Patchy Kinetic Sunyaev-Zel'dovich Effect with Controlled Reionization
  History and Morphology
  Using the novel semi-numerical code for reionization AMBER, we model the
patchy kinetic Sunyaev-Zel'dovich (kSZ) effect by directly specifying the
reionization history with the redshift midpoint $z_\mathrm{mid}$, duration
$\Delta_\mathrm{z}$, and asymmetry $A_\mathrm{z}$. We further control the
ionizing sources and radiation through the minimum halo mass $M_\mathrm{h}$ and
the radiation mean free path $\lambda_\mathrm{mfp}$. AMBER reproduces the free
electron number density and the patchy kSZ power spectrum of
radiation-hydrodynamic simulations at the target resolution ($1\,{\rm Mpc}/h$)
with matched reionization parameters. With a suite of $(2\,{\rm Gpc}/h)^3$
simulations using AMBER, we first constrain the redshift midpoint $6.0<z_{\rm
mid}<8.9$ using the Planck2018 Thomson optical depth result (95\% CL). Then,
assuming $z_{\rm mid}=8$, we find that the amplitude of $D^{\rm
pkSZ}_{\ell=3000}$ scales linearly with the duration of reionization
$\Delta_z$, and is consistent with the $1\sigma$ upper limit from the South
Pole Telescope (SPT) results up to $\Delta_z<5.1$ ($\Delta_z$ encloses $5\%$ to
$95\%$ ionization). Moreover, a shorter $\lambda_{\rm mfp}$ can lead to a $\sim
10\%$ lower $D^{\rm pkSZ}_{\ell=3000}$ and a flatter slope in the
$\Delta_z-D^{\rm pkSZ}_{\ell=3000}$ scaling relation, thereby affecting the
constraints on $\Delta_z$ at $\ell=3000$. Allowing $z_{\rm mid}$ and
$\lambda_{\rm mfp}$ to vary simultaneously, we get spectra consistent with the
SPT result ($95\%$ CL) up to $\Delta_z=12.8$ (but $A_z>8$ is needed to ensure
an end of reionization before $z=5.5$). We show that constraints on the
asymmetry require $\sim 0.1\,\mu k^2$ measurement accuracy at multipoles other
than $\ell=3000$. Finally, we find that the amplitude and shape of the kSZ
spectrum are only weakly sensitive to $M_h$ under a fixed reionization history
and radiation mean-free path.
