Table 3. Open in new tab Priors and...

		NB816	NB921
Parameter	Prior
log M_c/(h⁻¹ M_⊙)	None	11.75	\|$12.04^{+0.57}_{-0.32}$\|	11.93	\|$11.91^{+ 0.19} _{- 0.18}$\|
log M_min/(h⁻¹ M_⊙)	None	12.46	\|$12.61^{+0.32}_{-0.43}$\|	12.47	\|$12.57^{+0.29}_{-0.35}$\|
σ_log M	[0,1]	0.06	\|$0.40^{+0.28}_{-0.31}$\|	0.13	\|$0.17^{+ 0.15}_{- 0.10}$\|
α	1.00 ± 0.20	1.06	\|$1.03^{+0.12}_{-0.13}$\|	1.23	\|$1.12^{+ 0.13}_{- 0.12}$\|
\|$F_c^A$\|	[0, 0.5]	0.13	\|$0.26^{+0.16}_{-0.12}$\|	0.14	\|$0.26^{+ 0.15}_{- 0.13}$\|
\|$F_c^B$\|	[0,1]	0.95	\|$0.37^{+0.39}_{-0.28}$\|	0.90	\|$0.53^{+ 0.32}_{- 0.34}$\|
F_s	[0, 1]	0.98	\|$0.54^{+0.31}_{-0.34}$\|	0.73	\|$0.55^{+ 0.31}_{- 0.33}$\|
f_fake	0.140 ± 0.060	0.172	\|$0.140^{+0.048}_{-0.053}$\|	0.128	\|$0.104^{+ 0.043}_{- 0.041}$\|
χ²/ν (ν = 7)		2.17		0.856
Inferred quantity	Measurement
log n_g/(h⁻¹ Mpc)⁻³	−2.259 ± 0.068 (NB816)	−2.313	\|$-2.316^{+0.071}_{-0.073}$\|	−2.401	\|$-2.381^{+0.074}_{-0.073}$\|
	−2.344 ± 0.070 (NB921)
f_sat	—	0.308	\|$0.159^{+0.120}_{-0.047}$\|	0.242	\|$0.159^{ + 0.109}_{ - 0.049}$\|
b_eff	—	1.797	\|$1.700^{+0.084}_{-0.111}$\|	2.029	\|$1.981^{+0.072}_{-0.068}$\|
log M_eff/(h⁻¹ M_⊙)	—	12.831	\|$12.703^{+0.093}_{-0.071}$\|	12.699	\|$12.609^{+0.085}_{-0.051}$\|

NB816

NB921

Best fit

Posterior PDF

Best fit

Posterior PDF

Parameter

Prior

log M_c/(h⁻¹ M_⊙)

None

11.75

|$12.04^{+0.57}_{-0.32}$|

11.93

|$11.91^{+ 0.19} _{- 0.18}$|

log M_min/(h⁻¹ M_⊙)

None

12.46

|$12.61^{+0.32}_{-0.43}$|

12.47

|$12.57^{+0.29}_{-0.35}$|

σ_log M

[0,1]

0.06

|$0.40^{+0.28}_{-0.31}$|

0.13

|$0.17^{+ 0.15}_{- 0.10}$|

1.00 ± 0.20

1.06

|$1.03^{+0.12}_{-0.13}$|

1.23

|$1.12^{+ 0.13}_{- 0.12}$|

|$F_c^A$|

[0, 0.5]

0.13

|$0.26^{+0.16}_{-0.12}$|

0.14

|$0.26^{+ 0.15}_{- 0.13}$|

|$F_c^B$|

[0,1]

0.95

|$0.37^{+0.39}_{-0.28}$|

0.90

|$0.53^{+ 0.32}_{- 0.34}$|

F_s

[0, 1]

0.98

|$0.54^{+0.31}_{-0.34}$|

0.73

|$0.55^{+ 0.31}_{- 0.33}$|

f_fake

0.140 ± 0.060

0.172

|$0.140^{+0.048}_{-0.053}$|

0.128

|$0.104^{+ 0.043}_{- 0.041}$|

χ²/ν (ν = 7)

2.17

0.856

Inferred quantity

Measurement

log n_g/(h⁻¹ Mpc)⁻³

−2.259 ± 0.068 (NB816)

