  Electron acceleration to non-thermal energies is known to occur in low Mach
number (M<5) shocks in galaxy clusters and solar flares, but the electron
acceleration mechanism remains poorly understood. Using two-dimensional (2D)
particle-in-cell (PIC) plasma simulations, we showed in Paper I that electrons
are efficiently accelerated in low Mach number (M=3) quasi-perpendicular shocks
via a Fermi-like process. The electrons bounce between the upstream region and
the shock front, with each reflection at the shock resulting in energy gain via
shock drift acceleration. The upstream scattering is provided by oblique
magnetic waves, that are self-generated by the electrons escaping ahead of the
shock. In the present work, we employ additional 2D PIC simulations to address
the nature of the upstream oblique waves. We find that the waves are generated
by the shock-reflected electrons via the firehose instability, which is driven
by an anisotropy in the electron velocity distribution. We systematically
explore how the efficiency of wave generation and of electron acceleration
depend on the magnetic field obliquity, the flow magnetization (or
equivalently, the plasma beta), and the upstream electron temperature. We find
that the mechanism works for shocks with high plasma beta (>20) at nearly all
magnetic field obliquities, and for electron temperatures in the range relevant
for galaxy clusters. Our findings offer a natural solution to the conflict
between the bright radio synchrotron emission observed from the outskirts of
galaxy clusters and the low electron acceleration efficiency usually expected
in low Mach number shocks.
