Parametrizing the Reionization History with the Redshift Midpoint, Duration, and Asymmetry

A new parametrization of the reionization history is presented to facilitate robust comparisons between different observations and with theory. The evolution of the ionization fraction with redshift can be effectively captured by specifying the midpoint, duration, and asymmetry parameters. Lagrange interpolating functions are then used to construct analytical curves that exactly fit corresponding ionization points. The shape parametrizations are excellent matches to theoretical results from radiation-hydrodynamic simulations. The comparative differences for reionization observables are: ionization fraction $|Δx_\text{i}| \lesssim 0.03$, 21cm brightness temperature $|ΔT_\text{b}| \lesssim 0.7\, \text{mK}$, Thomson optical depth $|Δτ| \lesssim 0.001$, and patchy kinetic Sunyaev-Zel'dovich angular power $|ΔD_\ell | \lesssim 0.1\, μ\text{K}^2$. This accurate and flexible approach will allow parameter-space studies and self-consistent constraints on the reionization history from 21cm, CMB, and high-redshift galaxies and quasars.