5.5.1 Relationships with other photometric systems
Author(s): Josep Manel Carrasco, Michele Bellazzini
This section includes some transformations between Gaia photometry and other common photometric systems using Gaia EDR3 data. Hipparcos (ESA 1997), Tycho2 (Høg et al. 2000), SDSS12 (Alam et al. 2015), JohnsonCousins (Stetson 2000), 2MASS (Skrutskie et al. 2006) and GSC2.3 (Lasker et al. 2008) are included here.
Except for the JohnsonCousins system, for which all available sources were used due to its intrinsic quality, for the other systems only those sources with small magnitude error and small excess flux were used for the fitting.
In order to minimise the effect of the photometric noise on the derived relationships, only Gaia EDR3 sources with $$ mag were considered for the crossmatch, and only those with available photometry in all three Gaia passbands and in the external photometric systems were used.
Nevertheless, this dataset is not appropriate for SDSS12 transformations, as SDSS12 sources brighter than 14 mag are saturated. To avoid this problem, for SDSS12 transformations some Gaia EDR3 sources with $$ and only SDSS12 magnitudes fainter than 15 mag were used. For the GSC2.3 transformations, two different fittings were done, one using sources with $\delta \ge 0$, and the other with sources at $$, as the photometric systems in the two celestial hemispheres are somewhat different.
In order to obtain cleaner fittings, some filtering criteria were adopted in the production of the colourcolour diagrams. Detailed information on the filtering to produce the photometric relationships is given in Table 5.4 and Table 5.5.
The polynomial coefficients obtained with the resulting sources are listed in Table 5.6 and Table 5.7. The validity of the relationships derived from these fittings is, of course, only applicable within the colour intervals used to perform the fittings (see Table 5.8).
The photometric relationships derived between Gaia and Hipparcos, Tycho2, SDSS12, JohnsonCousins, 2MASS and GSC2.3 can be seen in Figure 5.20 to Figure 5.29.
The relationships presented here were obtained using preliminary data. Thus, some sources used here for the fitting might have been filtered out in the final production.
The purpose of these relationships is to provide a tool applicable to as wide as possible a population of stars, in order to obtain a crude estimation of their photometry when transforming from one system to another. There are cases in which different populations (particularly M type giants and dwarfs) show different behaviours in the colourcolour diagram. In these cases a single fitting was chosen, namely the one reproducing the most populated group for which the validity of the relationship holds over the widest colour range (M giants in this case). Thus, for many relationships shown here the extension to red colours is only valid for M giants and not for M dwarfs.
Hipparcos filtering  
$$, $e=\frac{{F}_{\mathrm{BP}}+{F}_{\mathrm{RP}}}{{F}_{G}}\le 1.3+0.06{({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})}^{2}$  
$G{H}_{P}=f(BV)$  $$, $$, $$, $BV\ne 0.0$, $$  89 460 sources 
$$  
$G{H}_{P}=f(VI)$  $$, $$, $VI\ne 0.0$, $$  98 910 sources 
$G{H}_{P}=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$, $$, $$, $$  97 800 sources 
${G}_{\mathrm{BP}}{H}_{P}=f(VI)$  $$, $$, $VI\ne 0.0$, $$  97 098 sources 
${G}_{\mathrm{RP}}{H}_{P}=f(VI)$  $$, $$, $VI\ne 0.0$, $$  97 534 sources 
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(VI)$  $$, $$, $VI\ne 0.0$,  96 771 sources 
$$, ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}>(VI)0.5$  
Tycho2 filtering  
$$, $e=\frac{{F}_{\mathrm{BP}}+{F}_{\mathrm{RP}}}{{F}_{G}}\le 1.3+0.06{({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})}^{2}$  
$G{V}_{T}=f({B}_{T}{V}_{T})$  $$, $$, $$  374 697 sources 
$G{V}_{T}\ge 0.3({B}_{T}{V}_{T})0.5$, $$  
