Table 1. Open in new tab Fit parameters...

R²

Spearman r

LoM-50

|$\log _{10} P_{\rm birth}/(\, {\rm K}\, {\rm cm}^{-3})$|

0.12 ± 0.00

−0.69 ± 0.02

0.96

0.99

<0.01

|$\log _{10}\sigma _e/(\, {\rm km}\, {\rm s}^{-1})$|

0.22 ± 0.05

−0.52 ± 0.11

0.22

0.48

<0.01

log₁₀Age/Gyr

0.34 ± 0.06

−0.32 ± 0.05

0.32

0.61

<0.01

log₁₀Z/Z_⊙

−0.18 ± 0.08

0.01 ± 0.02

0.08

−0.22

0.07

[Mg/Fe]

0.16 ± 0.10

−0.02 ± 0.01

0.04

0.21

0.09

log₁₀r_e/kpc

−0.04 ± 0.04

−0.01 ± 0.02

0.02

−0.06

0.65

log₁₀M_⋆,Chab

0.08 ± 0.03

−0.92 ± 0.29

0.12

0.38

<0.01

M_K − 5log₁₀h

−0.02 ± 0.01

−0.53 ± 0.25

0.06

−0.26

0.03

log₁₀M_BH/M_⋆

0.11 ± 0.02

0.31 ± 0.06

0.34

0.46

<0.01

|$\log _{10} \sigma _e^2/r_e\ [{\rm km^2\, s^{-2}\, kpc^{-1}}]$|

0.15 ± 0.02

−0.59 ± 0.09

0.37

0.56

<0.01

HiM-50

|$\log _{10} P_{\rm birth}/(\, {\rm K}\, {\rm cm}^{-3})$|

0.07 ± 0.01

−0.51 ± 0.03

0.87

0.91

<0.01

|$\log _{10}\sigma _e/(\, {\rm km}\, {\rm s}^{-1})$|

0.19 ± 0.08

−0.52 ± 0.15

0.18

0.48

<0.01

log₁₀Age/Gyr

0.34 ± 0.06

−0.38 ± 0.04

0.53

0.68

<0.01

log₁₀Z/Z_⊙

0.13 ± 0.06

−0.22 ± 0.04

0.15

0.39

0.04

[Mg/Fe]

0.39 ± 0.05

−0.19 ± 0.01

0.72

0.81

<0.01

log₁₀r_e/kpc

0.12 ± 0.08

−0.24 ± 0.06

0.09

0.24

0.21

log₁₀M_⋆,Chab

0.09 ± 0.04

−1.10 ± 0.40

0.17

0.36

0.06

M_K − 5log₁₀h

−0.02 ± 0.02

−0.66 ± 0.34

0.08

−0.21

0.26

log₁₀M_BH/M_⋆

−0.01 ± 0.02

−0.16 ± 0.06

<0.01

0.24

0.21

|$\log _{10} \sigma _e^2/r_e\ [{\rm km^2\, s^{-2}\, kpc^{-1}}]$|

0.08 ± 0.05

−0.40 ± 0.15

0.10

0.36

0.06

Table 1.

Open in new tab

Fit parameters to the r-band mass-to-light ratio excess, MLE_r, for mock C13 galaxies in our variable IMF simulations. Columns 2 and 3 show the result of a linear least-squares fit of the relation between each parameter (indicated in Column 1) individually and MLE_r, of the form MLE_r = ax + b. Column 4 shows the coefficient of determination, while columns 5 and 6 show the Spearman-r value and the corresponding p-value.

