Elly M. Berkhuijsen

Magnetic fields and spiral arms in the galaxy M51

We use new multiwavelength radio observations, made with the VLA and Effelsberg telescopes, to study the magnetic field of the nearby galaxy M51 on scales from 200 pc to several kpc. Interferometric and single-dish data are combined to obtain new maps at lambda lambda 3, 6 cm in total and polarized emission, and earlier lambda 20 cm data are rereduced. We compare the spatial distribution of the radio emission with observations of the neutral gas, derive radio spectral index and Faraday depolarization maps, and model the large-scale variation in Faraday rotation in order to deduce the structure of the regular magnetic field. We find that the lambda 20 cm emission from the disc is severely depolarized and that a dominating fraction of the observed polarized emission at lambda 6 cm must be due to anisotropic small-scale magnetic fields. Taking this into account, we derive two components for the regular magnetic field in this galaxy; the disc is dominated by a combination of azimuthal modes, m = 0 + 2, but in the halo only an m = 1 mode is required to fit the observations. We discuss how the observed arm-interarm contrast in radio intensities can be reconciled with evidence for strong gas compression in the spiral shocks. In the inner spiral arms, the strong arm-interarm contrasts in total and polarized radio emission are roughly consistent with expectations from shock compression of the regular and turbulent components of the magnetic field. However, the average arm-interam contrast, representative of the radii r > 2 kpc where the spiral arms are broader, is not compatible with straightforward compression: lower arm-interarm contrasts than expected may be due to resolution effects and decompression of the magnetic field as it leaves the arms. We suggest a simple method to estimate the turbulent scale in the magneto-ionic medium from the dependence of the standard deviation of the observed Faraday rotation measure on resolution. We thus obtain an estimate of 50 pc for the size of the turbulent eddies.

The magnetic field of M 31 from multi-wavelength radio polarization observations

The configuration of the regular magnetic field in M31 is deduced from radio polarization observations at the wavelengths �� 6, 11 and 20cm. By fitting the observed azimuthal distribution of polarization angles, we find that the regular magnetic field, averaged over scales 1-3kpc, is almost perfectly axisymmetric in the radial range 8 to 14kpc, and follows a spiral pattern with pitch angles of p ≃ −19 ◦ to p ≃ −8 ◦ . In the ring between 6 and 8kpc a perturbation of the dominant axisymmetric mode may be present, having the azimuthal wave number m = 2. A systematic analysis of the observed depolarization allows us to identify the main mechanism for wavelength dependent depolarization - Faraday rotation measure gradients arising in a magneto-ionic screen above the synchrotron disk. Modelling of the depolarization leads to constraints on the relative scale heights of the thermal and synchrotron emitting layers in M31; the thermal layer is found to be up to three times thicker than the synchrotron disk. The regular magnetic field must be coherent over a vertical scale at least similar to the scale height of the thermal layer, estimated to be hth ≃ 1kpc. Faraday effects offer a powerful method to detect thick magneto-ionic disks or halosaround spiral galaxies.

Scaling and correlation analysis of galactic images

ABSTRA C T Different scaling and autocorrelation characteristics and their application to astronomical images are discussed: the structure function, the autocorrelation function, Fourier spectra and wavelet spectra. The choice of the mathematical tool is of great importance for the scaling analysis of images. The structure function, for example, cannot resolve scales that are close to the dominating large-scale structures, and can lead to the wrong interpretation that a continuous range of scales with a power law exists. The traditional Fourier technique, applied to real data, gives very spiky spectra, in which the separation of real maxima and high harmonics can be difficult. We recommend as the optimal tool the wavelet spectrum with a suitable choice of the analysing wavelet. We introduce the wavelet cross-correlation function, which enables us to study the correlation between images as a function of scale. The crosscorrelation coefficient strongly depends on the scale. The classical cross-correlation coefficient can be misleading if a bright, extended central region or an extended disc exists in the galactic images. An analysis of the scaling and cross-correlation characteristics of nine optical and radio maps of the nearby spiral galaxy NGC 6946 is presented. The wavelet spectra allow us to separate structures on different scales like spiral arms and diffuse extended emission. Only the images of thermal radio emission and Ha emission give indications of three-dimensional Kolmogorov-type turbulence on the smallest resolved scales O160‐800 pcU. The crosscorrelations between the images of NGC 6946 show strong similarities between the images of total radio emission, red light and mid-infrared dust emission on all scales. The best correlation is found between total radio emission and dust emission. Thermal radio continuum and Ha emission are best correlated on a scale of about 1 arcmin . 1:6 kpc, the typical width of a spiral arm. On a similar scale, the images of polarized radio and Ha emission are anticorrelated, a fact that remains undetected with classical cross-correlation analysis.

