4.1. Distribution of thermal emission
In order to determine the equipartition magnetic field strength in selected regions of NGC 4449 we need to estimate the distribution of thermal emission in the galaxy. The spectral index computed between the maps of NGC 4449 at 8.46 GHz and 4.86 GHz changes from about -0.3 () in strongly star-forming regions to -1.1 locally in the outer southern region. Somewhat smaller variations are found by Klein et al. (1996), probably because of the much lower resolution used by these authors. Although Klein et al. (1996) found variations of the nonthermal spectral index between -0.5 in the central star-forming region to -0.8 in the eastern part of the halo, for our purpose it was sufficient to assume constant over the whole galaxy. Possible uncertainties due to this assumption were included in the errors. To determine the nonthermal spectral index we compared the radial distribution of the thermal brightness at 8.46 GHz and that in the H line (), convolved to the beam of . We found that they are identical for = -0.9. This value differs only by about 1.5 r.m.s. from the value obtained by Klein et al. (1996) from the radio spectrum, but agrees better with their estimate based on thermal flux obtained from the H emission.
The distribution of thermal fraction at 8.46 GHz in NGC 4449 (Fig. 6) shows clear peaks at the positions of bright star-forming complexes, reaches 80% there. After subtraction of the thermal emission these regions are still considerably brighter than the diffuse emission from the surroundings by some 40%. Away from bright star-forming complexes the emission is largely nonthermal, the free-free emission amounts to not more than 10%.
As an additional test of our assumption of constant over the galaxy's body we analyzed the point-to-point correlation between maps of the radio thermal flux at 8.46 GHz and that in the H line convolved to . We checked that, using the Monte-Carlo simulations of two-dimensional arrays of points convolved to various beams, values in map points separated by 1.2 times the beam size are correlated only by some 10 - 12% and are for our purposes almost independent. Therefore we used points separated by . In order to eliminate an artificial correlation caused by the radial decrease of all quantities, each map was divided by an axisymmetric model obtained by integrating the map in elliptical rings with the position angle and inclination taken from Table 1. A correlation slope significantly larger than 1 would mean that we have overestimated the thermal radio emission in strongly star-forming regions while in fact they have much flatter nonthermal spectra. Using the orthogonal regression we obtained , thus close to a linear relationship, though few regions deviate strongly from the best-fit line. This means that shows some place-to place variations, but our assumption of = constant does not introduce large, systematic errors in determining the thermal fraction. A detailed multi-dimensional analysis of both radio emission components involving the H, CO, HI and X-ray data will be the subject of a separate study.
4.2. Magnetic field strengths
To determine the magnetic field strengths in NGC 4449 from the synchrotron emission we assumed the equipartition conditions between magnetic fields and cosmic rays to be valid everywhere in the galaxy. Furthermore we adopted a proton-to-electron ratio of energy densities of 100 and a lower energy cutoff of cosmic ray electrons of 300 MeV. We assumed a face-on thickness of the nonthermal disk of 2 kpc, resulting from a typical scale height of galactic radio disks of 1 kpc (Hummel et al. 1991), determined by the propagation range of cosmic ray electrons. With the inclination of NGC 4449 from Table 1 this implies a mean pathlength through the galaxy of 2.8 kpc. The errors of estimated magnetic field strengths include an uncertainty of these quantities of a factor two. The thermal fractions were taken from results described in Sect. 4.1.
Under these assumptions we determined the mean magnetic field strength for the whole galaxy and for selected regions; the results are summarized in Table 2. Regular magnetic fields derived from the polarized intensity were found to reach locally up to G in the western magnetic "fan" and about G in the radio-bright part of the polarized ring. The total magnetic field in these regions, determined from the total power emission reaches G, comparable to that in the radio-brightest spiral galaxies (Beck et al. 1996b). A slow rotation of NGC 4449 accompanied by chaotic gas motions apparently does not exclude the existence of strong, regular magnetic fields.
Table 2. Magnetic fields in NGC 4449
4.3. Magnetic field structure
4.3.1. Magnetic field coherence
The presence of polarized emission alone does not provide a definite proof for dynamo-generated, spatially coherent magnetic fields. Substantial polarization may be also produced by random fields, made anisotropic by squeezing or stretching, e.g. by stellar winds or large-scale shocks from multiple supernova events, however, frequent field reversals along the line of sight would completely cancel the Faraday rotation. Non-zero rotation measures imply the magnetic fields in the observed galaxy coherent over scales much larger than the telescope beam.
