Core-collapse supernovae have been supposed to
be one of the most plausible sources of gravitational waves.
Based on a series of our magnetohydrodynamic core-collapse
simulations, we find that
the gravitational amplitudes at core bounce can
be within the detection limits for the currently running
laser-interferometers for a galactic supernova if the central core
rotates sufficiently rapidly.
This is regardless of the difference of the realistic
equations of state and the possible occurrence of the QCD phase
transition near core bounce. Even if the core rotates slowly, we point
out that the
gravitational waves generated from anisotropic neutrino radiation
in the postbounce phase due to the standing accretion shock
instability (SASI)
could be within the detection limits of the detectors in the next
generation such as LCGT and the advanced LIGO for the galactic source.
Since the waveforms significantly depend on the exploding scenarios,
our results suggest that we can obtain the information
about the long-veiled explosion mechanism from the gravitational wave signals.
Furthermore we discuss the gravitational wave background (GWB) from the
explosions of Pop III stars and show that the GWB from Pop III,
depending on their formation rates,
can be large enough to be within the detection limits
of future planned interferometers such as
DECIGO and BBO in the frequency interval of ~0.1-1 Hz.
This means that the detections of GW background from Pop III stars can
be an important tool to supply
the information about the star formation history in the early universe.