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 _mid , duration Δ _z , and asymmetry A _z . We further control the ionizing sources and radiation through the minimum halo mass M _h and the radiation mean free path λ _mfp . AMBER reproduces the free-electron number density and the patchy kSZ power spectrum of radiation–hydrodynamic simulations at the target resolution (1 Mpc h ^−1 ) with matched reionization parameters. With a suite of (2 Gpc/ h ) ^3 simulations using AMBER, we first constrain the redshift midpoint 6.0 < z _mid < 8.9 using the Planck 2018 Thomson optical depth result (95% CL). Then, assuming z _mid = 8, we find that the amplitude of ${D}_{{\ell }=3000}^{\mathrm{pkSZ}}$ scales linearly with the duration of reionization Δ _z and is consistent with the 1 σ upper limit from South Pole Telescope (SPT) results up to Δ _z < 5.1 (Δ _z encloses 5%–95% ionization). Moreover, a shorter λ _mfp can lead to a ∼10% lower ${D}_{{\ell }=3000}^{\mathrm{pkSZ}}$ and a flatter slope in the ${D}_{{\ell }=3000}^{\mathrm{pkSZ}}-{{\rm{\Delta }}}_{z}$ scaling relation, thereby affecting the constraints on Δ _z at ℓ = 3000. Allowing z _mid and λ _mfp to vary simultaneously, we get spectra consistent with the SPT result (95% CL) up to Δ _z = 12.8 (but A _z > 8 is needed to ensure the end of reionization before z = 5.5). We show that constraints on the asymmetry require ∼0.1 μ k ^2 measurement accuracy at multipoles other than ℓ = 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.