Table C.1
Values of Δχ2 corresponding to CL = (68.27, 95.45, 99.7%) as derived from the Monte-Carlo simulation of correlation functions.
| Δχ2: Lyα-only simulation | Δχ2: Complete simulation | |||||
| CL | 68.27% | 95.45% | 99.7% | 68.27% | 95.45% | 99.7% |
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| Cross | ||||||
| α∥ | 1.14 ± 0.02 | 4.76 ± 0.09 | 10.05 ± 0.53 | 1.16 ± 0.03 | 4.77 ± 0.10 | 10.5 ± 0.79 |
| α⊥ | 1.18 ± 0.02 | 4.86 ± 0.08 | 10.59 ± 0.43 | 1.23 ± 0.03 | 4.93 ± 0.11 | 10.16 ± 0.30 |
| b(1 + β)Lyα | 1.04 ± 0.02 | 4.13 ± 0.09 | 9.12 ± 0.25 | 1.04 ± 0.06 | 4.07 ± 0.22 | 9.52 ± 1.55 |
| β Lyα | 1.02 ± 0.01 | 4.07 ± 0.09 | 9.17 ± 0.27 | 1.00 ± 0.03 | 4.01 ± 0.23 | 8.91 ± 1.40 |
| (α∥,α⊥) | 2.62 ± 0.03 | 7.25 ± 0.05 | 12.93 ± 0.32 | 2.65 ± 0.04 | 7.24 ± 0.09 | 13.23 ± 0.43 |
|
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| Auto | ||||||
| α∥ | 1.14 ± 0.02 | 4.52 ± 0.10 | 10.68 ± 0.43 | 1.16 ± 0.02 | 4.66 ± 0.11 | 9.94 ± 0.48 |
| α⊥ | 1.20 ± 0.01 | 4.85 ± 0.08 | 10.84 ± 0.59 | 1.20 ± 0.03 | 4.87 ± 0.09 | 10.36 ± 0.34 |
| b(1 + β)Lyα | 0.98 ± 0.02 | 4.09 ± 0.09 | 9.25 ± 0.40 | 0.96 ± 0.02 | 3.82 ± 0.09 | 8.65 ± 0.43 |
| β Lyα | 0.99 ± 0.01 | 4.07 ± 0.07 | 9.48 ± 0.49 | 1.09 ± 0.02 | 4.42 ± 0.07 | 9.67 ± 0.56 |
| (α∥,α⊥) | 2.63 ± 0.03 | 7.13 ± 0.11 | 14.22 ± 0.74 | 2.65 ± 0.05 | 7.07 ± 0.12 | 13.63 ± 0.77 |
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| Combined | ||||||
| α ∥ | 1.08 ± 0.02 | 4.19 ± 0.05 | 9.73 ± 0.41 | 1.03 ± 0.03 | 4.20 ± 0.09 | 9.89 ± 0.46 |
| α ⊥ | 1.08 ± 0.02 | 4.37 ± 0.08 | 10.22 ± 0.53 | 1.11 ± 0.07 | 4.19 ± 0.32 | — |
| b(1 + β)Lyα | 1.03 ± 0.02 | 4.06 ± 0.09 | 9.41 ± 0.90 | 0.93 ± 0.04 | 3.77 ± 0.10 | 9.31 ± 1.01 |
| β Lyα | 1.00 ± 0.01 | 4.18 ± 0.06 | 9.18 ± 0.15 | 1.24 ± 0.05 | 4.79 ± 0.14 | 11.24 ± 0.64 |
| (α∥,α⊥) | 2.45 ± 0.02 | 6.58 ± 0.10 | 12.95 ± 0.44 | 2.47 ± 0.05 | 6.45 ± 0.11 | 13.5 ± 1.52 |
Notes. For the four fit variables x = (bLyα(1 + βLyα),βLyα,α∥,α⊥) and for the combination (α⊥,α∥), the table gives the range of 
that includes a percentage CL of the generated data sets. Values are given for fits of the cross- and auto-correlations and for the combined fits. In each of these three cases, values are given for the ~10 000 simulations with only Lyα absorption, and for the ~1000 “complete” simulations with metals, UV fluctuations, and QSO radiation. The uncertainties are statistical, reflecting the number of simulations. For the variables bLyα(1 + βLyα) and βLyα, Δχ2 is close to the nominal values (1,4,9) expected for Gaussian statistics. For α⊥ and α∥ the number is consistently higher than the nominal values, as is also the case for the combination (α⊥, α∥), which is consistently larger than the nominal values (2.29, 6.18, 11.82).
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