Summary of relevant quantities for our sample of broad H i (b ≥ 50 km s−1) 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 | 4 | |$130^{+103}_{-63}$| | |$86^{+69}_{-42}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.4^{+6.4}_{-4.4}$| | |$7.0^{+6.0}_{-4.1}$| |
| 3.0 | 630 | 0.04 | 0.04 | 0.06 | 4 | |$106^{+85}_{-52}$| | |$71^{+56}_{-34}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+5.2}_{-3.6}$| | |$5.7^{+4.9}_{-3.4}$| |
| 3.0 | 794 | 0.04 | 0.05 | 0.07 | 6 | |$131^{+78}_{-52}$| | |$87^{+52}_{-35}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.5^{+5.1}_{-3.9}$| | |$7.0^{+4.8}_{-3.7}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 6 | |$108^{+65}_{-43}$| | |$72^{+43}_{-29}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+4.2}_{-3.2}$| | |$5.8^{+4.0}_{-3.0}$| |
| 3.0 | 1313 | 0.04 | 0.07 | 0.11 | 6 | |$84^{+50}_{-33}$| | |$56^{+34}_{-22}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.8^{+3.3}_{-2.5}$| | |$4.5^{+3.1}_{-2.4}$| |
| 3.0 | 1724 | 0.04 | 0.09 | 0.13 | 6 | |$66^{+40}_{-26}$| | |$44^{+27}_{-18}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.8^{+2.6}_{-2.0}$| | |$3.6^{+2.5}_{-1.9}$| |
| 3.0 | 2264 | 0.04 | 0.12 | 0.17 | 7 | |$61^{+33}_{-23}$| | |$41^{+22}_{-15}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.5^{+2.2}_{-1.7}$| | |$3.3^{+2.1}_{-1.7}$| |
| 3.0 | 2972 | 0.04 | 0.14 | 0.21 | 7 | |$50^{+27}_{-19}$| | |$34^{+18}_{-13}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.9^{+1.8}_{-1.4}$| | |$2.7^{+1.7}_{-1.4}$| |
| 3.0 | 3903 | 0.04 | 0.16 | 0.24 | 8 | |$49^{+24}_{-17}$| | |$33^{+16}_{-11}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.8^{+1.7}_{-1.3}$| | |$2.6^{+1.6}_{-1.3}$| |
| 3.0 | 5125 | 0.04 | 0.18 | 0.27 | 8 | |$44^{+22}_{-15}$| | |$30^{+15}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.5^{+1.5}_{-1.2}$| | |$2.4^{+1.4}_{-1.2}$| |
| 3.0 | 6729 | 0.04 | 0.19 | 0.28 | 8 | |$41^{+20}_{-14}$| | |$28^{+14}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.4^{+1.4}_{-1.1}$| | |$2.3^{+1.4}_{-1.1}$| |
| 3.0 | 8835 | 0.04 | 0.22 | 0.32 | 8 | |$37^{+18}_{-13}$| | |$25^{+13}_{-9}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.1^{+1.3}_{-1.0}$| | |$2.0^{+1.2}_{-1.0}$| |
| 3.0 | 11601 | 0.04 | 0.25 | 0.36 | 9 | |$36^{+16}_{-12}$| | |$25^{+11}_{-8}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.0^{+1.2}_{-1.0}$| | |$2.0^{+1.1}_{-0.9}$| |
| 3.0 | 15232 | 0.04 | 0.30 | 0.42 | 10 | |$34^{+14}_{-11}$| | |$24^{+10}_{-7}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$1.9^{+1.1}_{-0.9}$| | |$1.9^{+1.0}_{-0.9}$| |
| 3.0 | 20000 | 0.04 | 0.33 | 0.47 | 11 | |$33^{+13}_{-10}$| | |$24^{+9}_{-7}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$1.9^{+1.0}_{-0.9}$| | |$1.9^{+1.0}_{-0.9}$| |
| 1.0 | 1000 | 0.04 | 0.01 | 0.02 | 2 | |$135^{+180}_{-89}$| | |$93^{+124}_{-62}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.7^{+10.6}_{-5.7}$| | |$7.5^{+10.3}_{-5.6}$| |
| 1.4 | 1000 | 0.04 | 0.03 | 0.04 | 4 | |$154^{+122}_{-75}$| | |$100^{+80}_{-48}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$8.8^{+7.6}_{-5.2}$| | |$8.1^{+7.0}_{-4.8}$| |
| 2.1 | 1000 | 0.04 | 0.04 | 0.06 | 5 | |$115^{+78}_{-50}$| | |$77^{+53}_{-34}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.6^{+5.0}_{-3.6}$| | |$6.3^{+4.7}_{-3.4}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 6 | |$108^{+65}_{-43}$| | |$72^{+43}_{-29}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+4.2}_{-3.2}$| | |$5.8^{+4.0}_{-3.0}$| |
