Summary of relevant quantities for our sample of total H i absorption lines.
| Δd . | Δv . | |$W_{\rm r}^{\rm min}$| . | Δz . | ΔX . | N . | |$\frac{{\rm d}N}{{\rm d}z}$| . | |$\frac{{\rm d}N}{{\rm d}X}$| . | |$\frac{{\rm d}N}{{\rm d}z}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}X}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}z}/\frac{{\rm d}N}{{\rm d}z}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}X}/\frac{{\rm d}N}{{\rm d}X}|_{\rm field}$| . |
|---|---|---|---|---|---|---|---|---|---|---|---|
| (Mpc) . | (km s−1) . | (Å) . | . | . | . | . | . | . | . | . | . |
| (1) . | (2) . | (3) . | (4) . | (5) . | (6) . | (7) . | (8) . | (9) . | (10) . | (11) . | (12) . |
| 3.0 | 500 | 0.04 | 0.03 | 0.05 | 11 | |$358^{+144}_{-107}$| | |$238^{+96}_{-71}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.9^{+1.2}_{-0.9}$| | |$2.7^{+1.1}_{-0.9}$| |
| 3.0 | 630 | 0.04 | 0.04 | 0.06 | 11 | |$293^{+118}_{-87}$| | |$195^{+78}_{-58}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.4^{+1.0}_{-0.7}$| | |$2.2^{+0.9}_{-0.7}$| |
| 3.0 | 794 | 0.04 | 0.05 | 0.07 | 14 | |$305^{+105}_{-81}$| | |$203^{+70}_{-54}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.5^{+0.9}_{-0.7}$| | |$2.3^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 16 | |$287^{+91}_{-71}$| | |$191^{+61}_{-47}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 3.0 | 1313 | 0.04 | 0.07 | 0.11 | 17 | |$237^{+73}_{-57}$| | |$159^{+49}_{-38}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.9^{+0.6}_{-0.5}$| | |$1.8^{+0.6}_{-0.5}$| |
| 3.0 | 1724 | 0.04 | 0.09 | 0.13 | 17 | |$188^{+58}_{-45}$| | |$126^{+39}_{-30}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.5}_{-0.4}$| | |$1.5^{+0.5}_{-0.4}$| |
| 3.0 | 2264 | 0.04 | 0.12 | 0.17 | 18 | |$156^{+46}_{-37}$| | |$105^{+31}_{-25}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.4}_{-0.3}$| | |$1.2^{+0.4}_{-0.3}$| |
| 3.0 | 2972 | 0.04 | 0.14 | 0.21 | 21 | |$151^{+41}_{-33}$| | |$101^{+27}_{-22}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.4}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 3.0 | 3903 | 0.04 | 0.16 | 0.24 | 25 | |$152^{+37}_{-30}$| | |$102^{+25}_{-20}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 3.0 | 5125 | 0.04 | 0.18 | 0.27 | 26 | |$143^{+34}_{-28}$| | |$97^{+23}_{-19}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.1^{+0.3}_{-0.2}$| |
| 3.0 | 6729 | 0.04 | 0.19 | 0.28 | 26 | |$134^{+32}_{-26}$| | |$91^{+22}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.1^{+0.3}_{-0.2}$| | |$1.1^{+0.3}_{-0.2}$| |
| 3.0 | 8835 | 0.04 | 0.22 | 0.32 | 32 | |$147^{+31}_{-26}$| | |$101^{+21}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.2}$| | |$1.2^{+0.3}_{-0.2}$| |
| 3.0 | 11601 | 0.04 | 0.25 | 0.36 | 38 | |$151^{+29}_{-24}$| | |$105^{+20}_{-17}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.2}$| | |$1.2^{+0.3}_{-0.2}$| |
| 3.0 | 15232 | 0.04 | 0.30 | 0.42 | 43 | |$146^{+26}_{-22}$| | |$103^{+18}_{-16}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.2}_{-0.2}$| | |$1.2^{+0.2}_{-0.2}$| |
| 3.0 | 20000 | 0.04 | 0.33 | 0.47 | 48 | |$145^{+24}_{-21}$| | |$103^{+17}_{-15}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.2}_{-0.2}$| | |$1.2^{+0.2}_{-0.2}$| |
| 1.0 | 1000 | 0.04 | 0.01 | 0.02 | 3 | |$203^{+199}_{-112}$| | |$140^{+137}_{-77}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+1.6}_{-0.9}$| | |$1.6^{+1.6}_{-0.9}$| |
| 1.4 | 1000 | 0.04 | 0.03 | 0.04 | 6 | |$231^{+139}_{-92}$| | |$150^{+90}_{-60}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.9^{+1.1}_{-0.8}$| | |$1.7^{+1.1}_{-0.7}$| |
| 2.1 | 1000 | 0.04 | 0.04 | 0.06 | 8 | |$184^{+91}_{-64}$| | |$124^{+61}_{-43}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.8}_{-0.5}$| | |$1.4^{+0.7}_{-0.5}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 16 | |$287^{+91}_{-71}$| | |$191^{+61}_{-47}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 4.1 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$280^{+89}_{-69}$| | |$187^{+59}_{-46}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 5.7 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$279^{+89}_{-69}$| | |$186^{+59}_{-46}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.1^{+0.7}_{-0.6}$| |
| 7.8 | 1000 | 0.04 | 0.07 | 0.10 | 16 | |$242^{+77}_{-60}$| | |$164^{+52}_{-41}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.0^{+0.7}_{-0.5}$| | |$1.9^{+0.6}_{-0.5}$| |