$G{V}_{T}=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$, $$, $$, $$  569 238 sources 
$G{B}_{T}=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$, $$, $$, $$  393 188 sources 
${G}_{\mathrm{BP}}{V}_{T}=f({B}_{T}{V}_{T})$  $$, $$, $$  375 086 sources 
${G}_{\mathrm{RP}}{V}_{T}=f({B}_{T}{V}_{T})$  $$, $$, $$  371 974 sources 
${G}_{\mathrm{RP}}{V}_{T}>2.1$  
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f({B}_{T}{V}_{T})$  $$, $$, $$, $$  370 974 sources 
$$  
SDSS12 filtering  
$G>13$ mag, $e\le 1.3+0.06{({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})}^{2}$, cl$=6$ (stars), $$ mag  
$Gg=f(gi)$  $g$, $i>15$ mag, $$  213 563 sources 
$Gr=f(ri)$  $r$, $i>15$ mag, $$,  213 497 sources 
$$  
$Gi=f(ri)$ $r$, $i>15$ mag,  212 293 sources  
$$  
${G}_{\mathrm{BP}}g=f(gi)$  $g$, $i>15$ mag, $$ mag,  34 903 sources 
$$  
${G}_{\mathrm{RP}}g=f(gi)$  $g$, $i>15$ mag, $$ mag  65 207 sources 
$$  
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(gi)$  $g$, $i>15$ mag, ${\sigma}_{{G}_{\mathrm{BP}}}$, $$ mag  35 111 sources 
$$  
$Gr=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  ${\sigma}_{{G}_{\mathrm{BP}}}$, $$ mag, $$  38 041 sources 
$r>15$ mag, $$  
$Gi=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $i>15$ mag, $Gi>0.3({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})0.5$  35 253 sources 
${\sigma}_{{G}_{\mathrm{BP}}}$, $$ mag  
$Gg=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $g>15$ mag, ${\sigma}_{{G}_{\mathrm{BP}}}$, $$ mag,  43 112 sources 
$$ 
JohnsonCousins filtering  
$GV=f(V{I}_{C})$  No filter  82 617 sources 
$GV=f(VR)$  $GV>0.150.5(VR)0.32{(VR)}^{2}$  42 503 sources 
$GV=f(BV)$  $GV>0.2+0.03(BV)0.32{(BV)}^{2}+0.01{(BV)}^{3}$  85 869 sources 
${G}_{\mathrm{BP}}V=f(V{I}_{C})$  No filter  82 617 sources 
${G}_{\mathrm{RP}}V=f(V{I}_{C})$  No filter  82 617 sources 
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(V{I}_{C})$  No filter  82 617 sources 
$GV=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  No filter  96 413 sources 
$GR=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $GR>0.15+0.51({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})0.23{({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})}^{2}+0.02{({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})}^{3}$  43 384 sources 
$G{I}_{C}=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  No filter  83 483 sources 
2MASS filtering  
$$, $e=\frac{{F}_{\mathrm{BP}}+{F}_{\mathrm{RP}}}{{F}_{G}}\le 1.3+0.06{({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})}^{2}$, ${Q}_{fl}=$”AAA”  
$G{K}_{S}=f(H{K}_{S})$  $$, ${\sigma}_{H}$ and $$,  1 697 974 sources 
$H{K}_{S}>0.11$, $G{K}_{S}\ge 13(H{K}_{S})1.5$  
${G}_{\mathrm{BP}}{K}_{S}=f(H{K}_{S})$  $$, ${\sigma}_{H}$ and $$, $$  1 110 501 sources 
${G}_{\mathrm{RP}}{K}_{S}=f(H{K}_{S})$  $$, ${\sigma}_{H}$ and $$  599 005 sources 
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(H{K}_{S})$  ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, ${\sigma}_{H}$, $$, $$  258 902 sources 
$G{K}_{S}=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  ${\sigma}_{G}$, ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$  238 171 sources 
$GH=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  ${\sigma}_{G}$, ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$  103 388 sources 
$GJ=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  ${\sigma}_{G}$, ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$  93 438 sources 
$G{K}_{S}=f(J{K}_{S})$  $$, ${\sigma}_{J}$ and $$  82 491 sources 
${G}_{\mathrm{BP}}{K}_{S}=f(J{K}_{S})$  $$, ${\sigma}_{J}$ and $$  72 118 sources 
${G}_{\mathrm{RP}}{K}_{S}=f(J{K}_{S})$  $$, ${\sigma}_{J}$ and $$  63 583 sources 
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(J{K}_{S})$  $$, $$, ${\sigma}_{J}$ and $$  55 884 sources 
GSC2.3 filtering  
