  Abridged: Using a suite of progenitor models, neutrino luminosities, and two-
dimensional (2D) simulations, we investigate the matter gravitational-wave (GW)
emission from postbounce phases of neutrino-driven core-collapse supernovae
(CCSNe). The relevant phases are prompt and steady-state convection, the
standing accretion shock instability (SASI), and asymmetric explosions. For the
stages before explosion, we propose a model for the source of GW emission.
Downdrafts of the postshock-convection/SASI region strike the protoneutron star
"surface" with large speeds and are decelerated by buoyancy forces. We find
that the GW amplitude is set by the magnitude of deceleration and, by
extension, the downdraft's speed and the vigor of postshock-convective/SASI
motions. However, the characteristic frequencies, which evolve from ~100 Hz
after bounce to ~300-400 Hz, are primarily independent of these speeds, but are
set by the deceleration timescale, which is in turn set by the buoyancy
frequency at the lower boundary of postshock convection. Consequently, the GW
characteristic frequencies are dependent upon a combination of core structure
attributes, specifically the dense-matter equation of state (EOS) and details
that determine the gradients at the boundary, including the accretion-rate
history, the EOS at subnuclear densities, and neutrino transport. During
explosion, the high frequency signal wanes and is replaced by a strong low
frequency, ~10s of Hz, signal that reveals the general morphology of the
explosion (i.e. prolate, oblate, or spherical). However, current and
near-future GW detectors are sensitive to GW power at frequencies >50 Hz.
Therefore, the signature of explosion will be the abrupt reduction of
detectable GW emission.