| 10.7 | 1000 | 0.04 | 0.08 | 0.12 | 17 | |$218^{+67}_{-53}$| | |$147^{+45}_{-35}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.8^{+0.6}_{-0.5}$| | |$1.7^{+0.5}_{-0.4}$| |
| 14.8 | 1000 | 0.04 | 0.09 | 0.14 | 19 | |$205^{+59}_{-47}$| | |$140^{+40}_{-32}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.7^{+0.5}_{-0.4}$| | |$1.6^{+0.5}_{-0.4}$| |
| 20.3 | 1000 | 0.04 | 0.11 | 0.16 | 21 | |$193^{+52}_{-42}$| | |$132^{+36}_{-29}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+0.5}_{-0.4}$| | |$1.5^{+0.4}_{-0.4}$| |
| 27.9 | 1000 | 0.04 | 0.12 | 0.17 | 23 | |$195^{+50}_{-40}$| | |$133^{+34}_{-28}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+0.4}_{-0.4}$| | |$1.5^{+0.4}_{-0.4}$| |
| 38.4 | 1000 | 0.04 | 0.15 | 0.22 | 27 | |$180^{+42}_{-35}$| | |$124^{+29}_{-24}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.4}_{-0.3}$| | |$1.4^{+0.4}_{-0.3}$| |
| 52.9 | 1000 | 0.04 | 0.17 | 0.24 | 27 | |$160^{+37}_{-31}$| | |$111^{+26}_{-21}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.3}_{-0.3}$| | |$1.3^{+0.3}_{-0.3}$| |
| 72.7 | 1000 | 0.04 | 0.19 | 0.28 | 29 | |$150^{+33}_{-28}$| | |$105^{+23}_{-19}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 100.0 | 1000 | 0.04 | 0.24 | 0.35 | 39 | |$160^{+30}_{-25}$| | |$113^{+21}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.3}_{-0.2}$| | |$1.3^{+0.3}_{-0.2}$| |
| 3.0 | 1000 | 0.03 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$139^{+26}_{-22}$| | |$100^{+19}_{-16}$| | |$2.0^{+0.7}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$139^{+26}_{-22}$| | |$100^{+19}_{-16}$| | |$2.0^{+0.7}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$136^{+26}_{-22}$| | |$97^{+18}_{-16}$| | |$2.1^{+0.8}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$132^{+26}_{-22}$| | |$94^{+18}_{-15}$| | |$2.1^{+0.8}_{-0.7}$| | |$2.0^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$125^{+25}_{-21}$| | |$89^{+18}_{-15}$| | |$2.3^{+0.8}_{-0.7}$| | |$2.1^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.06 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$125^{+25}_{-21}$| | |$89^{+18}_{-15}$| | |$2.1^{+0.8}_{-0.7}$| | |$2.0^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.07 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$121^{+25}_{-21}$| | |$87^{+18}_{-15}$| | |$2.2^{+0.8}_{-0.7}$| | |$2.0^{+0.8}_{-0.6}$| |
| 3.0 | 1000 | 0.08 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$121^{+25}_{-21}$| | |$87^{+18}_{-15}$| | |$2.2^{+0.8}_{-0.7}$| | |$2.0^{+0.8}_{-0.6}$| |
| 3.0 | 1000 | 0.09 | 0.06 | 0.09 | 14 | |$247^{+85}_{-65}$| | |$165^{+57}_{-44}$| | |$114^{+24}_{-20}$| | |$82^{+17}_{-14}$| | |$2.2^{+0.9}_{-0.7}$| | |$2.0^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.10 | 0.06 | 0.09 | 12 | |$212^{+81}_{-60}$| | |$141^{+54}_{-40}$| | |$96^{+22}_{-18}$| | |$69^{+16}_{-13}$| | |$2.2^{+1.0}_{-0.8}$| | |$2.0^{+0.9}_{-0.7}$| |
| 3.0 | 1000 | 0.11 | 0.06 | 0.09 | 12 | |$212^{+81}_{-60}$| | |$141^{+54}_{-40}$| | |$89^{+22}_{-18}$| | |$64^{+15}_{-13}$| | |$2.4^{+1.0}_{-0.9}$| | |$2.2^{+1.0}_{-0.8}$| |
| 3.0 | 1000 | 0.12 | 0.06 | 0.09 | 11 | |$194^{+78}_{-58}$| | |$129^{+52}_{-39}$| | |$82^{+21}_{-17}$| | |$59^{+15}_{-12}$| | |$2.4^{+1.1}_{-0.9}$| | |$2.2^{+1.0}_{-0.8}$| |
| 3.0 | 1000 | 0.14 | 0.06 | 0.09 | 11 | |$194^{+78}_{-58}$| | |$129^{+52}_{-39}$| | |$75^{+20}_{-16}$| | |$54^{+14}_{-12}$| | |$2.6^{+1.2}_{-1.0}$| | |$2.4^{+1.1}_{-0.9}$| |
| 3.0 | 1000 | 0.16 | 0.06 | 0.09 | 9 | |$159^{+73}_{-52}$| | |$106^{+48}_{-35}$| | |$61^{+19}_{-15}$| | |$43^{+13}_{-10}$| | |$2.6^{+1.4}_{-1.1}$| | |$2.4^{+1.3}_{-1.0}$| |
| 3.0 | 1000 | 0.18 | 0.06 | 0.09 | 8 | |$141^{+70}_{-49}$| | |$94^{+47}_{-33}$| | |$50^{+17}_{-13}$| | |$36^{+12}_{-9}$| | |$2.8^{+1.6}_{-1.3}$| | |$2.6^{+1.5}_{-1.2}$| |
| Δd . | Δv . | |$W_{\rm r}^{\rm min}$| . | Δz . | ΔX . | N . | |$\frac{{\rm d}N}{{\rm d}z}$| . | |$\frac{{\rm d}N}{{\rm d}X}$| . | |$\frac{{\rm d}N}{{\rm d}z}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}X}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}z}/\frac{{\rm d}N}{{\rm d}z}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}X}/\frac{{\rm d}N}{{\rm d}X}|_{\rm field}$| . |
|---|---|---|---|---|---|---|---|---|---|---|---|
| (Mpc) . | (km s−1) . | (Å) . | . | . | . | . | . | . | . | . | . |
| (1) . | (2) . | (3) . | (4) . | (5) . | (6) . | (7) . | (8) . | (9) . | (10) . | (11) . | (12) . |
