Chromatic effects in the 21 cm global signal from the cosmic dawn
  The redshifted 21 cm brightness distribution from neutral hydrogen is a
promising probe into the cosmic dark ages, cosmic dawn, and re-ionization.
LOFAR's Low Band Antennas (LBA) may be used in the frequency range 45 MHz to 85
MHz (30>z>16) to measure the sky averaged redshifted 21 cm brightness
temperature as a function of frequency, or equivalently, cosmic redshift. These
low frequencies are affected by strong Galactic foreground emission that is
observed through frequency dependent ionospheric and antenna beam distortions
which lead to chromatic mixing of spatial structure into spectral structure.
Using simple models, we show that (i) the additional antenna temperature due to
ionospheric refraction and absorption are at a \sim 1% level--- 2 to 3 orders
of magnitude higher than the expected 21 cm signal, and have an approximate
\nu^{-2} dependence, (ii) ionospheric refraction leads to a knee-like
modulation on the sky spectrum at \nu\approx 4\times plasma frequency. Using
more realistic simulations, we show that in the measured sky spectrum, more
than 50% of the 21 cm signal variance can be lost to confusion from foregrounds
and chromatic effects. We conclude that foregrounds and chromatic mixing may
not be subtracted as generic functions of frequency as previously thought, but
must rather be carefully modeled using additional priors and interferometric
measurements.
