  The quantification of all possible waves and instabilities in a given system
is of paramount importance, and knowledge of the full magnetohydrodynamic (MHD)
spectrum allows one to predict the (in)stability of a given equilibrium state.
This is highly relevant in many (astro)physical disciplines, and when applied
to the solar atmosphere it may yield various new insights in processes like
prominence formation and coronal loop oscillations. In this work we present a
detailed, high-resolution spectroscopic study of the solar atmosphere, where we
use our newly developed Legolas code to calculate the full spectrum with
corresponding eigenfunctions of equilibrium configurations that are based on
fully realistic solar atmospheric models, including gravity, optically thin
radiative losses and thermal conduction. Special attention is given to thermal
instabilities, known to be responsible for the formation of prominences,
together with a new outlook on the thermal and slow continua and how they
behave in different chromospheric and coronal regions. We show that thermal
instabilities are unavoidable in our solar atmospheric models and that there
exist certain regions where both the thermal, slow and fast modes all have
unstable wave mode solutions. We also encounter regions where the slow and
thermal continua become purely imaginary and merge on the imaginary axis. The
spectra discussed in this work illustrate clearly that thermal instabilities
(both discrete and continuum modes) and magneto-thermal overstable propagating
modes are ubiquitous throughout the solar atmosphere, and may well be
responsible for much of the observed fine-structuring and multi-thermal
dynamics.
