Excitation of stellar oscillations by gravitational waves: Hydrodynamic model and numerical results for the sun

Abstract

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 ≲ 10 -8 mm s-1, assuming GW strain amplitudes of h ≲ 10-20. It is shown that current models for an SBGW produced by cosmic strings, with ΩGW 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-1. This result lies close or within the amplitude range of 10-3-1 mm s -1 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. © 2011. The American Astronomical Society. All rights reserved.