Table 4: Surface brightness relations using $\it BVR{I}JHK$ based colors: $F_\lambda (C_\lambda - C_1) = a_\lambda (C_\lambda - C_1)+ b_\lambda$ . The 1 $\sigma$ errors in each coefficient are given in superscript, multiplied by 1000 to reduce the length of each line, i.e. -0.2944^2.4 stands for $-0.2944 \pm 0.0024$ . The standard deviation of the residuals $\sigma$ is listed for each SB relation, together with the reduced $\chi ^2$ of the fit and the total number of measurements $N_{\rm meas}$ taken into account (photometric data were unavailable for some stars).
$C_\lambda\ \downarrow$ $C_1\rightarrow B$ V R I J H K

a_B -0.2944^2.4 -0.1978^1.6 -0.1800^0.9 -0.1401^0.8 -0.1224^0.7 -0.1199^0.6

b_B 3.8813^1.1 3.8719^0.9 3.9283^0.6 3.9297^0.8 3.9423^0.8 3.9460^0.7

$\sigma_B / \chi^2_{\rm red}$ 0.017/1.20 0.008/0.46 0.015/1.41 0.015/0.65 0.014/0.63 0.015/0.75

$N_{\rm meas}$ 145 34 119 127 100 128

a_V 0.1956^1.8 -0.3789^10.0 -0.3077^2.4 -0.1759^1.4 -0.1379^1.0 -0.1336^0.8

b_V 3.8828^0.9 3.8516^2.2 3.9617^0.7 3.9407^0.7 3.9490^0.7 3.9530^0.6

$\sigma_V / \chi^2_{\rm red}$ 0.017/1.75 0.014/0.75 0.016/0.89 0.015/0.57 0.014/0.58 0.015/0.70

$N_{\rm meas}$ 145 34 119 127 100 128

a_R 0.0994^1.1 0.2868^8.0 -1.2894^26.4 -0.2240^3.2 -0.1458^1.6 -0.1386^1.5

b_R 3.8746^0.6 3.8554^1.7 4.3248^2.9 3.9532^0.7 3.9426^0.6 3.9430^0.6

$\sigma_R / \chi^2_{\rm red}$ 0.008/0.72 0.015/1.10 0.060/1.19 0.006/0.12 0.005/0.14 0.005/0.18

$N_{\rm meas}$ 34 34 34 34 34 34

a_I 0.0808^0.6 0.2105^1.9 1.8067^38.4 -0.2854^7.1 -0.1713^2.6 -0.1630^2.0

b_I 3.9304^0.4 3.9642^0.5 4.6102^4.3 3.9323^1.7 3.9491^0.9 3.9548^0.8

$\sigma_I / \chi^2_{\rm red}$ 0.015/2.23 0.016/1.37 0.089/1.35 0.013/0.34 0.010/0.40 0.013/0.50

$N_{\rm meas}$ 119 119 34 101 74 102

a_J 0.0399^0.6 0.0753^1.1 0.1243^2.2 0.1877^5.3 -0.2988^10.2 -0.2614^6.8

b_J 3.9295^0.6 3.9403^0.6 3.9536^0.5 3.9335^1.2 3.9679^1.7 3.9722^1.3

$\sigma_J / \chi^2_{\rm red}$ 0.015/0.89 0.015/0.86 0.006/0.20 0.013/0.54 0.015/0.21 0.016/0.29

$N_{\rm meas}$ 127 127 34 101 100 127

a_H 0.0223^0.5 0.0375^0.8 0.0460^1.1 0.0700^1.8 0.2060^7.2 -2.3858^309.8

b_H 3.9422^0.6 3.9487^0.5 3.9428^0.4 3.9480^0.7 3.9710^1.2 4.0653^8.4

$\sigma_H / \chi^2_{\rm red}$ 0.014/0.77 0.014/0.74 0.005/0.22 0.010/0.62 0.015/0.35 0.029/0.03

$N_{\rm meas}$ 100 100 34 74 100 100

a_K 0.0197^0.5 0.0331^0.7 0.0389^1.1 0.0618^1.4 0.1704^4.7 2.7121^354.8

b_K 3.9458^0.5 3.9524^0.5 3.9435^0.4 3.9539^0.5 3.9767^0.9 4.0970^9.6

$\sigma_K / \chi^2_{\rm red}$ 0.015/0.94 0.015/0.92 0.005/0.28 0.012/0.80 0.016/0.51 0.034/0.03