| 4.1 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$105^{+63}_{-42}$| | |$70^{+42}_{-28}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.0^{+4.1}_{-3.1}$| | |$5.7^{+3.9}_{-3.0}$| |
| 5.7 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$104^{+63}_{-42}$| | |$70^{+42}_{-28}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.0^{+4.1}_{-3.1}$| | |$5.6^{+3.9}_{-2.9}$| |
| 7.8 | 1000 | 0.04 | 0.07 | 0.10 | 6 | |$91^{+54}_{-36}$| | |$62^{+37}_{-25}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$5.2^{+3.6}_{-2.7}$| | |$5.0^{+3.4}_{-2.6}$| |
| 10.7 | 1000 | 0.04 | 0.08 | 0.12 | 6 | |$77^{+46}_{-31}$| | |$52^{+31}_{-21}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.4^{+3.0}_{-2.3}$| | |$4.2^{+2.9}_{-2.2}$| |
| 14.8 | 1000 | 0.04 | 0.09 | 0.14 | 7 | |$76^{+41}_{-28}$| | |$52^{+28}_{-19}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.3^{+2.7}_{-2.2}$| | |$4.2^{+2.7}_{-2.1}$| |
| 20.3 | 1000 | 0.04 | 0.11 | 0.16 | 7 | |$64^{+35}_{-24}$| | |$44^{+24}_{-16}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.7^{+2.3}_{-1.8}$| | |$3.6^{+2.3}_{-1.8}$| |
| 27.9 | 1000 | 0.04 | 0.12 | 0.17 | 7 | |$59^{+32}_{-22}$| | |$41^{+22}_{-15}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.4^{+2.1}_{-1.7}$| | |$3.3^{+2.1}_{-1.6}$| |
| 38.4 | 1000 | 0.04 | 0.15 | 0.22 | 8 | |$53^{+26}_{-19}$| | |$37^{+18}_{-13}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.1^{+1.8}_{-1.5}$| | |$3.0^{+1.8}_{-1.4}$| |
| 52.9 | 1000 | 0.04 | 0.17 | 0.24 | 8 | |$47^{+23}_{-16}$| | |$33^{+16}_{-11}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.7^{+1.6}_{-1.3}$| | |$2.7^{+1.6}_{-1.3}$| |
| 72.7 | 1000 | 0.04 | 0.19 | 0.28 | 8 | |$41^{+21}_{-14}$| | |$29^{+14}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.4^{+1.4}_{-1.1}$| | |$2.3^{+1.4}_{-1.1}$| |
| 100.0 | 1000 | 0.04 | 0.24 | 0.35 | 10 | |$41^{+18}_{-13}$| | |$29^{+12}_{-9}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.3^{+1.3}_{-1.1}$| | |$2.3^{+1.3}_{-1.1}$| |
| 3.0 | 1000 | 0.03 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.06 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.07 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.08 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.09 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.10 | 0.06 | 0.09 | 5 | |$88^{+60}_{-38}$| | |$59^{+40}_{-26}$| | |$14^{+11}_{-7}$| | |$10^{+8}_{-5}$| | |$6.2^{+5.8}_{-4.8}$| | |$5.8^{+5.4}_{-4.5}$| |
| 3.0 | 1000 | 0.11 | 0.06 | 0.09 | 5 | |$88^{+60}_{-38}$| | |$59^{+40}_{-26}$| | |$11^{+10}_{-6}$| | |$8^{+7}_{-4}$| | |$8.2^{+8.4}_{-7.3}$| | |$7.7^{+7.9}_{-6.8}$| |
| 3.0 | 1000 | 0.12 | 0.06 | 0.09 | 4 | |$71^{+56}_{-34}$| | |$47^{+37}_{-23}$| | |$11^{+10}_{-6}$| | |$8^{+7}_{-4}$| | |$6.6^{+7.3}_{-6.0}$| | |$6.1^{+6.8}_{-5.6}$| |
| 3.0 | 1000 | 0.14 | 0.06 | 0.09 | 4 | |$71^{+56}_{-34}$| | |$47^{+37}_{-23}$| | |$7^{+9}_{-5}$| | |$5^{+7}_{-3}$| | |$9.9^{+12.6}_{-9.9}$| | |$9.2^{+11.7}_{-9.2}$| |
| 3.0 | 1000 | 0.16 | 0.06 | 0.09 | 2 | |$35^{+47}_{-23}$| | |$24^{+31}_{-16}$| | |$4^{+8}_{-3}$| | |$3^{+6}_{-2}$| | |$9.9^{+20.5}_{-9.9}$| | |$9.2^{+19.1}_{-9.2}$| |
| 3.0 | 1000 | 0.18 | 0.06 | 0.09 | 2 | |$35^{+47}_{-23}$| | |$24^{+31}_{-16}$| | |$4^{+8}_{-3}$| | |$3^{+6}_{-2}$| | |$9.9^{+20.5}_{-9.9}$| | |$9.2^{+19.1}_{-9.2}$| |
