1 Introduction

The magnetic field strength, Alfvén velocity, and the plasma-to-magnetic pressure ratio $\beta$ are parameters that are essential for the comprehension of processes taking place in the solar corona. Unfortunately, a direct measurement of the magnetic field in a hot low-density coronal plasma by means of the Zeeman or Hanle effect is obstructed by many difficulties (for a brief survey see Lin et al. 2000). Although a big step forward was achieved recently (Lin et al. 2000) the measurements are still burdened by a low signal-to-noise ratio, low temporal and spatial resolution and can be performed only at low heights.

Most of the information about the coronal magnetic field strength is obtained by indirect methods, generally based on two different approaches: the coronal field can be inferred by extrapolating the measured photospheric field, or by analyzing various forms of coronal radio emission (for a review see, e.g., Dulk & McLean 1978; Krüger & Hildebrandt 1993).

In this paper we utilize the method proposed by Smerd et al. (1974, 1975). It is based on measurements of type II radio bursts, known to be excited by the coronal MHD shock waves. Type II bursts usually show the fundamental and harmonic emission band, both frequently being split in two parallel lanes (cf. Nelson & Melrose 1985). Smerd et al. (1974) proposed that the band-split is associated with the density jump at the shock front, which provides an estimate of the shock Mach number. On the other hand, the shock velocity can be estimated from the frequency drift of the burst, and the ratio of the two parameters gives the Alfvén velocity.

Although the method is quite simple it has not really been exploited after the paper by Smerd et al. (1975). It has been applied only occasionally, often in an indirect way (see e.g., Gopalswamy et al. 1986; Mann et al. 1995; Magdalenic & Vrsnak 2000; Vrsnak et al. 2001a). The reason could be found in the barely justified hypothesis on which it relies. The proposed upstream/downstream interpretation apparently had serious drawbacks and some other explanations seemed to be more appropriate (for a review and discussion see Vrsnak et al. 2001b; hereinafter Paper I). Eventually, the upstream/downstream interpretation was justified in Paper I analyzing type II bursts from interplanetary shocks reaching the Earth: several examples were found in which the extrapolation of the two band split lanes were pointing to the base and the ramp of the local plasma frequency jump caused by the shock passage.

Since type II bursts are excited by MHD shock waves sweeping through the corona on a global scale they have the advantage of not being restricted to a flaring region itself. Moreover, type II bursts associated with coronal mass ejections are observed not only in the metric wavelength range, but also at much longer, decametric-kilometric (Dm-km) wavelengths (e.g., Bougeret 1985). Consequently, they can be used to infer the magnetic field and Alfvén velocity in the upper corona where no other diagnostic tool is available, as well as in the interplanetary (IP) space where the magnetic field can be determined only occasionally by in situ measurements.

Several reasons motivated us to perform an analysis similar to the one presented by Smerd et al. (1974, 1975). First, the data set used by Smerd et al. (1974, 1975) was relatively small and the procedure was not appropriate: The analysis included only 9 events with the highest observed fundamental band frequency 80 MHz, and the Mach number was evaluated using the hydrodynamic approximation ( $\beta=\infty$). We have selected a two times as large a data set of 18 type II bursts embracing starting (fundamental band) frequencies up to 270 MHz, and a more detailed and more accurate analysis is performed.

A further motive was that such an analysis can resolve some open questions regarding the process of formation and evolution of coronal and IP shocks, i.e. the bias between the blast and piston formation mechanisms (see, e.g., Gopalswamy et al. 1998; Cliver et al. 1999).

Finally, the following analysis lays the ground for the proper treatment of the Dm-km type II bursts that provide information about the magnetic field in the upper corona and interplanetary space. Since the Dm-km type II shocks propagate on the solar wind environment that is considerably different from that of the corona, we delay their discussion for a separate paper.

In Sect. 2 we briefly describe the method and the approximations used. In order to make reading easy, the mathematical relations used are given in the Appendix. The observations, measurements, and procedure of data reduction are presented in Sect. 3. The results are presented and discussed in Sects. 4 and 5, respectively, and the conclusions are drawn in Sect. 6.