x	a	b	R²	Spearman r	p
LoM-50
\|$\log _{10} P_{\rm birth}/(\, {\rm K}\, {\rm cm}^{-3})$\|	0.12 ± 0.00	−0.69 ± 0.02	0.96	0.99	<0.01
\|$\log _{10}\sigma _e/(\, {\rm km}\, {\rm s}^{-1})$\|	0.22 ± 0.05	−0.52 ± 0.11	0.22	0.48	<0.01
log₁₀Age/Gyr	0.34 ± 0.06	−0.32 ± 0.05	0.32	0.61	<0.01
log₁₀Z/Z_⊙	−0.18 ± 0.08	0.01 ± 0.02	0.08	−0.22	0.07
[Mg/Fe]	0.16 ± 0.10	−0.02 ± 0.01	0.04	0.21	0.09
log₁₀r_e/kpc	−0.04 ± 0.04	−0.01 ± 0.02	0.02	−0.06	0.65
log₁₀M_⋆,Chab	0.08 ± 0.03	−0.92 ± 0.29	0.12	0.38	<0.01
M_K − 5log₁₀h	−0.02 ± 0.01	−0.53 ± 0.25	0.06	−0.26	0.03
log₁₀M_BH/M_⋆	0.11 ± 0.02	0.31 ± 0.06	0.34	0.46	<0.01
\|$\log _{10} \sigma _e^2/r_e\ [{\rm km^2\, s^{-2}\, kpc^{-1}}]$\|	0.15 ± 0.02	−0.59 ± 0.09	0.37	0.56	<0.01
HiM-50
\|$\log _{10} P_{\rm birth}/(\, {\rm K}\, {\rm cm}^{-3})$\|	0.07 ± 0.01	−0.51 ± 0.03	0.87	0.91	<0.01
\|$\log _{10}\sigma _e/(\, {\rm km}\, {\rm s}^{-1})$\|	0.19 ± 0.08	−0.52 ± 0.15	0.18	0.48	<0.01
log₁₀Age/Gyr	0.34 ± 0.06	−0.38 ± 0.04	0.53	0.68	<0.01
log₁₀Z/Z_⊙	0.13 ± 0.06	−0.22 ± 0.04	0.15	0.39	0.04
[Mg/Fe]	0.39 ± 0.05	−0.19 ± 0.01	0.72	0.81	<0.01
log₁₀r_e/kpc	0.12 ± 0.08	−0.24 ± 0.06	0.09	0.24	0.21
log₁₀M_⋆,Chab	0.09 ± 0.04	−1.10 ± 0.40	0.17	0.36	0.06
M_K − 5log₁₀h	−0.02 ± 0.02	−0.66 ± 0.34	0.08	−0.21	0.26
log₁₀M_BH/M_⋆	−0.01 ± 0.02	−0.16 ± 0.06	<0.01	0.24	0.21
\|$\log _{10} \sigma _e^2/r_e\ [{\rm km^2\, s^{-2}\, kpc^{-1}}]$\|	0.08 ± 0.05	−0.40 ± 0.15	0.10	0.36	0.06

x	a	b	R²	Spearman r	p
LoM-50
\|$\log _{10} P_{\rm birth}/(\, {\rm K}\, {\rm cm}^{-3})$\|	0.12 ± 0.00	−0.69 ± 0.02	0.96	0.99	<0.01
\|$\log _{10}\sigma _e/(\, {\rm km}\, {\rm s}^{-1})$\|	0.22 ± 0.05	−0.52 ± 0.11	0.22	0.48	<0.01
log₁₀Age/Gyr	0.34 ± 0.06	−0.32 ± 0.05	0.32	0.61	<0.01
log₁₀Z/Z_⊙	−0.18 ± 0.08	0.01 ± 0.02	0.08	−0.22	0.07
[Mg/Fe]	0.16 ± 0.10	−0.02 ± 0.01	0.04	0.21	0.09
log₁₀r_e/kpc	−0.04 ± 0.04	−0.01 ± 0.02	0.02	−0.06	0.65
log₁₀M_⋆,Chab	0.08 ± 0.03	−0.92 ± 0.29	0.12	0.38	<0.01
M_K − 5log₁₀h	−0.02 ± 0.01	−0.53 ± 0.25	0.06	−0.26	0.03
log₁₀M_BH/M_⋆	0.11 ± 0.02	0.31 ± 0.06	0.34	0.46	<0.01
\|$\log _{10} \sigma _e^2/r_e\ [{\rm km^2\, s^{-2}\, kpc^{-1}}]$\|	0.15 ± 0.02	−0.59 ± 0.09	0.37	0.56	<0.01
HiM-50
\|$\log _{10} P_{\rm birth}/(\, {\rm K}\, {\rm cm}^{-3})$\|	0.07 ± 0.01	−0.51 ± 0.03	0.87	0.91	<0.01
\|$\log _{10}\sigma _e/(\, {\rm km}\, {\rm s}^{-1})$\|	0.19 ± 0.08	−0.52 ± 0.15	0.18	0.48	<0.01
log₁₀Age/Gyr	0.34 ± 0.06	−0.38 ± 0.04	0.53	0.68	<0.01
log₁₀Z/Z_⊙	0.13 ± 0.06	−0.22 ± 0.04	0.15	0.39	0.04
[Mg/Fe]	0.39 ± 0.05	−0.19 ± 0.01	0.72	0.81	<0.01
log₁₀r_e/kpc	0.12 ± 0.08	−0.24 ± 0.06	0.09	0.24	0.21
log₁₀M_⋆,Chab	0.09 ± 0.04	−1.10 ± 0.40	0.17	0.36	0.06
M_K − 5log₁₀h	−0.02 ± 0.02	−0.66 ± 0.34	0.08	−0.21	0.26
log₁₀M_BH/M_⋆	−0.01 ± 0.02	−0.16 ± 0.06	<0.01	0.24	0.21
\|$\log _{10} \sigma _e^2/r_e\ [{\rm km^2\, s^{-2}\, kpc^{-1}}]$\|	0.08 ± 0.05	−0.40 ± 0.15	0.10	0.36	0.06

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