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.
