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We present upper limits on the 21 cm power spectrum at $z = 5.9$ calculatedfrom the model-independent limit on the neutral fraction of the intergalacticmedium of $x_{\rm H{\small I }} < 0.06 + 0.05\ (1\sigma)$ derived from darkpixel statistics of quasar absorption spectra. Using 21CMMC, a Markov chainMonte Carlo Epoch of Reionization analysis code, we explore the probabilitydistribution of 21 cm power spectra consistent with this constraint on theneutral fraction. We present 99 per cent confidence upper limits of$\Delta^2(k) < 10$ to $20\ {\rm mK}^2$ over a range of $k$ from 0.5 to $2.0\h{\rm Mpc}^{-1}$, with the exact limit dependent on the sampled $k$ mode. Thislimit can be used as a null test for 21 cm experiments: a detection of power at$z=5.9$ in excess of this value is highly suggestive of residual foregroundcontamination or other systematic errors affecting the analysis.

Upper Limits on the 21 cm Power Spectrum at z = 5.9 from Quasar Absorption Line Spectroscopy