| 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 | 4 | |$130^{+103}_{-63}$| | |$86^{+69}_{-42}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.4^{+6.4}_{-4.4}$| | |$7.0^{+6.0}_{-4.1}$| |
| 3.0 | 630 | 0.04 | 0.04 | 0.06 | 4 | |$106^{+85}_{-52}$| | |$71^{+56}_{-34}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+5.2}_{-3.6}$| | |$5.7^{+4.9}_{-3.4}$| |
| 3.0 | 794 | 0.04 | 0.05 | 0.07 | 6 | |$131^{+78}_{-52}$| | |$87^{+52}_{-35}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.5^{+5.1}_{-3.9}$| | |$7.0^{+4.8}_{-3.7}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 6 | |$108^{+65}_{-43}$| | |$72^{+43}_{-29}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+4.2}_{-3.2}$| | |$5.8^{+4.0}_{-3.0}$| |
| 3.0 | 1313 | 0.04 | 0.07 | 0.11 | 6 | |$84^{+50}_{-33}$| | |$56^{+34}_{-22}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.8^{+3.3}_{-2.5}$| | |$4.5^{+3.1}_{-2.4}$| |
| 3.0 | 1724 | 0.04 | 0.09 | 0.13 | 6 | |$66^{+40}_{-26}$| | |$44^{+27}_{-18}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.8^{+2.6}_{-2.0}$| | |$3.6^{+2.5}_{-1.9}$| |
| 3.0 | 2264 | 0.04 | 0.12 | 0.17 | 7 | |$61^{+33}_{-23}$| | |$41^{+22}_{-15}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.5^{+2.2}_{-1.7}$| | |$3.3^{+2.1}_{-1.7}$| |
| 3.0 | 2972 | 0.04 | 0.14 | 0.21 | 7 | |$50^{+27}_{-19}$| | |$34^{+18}_{-13}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.9^{+1.8}_{-1.4}$| | |$2.7^{+1.7}_{-1.4}$| |
| 3.0 | 3903 | 0.04 | 0.16 | 0.24 | 8 | |$49^{+24}_{-17}$| | |$33^{+16}_{-11}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.8^{+1.7}_{-1.3}$| | |$2.6^{+1.6}_{-1.3}$| |
| 3.0 | 5125 | 0.04 | 0.18 | 0.27 | 8 | |$44^{+22}_{-15}$| | |$30^{+15}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.5^{+1.5}_{-1.2}$| | |$2.4^{+1.4}_{-1.2}$| |
| 3.0 | 6729 | 0.04 | 0.19 | 0.28 | 8 | |$41^{+20}_{-14}$| | |$28^{+14}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.4^{+1.4}_{-1.1}$| | |$2.3^{+1.4}_{-1.1}$| |
| 3.0 | 8835 | 0.04 | 0.22 | 0.32 | 8 | |$37^{+18}_{-13}$| | |$25^{+13}_{-9}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.1^{+1.3}_{-1.0}$| | |$2.0^{+1.2}_{-1.0}$| |
| 3.0 | 11601 | 0.04 | 0.25 | 0.36 | 9 | |$36^{+16}_{-12}$| | |$25^{+11}_{-8}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.0^{+1.2}_{-1.0}$| | |$2.0^{+1.1}_{-0.9}$| |
| 3.0 | 15232 | 0.04 | 0.30 | 0.42 | 10 | |$34^{+14}_{-11}$| | |$24^{+10}_{-7}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$1.9^{+1.1}_{-0.9}$| | |$1.9^{+1.0}_{-0.9}$| |
| 3.0 | 20000 | 0.04 | 0.33 | 0.47 | 11 | |$33^{+13}_{-10}$| | |$24^{+9}_{-7}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$1.9^{+1.0}_{-0.9}$| | |$1.9^{+1.0}_{-0.9}$| |
| 1.0 | 1000 | 0.04 | 0.01 | 0.02 | 2 | |$135^{+180}_{-89}$| | |$93^{+124}_{-62}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.7^{+10.6}_{-5.7}$| | |$7.5^{+10.3}_{-5.6}$| |
| 1.4 | 1000 | 0.04 | 0.03 | 0.04 | 4 | |$154^{+122}_{-75}$| | |$100^{+80}_{-48}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$8.8^{+7.6}_{-5.2}$| | |$8.1^{+7.0}_{-4.8}$| |
| 2.1 | 1000 | 0.04 | 0.04 | 0.06 | 5 | |$115^{+78}_{-50}$| | |$77^{+53}_{-34}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.6^{+5.0}_{-3.6}$| | |$6.3^{+4.7}_{-3.4}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 6 | |$108^{+65}_{-43}$| | |$72^{+43}_{-29}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+4.2}_{-3.2}$| | |$5.8^{+4.0}_{-3.0}$| |
