We have computed the gravitational wave signal from supernova core collapse by using the most realistic input physics available at present. We start from state-of-the-art progenitor models of rotating and nonrotating massive stars and simulate the dynamics of their core collapse by integrating the equations of axisymmetric hydrodynamics, together with the Boltzmann equation for the neutrino transport, including an elaborate description of neutrino interactions, and a realistic equation of state. Using the Einstein quadrupole formula we compute the quadrupole wave amplitudes, the Fourier wave spectra, the amount of energy radiated in the form of gravitational waves, and the signal-to-noise ratios for the Laser Interferometer Gravitational-Wave Observatory (LIGO) I and the tuned Advanced LIGO (LIGO II) interferometers resulting from both nonradial mass motion and anisotropic neutrino emission. The simulations demonstrate that the dominant contribution to the gravitational wave signal is produced by neutrino-driven convection behind the supernova shock. For stellar cores rotating at the extreme of current stellar evolution predictions, the core bounce signal is detectable (S/N 7) with LIGO II for a supernova up to a distance of ~5 kpc, whereas the signal from postshock convection is observable (S/N 7) with LIGO II up to a distance of ~100 kpc and with LIGO I to a distance of ~5 kpc. If the core is nonrotating, its gravitational wave emission can be measured with LIGO II up to a distance of ~15 kpc (S/N 8), while the signal from the Ledoux convection in the deleptonizing nascent neutron star can be detected up to a distance of ~10 kpc (S/N 8). Both kinds of signals are generically produced by convection in any core-collapse supernova.

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