Analysis of spiral arms using anisotropic wavelets: gas, dust and magnetic fields in M51

Context. The origin of the spiral pattern of magnetic fields in disc galaxies is an open question. Aims. Comparison of the regular magnetic field orientation with the gaseous spiral arm pitch angles can tell us whether spiral shock compression is responsible for the magnetic spirals. We also wish to see whether the ridges of different components of the ISM show the large-scale, systematic shifts expected from density wave theory. Methods. We have developed a technique of isolating elongated structures in galactic images, such as spiral arms, using anisotropic wavelets and apply this to maps of the CO, infrared and radio continuum emission of the grand-design spiral galaxy M 51. Results. Systematic shifts between the ridges of CO, infrared and radio continuum emission that are several kpc long are identified, as well as large variations in pitch angle along spiral arms, of a few tens of degrees. We find two types of arms of polarized radio emission: one has a ridge close to the ridge of CO, with similar pitch angles for the CO and polarization spirals and the regular magnetic field; the other does not always coincide with the CO arm and its pitch angle differs from the orientation of its regular magnetic field. Conclusions. The offsets between ridges of regular magnetic field, dense gas and warm dust are compatible with the sequence expected from spiral density wave triggered star formation, with a delay of a few tens of millions of years between gas entering the shock and the formation of giant molecular clouds and a similar interval between the formation of the clouds and the emergence of young star clusters. At the position of the CO arms the orientation of the regular magnetic field is the same as the pitch angle of the spiral arm, but away from the gaseous arms the orientation of the regular field varies significantly. Spiral shock compression can explain the generation of one type of arm of strong polarized radio emission but a different mechanism is probably responsible for a second type of polarization arm.

Densities and filling factors of the diffuse ionized gas in the Solar neighbourhood

Aims. We analyse electron densities and filling factors of the diffuse ionized gas (DIG) in the Solar neighbourhood. Methods. We have combined dispersion measures and emission measures towards 38 pulsars at distances known to better than 50%, from which we derived the mean density in clouds, Nc, and their volume filling factor, Fv, averaged along the line of sight. The emission measures were corrected for absorption by dust and contributions from beyond the pulsar distance. Results. The scale height of the electron layer for our sample is 0.93±0.13 kpc and the midplane electron density is 0.023±0.004 cm −3 , in agreement with earlier results. The average density along the line of sight isne� = 0.018 ± 0.002 cm −3 and is nearly constant. Since � ne� = FvNc, an inverse relationship between Fv and Nc is expected. We find Fv(Nc) = (0.011 ± 0.003) N −1.20±0.13 c , which holds for the ranges Nc = 0.05− 1c m −3 and Fv = 0.4−0.01. Near the Galactic plane the dependence of Fv on Nc is significantly stronger than away from the plane. Fv does not systematically change along or perpendicular to the Galactic plane, but the spread about the mean value of 0.08 ± 0.02 is considerable. The total pathlength through the ionized regions increases linearly to about 80 pc towards |z| = 1 kpc. Conclusions. Our study of Fv and Nc of the DIG is the first one based on a sample of pulsars with known distances. We confirm the existence of a tight, nearly inverse correlation between Fv and Nc in the DIG. The exact form of this relation depends on the regions in the Galaxy probed by the pulsar sample. The inverse Fv-Nc relation is consistent with a hierarchical, fractal density distribution in the DIG caused by turbulence. The observed near constancy ofnethen is a signature of fractal structure in the ionized medium, which is most pronounced outside the thin disk.