| 4.1 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$105^{+63}_{-42}$| | |$70^{+42}_{-28}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.0^{+4.1}_{-3.1}$| | |$5.7^{+3.9}_{-3.0}$| |
| 5.7 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$104^{+63}_{-42}$| | |$70^{+42}_{-28}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.0^{+4.1}_{-3.1}$| | |$5.6^{+3.9}_{-2.9}$| |
| 7.8 | 1000 | 0.04 | 0.07 | 0.10 | 6 | |$91^{+54}_{-36}$| | |$62^{+37}_{-25}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$5.2^{+3.6}_{-2.7}$| | |$5.0^{+3.4}_{-2.6}$| |
| 10.7 | 1000 | 0.04 | 0.08 | 0.12 | 6 | |$77^{+46}_{-31}$| | |$52^{+31}_{-21}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.4^{+3.0}_{-2.3}$| | |$4.2^{+2.9}_{-2.2}$| |
| 14.8 | 1000 | 0.04 | 0.09 | 0.14 | 7 | |$76^{+41}_{-28}$| | |$52^{+28}_{-19}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.3^{+2.7}_{-2.2}$| | |$4.2^{+2.7}_{-2.1}$| |
| 20.3 | 1000 | 0.04 | 0.11 | 0.16 | 7 | |$64^{+35}_{-24}$| | |$44^{+24}_{-16}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.7^{+2.3}_{-1.8}$| | |$3.6^{+2.3}_{-1.8}$| |
| 27.9 | 1000 | 0.04 | 0.12 | 0.17 | 7 | |$59^{+32}_{-22}$| | |$41^{+22}_{-15}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.4^{+2.1}_{-1.7}$| | |$3.3^{+2.1}_{-1.6}$| |
| 38.4 | 1000 | 0.04 | 0.15 | 0.22 | 8 | |$53^{+26}_{-19}$| | |$37^{+18}_{-13}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.1^{+1.8}_{-1.5}$| | |$3.0^{+1.8}_{-1.4}$| |
| 52.9 | 1000 | 0.04 | 0.17 | 0.24 | 8 | |$47^{+23}_{-16}$| | |$33^{+16}_{-11}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.7^{+1.6}_{-1.3}$| | |$2.7^{+1.6}_{-1.3}$| |
| 72.7 | 1000 | 0.04 | 0.19 | 0.28 | 8 | |$41^{+21}_{-14}$| | |$29^{+14}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.4^{+1.4}_{-1.1}$| | |$2.3^{+1.4}_{-1.1}$| |
| 100.0 | 1000 | 0.04 | 0.24 | 0.35 | 10 | |$41^{+18}_{-13}$| | |$29^{+12}_{-9}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.3^{+1.3}_{-1.1}$| | |$2.3^{+1.3}_{-1.1}$| |
| 3.0 | 1000 | 0.03 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.06 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.07 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.08 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.09 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.10 | 0.06 | 0.09 | 5 | |$88^{+60}_{-38}$| | |$59^{+40}_{-26}$| | |$14^{+11}_{-7}$| | |$10^{+8}_{-5}$| | |$6.2^{+5.8}_{-4.8}$| | |$5.8^{+5.4}_{-4.5}$| |
| 3.0 | 1000 | 0.11 | 0.06 | 0.09 | 5 | |$88^{+60}_{-38}$| | |$59^{+40}_{-26}$| | |$11^{+10}_{-6}$| | |$8^{+7}_{-4}$| | |$8.2^{+8.4}_{-7.3}$| | |$7.7^{+7.9}_{-6.8}$| |
| 3.0 | 1000 | 0.12 | 0.06 | 0.09 | 4 | |$71^{+56}_{-34}$| | |$47^{+37}_{-23}$| | |$11^{+10}_{-6}$| | |$8^{+7}_{-4}$| | |$6.6^{+7.3}_{-6.0}$| | |$6.1^{+6.8}_{-5.6}$| |
| 3.0 | 1000 | 0.14 | 0.06 | 0.09 | 4 | |$71^{+56}_{-34}$| | |$47^{+37}_{-23}$| | |$7^{+9}_{-5}$| | |$5^{+7}_{-3}$| | |$9.9^{+12.6}_{-9.9}$| | |$9.2^{+11.7}_{-9.2}$| |
| 3.0 | 1000 | 0.16 | 0.06 | 0.09 | 2 | |$35^{+47}_{-23}$| | |$24^{+31}_{-16}$| | |$4^{+8}_{-3}$| | |$3^{+6}_{-2}$| | |$9.9^{+20.5}_{-9.9}$| | |$9.2^{+19.1}_{-9.2}$| |
| 3.0 | 1000 | 0.18 | 0.06 | 0.09 | 2 | |$35^{+47}_{-23}$| | |$24^{+31}_{-16}$| | |$4^{+8}_{-3}$| | |$3^{+6}_{-2}$| | |$9.9^{+20.5}_{-9.9}$| | |$9.2^{+19.1}_{-9.2}$| |
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 broad H i (b ≥ 50 km s−1) 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 | 4 | |$130^{+103}_{-63}$| | |$86^{+69}_{-42}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.4^{+6.4}_{-4.4}$| | |$7.0^{+6.0}_{-4.1}$| |
