  During the Epoch of Reionization (EoR), the ultraviolet radiation from the
first stars and galaxies ionised the neutral hydrogen of the intergalactic
medium, which can emit radiation through its 21 cm hyperfine transition. This
21 cm signal is a direct probe of the first light sources in the early
Universe. Measuring the 21 cm power spectrum is a key science goal for the
future Square Kilometre Array (SKA), however, observing and interpreting it is
a challenging task. Another high-potential probe of the EoR is the patchy
kinetic Sunyaev-Zel'dovich effect (pkSZ), observed as a foreground to the
primary cosmic microwave background temperature anisotropies on small scales.
Despite recent promising measurements by ground-based telescopes, placing
constraints on reionization from pkSZ observations is a non-trivial task,
subject to strong model dependence.
  In this work, we propose to alleviate the difficulties in observing and
interpreting the 21 cm and pkSZ power spectra by combining them. With a simple
yet effective parametric model that establishes a formal connection between
them, we are able to jointly fit mock 21 cm and pkSZ data points. We confirm
that these two observables provide complementary information on reionization,
leading to significantly improved constraints when combined. We demonstrate
that with as few as two measurements of the 21 cm power spectrum with 100 hours
of observations with the SKA, as well as a single $\ell=3000$ pkSZ data point,
we can reconstruct the reionization history of the Universe and its morphology.
We find that the reionization global history (morphology) is better constrained
with two 21 cm measurements at different redshifts (scales). Therefore, a
combined analysis of the two probes will give access to tighter constraints on
cosmic reionization even in the early stages of 21 cm detections.
