The damping factor, |$\mathcal {D}(k)$|, for a survey where 21-cm modes have k∥ and μ = |k∥|/k restricted to the ranges shown. The black lines (upper lines at high k) have no missing modes. Colored lines include the effect of the wedge with μmin = 0.56 and/or a cut in k∥; lines for k∥ ≥ 0.1 hMpc−1, μ ≥ 0, 0.56 are degenerate. The noise of the 21-cm modes, i.e. modes not in the wedge, is taken to be equivalent to |$b^2\,\bar{n}\simeq 3\times 10^{-3}\,h^3{\rm Mpc}^{-3}$| (see text). Two directions are shown: solid lines are along the line of sight (k∥ = k, k⊥ = 0) and dashed lines are transverse (k⊥ = k, k∥ = 0). Solid lines are ordered at large k according to k∥ ≥ 0, 0.02, 0.1, top to bottom, with μ ≥ 0 higher than μ ≥ 0.56 for each k∥ cut. Top: |$\mathcal {D}(k)$| for modes which are present (obeying k∥ and μmin cut), PN = ∞ or |$b^2 \bar{n}\rightarrow 0$| for missing modes. Bottom: the same cuts in k∥, μ, as above, but replacing the missing modes with an ELG survey with number density 3 × 10−4 h3 Mpc−3. For |${\mathcal {D}}(k=k_\perp )$|, the line order at large k top to bottom is the same as in the legend. Note in the top figure that with our approximations a small range of k∥ is improved when other modes are completely left out of reconstruction, an example of increasing noise increasing |$\mathcal {D}(k)$| for some k and suggesting that a different smoothing may help with better recovering those components.
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