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Helioseismology and Asteroseismology: Looking for Gravitational Waves in acoustic oscillations

Current helioseismology observations allow the determination of the frequencies and surface velocity amplitudes of solar acoustic modes with exceptionally high precision. In some cases, the frequency accuracy is better than one part in a million. We show that there is a distinct possibility that the quadrupole acoustic modes of low order could be excited by gravitational waves (GWs), if the GWs have a strain amplitude in the range $10^{-20}h_{-20}$ with $h_{-20}\sim 1$ or $h_{-20}\sim 10^{3}$, as predicted by several types of GW sources, such as galactic ultracompact binaries or extreme mass ratio inspirals and coalescence of black holes. If the damping rate at low order is $ 10^{-3}η_N$ $μ{\rm Hz}$, with $η_N\sim 10^{-3} $ - $1,$ as inferred from the theory of stellar pulsations, then GW radiation will lead to a maximum rms surface velocity amplitude of quadrupole modes of the order of $h_{-20}η_N^{-1}\sim$ $10^{-9}$ - $10^{-3}$ ${\rm cm\; s^{-1}}$, on the verge of what is currently detectable via helioseismology. The frequency and sensitivity range probed by helioseismological acoustic modes overlap with, and complement, the capabilities of eLISA for the brightest resolved ultracompact galactic binaries.