Band-splitting of coronal and interplanetary type II bursts - III. Physical conditions in the upper corona and interplanetary space

We analyse properties of 58 type II radio bursts recorded in the meter-to-kilometer wavelength range, focusing on episodes of band-split emission. The basic two parameters utilized are the frequency drift D-f = df/dt and the relative band-split BDW = Lambdaf/f of type II burst emission lanes. On average, in the meter-to-kilometer wavelength range Df increases with the emission frequency as D-f proportional to f(1.83), revealing that source velocities are smaller at larger heliocentric distances. The relative band-split shows a weak but statistically significant dependence on the emission frequency, BDW proportional to f(-0.06), indicating an increase of BDW with the heliocentric distance. Combining the shock velocity estimated from the frequency drift, with the Mach number inferred from the band-split, the Alfven speed and the magnetic field in the ambient plasma can be estimated as a function of the heliocentric distance r. However, the outcome directly depends on the coronal/interplanetary density model used, which is poorly known in the upper corona and the near-Sun interplanetary space. So, we invert the problem: utilizing the results of the previous paper where it was shown that beyond the heliocentric distance of two solar radii (r/r(circle dot) = R > 2) the average magnetic field decreases approximately as B proportional to R--2,R- we infer the density n(R) in the upper corona and near-Sun interplanetary space. The obtained empirical dependence n( R) is presented in the analytical form as a four-degree polynomial of 1/R, and is compared with some theoretical n(R) models, considering also a deviation from the B proportional to 1/R-2 scaling used. The model matches the five-fold Saito density model (representing the active region corona) with the n proportional to R-2 regime in the interplanetary space. Furthermore, it is shown that on average the magnetosonic speed attains a local minimum of v(ms) approximate to 400 km s(-1) around R = 3 and a broad local maximum of v(ms) approximate to 500 km s(-1) in the range R = 4-6, beyond which it gradually decreases to several tens km s(-1) at 1 a.u. The local minimum becomes even deeper if the super-radial expansion of the magnetic field is taken into account. The implications regarding the formation and evolution of shocks in the corona and upper corona are discussed in the framework of CME-piston and flare-blast scenarios. The inferred general decrease of type II burst source velocities and broadening of band-splits with distance is interpreted in terms of the deceleration of mass ejections driving the shocks in the decreasing vms environment.