| 3.0 | 630 | 0.04 | 0.04 | 0.06 | 4 | |$106^{+85}_{-52}$| | |$71^{+56}_{-34}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+5.2}_{-3.6}$| | |$5.7^{+4.9}_{-3.4}$| |
| 3.0 | 794 | 0.04 | 0.05 | 0.07 | 6 | |$131^{+78}_{-52}$| | |$87^{+52}_{-35}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.5^{+5.1}_{-3.9}$| | |$7.0^{+4.8}_{-3.7}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 6 | |$108^{+65}_{-43}$| | |$72^{+43}_{-29}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+4.2}_{-3.2}$| | |$5.8^{+4.0}_{-3.0}$| |
| 3.0 | 1313 | 0.04 | 0.07 | 0.11 | 6 | |$84^{+50}_{-33}$| | |$56^{+34}_{-22}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.8^{+3.3}_{-2.5}$| | |$4.5^{+3.1}_{-2.4}$| |
| 3.0 | 1724 | 0.04 | 0.09 | 0.13 | 6 | |$66^{+40}_{-26}$| | |$44^{+27}_{-18}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.8^{+2.6}_{-2.0}$| | |$3.6^{+2.5}_{-1.9}$| |
| 3.0 | 2264 | 0.04 | 0.12 | 0.17 | 7 | |$61^{+33}_{-23}$| | |$41^{+22}_{-15}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.5^{+2.2}_{-1.7}$| | |$3.3^{+2.1}_{-1.7}$| |
| 3.0 | 2972 | 0.04 | 0.14 | 0.21 | 7 | |$50^{+27}_{-19}$| | |$34^{+18}_{-13}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.9^{+1.8}_{-1.4}$| | |$2.7^{+1.7}_{-1.4}$| |
| 3.0 | 3903 | 0.04 | 0.16 | 0.24 | 8 | |$49^{+24}_{-17}$| | |$33^{+16}_{-11}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.8^{+1.7}_{-1.3}$| | |$2.6^{+1.6}_{-1.3}$| |
| 3.0 | 5125 | 0.04 | 0.18 | 0.27 | 8 | |$44^{+22}_{-15}$| | |$30^{+15}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.5^{+1.5}_{-1.2}$| | |$2.4^{+1.4}_{-1.2}$| |
| 3.0 | 6729 | 0.04 | 0.19 | 0.28 | 8 | |$41^{+20}_{-14}$| | |$28^{+14}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.4^{+1.4}_{-1.1}$| | |$2.3^{+1.4}_{-1.1}$| |
| 3.0 | 8835 | 0.04 | 0.22 | 0.32 | 8 | |$37^{+18}_{-13}$| | |$25^{+13}_{-9}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.1^{+1.3}_{-1.0}$| | |$2.0^{+1.2}_{-1.0}$| |
| 3.0 | 11601 | 0.04 | 0.25 | 0.36 | 9 | |$36^{+16}_{-12}$| | |$25^{+11}_{-8}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.0^{+1.2}_{-1.0}$| | |$2.0^{+1.1}_{-0.9}$| |
| 3.0 | 15232 | 0.04 | 0.30 | 0.42 | 10 | |$34^{+14}_{-11}$| | |$24^{+10}_{-7}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$1.9^{+1.1}_{-0.9}$| | |$1.9^{+1.0}_{-0.9}$| |
| 3.0 | 20000 | 0.04 | 0.33 | 0.47 | 11 | |$33^{+13}_{-10}$| | |$24^{+9}_{-7}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$1.9^{+1.0}_{-0.9}$| | |$1.9^{+1.0}_{-0.9}$| |
| 1.0 | 1000 | 0.04 | 0.01 | 0.02 | 2 | |$135^{+180}_{-89}$| | |$93^{+124}_{-62}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.7^{+10.6}_{-5.7}$| | |$7.5^{+10.3}_{-5.6}$| |
| 1.4 | 1000 | 0.04 | 0.03 | 0.04 | 4 | |$154^{+122}_{-75}$| | |$100^{+80}_{-48}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$8.8^{+7.6}_{-5.2}$| | |$8.1^{+7.0}_{-4.8}$| |
| 2.1 | 1000 | 0.04 | 0.04 | 0.06 | 5 | |$115^{+78}_{-50}$| | |$77^{+53}_{-34}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.6^{+5.0}_{-3.6}$| | |$6.3^{+4.7}_{-3.4}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 6 | |$108^{+65}_{-43}$| | |$72^{+43}_{-29}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+4.2}_{-3.2}$| | |$5.8^{+4.0}_{-3.0}$| |
| 4.1 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$105^{+63}_{-42}$| | |$70^{+42}_{-28}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.0^{+4.1}_{-3.1}$| | |$5.7^{+3.9}_{-3.0}$| |
