Abstract
Upper limits from the current generation of interferometers targeting 21-cm
emission from high redshifts have recently begun to rule out physically
realistic, though still extreme, models of the Epoch of Reionization (EoR).
While inferring the detailed properties of the first galaxies is one of the
most important motivations for 21-cm measurements, they can also provide useful
constraints on the properties of the intergalactic medium (IGM). Motivated by
this, we build a simple, phenomenological model for 21-cm fluctuations that
works directly in terms of IGM properties, which bypasses the computationally
expensive 3-D semi-numerical modeling generally employed in inference pipelines
and avoids explicit assumptions about galaxy properties. The key simplifying
assumptions are that (i) the ionization field is binary, and composed of
spherical bubbles with an abundance described well by a parametric bubble size
distribution, and (ii) that the spin temperature of the "bulk" IGM outside
bubbles is uniform. Despite the simplicity of the model, the mean ionized
fraction and spin temperature of the IGM recovered from mock 21-cm power
spectra generated with 21cmFAST are in qualitative agreement with the true
input values. This suggests that it is possible to obtain comparable
constraints on the IGM from 21-cm measurements using models with very different
assumptions, parameters, and priors. Our approach will thus be complementary to
semi-numerical models as upper limits continue to improve in the coming years.
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