger 1978, Habe and Ikeuchi 1980, Völk et al 1990, Breitschwerdt et a1 1991). These phenomena will naturally tend to drive significant outflow from galactic disks. At this point it is relevant to mention the more extreme case of a starburst nucleus, which creates an even stronger outflow, such as recently revealed in M82 (cf section 3.1 below).
The effectiveness of the standard - dynamo has been questioned from another standpoint by Kulsrud (1986), who points out that the galactic disk field is tied largely to the densest clouds, which are ipso facto the most neutral clouds, so that the cloud-field coupling is not strong enough to prevent the field from simply passing through the clouds with the largest kinetic energy density. Thus the competing effects just mentioned would, according to Kulsrud, prevent a tight wind-up, or significant dynamo field generation (cf also Kulsrud 1990).
These phenomena have two broad implications for extragalactic magnetic fields: (a) they appear to force a re-examination of how large scale fields are generated and amplified in galaxies - which is our concern in this section. (b) As we shall discuss in section 6, they may have profound implications for the origin and strength of extragalactic magnetic fields. If the slow-acting (over several × 108 yr) mean field - dynamo is not effective, or is regularly disrupted by enhanced star formation activity, then µG-level fields may have existed at the protogalaxy stage. As we discuss later, there is increasing evidence to suggest that this may have been the case. Meanwhile we review some further developments of the mean-field galactic dynamo theory.
2.3.6. A modified galactic dynamo incorporating the effects of ouflow. The energetic nature of the stellar events mentioned above will produce some vertical waviness in the galaxy disk field, thus permitting the dense gas to slide downward along the field lines, while the buoyant and energetic cosmic ray gas tends to inflate the outward-directed wave bulges (cf Mouschovias 1974, Parker 1966, 1979 pp 325-33, 1992, and Shibata et al 1989, 1990). This `bulging and looping' of the disk mean field lines is associated with an interstellar gas clumping scale of 500 pc over 2 × 107 yr - the characteristic lifetime of the star-forming complexes mentioned above. The ongoing generation of cosmic rays in the gaseous disk will produce ballooning loops of field, which are inflated outward at > 30 km s-1 to distances of 1 kpc, thus forming a halo above the disk (cf Parker 1966, 1990, 1992, Kahn 1991).
In Parker's (1992) proposed modified - dynamo, the resulting close-packed, and outwardly inflating loops provide a natural opportunity for rapid magnetic reconnection between opposing, vertically oriented magnetic field lines (see figure 6). This, plus the rapid outward diffusion of the close-packed magnetic lobes provide the diffusivity (t) which is otherwise difficult to physically justify on the `standard` dynamo model (section 2.3.5). Another `natural' feature of Parker's model is that the outwardly inflated magnetic loops can sever themselves, by reconnection, from the disk field. They then behave as `freely rotating' loops due to the Coriolis force. Further reconnection fuses the large number of loops into a large scale poloidal field. This scenario appears capable of explaining, a1 least qualitatively, the observed halo field geometry in Sukumar and Allen's (1991) observations of NGC 891, as do also the numerical models of Brandenburg et al (1992) and Elstner et al (1992). A key, and attractive aspect of Parker's modified - dynamo is that it is a fast dynamo, whose `speed' increases with disk activity (i.e. outflow force). Whereas the conventional mean-field dynamo amplifies the azimuthal disk field slowly over 109 yr or more, and is susceptible to inevitable disruption by outflow due to disk star formation activity, Parker's fast acting dynamo thrives on the outflow; indeed it is the source of the turbulent diffusivity. The more vigorous the outflow, the faster, and more effective is the dynamo action.
Figure 6. Illustration of the formation of vertical magnetic loops, inflated by cosmic rays and hot gas, which can detach by reconnection from the disk field (Parker 1994).