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.