Expected constraints on models of the epoch of reionization with the variance and skewness in redshifted 21cm-line fluctuations

Redshifted 21cm-line signal from neutral hydrogens in the intergalactic medium (IGM) gives a direct probe of the epoch of reionization (EoR). In this paper, we investigate the potential of the variance and skewness of the probability distribution function of the 21cm brightness temperature for constraining EoR models. These statistical quantities are simple, easy to calculate from the observed visibility and thus suitable for the early exploration of the EoR with ongoing telescopes such as the Murchison Widefield Array (MWA) and LOw Frequency ARray (LOFAR). We show, by performing Fisher analysis, that the variance and skewness at $z=7-9$ are complementary to each other to constrain the EoR model parameters such as the minimum virial temperature of halos which host luminous objects, ionizing efficiency and mean free path of ionizing photons in the IGM. Quantitatively, the constraining power highly depends on the quality of the foreground subtraction and calibration. We give a best case estimate of the constraints on the parameters, neglecting the systematics other than the thermal noise.