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Starting from a general relativistic framework a hydrodynamic formalism isderived that yields the mean-square amplitudes and rms surface velocities ofnormal modes of non-relativistic stars excited by arbitrary gravitational wave(GW) radiation. In particular, stationary GW fields are considered and theresulting formulae are evaluated for two general types of GW radiation:radiation from a particular astrophysical source (e.g., a binary system) and astochastic background of gravitational waves (SBGW). Expected sources andsignal strengths for both types of GW radiation are reviewed and discussed.Numerical results for the Sun show that low-order quadrupolar g modes areexcited more strongly than p modes by orders of magnitude. Maximal rms surfacevelocities 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 isshown 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 producemaximal solar g-mode rms surface velocities of 10^(-5)-10^(-3) mm/s. Thisresult lies close to or within the amplitude range of 10^(-3)-1 mm/s expectedfrom excitation by turbulent convection, which is currently considered to beresponsible for stellar g-mode excitation. It is concluded that studying g-modeobservations of stars other than the Sun, in which excitation by GWs could beeven more effective due to different stellar structures, might provide a newmethod to either detect GWs or to deduce a significant direct upper limit on anSBGW at intermediate frequencies between the pulsar bound and the bounds frominterferometric detectors on Earth.

Excitation of stellar oscillations by gravitational waves: hydrodynamic model and numerical results for the Sun