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Introduction

The measurement of line widths can provide information concerning ion temperatures, sub-resolution turbulent motions and velocity fluctuations associated with magnetohydrodynamic (MHD) waves in the corona. Line width variations combined with simultaneous electron density estimates, provides a very powerful diagnostic for the solar corona. In two previous papers we have reported such observations off the Western limb (Doyle et al. 1998; hereafter DBP) and above a Coronal Hole (Banerjee et al. 1998; hereafter BTDW) based on Si VIII lines observed with SUMER (Wilhelm et al. 1995) onboard SOHO. Doschek et al. (1997) have derived electron densities as a function of height in the north and south polar coronal holes. They find that for distances of a few arc seconds outside the solar limb, the average line of sight electron densities in the coronal holes are about a factor of 2 lower than in quiet sun regions. Electron densities similar to those derived from the Si VIII lines are reported by Fludra et al. (1999a,b) and Doyle et al. (1999) based on Si IX data obtained with the CDS instrument onboard SOHO (Harrison et al. 1995). Wilhelm et al. (1998) have deduced electron temperatures, densities and ion velocities in plumes and inter-plume regions of coronal holes. Recently Warren & Hassler (1999) have used Si III, Mg VIII, Si VIII and Mg IX line ratios for electron density measurements. In an earlier study, Hassler et al. (1990) presented line profiles of coronal lines from Mg X 609/625 Å up to $\sim$ 140,000 km above the limb.

In the coronal hole (see BTDW), the line width data show that the non-thermal line-of-sight velocity increases from $27 \ {\rm km \; s}^{-1}$ at 27 arc sec above the limb to $46 \; {\rm km \; s}^{-1}$ some 250 arc sec (i.e. $\sim$180,000 km) above the limb. The electron density shows a decrease from $1.1 \ 10^8 \ {\rm cm}^{-3}$ to $1.6 \ 10^7 \ {\rm cm}^{-3}$ over the same distance. It was shown by DBP and BTDW that the Si VIII non-thermal velocity was inversely proportional to the quadratic root of the electron density, in excellent agreement with that predicted for undamped radially propagating Alfvén waves. The Western limb data showed a similar trend. Several questions arise from this work, e.g. how representative are the Si VIII lines of coronal hole conditions near the limb? How do these observations of line width and electron density out to $1.25~R_{\odot}$ compare with measurements further off-limb? We address these issues by looking at additional SUMER data out to 1.38 $R_{\odot}$ coupled with measurements obtained from LASCO and UVCS. This allows us to investigate physical conditions of the solar corona and the coronal-heliospheric interface. Earlier observations of Skylab and more recently SOHO/UVCS observations (Cranmer et al. 1999) have established that the fast solar wind originates from coronal holes, while the slow wind is associated with bright equatorial streamers and a number of dramatic transient events such as coronal mass ejections (CMEs). We concentrate here on the coronal hole region in the solar minimum phase (during Nov-Dec '96). All solar wind modelling requires knowledge of both the electron density and non-thermal velocity at the base of the coronal hole as boundary conditions. We hope that our results will provide input parametric values for such solar wind modelling.