| 5.7 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$104^{+63}_{-42}$| | |$70^{+42}_{-28}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.0^{+4.1}_{-3.1}$| | |$5.6^{+3.9}_{-2.9}$| |
| 7.8 | 1000 | 0.04 | 0.07 | 0.10 | 6 | |$91^{+54}_{-36}$| | |$62^{+37}_{-25}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$5.2^{+3.6}_{-2.7}$| | |$5.0^{+3.4}_{-2.6}$| |
| 10.7 | 1000 | 0.04 | 0.08 | 0.12 | 6 | |$77^{+46}_{-31}$| | |$52^{+31}_{-21}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.4^{+3.0}_{-2.3}$| | |$4.2^{+2.9}_{-2.2}$| |
| 14.8 | 1000 | 0.04 | 0.09 | 0.14 | 7 | |$76^{+41}_{-28}$| | |$52^{+28}_{-19}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.3^{+2.7}_{-2.2}$| | |$4.2^{+2.7}_{-2.1}$| |
| 20.3 | 1000 | 0.04 | 0.11 | 0.16 | 7 | |$64^{+35}_{-24}$| | |$44^{+24}_{-16}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.7^{+2.3}_{-1.8}$| | |$3.6^{+2.3}_{-1.8}$| |
| 27.9 | 1000 | 0.04 | 0.12 | 0.17 | 7 | |$59^{+32}_{-22}$| | |$41^{+22}_{-15}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.4^{+2.1}_{-1.7}$| | |$3.3^{+2.1}_{-1.6}$| |
| 38.4 | 1000 | 0.04 | 0.15 | 0.22 | 8 | |$53^{+26}_{-19}$| | |$37^{+18}_{-13}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.1^{+1.8}_{-1.5}$| | |$3.0^{+1.8}_{-1.4}$| |
| 52.9 | 1000 | 0.04 | 0.17 | 0.24 | 8 | |$47^{+23}_{-16}$| | |$33^{+16}_{-11}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.7^{+1.6}_{-1.3}$| | |$2.7^{+1.6}_{-1.3}$| |
| 72.7 | 1000 | 0.04 | 0.19 | 0.28 | 8 | |$41^{+21}_{-14}$| | |$29^{+14}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.4^{+1.4}_{-1.1}$| | |$2.3^{+1.4}_{-1.1}$| |
| 100.0 | 1000 | 0.04 | 0.24 | 0.35 | 10 | |$41^{+18}_{-13}$| | |$29^{+12}_{-9}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.3^{+1.3}_{-1.1}$| | |$2.3^{+1.3}_{-1.1}$| |
| 3.0 | 1000 | 0.03 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.06 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.07 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.08 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.09 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.10 | 0.06 | 0.09 | 5 | |$88^{+60}_{-38}$| | |$59^{+40}_{-26}$| | |$14^{+11}_{-7}$| | |$10^{+8}_{-5}$| | |$6.2^{+5.8}_{-4.8}$| | |$5.8^{+5.4}_{-4.5}$| |
| 3.0 | 1000 | 0.11 | 0.06 | 0.09 | 5 | |$88^{+60}_{-38}$| | |$59^{+40}_{-26}$| | |$11^{+10}_{-6}$| | |$8^{+7}_{-4}$| | |$8.2^{+8.4}_{-7.3}$| | |$7.7^{+7.9}_{-6.8}$| |
| 3.0 | 1000 | 0.12 | 0.06 | 0.09 | 4 | |$71^{+56}_{-34}$| | |$47^{+37}_{-23}$| | |$11^{+10}_{-6}$| | |$8^{+7}_{-4}$| | |$6.6^{+7.3}_{-6.0}$| | |$6.1^{+6.8}_{-5.6}$| |
| 3.0 | 1000 | 0.14 | 0.06 | 0.09 | 4 | |$71^{+56}_{-34}$| | |$47^{+37}_{-23}$| | |$7^{+9}_{-5}$| | |$5^{+7}_{-3}$| | |$9.9^{+12.6}_{-9.9}$| | |$9.2^{+11.7}_{-9.2}$| |
| 3.0 | 1000 | 0.16 | 0.06 | 0.09 | 2 | |$35^{+47}_{-23}$| | |$24^{+31}_{-16}$| | |$4^{+8}_{-3}$| | |$3^{+6}_{-2}$| | |$9.9^{+20.5}_{-9.9}$| | |$9.2^{+19.1}_{-9.2}$| |
| 3.0 | 1000 | 0.18 | 0.06 | 0.09 | 2 | |$35^{+47}_{-23}$| | |$24^{+31}_{-16}$| | |$4^{+8}_{-3}$| | |$3^{+6}_{-2}$| | |$9.9^{+20.5}_{-9.9}$| | |$9.2^{+19.1}_{-9.2}$| |
| 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 | 4 | |$130^{+103}_{-63}$| | |$86^{+69}_{-42}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.4^{+6.4}_{-4.4}$| | |$7.0^{+6.0}_{-4.1}$| |
