Constraining the redshifted 21-cm signal with the unresolved soft X-ray
  background
  We use the observed unresolved cosmic X-ray background (CXRB) in the 0.5-2
keV band and existing upper limits on the 21-cm power spectrum to constrain the
high-redshift population of X-ray sources, focusing on their effect on the
thermal history of the Universe and the cosmic 21-cm signal. Because the
properties of these sources are poorly constrained, we consider hot gas, X-ray
binaries and mini-quasars (i.e., sources with soft or hard X-ray spectra) as
possible candidates. We find that (1) the soft-band CXRB sets an upper limit on
the X-ray efficiency of sources that existed before the end of reionization,
which is one-to-two orders of magnitude higher than typically assumed
efficiencies, (2) hard sources are more effective in generating the CXRB than
the soft ones, (3) the commonly-assumed limit of saturated heating is not valid
during the first half of reionization in the case of hard sources, with any
allowed value of X-ray efficiency, (4) the maximal allowed X-ray efficiency
sets a lower limit on the depth of the absorption trough in the global 21-cm
signal and an upper limit on the height of the emission peak, while in the
21-cm power spectrum it sets a minimum amplitude and frequency for the
high-redshift peaks, and (5) the existing upper limit on the 21-cm power
spectrum sets a lower limit on the X-ray efficiency for each model. When
combined with the 21-cm global signal, the CXRB will be useful for breaking
degeneracies and helping constrain the nature of high-redshift heating sources.
