The chromosphere of the Sun is a temporally and spatially very varying
medium for which the assumption of ionisation equilibrium is
Our aim is to determine the dominant processes and timescales for the
ionisation equilibrium of calcium under solar chromo- spheric
The study is based on numerical simulations with the RADYN
code, which combines hydrodynamics with a detailed so- lution of the
radiative transfer equation. The calculations include a detailed
non-equilibrium treatment of hydrogen, calcium, and helium.
Next to an hour long simulation sequence, additional simulations are
produced, for which the stratification is slightly perturbed so that a
ionisation relaxation timescale can be determined.
The simulations are characterised by upwards propagating shock waves,
which cause strong temperature fluctuations and variations of the
(non-equilibrium) ionisation degree of calcium.
The passage of a hot shock front leads to a strong net ionisation of
Ca II, rapidly followed by net recombination. The relax- ation
timescale of the calcium ionisation state is found to be of the order
of a few seconds at the top of the photosphere and 10 to 30 s in the
upper chromosphere. At heights around 1 Mm, we find typical values
around 60 s and in extreme cases up to ~150 s. Generally, the
timescales are significantly reduced in the wakes of ubiquitous hot
shock fronts. The timescales can be reliably determined from a simple
analysis of the eigenvalues of the transition rate matrix. The
timescales are dominated by the radiative recombination from Ca III
into the metastable Ca II energy levels of the 4d 2 D term. These
transitions depend strongly on the density of free electrons and
therefore on the (non-equilibrium) ionisation degree of hydrogen,
which is the main electron donor.
The ionisation/recombination timescales derived here are too long for
the assumption of an instantaneous ionisation equilibrium to be valid
and, on the other hand, are not long enough to warrant an assumption
of a constant ionisation fraction. Fortunately, the ionisation degree
of Ca II remains small in the height range, where the cores of the H,
K, and the infrared triplet lines are formed. We conclude that the
difference due to a detailed treatment of Ca ionisation has only
negligible impact on the modelling of spectral lines of Ca II and the
plasma properties under the conditions in the quiet solar
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