| 3.0 | 500 | 0.04 | 0.03 | 0.05 | 11 | |$358^{+144}_{-107}$| | |$238^{+96}_{-71}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.9^{+1.2}_{-0.9}$| | |$2.7^{+1.1}_{-0.9}$| |
| 3.0 | 630 | 0.04 | 0.04 | 0.06 | 11 | |$293^{+118}_{-87}$| | |$195^{+78}_{-58}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.4^{+1.0}_{-0.7}$| | |$2.2^{+0.9}_{-0.7}$| |
| 3.0 | 794 | 0.04 | 0.05 | 0.07 | 14 | |$305^{+105}_{-81}$| | |$203^{+70}_{-54}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.5^{+0.9}_{-0.7}$| | |$2.3^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 16 | |$287^{+91}_{-71}$| | |$191^{+61}_{-47}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 3.0 | 1313 | 0.04 | 0.07 | 0.11 | 17 | |$237^{+73}_{-57}$| | |$159^{+49}_{-38}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.9^{+0.6}_{-0.5}$| | |$1.8^{+0.6}_{-0.5}$| |
| 3.0 | 1724 | 0.04 | 0.09 | 0.13 | 17 | |$188^{+58}_{-45}$| | |$126^{+39}_{-30}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.5}_{-0.4}$| | |$1.5^{+0.5}_{-0.4}$| |
| 3.0 | 2264 | 0.04 | 0.12 | 0.17 | 18 | |$156^{+46}_{-37}$| | |$105^{+31}_{-25}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.4}_{-0.3}$| | |$1.2^{+0.4}_{-0.3}$| |
| 3.0 | 2972 | 0.04 | 0.14 | 0.21 | 21 | |$151^{+41}_{-33}$| | |$101^{+27}_{-22}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.4}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 3.0 | 3903 | 0.04 | 0.16 | 0.24 | 25 | |$152^{+37}_{-30}$| | |$102^{+25}_{-20}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 3.0 | 5125 | 0.04 | 0.18 | 0.27 | 26 | |$143^{+34}_{-28}$| | |$97^{+23}_{-19}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.1^{+0.3}_{-0.2}$| |
| 3.0 | 6729 | 0.04 | 0.19 | 0.28 | 26 | |$134^{+32}_{-26}$| | |$91^{+22}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.1^{+0.3}_{-0.2}$| | |$1.1^{+0.3}_{-0.2}$| |
| 3.0 | 8835 | 0.04 | 0.22 | 0.32 | 32 | |$147^{+31}_{-26}$| | |$101^{+21}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.2}$| | |$1.2^{+0.3}_{-0.2}$| |
| 3.0 | 11601 | 0.04 | 0.25 | 0.36 | 38 | |$151^{+29}_{-24}$| | |$105^{+20}_{-17}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.2}$| | |$1.2^{+0.3}_{-0.2}$| |
| 3.0 | 15232 | 0.04 | 0.30 | 0.42 | 43 | |$146^{+26}_{-22}$| | |$103^{+18}_{-16}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.2}_{-0.2}$| | |$1.2^{+0.2}_{-0.2}$| |
| 3.0 | 20000 | 0.04 | 0.33 | 0.47 | 48 | |$145^{+24}_{-21}$| | |$103^{+17}_{-15}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.2}_{-0.2}$| | |$1.2^{+0.2}_{-0.2}$| |
| 1.0 | 1000 | 0.04 | 0.01 | 0.02 | 3 | |$203^{+199}_{-112}$| | |$140^{+137}_{-77}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+1.6}_{-0.9}$| | |$1.6^{+1.6}_{-0.9}$| |
| 1.4 | 1000 | 0.04 | 0.03 | 0.04 | 6 | |$231^{+139}_{-92}$| | |$150^{+90}_{-60}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.9^{+1.1}_{-0.8}$| | |$1.7^{+1.1}_{-0.7}$| |
| 2.1 | 1000 | 0.04 | 0.04 | 0.06 | 8 | |$184^{+91}_{-64}$| | |$124^{+61}_{-43}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.8}_{-0.5}$| | |$1.4^{+0.7}_{-0.5}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 16 | |$287^{+91}_{-71}$| | |$191^{+61}_{-47}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 4.1 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$280^{+89}_{-69}$| | |$187^{+59}_{-46}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 5.7 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$279^{+89}_{-69}$| | |$186^{+59}_{-46}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.1^{+0.7}_{-0.6}$| |
| 7.8 | 1000 | 0.04 | 0.07 | 0.10 | 16 | |$242^{+77}_{-60}$| | |$164^{+52}_{-41}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.0^{+0.7}_{-0.5}$| | |$1.9^{+0.6}_{-0.5}$| |
| 10.7 | 1000 | 0.04 | 0.08 | 0.12 | 17 | |$218^{+67}_{-53}$| | |$147^{+45}_{-35}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.8^{+0.6}_{-0.5}$| | |$1.7^{+0.5}_{-0.4}$| |
| 14.8 | 1000 | 0.04 | 0.09 | 0.14 | 19 | |$205^{+59}_{-47}$| | |$140^{+40}_{-32}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.7^{+0.5}_{-0.4}$| | |$1.6^{+0.5}_{-0.4}$| |
| 20.3 | 1000 | 0.04 | 0.11 | 0.16 | 21 | |$193^{+52}_{-42}$| | |$132^{+36}_{-29}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+0.5}_{-0.4}$| | |$1.5^{+0.4}_{-0.4}$| |
| 27.9 | 1000 | 0.04 | 0.12 | 0.17 | 23 | |$195^{+50}_{-40}$| | |$133^{+34}_{-28}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+0.4}_{-0.4}$| | |$1.5^{+0.4}_{-0.4}$| |
