  Starting from a general relativistic framework a hydrodynamic formalism is
derived that yields the mean-square amplitudes and rms surface velocities of
normal modes of non-relativistic stars excited by arbitrary gravitational wave
(GW) radiation. In particular, stationary GW fields are considered and the
resulting formulae are evaluated for two general types of GW radiation:
radiation from a particular astrophysical source (e.g., a binary system) and a
stochastic background of gravitational waves (SBGW). Expected sources and
signal strengths for both types of GW radiation are reviewed and discussed.
Numerical results for the Sun show that low-order quadrupolar g modes are
excited more strongly than p modes by orders of magnitude. Maximal rms surface
velocities in the case of excitation by astrophysical sources are found to be v
{\le} 10^(-8) mm/s, assuming GW strain amplitudes of h {\le} 10^(-20). It is
shown that current models for an SBGW produced by cosmic strings, with Omega_GW
~ 10^(-8)-10^(-5) in the frequency range of solar g modes, are able to produce
maximal solar g-mode rms surface velocities of 10^(-5)-10^(-3) mm/s. This
result lies close to or within the amplitude range of 10^(-3)-1 mm/s expected
from excitation by turbulent convection, which is currently considered to be
responsible for stellar g-mode excitation. It is concluded that studying g-mode
observations of stars other than the Sun, in which excitation by GWs could be
even more effective due to different stellar structures, might provide a new
method to either detect GWs or to deduce a significant direct upper limit on an
SBGW at intermediate frequencies between the pulsar bound and the bounds from
interferometric detectors on Earth.
