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A new parametrization of the reionization history is presented to facilitaterobust comparisons between different observations and with theory. Theevolution of the ionization fraction with redshift can be effectively capturedby specifying the midpoint, duration, and asymmetry parameters. Lagrangeinterpolating functions are then used to construct analytical curves thatexactly fit corresponding ionization points. The shape parametrizations areexcellent matches to theoretical results from radiation-hydrodynamicsimulations. The comparative differences for reionization observables are:ionization fraction $|\Delta x_\text{i}| \lesssim 0.03$, 21cm brightnesstemperature $|\Delta T_\text{b}| \lesssim 0.7\, \text{mK}$, Thomson opticaldepth $|\Delta \tau| \lesssim 0.001$, and patchy kinetic Sunyaev-Zel'dovichangular power $|\Delta D_\ell | \lesssim 0.1\, \mu\text{K}^2$. This accurateand flexible approach will allow parameter-space studies and self-consistentconstraints on the reionization history from 21cm, CMB, and high-redshiftgalaxies and quasars.

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