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Observations of the frequency dependence of the global brightness temperatureof the redshifted 21 cm line of neutral hydrogen may be possible with singledipole experiments. In this paper, we develop a Fisher matrix formalism forcalculating the sensitivity of such instruments to the 21 cm signal fromreionization and the dark ages. We show that rapid reionization histories withduration delta z< 2 can be constrained, provided that local foregrounds can bewell modelled by low order polynomials. It is then shown that observations inthe range nu = 50 - 100 MHz can feasibly constrain the Lyman alpha and X-rayemissivity of the first stars forming at z = 15 - 25, provided that systematictemperature residuals can be controlled to less than 1 mK. Finally, wedemonstrate the difficulty of detecting the 21 cm signal from the dark agesbefore star formation.

Constraining the unexplored period between reionization and the dark ages with observations of the global 21 cm signal