How cosmic ray electron propagation affects radio–far-infrared correlations in M 31 and M 33

We investigate the effect of propagation of cosmic-ray electrons (CRE) on the nonthermal (synchrotron) - far-infrared correlations in M31 and M33. The thermal (TH) and nonthermal (NTH) emission components of the radio continuum emission at 1.4 GHz and one higher frequency are compared with dust emission from M31 and M33 using Spitzer data. In both galaxies the TH emission is linearly correlated with the emission from warm dust (24 \mu m, 70 \mu m), but the power laws of the NTH-FIR correlations have exponents b < 1 that increase with increasing frequency. Furthermore, the values of b for M33 are significantly smaller (b ~ 0.4) than those for M31 (b ~ 0.6). We interpret the differences in b as differences in the diffusion length of the CRE. We estimate the diffusion length in two ways: (1) by smoothing the NTH emission at the higher frequency until the correlation with NTH emission at 1.4 GHz has b = 1, and (2) by smoothing the TH emission until the correlation with the NTH emission at the same frequency has b = 1, assuming that the TH emission represents the source distribution of the CRE. Our smoothing experiments show that M31 only has a thin NTH disk with a scale height of h = 0.3-0.4 kpc at 1.4 GHz, whereas M33 has a similar thin disk as well as a thick disk with scale height h_thick ~ 2 kpc. In the thin disks, the (deprojected) diffusion length at 1.4 GHz is ~ 1.5 kpc, yielding a diffusion coefficient of ~ 2 10^28 cm^2/s. The structure, strength and regularity of the magnetic field in a galaxy as well as the existence of a thick disk determine the diffusion of the CRE, and hence, the power-law exponent of the NTH-FIR correlations.

THE GALACTIC CONTINUUM SPURS AND NEUTRAL HYDROGEN.

So far no association has been found between the features of the galactic continuum radiation known as the spurs and the distribution of neutral hydrogen. McGee, Murray and Milton1 give contour maps of the peak brightness temperature of profiles of low velocity neutral hydrogen, and if the position of the steep outer gradient of the continuum radiation from the North Polar Spur, obtained from the best data at present available2–4, is plotted on these maps (Fig. 1), a correlation is immediately apparent. The line of outer gradient coincides with a spur feature in the neutral hydrogen distribution. Also plotted on Fig. 1 is the outer gradient of the continuum ridge at +10° declination, taken from ref. 4. The ridges P and U from ref. 5 are included up to the limit of that survey at R.A. = 16 h. All these ridges are in close coincidence with similar hydrogen features. A section through the neutral hydrogen and continuum distributions for the North Polar Spur edge at bII = +45° is shown in Fig. 2.

Probability distribution functions of gas in M31 and M51

We present probability distribution functions (PDFs) of the surface densities of ionized and neutral gas in the nearby spiral galaxies M31 and M51, as well as of dust emission and extinction Av in M31. The PDFs are close to lognormal and those for HI and Av in M31 are nearly identical. However, the PDFs for H2 are wider than the HI PDFs and the M51 PDFs have larger dispersions than those for M31. We use a simple model to determine how the PDFs are changed by variations in the line-of-sight (LOS) pathlength L through the gas, telescope resolution and the volume filling factor of the gas, f_v. In each of these cases the dispersion sigma of the lognormal PDF depends on the variable with a negative power law. We also derive PDFs of mean LOS volume densities of gas components in M31 and M51. Combining these with the volume density PDFs for different components of the ISM in the Milky Way (MW), we find that sigma decreases with increasing length L with an exponent of -0.76 +/- 0.06, which is steeper than expected. We show that the difference is due to variations in f_v. As f_v is similar in M31, M51 and the MW, the density structure in the gas in these galaxies must be similar. Finally, we demonstrate that an increase in f_v with increasing distance to the Galactic plane explains the decrease in sigma with latitude of the PDFs of emission measure and FUV emission observed for the MW.

Magnetic Fields and Spiral Structure

Interstellar magnetic fields are known to be a constraint for star formation, but their influence on the formation of spiral structures and the evolution of galaxies is generally neglected. Structure, strength and degree of uniformity of interstellar magnetic fields can be determined by measuring the linearly polarised radio continuum emission at several frequencies (e.g. Beck, 1982). Results for 7 galaxies observed until now with the Effelsberg and Westerbork radio telescopes are given in the table. The Milky Way is also included for comparison.

Erratum: Faraday ghosts: depolarization canals in the Galactic radio emission

Narrow, elongated regions of very low polarized intensity -- so-called canals -- have recently been observed by several authors at decimeter wavelengths in various directions in the Milky Way, but their origin remains enigmatic. We show that the canals arise from depolarization by differential Faraday rotation in the interstellar medium and that they represent level lines of Faraday rotation measure RM, a random function of position in the sky. Statistical properties of the separation of canals depend on the autocorrelation function of RM, and so provide a useful tool for studies of interstellar turbulence.