−2.313

|$-2.316^{+0.071}_{-0.073}$|

−2.401

|$-2.381^{+0.074}_{-0.073}$|

−2.344 ± 0.070 (NB921)

f_sat

—

0.308

|$0.159^{+0.120}_{-0.047}$|

0.242

|$0.159^{ + 0.109}_{ - 0.049}$|

b_eff

—

1.797

|$1.700^{+0.084}_{-0.111}$|

2.029

|$1.981^{+0.072}_{-0.068}$|

log M_eff/(h⁻¹ M_⊙)

—

12.831

|$12.703^{+0.093}_{-0.071}$|

12.699

|$12.609^{+0.085}_{-0.051}$|

		NB816	NB921
Parameter	Prior
log M_c/(h⁻¹ M_⊙)	None	11.75	\|$12.04^{+0.57}_{-0.32}$\|	11.93	\|$11.91^{+ 0.19} _{- 0.18}$\|
log M_min/(h⁻¹ M_⊙)	None	12.46	\|$12.61^{+0.32}_{-0.43}$\|	12.47	\|$12.57^{+0.29}_{-0.35}$\|
σ_log M	[0,1]	0.06	\|$0.40^{+0.28}_{-0.31}$\|	0.13	\|$0.17^{+ 0.15}_{- 0.10}$\|
α	1.00 ± 0.20	1.06	\|$1.03^{+0.12}_{-0.13}$\|	1.23	\|$1.12^{+ 0.13}_{- 0.12}$\|
\|$F_c^A$\|	[0, 0.5]	0.13	\|$0.26^{+0.16}_{-0.12}$\|	0.14	\|$0.26^{+ 0.15}_{- 0.13}$\|
\|$F_c^B$\|	[0,1]	0.95	\|$0.37^{+0.39}_{-0.28}$\|	0.90	\|$0.53^{+ 0.32}_{- 0.34}$\|
F_s	[0, 1]	0.98	\|$0.54^{+0.31}_{-0.34}$\|	0.73	\|$0.55^{+ 0.31}_{- 0.33}$\|
f_fake	0.140 ± 0.060	0.172	\|$0.140^{+0.048}_{-0.053}$\|	0.128	\|$0.104^{+ 0.043}_{- 0.041}$\|
χ²/ν (ν = 7)		2.17		0.856
Inferred quantity	Measurement
log n_g/(h⁻¹ Mpc)⁻³	−2.259 ± 0.068 (NB816)	−2.313	\|$-2.316^{+0.071}_{-0.073}$\|	−2.401	\|$-2.381^{+0.074}_{-0.073}$\|
	−2.344 ± 0.070 (NB921)
f_sat	—	0.308	\|$0.159^{+0.120}_{-0.047}$\|	0.242	\|$0.159^{ + 0.109}_{ - 0.049}$\|
b_eff	—	1.797	\|$1.700^{+0.084}_{-0.111}$\|	2.029	\|$1.981^{+0.072}_{-0.068}$\|
log M_eff/(h⁻¹ M_⊙)	—	12.831	\|$12.703^{+0.093}_{-0.071}$\|	12.699	\|$12.609^{+0.085}_{-0.051}$\|

Table 3.

