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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 ν^{-2} dependence, (ii) ionospheric refraction leads to a knee-like modulation on the sky spectrum at ν\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.