The [C II] line emission as an interstellar medium probe in the MARIGOLD galaxies

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Table 5.

Coefficients for the PCA-based prescriptions for estimating the molecular gas mass at different redshifts.

z	a	b	c	d	e	1 σ dispersion (dex)
						PCA	M_mol–L_[C II]	PCA ^( * )	M_mol– $L_{[C I I]}^{()}$ $L_{[\mathrm{C}{\small { {\text{ II}}}}]}\,^{()}$
PCA: $M_{mol} - L_{[C I I]} - {SFR}_{5} - {SFR}_{200} - Z$ $M_{\mathrm{mol}}{-}L_{[\mathrm{C}{\small { {\text{ II}}}}]}{-}{\mathrm{SFR}_{5}}{-}{\mathrm{SFR}_{200}}{-}Z$

7	0.50 ± 0.15	0.79 ± 0.08	−0.16 ± 0.31	+0.04 ± 0.26	4.39 ± 2.80	0.20	0.45	0.28	0.47
6	0.42 ± 0.08	0.73 ± 0.02	−0.02 ± 0.10	−0.03 ± 0.07	5.46 ± 0.87	0.17	0.41	0.24	0.42
5	0.45 ± 0.04	0.65 ± 0.01	−0.00 ± 0.04	−0.03 ± 0.03	5.27 ± 0.35	0.13	0.36	0.20	0.37
4	0.47 ± 0.03	0.59 ± 0.01	+0.01 ± 0.03	+0.09 ± 0.02	4.11 ± 0.26	0.13	0.30	0.20	0.32
3	0.57 ± 0.02	0.59 ± 0.01	−0.06 ± 0.02	+0.13 ± 0.02	3.12 ± 0.17	0.11	0.25	0.19	0.28

PCA: $M_{mol} - L_{[C I I]} - {SFR}_{5}$ $M_{\mathrm{mol}}{-}L_{[\mathrm{C}{\small { {\text{ II}}}}]}{-}{\mathrm{SFR}_{5}}$

7	0.41 ± 0.03	0.76 ± 0.02	–	–	5.33 ± 0.17	0.20	0.45	0.28	0.47
6	0.40 ± 0.02	0.73 ± 0.02	–	–	5.41 ± 0.14	0.17	0.41	0.25	0.42
5	0.44 ± 0.01	0.65 ± 0.01	–	–	5.13 ± 0.08	0.13	0.36	0.21	0.37
4	0.52 ± 0.01	0.59 ± 0.01	–	–	4.49 ± 0.08	0.13	0.30	0.20	0.32
3	0.57 ± 0.01	0.58 ± 0.01	–	–	4.17 ± 0.08	0.11	0.25	0.19	0.28

Notes. We use the general expression: $\log (M_{mol} / M_{⊙}) = a \log (L_{[C I I]} / L_{⊙}) + b \log ({SFR}_{5} / M_{⊙} {yr}^{- 1}) + c \log ({SFR}_{200} / M_{⊙} {yr}^{- 1}) + d [12 + \log (O / H)] + e$ $\mathrm{log} (M_{\mathrm{mol}}/{\mathrm{M_{\odot}}}) = a \, \mathrm{log} (L_{[\mathrm{C}{\small { {\text{ II}}}}]}/\mathrm{L_{\odot}}) + b \,\mathrm{log} ({\mathrm{SFR}}_{5}/{\mathrm{M_{\odot} \, yr^{-1}}}) + c \,\mathrm{log} ({\mathrm{SFR}}_{200}/{\mathrm{M_{\odot} \, yr^{-1}}}) + d \, [\mathrm{12+log(O/H)}] + e$ . We also include results obtained for two simpler 3-variable PCA using M_mol, L_[C II], and SFR₅. Errors on the coefficients are obtained from bootstrapping with replacement with a 1000 iterations. The seventh and eighth columns enlist the standard deviation of the offset between the true and predicted M_mol when using the PCA-based and the best fit M_mol–L_[C II] relations, respectively (see Fig. 12), while the last two (denoted by a ( * )) enlist the same when accounting for typical observational uncertainties (see text).

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