$G>13$, $e=\frac{{F}_{\mathrm{BP}}+{F}_{\mathrm{RP}}}{{F}_{G}}\le 1.3+0.06{({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})}^{2}$  
$JF=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$, $$, $\delta \ge 0$  7049 sources 
$JF=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$, $$, $$  13 174 sources 
$GJ=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  ${\sigma}_{G}$, ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$, $\delta \ge 0$,  9537 sources 
$$  
$GJ=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  ${\sigma}_{G}$, ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$, $$,  25 973 sources 
$$  
$GF=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  ${\sigma}_{G}$, ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$, $\delta \ge 0$, $$  7921 sources 
$GF=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  ${\sigma}_{G}$, ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$, $$, $$  11 911 sources 
$GF=f(JF)$  $$, $$, $$, $\delta \ge 0$, $JF>0.4$  18 453 sources 
$GF=f(JF)$  $$, $$, $$, $$, $$  24 423 sources 
$GJ=f(JF)$  $$, $$, $$, $\delta \ge 0$, $$  18 378 sources 
$GJ=f(JF)$  $$, $$, $$, $$, $$  28 208 sources 
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(JF)$  ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$, $$, $\delta \ge 0$,  6851 sources 
$$  
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(JF)$  ${\sigma}_{{G}_{\mathrm{BP}}}$ and $$, $$, $$, $$,  9798 sources 
$$ 
Hipparcos relationships  
$\mathbf{B}\mathbf{V}$  ${\left(\mathbf{B}\mathbf{V}\right)}^{\mathrm{\U0001d7d0}}$  ${\left(\mathbf{B}\mathbf{V}\right)}^{\mathrm{\U0001d7d1}}$  $\sigma $  
$GHp$  0.02392  0.4069  0.04569  0.0452  0.02417  
$\mathbf{V}\mathbf{I}$  ${\left(\mathbf{V}\mathbf{I}\right)}^{\mathrm{\U0001d7d0}}$  ${\left(\mathbf{V}\mathbf{I}\right)}^{\mathrm{\U0001d7d1}}$  $\sigma $  
$GHp$  0.01546  0.4308  0.01872    0.08191  
${G}_{\mathrm{BP}}Hp$  0.02696  0.1086  0.009148  0.004715  0.06  
${G}_{\mathrm{RP}}Hp$  0.006437  1.194  0.09962    0.1024  
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$  0.01612  1.274  0.08143    0.082  
${\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d0}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d1}}$  $\sigma $  
$GHp$  0.01008  0.2309  0.1300  0.01894  0.06066  
Tycho2 relationships  
${\mathbf{B}}_{\mathbf{T}}{\mathbf{V}}_{\mathbf{T}}$  ${\left({\mathbf{B}}_{\mathbf{T}}{\mathbf{V}}_{\mathbf{T}}\right)}^{\mathrm{\U0001d7d0}}$  ${\left({\mathbf{B}}_{\mathbf{T}}{\mathbf{V}}_{\mathbf{T}}\right)}^{\mathrm{\U0001d7d1}}$  $\sigma $  
$G{V}_{T}$  0.01072  0.2870  0.05807  0.06791  0.06084  
${G}_{\mathrm{BP}}{V}_{T}$  0.01868  0.2682  0.1366  0.01272  0.04127  
${G}_{\mathrm{RP}}{V}_{T}$  0.04424  1.197  0.4948  0.1757  0.09359  
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$  0.02621  1.458  0.6176  0.1817  0.06834  
${\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d0}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d1}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d2}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d3}}$  $\sigma $  
$G{V}_{T}$  0.01077  0.0682  0.2387  0.02342      0.05350 
$G{B}_{T}$  0.004288  0.8547  0.1244  0.9085  0.4843  0.06814  0.07063 
SDSS12 relationships  
$\mathbf{g}\mathbf{i}$  ${\left(\mathbf{g}\mathbf{i}\right)}^{\mathrm{\U0001d7d0}}$  ${\left(\mathbf{g}\mathbf{i}\right)}^{\mathrm{\U0001d7d1}}$  $\sigma $  
$Gg$  0.1064  0.4964  0.09339  0.004444  0.0872  
${G}_{\mathrm{BP}}g$  0.06213  0.2059  0.06478  0.007264  0.02944  
${G}_{\mathrm{RP}}g$  0.3306  0.9847  0.02874  0.002112  0.04958  
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$  0.3971  0.777  0.04164  0.008237  0.03846  

$\mathbf{r}\mathbf{i}$  ${\left(\mathbf{r}\mathbf{i}\right)}^{\mathrm{\U0001d7d0}}$  ${\left(\mathbf{r}\mathbf{i}\right)}^{\mathrm{\U0001d7d1}}$  $\sigma $  
$Gr$  0.01664  0.2662  0.649  0.08227  0.123  
