  Poorly understood "baryonic physics" impacts our ability to predict the power
spectrum of the kinetic Sunyaev-Zel'dovich (kSZ) effect. We study this in one
sample high resolution simulation of galaxy formation and feedback, Illustris.
The high resolution of Illustris allows us to probe the kSZ power spectrum on
multipoles $\ell =10^3-3\times 10^4$. Strong AGN feedback in Illustris nearly
wipes out gas fluctuations at $k\gtrsim1~h~\rm{Mpc}^{-1}$ and at late times,
likely somewhat under predicting the kSZ power generated at $z\lesssim 1$. The
post-reionization kSZ power spectrum for Illustris is well-fit by
$\mathcal{D}^{z<6}_{\ell} = 1.38[\ell/3000]^{0.21}~\mu K^2$ over
$3000\lesssim\ell\lesssim10000$, somewhat lower than most other reported values
but consistent with the analysis of Shaw et al. Our analysis of the bias of
free electrons reveals subtle effects associated with the multi-phase gas
physics and stellar fractions that affect even linear scales. In particular
there are fewer electrons in biased galaxies, due to gas cooling and star
formation, and this leads to an electron bias less than one even at low
wavenumbers. The combination of bias and electron fraction that determines the
overall suppression is relatively constant, $f_e^2b^2_{e0} \sim 0.7$, but more
simulations are needed to see if this is Illustris-specific. By separating the
kSZ power into different terms, we find at least $6\, (10)\%$ of the signal at
$\ell=3000\, (10000)$ comes from non-Gaussian connected four-point density and
velocity correlations, $\left<\delta v \delta v\right>_{c}$, even without
correcting for the Illustris simulation box size. A challenge going forward
will be to accurately model long-wave velocity modes simultaneously with
Illustris-like high resolution to capture the complexities of galaxy formation
and its correlations with large scale flows.
