1 Introduction

Giant radio galaxies (GRGs) are the largest radio sources in the Universe which are associated with active galactic nuclei (AGN). A common definition for GRGs is that they are radio sources with a linear size above 12 Mpc. These enormous sizes make them interesting objects to study. Why are they so large? Is it because they grow much faster than other radio galaxies, or are they extremely old radio sources? Which are the properties of their progenitors? Also, because their size is so extreme, they allow us to study their radio structures in detail and to use them as probes of the gaseous environment of their host galaxies on scales of a few hundred kpc to a few Mpc.

Since their discovery in the early seventies, several individual GRGs have been the subject of detailed radio studies at a variety of wavelengths and resolutions (e.g. 3C236 by Strom & Willis 1980 and Barthel et al. 1985; NGC315 by Willis et al. 1981, NGC6251 by Perley et al. 1984). However, systematic studies of GRGs as a population have always been hampered by the small number of sources available and by non-uniform selection effects. Since GRGs are large and their radio emission is not very powerful their surface brightness is relatively low. This makes them difficult objects to detect or recognize in most large-scale radio surveys. As a result, a large fraction of the known GRGs have been discovered serendipitously (e.g. Hine 1979; de Bruyn 1989), hence the difficulty in obtaining a uniformly selected sample. The most uniform dataset on GRGs available yet is that of 10.5-GHz observations with the 100-m Effelsberg telescope (Klein et al. 1994; Saripalli et al. 1996; Mack et al. 1997). All sources have been observed in the same way and at similar sensitivities ( RMS-noise $\sim 1$ mJy beam^-1), so that the results can be easily compared to each other.

In Paper I (Schoenmakers et al. 1900a; see also Schoenmakers 1999) we present a new sample of 47 GRGs selected from the 325-MHz WENSS survey (Rengelink et al. 1997). In this paper, we will define a complete subsample of 26 sources with a 325-MHz flux density above 1 Jy. This is the largest complete sample of GRGs, with well understood selection effects (see Paper I), yet compiled. We have used this sample for several follow-up studies, among which a study of their radio properties using multi-frequency radio data. For this purpose, we have obtained new 10.5-GHz radio data of 18 of these sources using observations with the 100-m Effelsberg telescope; the 8 remaining sources have already been observed with this instrument (Klein et al. 1994; Saripalli et al. 1996; Mack et al. 1997). We have used these data to investigate the high-frequency radio morphology, the magnetic field configuration and, combined with data obtained at lower frequencies, the spectral index distribution and spectral ages (e.g. Mack et al. 1998). The analysis and results of this study are presented here. Subsequent papers will deal with the optical properties of the AGN and their relation with the radio structure, and with the evolution of GRGs, both in terms of cosmological evolution as in terms of intrinsic radio source evolution.

In Sect. 2 we present the complete sample of GRGs and discuss some of its characteristics. Section 3 presents the new 10.5-GHz radio data and lower frequency data for the sources in the sample. In Sect. 4 we derive several source asymmetry parameters and investigate the presence of correlations between these. The ages and lobe advance velocities of several GRGs are derived in Sect. 5, and the energy densities and lobe pressures are derived in Sect. 6. In Sect. 7 we discuss the results, focusing on the spectral ages and the environment of the GRGs. Our conclusions are presented in Sect. 8.

Throughout this paper, a spectral index $\alpha$ is defined according to the relation $S_{\nu} \propto \nu^{\alpha}$ between flux density S and frequency $\nu$.