  To further confirm the causality and stability of a second-order hyperbolic
system of partial differential equations that models the relativistic dynamics
of barotropic fluids with viscosity and heat conduction (H. Freist\"uhler and
B. Temple, J. Math. Phys. 59 (2018)), this paper studies the Fourier-Laplace
modes of this system and shows that all such modes, relative to arbitrary
Lorentz frames, (a) decay with increasing time and (b) travel at subluminal
speeds. Stability is also shown for the related model of non-barotropic fluids
(H. Freist\"uhler and B. Temple. Proc. R. Soc. A 470 (2014) and Proc. R. Soc. A
473 (2017)). Even though these properties had been known for a while in the
sense of numerical evidence, the fully analytical proofs for the subluminality
of modes of arbitrary wave numbers in arbitrary frames given here appear to be
the first regarding any five-field formulation of dissipative relativistic
fluid dynamics.