Open in new tab

Priors and constraints of the HOD parameters for the Geach model.*

		NB816		NB921
		Best fit	Posterior PDF	Best fit	Posterior PDF
Parameter	Prior
log M_c/(h⁻¹ M_⊙)	None	11.75	\|$12.04^{+0.57}_{-0.32}$\|	11.93	\|$11.91^{+ 0.19} _{- 0.18}$\|
log M_min/(h⁻¹ M_⊙)	None	12.46	\|$12.61^{+0.32}_{-0.43}$\|	12.47	\|$12.57^{+0.29}_{-0.35}$\|
σ_log M	[0,1]	0.06	\|$0.40^{+0.28}_{-0.31}$\|	0.13	\|$0.17^{+ 0.15}_{- 0.10}$\|
α	1.00 ± 0.20	1.06	\|$1.03^{+0.12}_{-0.13}$\|	1.23	\|$1.12^{+ 0.13}_{- 0.12}$\|
\|$F_c^A$\|	[0, 0.5]	0.13	\|$0.26^{+0.16}_{-0.12}$\|	0.14	\|$0.26^{+ 0.15}_{- 0.13}$\|
\|$F_c^B$\|	[0,1]	0.95	\|$0.37^{+0.39}_{-0.28}$\|	0.90	\|$0.53^{+ 0.32}_{- 0.34}$\|
F_s	[0, 1]	0.98	\|$0.54^{+0.31}_{-0.34}$\|	0.73	\|$0.55^{+ 0.31}_{- 0.33}$\|
f_fake	0.140 ± 0.060	0.172	\|$0.140^{+0.048}_{-0.053}$\|	0.128	\|$0.104^{+ 0.043}_{- 0.041}$\|
χ²/ν (ν = 7)		2.17		0.856
Inferred quantity	Measurement
log n_g/(h⁻¹ Mpc)⁻³	−2.259 ± 0.068 (NB816)	−2.313	\|$-2.316^{+0.071}_{-0.073}$\|	−2.401	\|$-2.381^{+0.074}_{-0.073}$\|
	−2.344 ± 0.070 (NB921)
f_sat	—	0.308	\|$0.159^{+0.120}_{-0.047}$\|	0.242	\|$0.159^{ + 0.109}_{ - 0.049}$\|
b_eff	—	1.797	\|$1.700^{+0.084}_{-0.111}$\|	2.029	\|$1.981^{+0.072}_{-0.068}$\|
log M_eff/(h⁻¹ M_⊙)	—	12.831	\|$12.703^{+0.093}_{-0.071}$\|	12.699	\|$12.609^{+0.085}_{-0.051}$\|

		NB816		NB921
		Best fit	Posterior PDF	Best fit	Posterior PDF
Parameter	Prior
log M_c/(h⁻¹ M_⊙)	None	11.75	\|$12.04^{+0.57}_{-0.32}$\|	11.93	\|$11.91^{+ 0.19} _{- 0.18}$\|
log M_min/(h⁻¹ M_⊙)	None	12.46	\|$12.61^{+0.32}_{-0.43}$\|	12.47	\|$12.57^{+0.29}_{-0.35}$\|
σ_log M	[0,1]	0.06	\|$0.40^{+0.28}_{-0.31}$\|	0.13	\|$0.17^{+ 0.15}_{- 0.10}$\|
α	1.00 ± 0.20	1.06	\|$1.03^{+0.12}_{-0.13}$\|	1.23	\|$1.12^{+ 0.13}_{- 0.12}$\|
\|$F_c^A$\|	[0, 0.5]	0.13	\|$0.26^{+0.16}_{-0.12}$\|	0.14	\|$0.26^{+ 0.15}_{- 0.13}$\|
\|$F_c^B$\|	[0,1]	0.95	\|$0.37^{+0.39}_{-0.28}$\|	0.90	\|$0.53^{+ 0.32}_{- 0.34}$\|
F_s	[0, 1]	0.98	\|$0.54^{+0.31}_{-0.34}$\|	0.73	\|$0.55^{+ 0.31}_{- 0.33}$\|
f_fake	0.140 ± 0.060	0.172	\|$0.140^{+0.048}_{-0.053}$\|	0.128	\|$0.104^{+ 0.043}_{- 0.041}$\|
χ²/ν (ν = 7)		2.17		0.856
Inferred quantity	Measurement
log n_g/(h⁻¹ Mpc)⁻³	−2.259 ± 0.068 (NB816)	−2.313	\|$-2.316^{+0.071}_{-0.073}$\|	−2.401	\|$-2.381^{+0.074}_{-0.073}$\|
	−2.344 ± 0.070 (NB921)
f_sat	—	0.308	\|$0.159^{+0.120}_{-0.047}$\|	0.242	\|$0.159^{ + 0.109}_{ - 0.049}$\|
b_eff	—	1.797	\|$1.700^{+0.084}_{-0.111}$\|	2.029	\|$1.981^{+0.072}_{-0.068}$\|
log M_eff/(h⁻¹ M_⊙)	—	12.831	\|$12.703^{+0.093}_{-0.071}$\|	12.699	\|$12.609^{+0.085}_{-0.051}$\|

In the “Prior” column the ranges specified in brackets are for uniform priors while for the others we quote the mean and standard deviation of the Gaussian priors. The “Best fit” column shows the parameter set which gives the minimum value of χ². In the “Posterior PDF” column the central value is a median and the error means the 16th–84th percentiles after the other parameters are marginalized over. The measured number density log n_g includes non-[O ii] emitters, and thus its best-fitting values differ from the measure ones by log (1 − f_fake) ∼ −0.06.

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