| 38.4 | 1000 | 0.04 | 0.15 | 0.22 | 27 | |$180^{+42}_{-35}$| | |$124^{+29}_{-24}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.4}_{-0.3}$| | |$1.4^{+0.4}_{-0.3}$| |
| 52.9 | 1000 | 0.04 | 0.17 | 0.24 | 27 | |$160^{+37}_{-31}$| | |$111^{+26}_{-21}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.3}_{-0.3}$| | |$1.3^{+0.3}_{-0.3}$| |
| 72.7 | 1000 | 0.04 | 0.19 | 0.28 | 29 | |$150^{+33}_{-28}$| | |$105^{+23}_{-19}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 100.0 | 1000 | 0.04 | 0.24 | 0.35 | 39 | |$160^{+30}_{-25}$| | |$113^{+21}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.3}_{-0.2}$| | |$1.3^{+0.3}_{-0.2}$| |
| 3.0 | 1000 | 0.03 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$139^{+26}_{-22}$| | |$100^{+19}_{-16}$| | |$2.0^{+0.7}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$139^{+26}_{-22}$| | |$100^{+19}_{-16}$| | |$2.0^{+0.7}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$136^{+26}_{-22}$| | |$97^{+18}_{-16}$| | |$2.1^{+0.8}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$132^{+26}_{-22}$| | |$94^{+18}_{-15}$| | |$2.1^{+0.8}_{-0.7}$| | |$2.0^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$125^{+25}_{-21}$| | |$89^{+18}_{-15}$| | |$2.3^{+0.8}_{-0.7}$| | |$2.1^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.06 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$125^{+25}_{-21}$| | |$89^{+18}_{-15}$| | |$2.1^{+0.8}_{-0.7}$| | |$2.0^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.07 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$121^{+25}_{-21}$| | |$87^{+18}_{-15}$| | |$2.2^{+0.8}_{-0.7}$| | |$2.0^{+0.8}_{-0.6}$| |
| 3.0 | 1000 | 0.08 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$121^{+25}_{-21}$| | |$87^{+18}_{-15}$| | |$2.2^{+0.8}_{-0.7}$| | |$2.0^{+0.8}_{-0.6}$| |
| 3.0 | 1000 | 0.09 | 0.06 | 0.09 | 14 | |$247^{+85}_{-65}$| | |$165^{+57}_{-44}$| | |$114^{+24}_{-20}$| | |$82^{+17}_{-14}$| | |$2.2^{+0.9}_{-0.7}$| | |$2.0^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.10 | 0.06 | 0.09 | 12 | |$212^{+81}_{-60}$| | |$141^{+54}_{-40}$| | |$96^{+22}_{-18}$| | |$69^{+16}_{-13}$| | |$2.2^{+1.0}_{-0.8}$| | |$2.0^{+0.9}_{-0.7}$| |
| 3.0 | 1000 | 0.11 | 0.06 | 0.09 | 12 | |$212^{+81}_{-60}$| | |$141^{+54}_{-40}$| | |$89^{+22}_{-18}$| | |$64^{+15}_{-13}$| | |$2.4^{+1.0}_{-0.9}$| | |$2.2^{+1.0}_{-0.8}$| |
| 3.0 | 1000 | 0.12 | 0.06 | 0.09 | 11 | |$194^{+78}_{-58}$| | |$129^{+52}_{-39}$| | |$82^{+21}_{-17}$| | |$59^{+15}_{-12}$| | |$2.4^{+1.1}_{-0.9}$| | |$2.2^{+1.0}_{-0.8}$| |
| 3.0 | 1000 | 0.14 | 0.06 | 0.09 | 11 | |$194^{+78}_{-58}$| | |$129^{+52}_{-39}$| | |$75^{+20}_{-16}$| | |$54^{+14}_{-12}$| | |$2.6^{+1.2}_{-1.0}$| | |$2.4^{+1.1}_{-0.9}$| |
| 3.0 | 1000 | 0.16 | 0.06 | 0.09 | 9 | |$159^{+73}_{-52}$| | |$106^{+48}_{-35}$| | |$61^{+19}_{-15}$| | |$43^{+13}_{-10}$| | |$2.6^{+1.4}_{-1.1}$| | |$2.4^{+1.3}_{-1.0}$| |
| 3.0 | 1000 | 0.18 | 0.06 | 0.09 | 8 | |$141^{+70}_{-49}$| | |$94^{+47}_{-33}$| | |$50^{+17}_{-13}$| | |$36^{+12}_{-9}$| | |$2.8^{+1.6}_{-1.3}$| | |$2.6^{+1.5}_{-1.2}$| |
Notes. (1) Maximum transverse separation between cluster-pair axes and the Q1410 sightline (see Section 5.1). (2) Maximum velocity difference to any cluster pair within Δd from the Q1410 sightline (see Section 5.1). (3) Minimum rest-frame equivalent width (see Section 5.1). (4) Redshift path (see Section 5.1 and Appendix C). (5) Absorption distance (see Appendix C). (6) Total number of absorption components having |$W_{\rm r} \ge W^{\rm min}_{{\rm r}}$| within Δd and Δv from cluster pairs (see Section 5.1). (7) Redshift number density associated with absorption components having |$W_{\rm r} \ge W^{\rm min}_{{\rm r}}$| within Δd and Δv from cluster pairs (see Section 5.1). (8) Absorption distance number density to absorption components having |$W_{{\rm r}} \ge W^{\rm min}_{{\rm r}}$| within Δd and Δv from cluster pairs (analogous to dN/dz but see also Appendix C). (9) Field expectation for the redshift number density (see Section 5.2). (10) Field expectation for the absorption distance number density (see Section 5.2). (11) Excess of the measured redshift number density compared to the field expectation (see Section 6.2). (12) Excess of the measured absorption distance number density compared to the field expectation (see Section 6.2).
