Calcium to hydrogen line ratios in solar prominences

The ratio of Ca II 8542 Å to Hβ line intensities has been used for a long time to diagnose the gas pressure in solar prominences. In this paper we reconsider the theoretical dependence of $E(8542)/E($H$\beta)$ on the gas pressure, as originally computed by Heasley & Milkey (1978), and extend this theoretical correlation to higher pressures. Firstly, we revise the formation of calcium lines in prominences, using in parallel two independently developed NLTE radiative transfer codes. Computations consist of two subsequent steps: (i) the formation of hydrogen spectrum (treated in a similar way as in Gouttebroze et al. 1993), and (ii) the formation of calcium lines, using the electron-density structure obtained in step (i). The influence of hydrogen Lyman lines on Ca II to Ca III ionization is found to be very important for the determination of calcium-to-hydrogen line ratios. In particular, the intensities obtained for calcium lines at low pressures are significantly lower than those obtained by Heasley & Milkey (1978), which is the result of a greater Ca III/Ca II ratio. Our numerical results have been further checked against an approximate analytical model. Secondly, we have performed an extended computation using a large grid of models covering different temperatures, gas pressures, geometrical thicknesses, microturbulent velocities and prominence altitudes. For temperatures lower than 10 000 K and pressures lower than 0.1 dyn cm-2, the line ratio $E(8542)/E($H$\beta)$ undergoes only small variations, remaining between 0.2 and 0.3. At higher pressures (0.1 to 1 dyn cm-2), the behaviour of this ratio appears to be strongly dependent on temperature: rapidly increasing below 6000 K, moderately increasing between 6000 and 8000 K, and generally decreasing at higher temperatures. A comparison of the present models with recent observations of Stellmacher & Wiehr (2000) suggests the existence of cool prominence structures with temperatures around 6000 K and gas pressures higher than 0.1 dyn cm-2.