Annu. Rev. Astron. Astrophys. 2002. 40: 319-348 Copyright © 2002 by Annual Reviews. All rights reserved

9. FIELD ORIGIN

When attempting to understand the behavior of cosmic magnetic fields, a critical characteristic to keep in mind is their longevity. The Spitzer conductivity (Spitzer 1962) of the ICM is: ~ 3× 10¹⁸ sec^-1 (for comparison, the conductivity of liquid mercury at room temperature is 10¹⁶ sec^-1). The timescale for magnetic diffusion in the ICM is then: _diff = 4 (L / c)² ~ 10³⁶ (L / 10 kpc)² years, where L is the spatial scale for magnetic fluctuations. The magnetic Reynold's number is: R_m = _diff / _conv ~ 10²⁹ (L / 10 kpc) (V / 1000 km s^-1), where _conv = the convective timescale = L / V, and V is the bulk fluid velocity. The essentially infinite diffusion timescale for the fields implies that once a field is generated within the ICM, it will remain extant unless some anomalous resistive process occurs e.g., reconnection via plasma wave generation in shocks.

Perhaps the simplest origin for cluster magnetic fields is compression of an intergalactic field. Clusters have present day overdensities ~ 10³. In order to get B_ICM > 10^-7G by adiabatic compression (B ^2/3) then requires IGM fields B_IGM > 10^-9 µG.

Of course, this solution merely pushes the field origin problem from the ICM into the IGM. An upper limit to IGM fields of 10^-9G is set by Faraday rotation measurements of high z radio loud QSOs, assuming a cell size of order 1 Mpc (Kronberg 1996, Blasi, Burles, & Olinto 1999). A limit to IGM magnetic fields at the time of recombination can also be set by considering their affect on the CMB. Dynamically significant magnetic fields will exert an anisotropic pressure on the gas, which must be balanced by gravity. Detailed studies of this phenomenon in the context of recent measurements of the CMB anisotropies shows that the comoving IGM fields ³ must be less than a few× 10^-9 G (Barrow, Ferreira, & Silk 1997, Clarkson & Coley 2001, Adams et al. 1996). A co-moving field of 10^-9 G at recombination would lead to Faraday rotation of the polarized CMB emission by 1° at an observing frequency of 30 GHz, a measurement that is within reach of future instrumentation (Kosowsky & Loeb 1996, Grasso and Rubinstein 2001). Considerations of primordial nucleosynthesis and the affect of magnetic fields on weak interactions and electron densities imply upper limits to comoving IGM fields of 10^-7 G (Grasso and Rubinstein 1995).

The origin of IGM magnetic fields has been considered by many authors. One class of models involves large scale field generation prior to recombination. An excellent review of pre-recombination magnetic field generation is presented by Grasso and Rubinstein (2001). Early models for pre-recombination field generation involved the hydrodynamical (`Biermann') battery effect (Biermann 1950). In general, the hydrodynamic battery involves charge separation arising from the fact that electrons and protons have the same charge, but very different masses. For instance, protons will have larger Coulomb stopping distances than electrons, and be less affected by photon drag. Harrison (1970) suggested that photon drag on protons relative to electrons in vortical turbulence during the radiation era could lead to charge separation, and hence magnetic field generation by electric currents. Subsequent authors have argued strongly against vortical density perturbations just prior to recombination, since vortical (and higher order) density perturbations decay rapidly with the expansion of the universe (Rees 1987). This idea has been revisited recently in the context of vortical turbulence generated by moving cosmic strings (Vachaspati & Vilenkin 1991, Avelino & Shellard 1995). Other mechanisms for field generation prior to recombination include battery affects during the quark-hadron (QCD) phase transition (Quashnock, Loeb, & Spergel 1989), dynamo mechanisms during the electro-weak (QED) phase transition (Baym, Bödeker, & McLerran 1996), and mechanisms relating to the basic physics of inflation (Turner & Widrow 1988).

A problem with all these mechanisms is the survivability of the fields on relevant scales during the radiation era. Battaner & Lesch (2000) argue that magnetic and photon diffusion will destroy fields on comoving scales few Mpc during this epoch, thereby requiring generation of the fields in the post-recombination universe by normal plasma processes during proto-galactic evolution (see also Lesch & Birk 1998).

Models for post-recombination IGM magnetic field generation typically involve ejection of the fields from normal or active galaxies (Kronberg 1996, Rees 1989). A simple but cogent argument in this case is that the metalicity of the ICM is typically about 30% solar, implying that cluster atmospheres have been polluted by outflows from galaxies (Aguirre et al. 2001). A natural extension of this idea would be to include magnetic fields in the outflows (Goldshmidt & Rephaeli 1993). It has also been suggested that IGM fields could be generated through turbulent dynamo processes and/or shocks occurring during structure formation (Zweibel 1988, Kulsrud et al. 1997, Waxman & Loeb 2000), or by battery effects during the epoch of reionization (Gnedin et al. 2000).

Seed magnetic fields will arise in the earliest stars via the normal gas kinematical Biermann battery mechanism. These fields are amplified by the - dynamo operating in stellar convective atmospheres (Parker 1979), and then are ejected into the ISM by stellar outflows and supernova explosions. The ISM fields can then be injected into the IGM by winds from active star forming galaxies (Heckman 2001). Kronberg, Lesch, & Hopp (1999) consider this problem in detail and show that a population of dwarf starburst galaxies at z 6 could magnetize almost 50% of the universe, but that at lower redshifts the IGM volume is too large for galaxy outflows to affect a significant fraction of the volume.