Summary of relevant quantities for our sample of total H i absorption lines.
| Δd . | Δv . | |$W_{\rm r}^{\rm min}$| . | Δz . | ΔX . | N . | |$\frac{{\rm d}N}{{\rm d}z}$| . | |$\frac{{\rm d}N}{{\rm d}X}$| . | |$\frac{{\rm d}N}{{\rm d}z}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}X}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}z}/\frac{{\rm d}N}{{\rm d}z}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}X}/\frac{{\rm d}N}{{\rm d}X}|_{\rm field}$| . |
|---|---|---|---|---|---|---|---|---|---|---|---|
| (Mpc) . | (km s−1) . | (Å) . | . | . | . | . | . | . | . | . | . |
| (1) . | (2) . | (3) . | (4) . | (5) . | (6) . | (7) . | (8) . | (9) . | (10) . | (11) . | (12) . |
| 3.0 | 500 | 0.04 | 0.03 | 0.05 | 11 | |$358^{+144}_{-107}$| | |$238^{+96}_{-71}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.9^{+1.2}_{-0.9}$| | |$2.7^{+1.1}_{-0.9}$| |
| 3.0 | 630 | 0.04 | 0.04 | 0.06 | 11 | |$293^{+118}_{-87}$| | |$195^{+78}_{-58}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.4^{+1.0}_{-0.7}$| | |$2.2^{+0.9}_{-0.7}$| |
| 3.0 | 794 | 0.04 | 0.05 | 0.07 | 14 | |$305^{+105}_{-81}$| | |$203^{+70}_{-54}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.5^{+0.9}_{-0.7}$| | |$2.3^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 16 | |$287^{+91}_{-71}$| | |$191^{+61}_{-47}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 3.0 | 1313 | 0.04 | 0.07 | 0.11 | 17 | |$237^{+73}_{-57}$| | |$159^{+49}_{-38}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.9^{+0.6}_{-0.5}$| | |$1.8^{+0.6}_{-0.5}$| |
| 3.0 | 1724 | 0.04 | 0.09 | 0.13 | 17 | |$188^{+58}_{-45}$| | |$126^{+39}_{-30}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.5}_{-0.4}$| | |$1.5^{+0.5}_{-0.4}$| |
| 3.0 | 2264 | 0.04 | 0.12 | 0.17 | 18 | |$156^{+46}_{-37}$| | |$105^{+31}_{-25}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.4}_{-0.3}$| | |$1.2^{+0.4}_{-0.3}$| |
| 3.0 | 2972 | 0.04 | 0.14 | 0.21 | 21 | |$151^{+41}_{-33}$| | |$101^{+27}_{-22}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.4}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 3.0 | 3903 | 0.04 | 0.16 | 0.24 | 25 | |$152^{+37}_{-30}$| | |$102^{+25}_{-20}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 3.0 | 5125 | 0.04 | 0.18 | 0.27 | 26 | |$143^{+34}_{-28}$| | |$97^{+23}_{-19}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.1^{+0.3}_{-0.2}$| |
| 3.0 | 6729 | 0.04 | 0.19 | 0.28 | 26 | |$134^{+32}_{-26}$| | |$91^{+22}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.1^{+0.3}_{-0.2}$| | |$1.1^{+0.3}_{-0.2}$| |
| 3.0 | 8835 | 0.04 | 0.22 | 0.32 | 32 | |$147^{+31}_{-26}$| | |$101^{+21}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.2}$| | |$1.2^{+0.3}_{-0.2}$| |
| 3.0 | 11601 | 0.04 | 0.25 | 0.36 | 38 | |$151^{+29}_{-24}$| | |$105^{+20}_{-17}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.2}$| | |$1.2^{+0.3}_{-0.2}$| |
| 3.0 | 15232 | 0.04 | 0.30 | 0.42 | 43 | |$146^{+26}_{-22}$| | |$103^{+18}_{-16}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.2}_{-0.2}$| | |$1.2^{+0.2}_{-0.2}$| |
| 3.0 | 20000 | 0.04 | 0.33 | 0.47 | 48 | |$145^{+24}_{-21}$| | |$103^{+17}_{-15}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.2}_{-0.2}$| | |$1.2^{+0.2}_{-0.2}$| |
| 1.0 | 1000 | 0.04 | 0.01 | 0.02 | 3 | |$203^{+199}_{-112}$| | |$140^{+137}_{-77}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+1.6}_{-0.9}$| | |$1.6^{+1.6}_{-0.9}$| |
| 1.4 | 1000 | 0.04 | 0.03 | 0.04 | 6 | |$231^{+139}_{-92}$| | |$150^{+90}_{-60}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.9^{+1.1}_{-0.8}$| | |$1.7^{+1.1}_{-0.7}$| |
| 2.1 | 1000 | 0.04 | 0.04 | 0.06 | 8 | |$184^{+91}_{-64}$| | |$124^{+61}_{-43}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.8}_{-0.5}$| | |$1.4^{+0.7}_{-0.5}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 16 | |$287^{+91}_{-71}$| | |$191^{+61}_{-47}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 4.1 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$280^{+89}_{-69}$| | |$187^{+59}_{-46}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 5.7 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$279^{+89}_{-69}$| | |$186^{+59}_{-46}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.1^{+0.7}_{-0.6}$| |
| 7.8 | 1000 | 0.04 | 0.07 | 0.10 | 16 | |$242^{+77}_{-60}$| | |$164^{+52}_{-41}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.0^{+0.7}_{-0.5}$| | |$1.9^{+0.6}_{-0.5}$| |