$Gi$  0.01066  1.298  0.7595  0.1492  0.07112  
${\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d0}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d1}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d2}}$  $\sigma $  
$Gr$  0.09837  0.08592  0.1907  0.1701  0.02263  0.03776  
$Gi$  0.293  0.6404  0.09609  0.002104  0.04092  
$Gg$  0.2199  0.6365  0.1548  0.0064  0.0745 
JohnsonCousins relationships  
$\mathbf{V}{\mathbf{I}}_{\mathbf{C}}$  ${\left(\mathbf{V}{\mathbf{I}}_{\mathbf{C}}\right)}^{\mathrm{\U0001d7d0}}$  ${\left(\mathbf{V}{\mathbf{I}}_{\mathbf{C}}\right)}^{\mathrm{\U0001d7d1}}$  ${\left(\mathbf{V}{\mathbf{I}}_{\mathbf{C}}\right)}^{\mathrm{\U0001d7d2}}$  $\sigma $  
$GV$  0.01597  0.02809  0.2483  0.03656  0.002939  0.0272 
${G}_{\mathrm{BP}}V$  0.0143  0.3564  0.1332  0.01212  0.0371  
${G}_{\mathrm{RP}}V$  0.01868  0.9028  0.005321  0.004186  0.03784  
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$  0.03298  1.259  0.1279  0.01631  0.04459  
$\mathbf{V}\mathbf{R}$  ${\left(\mathbf{V}\mathbf{R}\right)}^{\mathrm{\U0001d7d0}}$  ${\left(\mathbf{V}\mathbf{R}\right)}^{\mathrm{\U0001d7d1}}$  $\sigma $  
$GV$  0.03088  0.04653  0.8794  0.1733  0.0352  
$\mathbf{B}\mathbf{V}$  ${\left(\mathbf{B}\mathbf{V}\right)}^{\mathrm{\U0001d7d0}}$  ${\left(\mathbf{B}\mathbf{V}\right)}^{\mathrm{\U0001d7d1}}$  $\sigma $  
$GV$  0.04749  0.0124  0.2901  0.02008  0.04772  
${\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d0}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d1}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d2}}$  $\sigma $  
$GV$  0.02704  0.01424  0.2156  0.01426  0.03017  
$GR$  0.02275  0.3961  0.1243  0.01396  0.003775  0.03167 
$G{I}_{C}$  0.01753  0.76  0.0991  0.03765  
2MASS relationships  
$\mathbf{H}{\mathbf{K}}_{\mathbf{S}}$  ${\left(\mathbf{H}{\mathbf{K}}_{\mathbf{S}}\right)}^{\mathrm{\U0001d7d0}}$  $\sigma $  
$G{K}_{S}$  0.5594  11.09  3.040  0.3743  
${G}_{\mathrm{BP}}{K}_{S}$  0.5922  15.36  1.691  0.499  
${G}_{\mathrm{RP}}{K}_{S}$  0.1882  10.3  3.976  0.2956  
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$  0.1836  8.456  3.781  0.2361  
${\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d0}}$  $\sigma $  
$G{K}_{S}$  0.0981  2.089  0.1579  0.08553  
$GH$  0.1048  2.011  0.1758  0.07805  
$GJ$  0.01798  1.389  0.09338  0.04762  
$\mathbf{J}{\mathbf{K}}_{\mathbf{S}}$  ${\left(\mathbf{J}{\mathbf{K}}_{\mathbf{S}}\right)}^{2}$  ${\left(\mathbf{J}{\mathbf{K}}_{\mathbf{S}}\right)}^{3}$  ${\left(\mathbf{J}{\mathbf{K}}_{\mathbf{S}}\right)}^{4}$  $\sigma $  
$G{K}_{S}$  0.1683  3.803  1.45  0.7867  0.1309  
${G}_{\mathrm{BP}}{K}_{S}$  0.1777  5.28  4.384  4.451  1.273  0.174 
${G}_{\mathrm{RP}}{K}_{S}$  0.08089  2.655  1.488  1.618  0.5068  0.07997 
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$  0.09396  2.581  2.782  2.788  0.8027  0.09668 
GSC2.3 relationships  
${\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}$  ${\left({\mathbf{G}}_{\mathrm{BP}}{\mathbf{G}}_{\mathrm{RP}}\right)}^{\mathrm{\U0001d7d0}}$  $\sigma $  
$JF$ ($\delta \ge 0.0$)  0.02223  1.225  0.06094  0.2791  
$JF$ ($$)  0.03718  1.25  0.1079  0.6247  
$GJ$ ($\delta \ge 0.0$)  0.1535  0.8585  0.09095  0.2032  
$GJ$ ($$)  0.1819  0.9921  0.01864  0.1857  
$GF$ ($\delta \ge 0.0$)  0.1601  0.2267  0.09907  0.1652  
$GF$ ($$)  0.003457  0.3588  0.1429  0.2118  
$\mathbf{J}\mathbf{F}$  ${\left(\mathbf{J}\mathbf{F}\right)}^{2}$  $\sigma $  
$GF$ ($\delta \ge 0.0$)  0.006076  0.3817  0.08016  0.292  
$GF$ ($$)  0.01069  0.2919  0.09112  0.1999  
$GJ$ ($\delta \ge 0.0$)  0.02773  0.6432  0.07362  0.2858  
$GJ$ ($$)  0.01615  0.6868  0.0654  0.2697  
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$ ($\delta \ge 0.0$)  0.42  0.398  0.1181  0.1658  
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$ ($$)  0.4719  0.4315  0.1111  0.1775 
Hipparcos relationships  Tycho2 relationships  