$N_{\rm meas}$ 128 128 34 102 127 100

**Table 4:** Surface brightness relations using $\it BVR{I}JHK$ based colors: $F_\lambda (C_\lambda - C_1) = a_\lambda (C_\lambda - C_1)+ b_\lambda$ . The 1 $\sigma$ errors in each coefficient are given in superscript, *multiplied by 1000* to reduce the length of each line, i.e. -0.2944^2.4 stands for $-0.2944 \pm 0.0024$ . The standard deviation of the residuals $\sigma$ is listed for each SB relation, together with the reduced $\chi ^2$ of the fit and the total number of measurements $N_{\rm meas}$ taken into account (photometric data were unavailable for some stars).
$C_\lambda\ \downarrow$	$C_1\rightarrow B$	V	R	I	J	H	K
a_B		-0.2944^2.4	-0.1978^1.6	-0.1800^0.9	-0.1401^0.8	-0.1224^0.7	-0.1199^0.6
b_B		3.8813^1.1	3.8719^0.9	3.9283^0.6	3.9297^0.8	3.9423^0.8	3.9460^0.7
$\sigma_B / \chi^2_{\rm red}$		0.017/1.20	0.008/0.46	0.015/1.41	0.015/0.65	0.014/0.63	0.015/0.75
$N_{\rm meas}$		145	34	119	127	100	128
a_V	0.1956^1.8		-0.3789^10.0	-0.3077^2.4	-0.1759^1.4	-0.1379^1.0	-0.1336^0.8
b_V	3.8828^0.9		3.8516^2.2	3.9617^0.7	3.9407^0.7	3.9490^0.7	3.9530^0.6
$\sigma_V / \chi^2_{\rm red}$	0.017/1.75		0.014/0.75	0.016/0.89	0.015/0.57	0.014/0.58	0.015/0.70
$N_{\rm meas}$	145		34	119	127	100	128
a_R	0.0994^1.1	0.2868^8.0		-1.2894^26.4	-0.2240^3.2	-0.1458^1.6	-0.1386^1.5
b_R	3.8746^0.6	3.8554^1.7		4.3248^2.9	3.9532^0.7	3.9426^0.6	3.9430^0.6
$\sigma_R / \chi^2_{\rm red}$	0.008/0.72	0.015/1.10		0.060/1.19	0.006/0.12	0.005/0.14	0.005/0.18
$N_{\rm meas}$	34	34		34	34	34	34
a_I	0.0808^0.6	0.2105^1.9	1.8067^38.4		-0.2854^7.1	-0.1713^2.6	-0.1630^2.0
b_I	3.9304^0.4	3.9642^0.5	4.6102^4.3		3.9323^1.7	3.9491^0.9	3.9548^0.8
$\sigma_I / \chi^2_{\rm red}$	0.015/2.23	0.016/1.37	0.089/1.35		0.013/0.34	0.010/0.40	0.013/0.50
$N_{\rm meas}$	119	119	34		101	74	102
a_J	0.0399^0.6	0.0753^1.1	0.1243^2.2	0.1877^5.3		-0.2988^10.2	-0.2614^6.8
b_J	3.9295^0.6	3.9403^0.6	3.9536^0.5	3.9335^1.2		3.9679^1.7	3.9722^1.3
$\sigma_J / \chi^2_{\rm red}$	0.015/0.89	0.015/0.86	0.006/0.20	0.013/0.54		0.015/0.21	0.016/0.29
$N_{\rm meas}$	127	127	34	101		100	127
a_H	0.0223^0.5	0.0375^0.8	0.0460^1.1	0.0700^1.8	0.2060^7.2		-2.3858^309.8
b_H	3.9422^0.6	3.9487^0.5	3.9428^0.4	3.9480^0.7	3.9710^1.2		4.0653^8.4
$\sigma_H / \chi^2_{\rm red}$	0.014/0.77	0.014/0.74	0.005/0.22	0.010/0.62	0.015/0.35		0.029/0.03
$N_{\rm meas}$	100	100	34	74	100		100
a_K	0.0197^0.5	0.0331^0.7	0.0389^1.1	0.0618^1.4	0.1704^4.7	2.7121^354.8
b_K	3.9458^0.5	3.9524^0.5	3.9435^0.4	3.9539^0.5	3.9767^0.9	4.0970^9.6
$\sigma_K / \chi^2_{\rm red}$	0.015/0.94	0.015/0.92	0.005/0.28	0.012/0.80	0.016/0.51	0.034/0.03
$N_{\rm meas}$	128	128	34	102	127	100

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