| 10.7 | 1000 | 0.04 | 0.08 | 0.12 | 17 | |$218^{+67}_{-53}$| | |$147^{+45}_{-35}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.8^{+0.6}_{-0.5}$| | |$1.7^{+0.5}_{-0.4}$| |
| 14.8 | 1000 | 0.04 | 0.09 | 0.14 | 19 | |$205^{+59}_{-47}$| | |$140^{+40}_{-32}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.7^{+0.5}_{-0.4}$| | |$1.6^{+0.5}_{-0.4}$| |
| 20.3 | 1000 | 0.04 | 0.11 | 0.16 | 21 | |$193^{+52}_{-42}$| | |$132^{+36}_{-29}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+0.5}_{-0.4}$| | |$1.5^{+0.4}_{-0.4}$| |
| 27.9 | 1000 | 0.04 | 0.12 | 0.17 | 23 | |$195^{+50}_{-40}$| | |$133^{+34}_{-28}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+0.4}_{-0.4}$| | |$1.5^{+0.4}_{-0.4}$| |
| 38.4 | 1000 | 0.04 | 0.15 | 0.22 | 27 | |$180^{+42}_{-35}$| | |$124^{+29}_{-24}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.4}_{-0.3}$| | |$1.4^{+0.4}_{-0.3}$| |
| 52.9 | 1000 | 0.04 | 0.17 | 0.24 | 27 | |$160^{+37}_{-31}$| | |$111^{+26}_{-21}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.3}_{-0.3}$| | |$1.3^{+0.3}_{-0.3}$| |
| 72.7 | 1000 | 0.04 | 0.19 | 0.28 | 29 | |$150^{+33}_{-28}$| | |$105^{+23}_{-19}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 100.0 | 1000 | 0.04 | 0.24 | 0.35 | 39 | |$160^{+30}_{-25}$| | |$113^{+21}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.3}_{-0.2}$| | |$1.3^{+0.3}_{-0.2}$| |
| 3.0 | 1000 | 0.03 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$139^{+26}_{-22}$| | |$100^{+19}_{-16}$| | |$2.0^{+0.7}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$139^{+26}_{-22}$| | |$100^{+19}_{-16}$| | |$2.0^{+0.7}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$136^{+26}_{-22}$| | |$97^{+18}_{-16}$| | |$2.1^{+0.8}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$132^{+26}_{-22}$| | |$94^{+18}_{-15}$| | |$2.1^{+0.8}_{-0.7}$| | |$2.0^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$125^{+25}_{-21}$| | |$89^{+18}_{-15}$| | |$2.3^{+0.8}_{-0.7}$| | |$2.1^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.06 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$125^{+25}_{-21}$| | |$89^{+18}_{-15}$| | |$2.1^{+0.8}_{-0.7}$| | |$2.0^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.07 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$121^{+25}_{-21}$| | |$87^{+18}_{-15}$| | |$2.2^{+0.8}_{-0.7}$| | |$2.0^{+0.8}_{-0.6}$| |
| 3.0 | 1000 | 0.08 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$121^{+25}_{-21}$| | |$87^{+18}_{-15}$| | |$2.2^{+0.8}_{-0.7}$| | |$2.0^{+0.8}_{-0.6}$| |
| 3.0 | 1000 | 0.09 | 0.06 | 0.09 | 14 | |$247^{+85}_{-65}$| | |$165^{+57}_{-44}$| | |$114^{+24}_{-20}$| | |$82^{+17}_{-14}$| | |$2.2^{+0.9}_{-0.7}$| | |$2.0^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.10 | 0.06 | 0.09 | 12 | |$212^{+81}_{-60}$| | |$141^{+54}_{-40}$| | |$96^{+22}_{-18}$| | |$69^{+16}_{-13}$| | |$2.2^{+1.0}_{-0.8}$| | |$2.0^{+0.9}_{-0.7}$| |
| 3.0 | 1000 | 0.11 | 0.06 | 0.09 | 12 | |$212^{+81}_{-60}$| | |$141^{+54}_{-40}$| | |$89^{+22}_{-18}$| | |$64^{+15}_{-13}$| | |$2.4^{+1.0}_{-0.9}$| | |$2.2^{+1.0}_{-0.8}$| |
| 3.0 | 1000 | 0.12 | 0.06 | 0.09 | 11 | |$194^{+78}_{-58}$| | |$129^{+52}_{-39}$| | |$82^{+21}_{-17}$| | |$59^{+15}_{-12}$| | |$2.4^{+1.1}_{-0.9}$| | |$2.2^{+1.0}_{-0.8}$| |
| 3.0 | 1000 | 0.14 | 0.06 | 0.09 | 11 | |$194^{+78}_{-58}$| | |$129^{+52}_{-39}$| | |$75^{+20}_{-16}$| | |$54^{+14}_{-12}$| | |$2.6^{+1.2}_{-1.0}$| | |$2.4^{+1.1}_{-0.9}$| |
| 3.0 | 1000 | 0.16 | 0.06 | 0.09 | 9 | |$159^{+73}_{-52}$| | |$106^{+48}_{-35}$| | |$61^{+19}_{-15}$| | |$43^{+13}_{-10}$| | |$2.6^{+1.4}_{-1.1}$| | |$2.4^{+1.3}_{-1.0}$| |
| 3.0 | 1000 | 0.18 | 0.06 | 0.09 | 8 | |$141^{+70}_{-49}$| | |$94^{+47}_{-33}$| | |$50^{+17}_{-13}$| | |$36^{+12}_{-9}$| | |$2.8^{+1.6}_{-1.3}$| | |$2.6^{+1.5}_{-1.2}$| |
| Δd . | Δv . | |$W_{\rm r}^{\rm min}$| . | Δz . | ΔX . | N . | |$\frac{{\rm d}N}{{\rm d}z}$| . | |$\frac{{\rm d}N}{{\rm d}X}$| . | |$\frac{{\rm d}N}{{\rm d}z}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}X}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}z}/\frac{{\rm d}N}{{\rm d}z}|_{\rm field}$| . | |$\frac{{\rm d}N}{{\rm d}X}/\frac{{\rm d}N}{{\rm d}X}|_{\rm field}$| . |
|---|---|---|---|---|---|---|---|---|---|---|---|
| (Mpc) . | (km s−1) . | (Å) . | . | . | . | . | . | . | . | . | . |
| (1) . | (2) . | (3) . | (4) . | (5) . | (6) . | (7) . | (8) . | (9) . | (10) . | (11) . | (12) . |
