  In the innermost regions of low-luminosity accretion flows, including Sgr A*
at the center of our Galaxy, the frequency of Coulomb collisions is so low that
the plasma is two-temperature, with the ions substantially hotter than the
electrons. This paradigm assumes that Coulomb collisions are the only channel
for transferring the ion energy to the electrons. In this work, the second of a
series, we assess the efficiency of electron heating by ion velocity-space
instabilities in collisionless accretion flows. The instabilities are seeded by
the pressure anisotropy induced by magnetic field amplification, coupled to the
adiabatic invariance of the particle magnetic moments. Using two-dimensional
(2D) particle-in-cell (PIC) simulations, we showed in Paper I that if the
electron-to-ion temperature ratio is < 0.2, the ion cyclotron instability is
the dominant mode for values of ion beta_i ~ 5-30 (here, beta_i is the ratio of
ion thermal pressure to magnetic pressure), as appropriate for the midplane of
low-luminosity accretion flows. In this work, we employ analytical theory and
1D PIC simulations (with the box aligned with the fastest growing wavevector of
the ion cyclotron mode) to fully characterize how the electron heating
efficiency during the growth of the ion cyclotron instability depends on the
electron-to-proton temperature ratio, the plasma beta, the Alfven speed, the
amplification rate of the mean field (in units of the ion Larmor frequency) and
the proton-to-electron mass ratio. Our findings can be incorporated as a
physically-grounded sub-grid model into global fluid simulations of
low-luminosity accretion flows, thus helping to assess the validity of the
two-temperature assumption.