Although the values of RM in individual points of our Faraday rotation map (Fig. 5) do not exceed the errors by much, we note that they deviate coherently from zero, forming large domains of constant RM sign (both positive and negative). These regions with mean RM of rad/m2 are up to 20 times larger than the telescope beam area. A correction for the foreground rotation of -35 rad/m2 was estimated from background sources present in our map and checked with the galactic RM map by Simard-Normandin & Kronberg (1980). At the galactic latitude of NGC 4449 of the existence of foreground rotation structures changing sign over angular scales of - with an amplitude of 100 rad/m2, correlated with particular features in the galaxy's polarized intensity, is unlikely. Thus, the observed Faraday effects almost certainly originate inside NGC 4449.
To check quantitatively the coherence of the non-zero Faraday rotation we computed values of RM and its error in a grid of points separated by (1.2 times the beam size). In case of a lack of systematic Faraday rotation such points would show only little correlation (see Sect. 4.1) and the variable defined as RM/ is expected to fluctuate randomly from point to point with a zero mean and unity variance. However, we found that its mean value deviates from zero in the eastern polarized ridge by more than as well as in the western "fan" by more than , being the r.m.s. error of mean RM in a given region. This implies that the probability of creating at random such large non-zero RM domains is less than . In the eastern, weaker "fan", the deviation amounts to only (the probability of a random occurrence of non-zero RM of 10%), because of a worse signal-to-noise ratio. The results were found to be independent of the assumed foreground rotation. Thus we conclude that NGC 4449 contains genuine unidirectional fields, rather than stretched and compressed random magnetic field. The latter one would have different sky-projected components yielding a substantial polarization while the line-of-sight component would frequently change sign which would cancel any systematic Faraday rotation. We note that the growth of galaxy-scale coherent, unidirectional fields lies at the foundations of the dynamo process.
4.3.2. Magnetic field geometry
Figs. 7a and b presents the distribution of magnetic field orientations in the azimuth-ln(R) frame (R being the radial distance form galaxy's optical centre), in which the logarithmic spiral appears as a set of straight lines inclined by the spiral's pitch angle. At 8.46 GHz (little Faraday rotation) we clearly see a combination of the radial field in the inner region out to ln(R) of 0.5 - 0.6 and a more azimuthal one at larger radii. However, at this frequency the picture in the outer galaxy regions becomes rather noisy. A comparison of Figs. 7a and b shows that Faraday rotation does not much change the global field picture in the inner region where the ionized gas density is highest and Faraday effects strongest. Thus, the 4.86 GHz data alone can be safely used in the galaxy outskirts.
Fig. 7b shows a very well ordered field in the polarized ring with the magnetic pitch angle keeping a constant sign over most of azimuthal angles (except a low signal-to-noise region at azimuths of - and ln(R) ). The value of is on average, with local variations. It resembles a somewhat distorted magnetic spiral with a substantial radial component. This, like in rapidly rotating spiral galaxies, may signify dynamo-type fields (Urbanik et al. 1997), while the random field pushed away from the galaxy and squeezed by an expanding gaseous shell would yield the observed B-vectors parallel to the shell. Nevertheless, the pitch angles show some place-to-place changes, possibly due to processes like local outflows or compressions. The strongest distortion of the spiral - the region of nearly pure toroidal magnetic field at azimuthal angles , ln(R) coincides with the densest HI clump and a region of star formation. The analysis of recent CO data (Kohle et al. in preparation) suggests strong gas compression possibly due to external interactions. We note also an opposite sign of Faraday rotation at both ends of the major axis, which is typical for axisymmetric magnetic fields.
The radial magnetic "fans" are structural elements not observed in spiral galaxies. They may be due to magnetic fields pulled out from the central star-forming region by gas outflows. Evidence for radial gas flows in NGC 4449 was indeed found by Martin (1998, 1999). However, in case of an initially random magnetic field (e.g. injected by supernovae) being stretched by gas flows, the "fans" would contain interspersed magnetic lines directed towards and outwards from the star-forming complex, yielding no significant Faraday rotation (see Sect. 4.3.1). Thus if the radial "fans" would result from the gaseous wind, a large-scale, coherent preexisting magnetic field would still be required, like one resulting from the dynamo process.