| 3.0 | 500 | 0.04 | 0.03 | 0.05 | 11 | |$358^{+144}_{-107}$| | |$238^{+96}_{-71}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.9^{+1.2}_{-0.9}$| | |$2.7^{+1.1}_{-0.9}$| |
| 3.0 | 630 | 0.04 | 0.04 | 0.06 | 11 | |$293^{+118}_{-87}$| | |$195^{+78}_{-58}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.4^{+1.0}_{-0.7}$| | |$2.2^{+0.9}_{-0.7}$| |
| 3.0 | 794 | 0.04 | 0.05 | 0.07 | 14 | |$305^{+105}_{-81}$| | |$203^{+70}_{-54}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.5^{+0.9}_{-0.7}$| | |$2.3^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 16 | |$287^{+91}_{-71}$| | |$191^{+61}_{-47}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 3.0 | 1313 | 0.04 | 0.07 | 0.11 | 17 | |$237^{+73}_{-57}$| | |$159^{+49}_{-38}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.9^{+0.6}_{-0.5}$| | |$1.8^{+0.6}_{-0.5}$| |
| 3.0 | 1724 | 0.04 | 0.09 | 0.13 | 17 | |$188^{+58}_{-45}$| | |$126^{+39}_{-30}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.5}_{-0.4}$| | |$1.5^{+0.5}_{-0.4}$| |
| 3.0 | 2264 | 0.04 | 0.12 | 0.17 | 18 | |$156^{+46}_{-37}$| | |$105^{+31}_{-25}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.4}_{-0.3}$| | |$1.2^{+0.4}_{-0.3}$| |
| 3.0 | 2972 | 0.04 | 0.14 | 0.21 | 21 | |$151^{+41}_{-33}$| | |$101^{+27}_{-22}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.4}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 3.0 | 3903 | 0.04 | 0.16 | 0.24 | 25 | |$152^{+37}_{-30}$| | |$102^{+25}_{-20}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 3.0 | 5125 | 0.04 | 0.18 | 0.27 | 26 | |$143^{+34}_{-28}$| | |$97^{+23}_{-19}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.1^{+0.3}_{-0.2}$| |
| 3.0 | 6729 | 0.04 | 0.19 | 0.28 | 26 | |$134^{+32}_{-26}$| | |$91^{+22}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.1^{+0.3}_{-0.2}$| | |$1.1^{+0.3}_{-0.2}$| |
| 3.0 | 8835 | 0.04 | 0.22 | 0.32 | 32 | |$147^{+31}_{-26}$| | |$101^{+21}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.2}$| | |$1.2^{+0.3}_{-0.2}$| |
| 3.0 | 11601 | 0.04 | 0.25 | 0.36 | 38 | |$151^{+29}_{-24}$| | |$105^{+20}_{-17}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.2}$| | |$1.2^{+0.3}_{-0.2}$| |
| 3.0 | 15232 | 0.04 | 0.30 | 0.42 | 43 | |$146^{+26}_{-22}$| | |$103^{+18}_{-16}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.2}_{-0.2}$| | |$1.2^{+0.2}_{-0.2}$| |
| 3.0 | 20000 | 0.04 | 0.33 | 0.47 | 48 | |$145^{+24}_{-21}$| | |$103^{+17}_{-15}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.2}_{-0.2}$| | |$1.2^{+0.2}_{-0.2}$| |
| 1.0 | 1000 | 0.04 | 0.01 | 0.02 | 3 | |$203^{+199}_{-112}$| | |$140^{+137}_{-77}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+1.6}_{-0.9}$| | |$1.6^{+1.6}_{-0.9}$| |
| 1.4 | 1000 | 0.04 | 0.03 | 0.04 | 6 | |$231^{+139}_{-92}$| | |$150^{+90}_{-60}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.9^{+1.1}_{-0.8}$| | |$1.7^{+1.1}_{-0.7}$| |
| 2.1 | 1000 | 0.04 | 0.04 | 0.06 | 8 | |$184^{+91}_{-64}$| | |$124^{+61}_{-43}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.8}_{-0.5}$| | |$1.4^{+0.7}_{-0.5}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 16 | |$287^{+91}_{-71}$| | |$191^{+61}_{-47}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 4.1 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$280^{+89}_{-69}$| | |$187^{+59}_{-46}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.2^{+0.7}_{-0.6}$| |
| 5.7 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$279^{+89}_{-69}$| | |$186^{+59}_{-46}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.3^{+0.8}_{-0.6}$| | |$2.1^{+0.7}_{-0.6}$| |
| 7.8 | 1000 | 0.04 | 0.07 | 0.10 | 16 | |$242^{+77}_{-60}$| | |$164^{+52}_{-41}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$2.0^{+0.7}_{-0.5}$| | |$1.9^{+0.6}_{-0.5}$| |
| 10.7 | 1000 | 0.04 | 0.08 | 0.12 | 17 | |$218^{+67}_{-53}$| | |$147^{+45}_{-35}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.8^{+0.6}_{-0.5}$| | |$1.7^{+0.5}_{-0.4}$| |
| 14.8 | 1000 | 0.04 | 0.09 | 0.14 | 19 | |$205^{+59}_{-47}$| | |$140^{+40}_{-32}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.7^{+0.5}_{-0.4}$| | |$1.6^{+0.5}_{-0.4}$| |
| 20.3 | 1000 | 0.04 | 0.11 | 0.16 | 21 | |$193^{+52}_{-42}$| | |$132^{+36}_{-29}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+0.5}_{-0.4}$| | |$1.5^{+0.4}_{-0.4}$| |
| 27.9 | 1000 | 0.04 | 0.12 | 0.17 | 23 | |$195^{+50}_{-40}$| | |$133^{+34}_{-28}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.6^{+0.4}_{-0.4}$| | |$1.5^{+0.4}_{-0.4}$| |