De Young (1992) and Rephaeli (1988) show that galaxy outflows, and/or gas stripping by the ICM, in present day clusters are insufficient to be solely responsible for cluster fields ~ 1 µG without invoking subsequent dynamo amplification of the fields by about an order of magnitude in the cluster atmosphere. A simple argument in this case is that the mean density ratio of the ICM versus the ISM, ~ 0.01, such that ICM fields would be weaker than ISM fields by ^2/3 ~ 0.05, corresponding to maximum ICM fields of 0.2 to 0.5 µG.

Fields can be ejected from Active Galactic Nuclei (AGN) by relativistic outflows (radio jets) and Broad Absorption Line outflows (BALs) (Rees & Setti 1968, Daly & Loeb 1990). The ultimate origin of the fields in this case may be a seed field generated by a gas kinematic battery operating in the dense accretion disk around the massive black hole, plus subsequent amplification by an - dynamo in the rotating disk (Colgate & Li 2000). Detailed consideration of this problem (Furlanetto & Loeb 2001, Kronberg et al. 2001) using the statistics for high z QSO populations shows that by z ~ 3, between 5% and 20% of the IGM may be permeated by fields with energy densities corresponding to 10% the thermal energy density of the photo-ionized IGM at 10⁴ K, corresponding to comoving field strengths of order 10^-9 µG.

Kronberg et al. (2001) point out that powerful double radio sources such as Cygnus A (radio luminosities ~ 10⁴⁵ erg s^-1) typically have total magnetic energies of about 10% that of the ICM as a whole. Hence, about ten powerful double radio sources over a cluster lifetime would be adequate to magnetize the cluster at the µG level.

Galaxy turbulent wakes have been proposed as a means of amplifying cluster magnetic fields (Jaffe 1980, Tribble 1993, Ruzmaikin, Sokolov, & Shukurov 1989). The problem in this case is that the energy appears to be insufficient, with expected field strengths of at most ~ 0.1µG. Also, the size scale of the dominant magnetic structures is predicted to be significantly smaller than the 5 to 10 kpc scale sizes observed (Goldshmidt & Rephaeli 1993, De Young 1992).

Cluster mergers are the most energetic events in the universe since the big bang, releasing of order 10⁶⁴ ergs in gravitational binding energy (Sarazin 2001a). For comparison, the total thermal energy in the cluster atmosphere is ~ 10⁶³ (M_gas / 10¹⁴ M) (T / 5 × 10⁷ K) ergs, and the total energy contained in the cluster magnetic fields is ~ 10⁶⁰ (B / 1 µG)² ergs. Hence, only a fraction of a percent of the cluster merger energy need be converted into magnetic fields. One possibility for merger-generated magnetic fields is a rotational dynamo associated with helical turbulence driven by off-center cluster mergers. This mechanism requires net cluster rotation - a phenomenon that has yet to be seen in cluster galaxy velocity fields (cf. Dupke & Bregman 2001). The lack of observed rotation for clusters suggests low impact parameters for mergers ( 100 kpc) on average (Sarazin 2001a), as might arise if most mergers occur along filamentary large scale structure (Evrard & Gioia 2001). The energetics of even slightly off-center cluster mergers is adequate to generate magnetic fields at the level observed, but the slow cluster rotation velocities ( 100 km s^-1) imply only one or two rotations in a Hubble time (Colgate & Li 2000), which is insufficient for mean field generation via the inverse cascade of the - dynamo (Parker 1979).

A general treatment of the problem of magnetic field evolution during cluster formation comes from numerical studies of heirarchical merging of large scale structure including an initial intergalactic field ~ 10^-9 G (Dolag & Schindler 2000, Roettiger, Stone, & Burns 1999). These studies show that a combination of adiabatic compression and non-linear amplification in shocks during cluster mergers may lead to ICM mean fields of order 1 µG.

A related phenomenon is field amplification by (possible) cooling flows. Soker & Sarazin (1990) have considered this mechanism in detail, and show that the amplification could be a factor of ten or larger in the inner 10's of kpc. They predict a strong increase in RMs with radius ( r²), with centrally peaked radio halos. Such an increase may explain the extreme RM values seen in powerful radio sources at the centers of cooling flow clusters (see Section 3.1), although the existence of gas inflow in these systems remains a topic of debate (Binney 2001).

Overall, there are a number of plausible methods for generating cluster magnetic fields, ranging from injection of fields into the IGM (or early ICM) by active star forming galaxies and/or radio jets at high redshift, to field amplification by cluster mergers. It is likely that a combination of these phenomena give rise to the µG fields observed in nearby cluster atmospheres. Tests of these mechanisms will require observations of (proto-) cluster atmospheres at high redshift, and a better understanding of the general IGM field.

Acknowledgements

We thank Juan Uson and Ken Kellermann for suggesting this review topic. We are grateful to Stirling Colgate, Steve Cowley, Luigina Feretti, Bill Forman, Gabriele Giovannini, Federica Govoni, Avi Loeb, Hui Li, Vahe Petrosian, and Robert Zavala for insightful corrections and comments on initial drafts of this manuscript. We also thank Rick Perley, John Dreher, and Frazer Owen for fostering our initial studies of cluster magnetic fields. We thank G. Giovannini, T. Clarke, J. Bagchi, Y. Rephaeli, and A. Vikhlinin for permission to reproduce some of the figures shown in this review. Finally, we thank Wayne Hu for the style files used to make this preprint.

The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under a cooperative agreement by Associated Universities, Inc. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, Caltech, under contract with NASA. This research has made extensive use of NASA's Astrophysics Data System Bibliographic Services.

² For > 300, IC losses dominate (or synchrotron losses for B > 2.3 (1 + z)² µG), while for lower electrons Brehmstrahlung losses dominate in cluster environments (Sarazin 2001b). Back.

³ Comoving fields correspond to equivalent present epoch field strengths, i.e. corrected for cosmic expansion assuming flux freezing. Back.