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Astron. Astrophys. 318, 700-720 (1997)

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2. The observational database

2.1. The data

The observations of the spiral galaxy M 51 which we discuss below were obtained at the wavelengths 2.8 cm (Neininger 1992a), 6.2 cm (Neininger et al. 1993a), 18.0 cm and 20.5 cm (Horellou et al. 1992). In contrast to earlier discussions of these observations, here we analyze the observations for all four wavelengths simultaneously.

The 2.8 cm data are single-dish measurements obtained with the 100-m Effelsberg radio telescope. The other data sets were obtained with the VLA in its D-array. This imposes some restrictions for the use of the 6.2 cm data since at this wavelength the diameter of the primary beam of the VLA is 9 arcmin, which corresponds to a diameter of 25 kpc in the plane of M 51. Therefore, we considered the measurements at 6.2 cm to be reliable up to a radius of 9 kpc chosen to be somewhat smaller than the radius of the primary beam, and we did not use them at larger radii.

At all wavelengths the data were smoothed to a final resolution of [FORMULA] corresponding to [FORMULA] in the plane of M 51. Fig. 1 shows the observed E-vectors rotated by [FORMULA], superimposed onto an optical picture of M 51.

[FIGURE] Fig. 1a-d. Maps of the E-vectors rotated by [FORMULA] observed at [FORMULA] 2.8 cm (a, upper left), 6.2 cm (b, upper right), 18.0 cm (c, bottom left) and 20.5 cm (d, bottom right). The length of the vectors is proportional to the observed polarized intensity. They are shown superimposed onto an optical picture (Lick Observatory) of M 51. All maps were smoothed to an angular resolution of [FORMULA]

2.2. Data averaging in sectors

Following an usual procedure in the studies of regular magnetic fields in external galaxies, the galaxy was divided into several rings and we considered the values of polarization angle averaged in sectors in each ring, [FORMULA], where the subscript n refers to the wavelength and i to the sector. Here we chose the rings between the galactocentric distances [FORMULA], 6, 9, 12 and [FORMULA] ; within each ring sectors of an opening angle of [FORMULA] were used. The azimuthal angle [FORMULA] was measured counterclockwise from the northern major axis. Throughout the paper we specify sectors by their median value of [FORMULA].

The input values from the observations were obtained by calculating separately the averages of the Stokes parameters Q and U over all the points of the regular data grid that lie in the specified sector. All data are slightly oversampled with a gridding interval of one third of the full width at half maximum (FWHM) of the Gaussian beam. After the averaging the polarized intensity and the polarization angle of the observed E -field, [FORMULA], were calculated using the mean Q and U values for each sector. The zero level of the polarized intensity was corrected for polarized noise (Wardle & Kronberg 1974). The [FORMULA] ambiguity in polarization angles was resolved by requiring that the difference in the values of [FORMULA] in neighboring sectors is minimum.

A lower estimate of the uncertainty of [FORMULA] is provided by the statistical noise in the Q and U maps. In addition an independent error calculation was used: in each sector the standard deviation, denoted as [FORMULA], of the data points around the sector average was determined and used as an estimate of the uncertainty of the corresponding mean value, [FORMULA]. Only if its value was less than the statistical noise value (which is usually not the case), the latter was adopted. For sectors with less than five data points these were used only to calculate the mean value. The standard deviation was then computed after combining the adjacent sectors within a ring until the total number of the data points was at least five. The resulting error was calculated as [FORMULA], where summation was carried out over the sectors involved, whose number is K, and [FORMULA] are undersampled standard deviations for individual sectors. This error was then assigned to all the sectors involved.

Earlier analyses by Ruzmaikin et al. (1990) and Sokoloff et al. (1992), based on a similar approach, used model values of the data errors. Here we use the errors obtained from observational data which makes our results more reliable. (We note, however, that the model calculations of [FORMULA] of the earlier analyses proved to be reasonable.)

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998