| 38.4 | 1000 | 0.04 | 0.15 | 0.22 | 27 | |$180^{+42}_{-35}$| | |$124^{+29}_{-24}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.5^{+0.4}_{-0.3}$| | |$1.4^{+0.4}_{-0.3}$| |
| 52.9 | 1000 | 0.04 | 0.17 | 0.24 | 27 | |$160^{+37}_{-31}$| | |$111^{+26}_{-21}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.3}_{-0.3}$| | |$1.3^{+0.3}_{-0.3}$| |
| 72.7 | 1000 | 0.04 | 0.19 | 0.28 | 29 | |$150^{+33}_{-28}$| | |$105^{+23}_{-19}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.2^{+0.3}_{-0.3}$| | |$1.2^{+0.3}_{-0.3}$| |
| 100.0 | 1000 | 0.04 | 0.24 | 0.35 | 39 | |$160^{+30}_{-25}$| | |$113^{+21}_{-18}$| | |$123^{+26}_{-23}$| | |$87^{+18}_{-16}$| | |$1.3^{+0.3}_{-0.2}$| | |$1.3^{+0.3}_{-0.2}$| |
| 3.0 | 1000 | 0.03 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$139^{+26}_{-22}$| | |$100^{+19}_{-16}$| | |$2.0^{+0.7}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$139^{+26}_{-22}$| | |$100^{+19}_{-16}$| | |$2.0^{+0.7}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$136^{+26}_{-22}$| | |$97^{+18}_{-16}$| | |$2.1^{+0.8}_{-0.6}$| | |$1.9^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$132^{+26}_{-22}$| | |$94^{+18}_{-15}$| | |$2.1^{+0.8}_{-0.7}$| | |$2.0^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 16 | |$282^{+90}_{-70}$| | |$188^{+60}_{-47}$| | |$125^{+25}_{-21}$| | |$89^{+18}_{-15}$| | |$2.3^{+0.8}_{-0.7}$| | |$2.1^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.06 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$125^{+25}_{-21}$| | |$89^{+18}_{-15}$| | |$2.1^{+0.8}_{-0.7}$| | |$2.0^{+0.7}_{-0.6}$| |
| 3.0 | 1000 | 0.07 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$121^{+25}_{-21}$| | |$87^{+18}_{-15}$| | |$2.2^{+0.8}_{-0.7}$| | |$2.0^{+0.8}_{-0.6}$| |
| 3.0 | 1000 | 0.08 | 0.06 | 0.09 | 15 | |$265^{+88}_{-68}$| | |$176^{+58}_{-45}$| | |$121^{+25}_{-21}$| | |$87^{+18}_{-15}$| | |$2.2^{+0.8}_{-0.7}$| | |$2.0^{+0.8}_{-0.6}$| |
| 3.0 | 1000 | 0.09 | 0.06 | 0.09 | 14 | |$247^{+85}_{-65}$| | |$165^{+57}_{-44}$| | |$114^{+24}_{-20}$| | |$82^{+17}_{-14}$| | |$2.2^{+0.9}_{-0.7}$| | |$2.0^{+0.8}_{-0.7}$| |
| 3.0 | 1000 | 0.10 | 0.06 | 0.09 | 12 | |$212^{+81}_{-60}$| | |$141^{+54}_{-40}$| | |$96^{+22}_{-18}$| | |$69^{+16}_{-13}$| | |$2.2^{+1.0}_{-0.8}$| | |$2.0^{+0.9}_{-0.7}$| |
| 3.0 | 1000 | 0.11 | 0.06 | 0.09 | 12 | |$212^{+81}_{-60}$| | |$141^{+54}_{-40}$| | |$89^{+22}_{-18}$| | |$64^{+15}_{-13}$| | |$2.4^{+1.0}_{-0.9}$| | |$2.2^{+1.0}_{-0.8}$| |
| 3.0 | 1000 | 0.12 | 0.06 | 0.09 | 11 | |$194^{+78}_{-58}$| | |$129^{+52}_{-39}$| | |$82^{+21}_{-17}$| | |$59^{+15}_{-12}$| | |$2.4^{+1.1}_{-0.9}$| | |$2.2^{+1.0}_{-0.8}$| |
| 3.0 | 1000 | 0.14 | 0.06 | 0.09 | 11 | |$194^{+78}_{-58}$| | |$129^{+52}_{-39}$| | |$75^{+20}_{-16}$| | |$54^{+14}_{-12}$| | |$2.6^{+1.2}_{-1.0}$| | |$2.4^{+1.1}_{-0.9}$| |
| 3.0 | 1000 | 0.16 | 0.06 | 0.09 | 9 | |$159^{+73}_{-52}$| | |$106^{+48}_{-35}$| | |$61^{+19}_{-15}$| | |$43^{+13}_{-10}$| | |$2.6^{+1.4}_{-1.1}$| | |$2.4^{+1.3}_{-1.0}$| |
| 3.0 | 1000 | 0.18 | 0.06 | 0.09 | 8 | |$141^{+70}_{-49}$| | |$94^{+47}_{-33}$| | |$50^{+17}_{-13}$| | |$36^{+12}_{-9}$| | |$2.8^{+1.6}_{-1.3}$| | |$2.6^{+1.5}_{-1.2}$| |
Notes. (1) Maximum transverse separation between cluster-pair axes and the Q1410 sightline (see Section 5.1). (2) Maximum velocity difference to any cluster pair within Δd from the Q1410 sightline (see Section 5.1). (3) Minimum rest-frame equivalent width (see Section 5.1). (4) Redshift path (see Section 5.1 and Appendix C). (5) Absorption distance (see Appendix C). (6) Total number of absorption components having |$W_{\rm r} \ge W^{\rm min}_{{\rm r}}$| within Δd and Δv from cluster pairs (see Section 5.1). (7) Redshift number density associated with absorption components having |$W_{\rm r} \ge W^{\rm min}_{{\rm r}}$| within Δd and Δv from cluster pairs (see Section 5.1). (8) Absorption distance number density to absorption components having |$W_{{\rm r}} \ge W^{\rm min}_{{\rm r}}$| within Δd and Δv from cluster pairs (analogous to dN/dz but see also Appendix C). (9) Field expectation for the redshift number density (see Section 5.2). (10) Field expectation for the absorption distance number density (see Section 5.2). (11) Excess of the measured redshift number density compared to the field expectation (see Section 6.2). (12) Excess of the measured absorption distance number density compared to the field expectation (see Section 6.2).
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