| 3.0 | 630 | 0.04 | 0.04 | 0.06 | 4 | |$106^{+85}_{-52}$| | |$71^{+56}_{-34}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+5.2}_{-3.6}$| | |$5.7^{+4.9}_{-3.4}$| |
| 3.0 | 794 | 0.04 | 0.05 | 0.07 | 6 | |$131^{+78}_{-52}$| | |$87^{+52}_{-35}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.5^{+5.1}_{-3.9}$| | |$7.0^{+4.8}_{-3.7}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 6 | |$108^{+65}_{-43}$| | |$72^{+43}_{-29}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+4.2}_{-3.2}$| | |$5.8^{+4.0}_{-3.0}$| |
| 3.0 | 1313 | 0.04 | 0.07 | 0.11 | 6 | |$84^{+50}_{-33}$| | |$56^{+34}_{-22}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.8^{+3.3}_{-2.5}$| | |$4.5^{+3.1}_{-2.4}$| |
| 3.0 | 1724 | 0.04 | 0.09 | 0.13 | 6 | |$66^{+40}_{-26}$| | |$44^{+27}_{-18}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.8^{+2.6}_{-2.0}$| | |$3.6^{+2.5}_{-1.9}$| |
| 3.0 | 2264 | 0.04 | 0.12 | 0.17 | 7 | |$61^{+33}_{-23}$| | |$41^{+22}_{-15}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.5^{+2.2}_{-1.7}$| | |$3.3^{+2.1}_{-1.7}$| |
| 3.0 | 2972 | 0.04 | 0.14 | 0.21 | 7 | |$50^{+27}_{-19}$| | |$34^{+18}_{-13}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.9^{+1.8}_{-1.4}$| | |$2.7^{+1.7}_{-1.4}$| |
| 3.0 | 3903 | 0.04 | 0.16 | 0.24 | 8 | |$49^{+24}_{-17}$| | |$33^{+16}_{-11}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.8^{+1.7}_{-1.3}$| | |$2.6^{+1.6}_{-1.3}$| |
| 3.0 | 5125 | 0.04 | 0.18 | 0.27 | 8 | |$44^{+22}_{-15}$| | |$30^{+15}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.5^{+1.5}_{-1.2}$| | |$2.4^{+1.4}_{-1.2}$| |
| 3.0 | 6729 | 0.04 | 0.19 | 0.28 | 8 | |$41^{+20}_{-14}$| | |$28^{+14}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.4^{+1.4}_{-1.1}$| | |$2.3^{+1.4}_{-1.1}$| |
| 3.0 | 8835 | 0.04 | 0.22 | 0.32 | 8 | |$37^{+18}_{-13}$| | |$25^{+13}_{-9}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.1^{+1.3}_{-1.0}$| | |$2.0^{+1.2}_{-1.0}$| |
| 3.0 | 11601 | 0.04 | 0.25 | 0.36 | 9 | |$36^{+16}_{-12}$| | |$25^{+11}_{-8}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.0^{+1.2}_{-1.0}$| | |$2.0^{+1.1}_{-0.9}$| |
| 3.0 | 15232 | 0.04 | 0.30 | 0.42 | 10 | |$34^{+14}_{-11}$| | |$24^{+10}_{-7}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$1.9^{+1.1}_{-0.9}$| | |$1.9^{+1.0}_{-0.9}$| |
| 3.0 | 20000 | 0.04 | 0.33 | 0.47 | 11 | |$33^{+13}_{-10}$| | |$24^{+9}_{-7}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$1.9^{+1.0}_{-0.9}$| | |$1.9^{+1.0}_{-0.9}$| |
| 1.0 | 1000 | 0.04 | 0.01 | 0.02 | 2 | |$135^{+180}_{-89}$| | |$93^{+124}_{-62}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$7.7^{+10.6}_{-5.7}$| | |$7.5^{+10.3}_{-5.6}$| |
| 1.4 | 1000 | 0.04 | 0.03 | 0.04 | 4 | |$154^{+122}_{-75}$| | |$100^{+80}_{-48}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$8.8^{+7.6}_{-5.2}$| | |$8.1^{+7.0}_{-4.8}$| |
| 2.1 | 1000 | 0.04 | 0.04 | 0.06 | 5 | |$115^{+78}_{-50}$| | |$77^{+53}_{-34}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.6^{+5.0}_{-3.6}$| | |$6.3^{+4.7}_{-3.4}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.08 | 6 | |$108^{+65}_{-43}$| | |$72^{+43}_{-29}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.1^{+4.2}_{-3.2}$| | |$5.8^{+4.0}_{-3.0}$| |
| 4.1 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$105^{+63}_{-42}$| | |$70^{+42}_{-28}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.0^{+4.1}_{-3.1}$| | |$5.7^{+3.9}_{-3.0}$| |