Alternatively, the observed magnetic field structure in NGC 4449 can be qualitatively explained by classical dynamo-generated fields. In addition to a toroidal field running around the disk, the classical dynamo process also generates a poloidal field with lines of force forming closed loop-like structures perpendicular to the disk plane and with diameters comparable to the galaxy radius (Donner & Brandenburg 1990). They are due to a radial field component, Br, turning into a vertical one, Bz, close to the centre and in the disk outskirts. The conservation of magnetic flux leads to Bz being always much stronger in the central region than in the outer disk. In large spiral galaxies the vertical segments of the poloidal field loops with the strongest Bz probably lie at heights - 3 kpc. This is too high to see the vertical magnetic field in synchrotron emission, as the latter has a vertical scale height of about 1 kpc (Hummel et al. 1991) due to a limited propagation range of cosmic ray electrons. As an exception NGC 4631 has a much larger scale height and dominating vertical fields in its inner regions (Hummel et al. 1991).
With its bright star-forming disk of about 4 kpc diameter NGC 4449 is several times smaller than normal spirals. If it had a classical poloidal dynamo-type magnetic field, its magnetic lines would make closed loop-like structures with a vertical size of about 1 - 1.5 kpc. The maximum Bz would occur at some hundreds of parsecs above the galaxy's plane, well within the propagation range of radio-emitting electrons, making vertical fields visible in emission. The intense star formation in NGC 4449 and its low gravitational potential may give rise to galactic winds which may additionally enhance the generation of vertical magnetic fields (Brandenburg et al. 1993). With the inclination of NGC 4449 (Table 1) a strong poloidal field in the central part of NGC 4449, projected to the sky plane, may give rise to the observed radial magnetic "fans". A detailed MHD model of magnetic field evolution in NGC 4449 is a subject of a separate study (Otmianowska-Mazur et al., in prep.). We note also that superimposed on the global magnetic field, smaller-scale ( 0.5 kpc or in our map) local phenomena (e.g. magnetized shells or giant magnetic loops caused by Parker instabilities, Klein et al. 1996) may be present, as well. They may explain e.g. local RM reversals, like that seen in the eastern "fan" at , .
Although the dynamo process constitutes some possibility to explain the magnetic field structure in NGC 4449, the question arises how the dynamo mechanism can work in this galaxy. Despite some evidence for the dynamo action strong regular magnetic fields are hard to explain by classical dynamo models which, given the weak signs of rotation of NGC 4449, yield growth rates of the regular magnetic field at least an order of magnitude smaller than in rapidly rotating spirals (see e.g. Brandenburg & Urpin 1998). Estimates kindly provided by Dr Anvar Shukurov indicate that for the rotation speed and dimensions of NGC 4449 the classical, Coriolis force-driven -effect is too weak for the onset of either or dynamo (see Ruzmaikin et al. 1988for definitions). Faster field amplification is predicted by a recent concept of the dynamo driven by magnetic buoyancy and sheared Parker instabilities (e.g. Moss et al. 1999). Crude estimates of its efficiency by A. Shukurov (priv. comm.) show that the dynamo process is easily excited throughout most of the galaxy's body. However, what kind of structure is generated in such conditions remains still an open question and will be a subject of separate analytical and numerical studies.
Among other possibilities we can mention e.g. fast dynamos (Parker 1992), interrelations between small-scale velocity and magnetic field perturbations caused by specific instabilities (Brandenburg & Urpin 1998) or even magnetic field amplification without any -effect at all (Blackman 1998). As in these concepts ordered rotation is still needed it is not known how they would work in the complex velocity field of NGC 4449. In summary, our work provides arguments in support of non-standard magnetic field generation mechanisms, though some elements of its structure may be due to gas outflow processes. Still a lot of theoretical work is needed to understand how a classical mixture of poloidal and toroidal fields, similar to that in rapidly rotating spirals can arise in a slowly and chaotically rotating object. Nevertheless, it seems that the existence of strong, dynamically important magnetic fields in dwarf irregulars cannot be ignored.
© European Southern Observatory (ESO) 2000
Online publication: March 17, 2000