CMB constraints on a physical model of reionization
  We study constraints on allowed reionization histories by comparing
predictions of a physical semi-numerical model with secondary temperature and
polarization anisotropies of the cosmic microwave background (CMB). Our model
has four free parameters characterizing the evolution of ionizing efficiency
$\zeta$ and the minimum mass $M_{\mathrm{min}}$ of haloes that can produce
ionizing radiation. Comparing the model predictions with the presently
available data of the optical depth $\tau$ and kinematic Sunyaev-Zeldovich
signal, we find that we can already rule out a significant region of the
parameter space. We limit the duration of reionization $\Delta
z=1.30^{+0.19}_{-0.60}$ ($\Delta z < 2.9$ at $99\%$ C.L.), one of the tightest
constraints on the parameter. The constraints mildly favour $M_{\mathrm{min}}
\gtrsim 10^9 \mathrm{M}_{\odot}$ (at $68\%$ C.L.) at $z \sim 8$, thus
indicating the presence of reionization feedback. Our analysis provides an
upper bound on the secondary $B$-mode amplitude $D_{l=200}^{BB}<18$ nK$^2$ at
$99\%$ C.L. We also study how the constraints can be further tightened with
upcoming space and ground-based CMB missions. Our study, which relies solely on
CMB data, has implications not only for upcoming CMB surveys for detecting
primordial gravitational waves but also redshifted 21 cm studies.