| 5.7 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$104^{+63}_{-42}$| | |$70^{+42}_{-28}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$6.0^{+4.1}_{-3.1}$| | |$5.6^{+3.9}_{-2.9}$| |
| 7.8 | 1000 | 0.04 | 0.07 | 0.10 | 6 | |$91^{+54}_{-36}$| | |$62^{+37}_{-25}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$5.2^{+3.6}_{-2.7}$| | |$5.0^{+3.4}_{-2.6}$| |
| 10.7 | 1000 | 0.04 | 0.08 | 0.12 | 6 | |$77^{+46}_{-31}$| | |$52^{+31}_{-21}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.4^{+3.0}_{-2.3}$| | |$4.2^{+2.9}_{-2.2}$| |
| 14.8 | 1000 | 0.04 | 0.09 | 0.14 | 7 | |$76^{+41}_{-28}$| | |$52^{+28}_{-19}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$4.3^{+2.7}_{-2.2}$| | |$4.2^{+2.7}_{-2.1}$| |
| 20.3 | 1000 | 0.04 | 0.11 | 0.16 | 7 | |$64^{+35}_{-24}$| | |$44^{+24}_{-16}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.7^{+2.3}_{-1.8}$| | |$3.6^{+2.3}_{-1.8}$| |
| 27.9 | 1000 | 0.04 | 0.12 | 0.17 | 7 | |$59^{+32}_{-22}$| | |$41^{+22}_{-15}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.4^{+2.1}_{-1.7}$| | |$3.3^{+2.1}_{-1.6}$| |
| 38.4 | 1000 | 0.04 | 0.15 | 0.22 | 8 | |$53^{+26}_{-19}$| | |$37^{+18}_{-13}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$3.1^{+1.8}_{-1.5}$| | |$3.0^{+1.8}_{-1.4}$| |
| 52.9 | 1000 | 0.04 | 0.17 | 0.24 | 8 | |$47^{+23}_{-16}$| | |$33^{+16}_{-11}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.7^{+1.6}_{-1.3}$| | |$2.7^{+1.6}_{-1.3}$| |
| 72.7 | 1000 | 0.04 | 0.19 | 0.28 | 8 | |$41^{+21}_{-14}$| | |$29^{+14}_{-10}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.4^{+1.4}_{-1.1}$| | |$2.3^{+1.4}_{-1.1}$| |
| 100.0 | 1000 | 0.04 | 0.24 | 0.35 | 10 | |$41^{+18}_{-13}$| | |$29^{+12}_{-9}$| | |$18^{+13}_{-10}$| | |$12^{+9}_{-7}$| | |$2.3^{+1.3}_{-1.1}$| | |$2.3^{+1.3}_{-1.1}$| |
| 3.0 | 1000 | 0.03 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.04 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.05 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.06 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.07 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.08 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.09 | 0.06 | 0.09 | 6 | |$106^{+63}_{-42}$| | |$71^{+42}_{-28}$| | |$18^{+12}_{-8}$| | |$13^{+9}_{-6}$| | |$5.9^{+4.9}_{-4.1}$| | |$5.5^{+4.5}_{-3.8}$| |
| 3.0 | 1000 | 0.10 | 0.06 | 0.09 | 5 | |$88^{+60}_{-38}$| | |$59^{+40}_{-26}$| | |$14^{+11}_{-7}$| | |$10^{+8}_{-5}$| | |$6.2^{+5.8}_{-4.8}$| | |$5.8^{+5.4}_{-4.5}$| |
| 3.0 | 1000 | 0.11 | 0.06 | 0.09 | 5 | |$88^{+60}_{-38}$| | |$59^{+40}_{-26}$| | |$11^{+10}_{-6}$| | |$8^{+7}_{-4}$| | |$8.2^{+8.4}_{-7.3}$| | |$7.7^{+7.9}_{-6.8}$| |
| 3.0 | 1000 | 0.12 | 0.06 | 0.09 | 4 | |$71^{+56}_{-34}$| | |$47^{+37}_{-23}$| | |$11^{+10}_{-6}$| | |$8^{+7}_{-4}$| | |$6.6^{+7.3}_{-6.0}$| | |$6.1^{+6.8}_{-5.6}$| |
| 3.0 | 1000 | 0.14 | 0.06 | 0.09 | 4 | |$71^{+56}_{-34}$| | |$47^{+37}_{-23}$| | |$7^{+9}_{-5}$| | |$5^{+7}_{-3}$| | |$9.9^{+12.6}_{-9.9}$| | |$9.2^{+11.7}_{-9.2}$| |
| 3.0 | 1000 | 0.16 | 0.06 | 0.09 | 2 | |$35^{+47}_{-23}$| | |$24^{+31}_{-16}$| | |$4^{+8}_{-3}$| | |$3^{+6}_{-2}$| | |$9.9^{+20.5}_{-9.9}$| | |$9.2^{+19.1}_{-9.2}$| |
| 3.0 | 1000 | 0.18 | 0.06 | 0.09 | 2 | |$35^{+47}_{-23}$| | |$24^{+31}_{-16}$| | |$4^{+8}_{-3}$| | |$3^{+6}_{-2}$| | |$9.9^{+20.5}_{-9.9}$| | |$9.2^{+19.1}_{-9.2}$| |
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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