  We present 2D hydrodynamic simulations of the long-time accretion phase of a
15 solar mass star after core bounce and before the launch of a supernova
explosion. Our simulations are performed with the Prometheus-Vertex code,
employing multi-flavor, energy-dependent neutrino transport and an effective
relativistic gravitational potential. Testing the influence of a stiff and a
soft equation of state for hot neutron star matter, we find that the non-radial
mass motions in the supernova core due to the standing accretion shock
instability (SASI) and convection impose a time variability on the neutrino and
gravitational-wave signals. These variations have larger amplitudes as well as
higher frequencies in the case of a more compact nascent neutron star. After
the prompt shock-breakout burst of electron neutrinos, a more compact accreting
remnant radiates neutrinos with higher luminosities and larger mean energies.
The observable neutrino emission in the direction of SASI shock oscillations
exhibits a modulation of several 10% in the luminosities and ~1 MeV in the mean
energies with most power at typical SASI frequencies of 20-100 Hz. At times
later than 50-100 ms after bounce the gravitational-wave amplitude is dominated
by the growing low-frequency (<200 Hz) signal associated with anisotropic
neutrino emission. A high-frequency wave signal is caused by nonradial gas
flows in the outer neutron star layers, which are stirred by anisotropic
accretion from the SASI and convective regions. The gravitational-wave power
then peaks at about 300-800 Hz with distinctively higher spectral frequencies
originating from the more compact and more rapidly contracting neutron star.
The detectability of the SASI effects in the neutrino and gravitational-wave
signals is briefly discussed. (abridged)