$G{H}_{P}=f(BV)$  $$  $G{V}_{T}=f({B}_{T}{V}_{T})$  $$ 
$G{H}_{P}=f(VI)$  $$  $G{V}_{T}=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$ 
$G{H}_{P}=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$  $G{B}_{T}=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$ 
${G}_{\mathrm{BP}}{H}_{P}=f(VI)$  $$  ${G}_{\mathrm{BP}}{V}_{T}=f({B}_{T}{V}_{T})$  $$ 
${G}_{\mathrm{RP}}{H}_{P}=f(VI)$  $$  ${G}_{\mathrm{RP}}{V}_{T}=f({B}_{T}{V}_{T})$  $$ 
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(VI)$  $$  ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f({B}_{T}{V}_{T})$  $$ 
SDSS12 relationships  JohnsonCousins relationships  
$Gg=f(gi)$  $$  $GV=f(V{I}_{C})$  $$ 
$Gr=f(ri)$  $$  $GV=f(VR)$  $$ 
$Gi=f(ri)$  $$  $GV=f(BV)$  $$ 
${G}_{\mathrm{BP}}g=f(gi)$  $$  ${G}_{\mathrm{BP}}V=f(V{I}_{C})$  $$ 
${G}_{\mathrm{RP}}r=f(ri)$  $$  ${G}_{\mathrm{RP}}V=f(V{I}_{C})$  $$ 
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(gi)$  $$  ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(V{I}_{C})$  $$ 
$Gr=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$  $GV=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$ 
$Gi=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$  $GR=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$ 
$Gg=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$  $G{I}_{C}=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$ 
GSC2.3 relationships  2MASS relationships  
$JF=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$, $\delta \ge 0$  $$  $G{K}_{S}=f(H{K}_{S})$  $$ 
$JF=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$, $$  $$  ${G}_{\mathrm{BP}}{K}_{S}=f(H{K}_{S})$  $$ 
$GJ=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$, $\delta \ge 0$  $$  ${G}_{\mathrm{RP}}{K}_{S}=f(H{K}_{S})$  $$ 
$GJ=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$, $$  $$  ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(H{K}_{S})$  $$ 
$GJ=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$, $\delta \ge 0$  $$  $G{K}_{S}=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$ 
$GJ=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$, $$  $$  $GH=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$ 
$GF=f(JF)$, $\delta \ge 0$  $$  $GJ=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$  $$ 
$GF=f(JF)$, $$  $$  $G{K}_{S}=f(J{K}_{S})$  $$ 
$GJ=f(JF)$, $\delta \ge 0$  $$  ${G}_{\mathrm{BP}}{K}_{S}=f(J{K}_{S})$  $$ 
$GJ=f(JF)$, $$  $$  ${G}_{\mathrm{RP}}{K}_{S}=f(J{K}_{S})$  $$ 
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(JF)$ , $\delta \ge 0$  $$  ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(J{K}_{S})$  $$ 
${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(JF)$ , $$  $$  
${}^{i}$ $GV=f(BV)$ is only valid for M giants when $BV>1.3$.  ${}^{j}$ $GR=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$ is only valid for M giants when ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}>2.0$.  
${}^{g}$ $Gg=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$ is only valid for M giants when ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}>2.0$.  ${}^{h}$ $GV=f(VR)$ is only valid for M giants when $VR>0.9$.  
${}^{e}$ ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f(gi)$ is only valid for M giants when ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}>2.25$.  ${}^{f}$ $Gr=f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$ is only valid for M giants when ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}>2.0$.  
${}^{c}$ ${G}_{\mathrm{RP}}{V}_{T}=f({B}_{T}{V}_{T})$ is only valid for M giants when ${B}_{T}{V}_{T}>1.7$.  ${}^{d}$ ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}=f({B}_{T}{V}_{T})$ is only valid for M giants when ${B}_{T}{V}_{T}>1.7$.  
${}^{a}$ $G{H}_{P}=f(BV)$ is only valid for M giants when $BV>1.4$  ${}^{b}$ $G{V}_{T}=f({B}_{T}{V}_{T})$ is only valid for M giants when ${B}_{T}{V}_{T}>1.7$. 