Author(s): Josep M. Carrasco
This section includes some photometric transformations from Gaia passbands to other common photometric systems using Gaia DR2 data. Hipparcos (ESA (1997)), Tycho-2 (Høg et al. (2000)), SDSS12 (Alam et al. (2015)), Johnson-Cousins(Landolt (2009)), 2MASS (Skrutskie et al. (2006)) and GSC2.3 (Lasker et al. (2008)) are included here.
Only those sources with small magnitude error and small excess flux (see Sec. 5.5.2) were used for the fitting. Gaia DR2 sources were cross-matched with G<13 mag (in order to limit the influence of the photometric noise in the derived relationships), considering those having available photometry in the external photometric systems. 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 we used some Gaia DR2 sources with σG<0.003 and SDSS12 magnitudes fainter than 15th. For GSC2.3 transformations, two different fittings were done, one using sources with δ>0, and another with δ<0, as the photometric system is not equal in the two celestial hemispheres.
In order to obtain cleaner fittings, some filtering criteria were added to produce each colour-colour diagram. The data filtering to produce the photometric relationships can be checked in Table 5.5 and Table 5.6. The polynomial coefficients obtained with the resulting sources are included in Table 5.7 and Table 5.8. The validity of these fittings is, of course, only applicable in the colour intervals used to do the fitting (see Table 5.9).
Tycho-2 filtering | ||
Non-variable sources, G<13, e≤1.5+0.03(GBP-GRP)2 | ||
G-VT=f(BT-VT) | σG<0.01, σBT<0.05, σVT<0.05 | 345 837 sources |
G-VT≥-0.3(BT-VT)-0.5, BT-VT<2.5 | ||
G-VT=f(GBP-GRP) | σVT<0.05, σG<0.01, σGBP<0.01, σGRP<0.01 | 529 127 sources |
G-BT=f(GBP-GRP) | σBT<0.05, σG<0.01, σGBP<0.01, σGRP<0.01 | 362 674 sources |
GBP-VT=f(BT-VT) | σBT<0.05, σVT<0.05, σGBP<0.01 | 345 121 sources |
GRP-VT=f(BT-VT) | σBT<0.05, σVT<0.05, σGRP<0.01 | 342 140 sources |
GRP-VT>-2.1 | ||
GBP-GRP=f(BT-VT) | σBT<0.05, σVT<0.05, σGBP<0.01, σGRP<0.01 | 340 775 sources |
GBP-GRP<2.1 | ||
Hipparcos filtering | ||
Non-variable sources, G<13, e≤1.5+0.03(GBP-GRP)2 | ||
G-HP=f(B-V) | σG<0.01, σHP<0.1, σB-V<0.1, B-V≠0.0, B-V<2.0 | 69 616 sources |
-0.4(B-V)-0.17<G-HP<-0.4(B-V)+0.05 | ||
G-HP=f(V-I) | σG<0.01, σHP<0.1, V-I≠0.0 | 78 012 sources |
G-HP=f(GBP-GRP) | σHP<0.1, σG<0.01, σGBP<0.01, σGRP<0.01 | 76 930 sources |
GBP-HP=f(V-I) | σHP<0.1, σGBP<0.01, V-I≠0.0 | 76 428 sources |
GRP-HP=f(V-I) | σHP<0.1, σGRP<0.01, V-I≠0.0 | 76 660 sources |
GBP-GRP=f(V-I) | σGBP<0.1, σGRP<0.01, V-I≠0.0 | 76 037 sources |
SDSS12 filtering | ||
Non-variable sources, e≤1.3+0.06(GBP-GRP)2, cl=6 (stars), σG<0.003 mag | ||
G-g=f(g-i) diagram | g, i>15 mag, G>6.5 mag, σg, σi<0.01 mag, | 279 458 sources |
-(g-i)-0.6<G-g<-(g-i)+1 | ||
G-g=f(g-r) diagram | g, r>15 mag, G>6.5 mag, σg, σr<0.01 mag | 296 068 sources |
-1.3(g-r)-0.5<G-g | ||
G-r=f(r-i) diagram | r, i>15 mag, G>6.5 mag, σr, σi<0.01 mag | 375 806 sources |
G-r<0.7(r-i)+0.12 | ||
G-i=f(r-i) diagram | r, i>15 mag, G>6.5 mag, σr, σi<0.01 mag | 375 593 sources |
(r-i)-1.1<G-i<1.7(r-i)+0.12 | ||
GBP-r=f(r-i) diagram | r, i>15 mag, GBP>4.0 mag, σr, σi, σGBP<0.01 mag | 149 631 sources |
GBP-r<1, 0.7(r-i)-0.5<GBP-r<1.7(r-i)+0.4 | ||
GRP-r=f(r-i) diagram | r, i>15 mag, GRP>4.0 mag, σr, σi, σGRP<0.01 mag | 286 712 sources |
-1.6(r-i)-0.6<GRP-r | ||
GBP-GRP=f(r-i) diagram | r, i>15 mag, GBP, GRP>4.0 mag, σr, σi, σGBP, σGRP<0.01 mag | 147 779 sources |
1.7(r-i)<GBP-GRP<2.5(r-i)+1.0 | ||
G-r=f(GBP-GRP) diagram | r>15 mag, GBP, GRP>4.0 mag, G>6.5 mag | 161 123 sources |
σr, σGBP, σGRP<0.01 mag, G-r<-0.7(GBP-GRP)+1.37 | ||
G-i=f(GBP-GRP) diagram | i>15 mag, GBP, GRP>4.0 mag, G>6.5 mag | 149 928 sources |
σi, σGBP, σGRP<0.01 mag | ||
G-g=f(GBP-GRP) diagram | g>15 mag, GBP, GRP>4.0 mag, G>6.5 mag | 186 540 sources |
σg, σGBP, σGRP<0.01 mag, G-g<-1.4(GBP-GRP)+1.5 |
Johnson-Cousins filtering | ||
Non-variable sources, G<13, e≤1.5+0.03(GBP-GRP)2 | ||
G-V=f(V-I) | σG<0.01 | 402 sources |
GBP-V=f(V-I) | σGBP<0.01 | 398 sources |
GRP-V=f(V-I) | σGRP<0.01 | 400 sources |
GBP-GRP=f(V-I) | σGBP<0.01,σGRP<0.01 | 398 sources |
G-V=f(V-R) | σG<0.01 | 402 sources |
G-V=f(B-V) | σG<0.01 | 402 sources |
G-V=f(GBP-GRP) | σG<0.01, σGBP<0.01, σGRP<0.01 | 398 sources |
G-R=f(GBP-GRP) | σG<0.01, σGBP<0.01, σGRP<0.01 | 398 sources |
G-I=f(GBP-GRP) | σG<0.01, σGBP<0.01, σGRP<0.01 | 398 sources |
2MASS filtering | ||
Non-variable sources, G<13, e≤1.5+0.03(GBP-GRP)2 | ||
G-K=f(H-K) | σG<0.01, σH and σK<0.03, G-K≥13(H-K)-1.5 | 5 242 124 sources |
GBP-K=f(H-K) | σGBP<0.01, σH and σK<0.03, H-K<0.6 | 5 177 073 sources |
GRP-K=f(H-K) | σGRP<0.01, σH and σK<0.03 | 5 209 578 sources |
GBP-GRP=f(H-K) | σGBP and σGRP<0.01, σH and σK<0.03 | 5 172 134 sources |
G-K=f(GBP-GRP) | σG, σGBP and σGRP<0.01, σK<0.03 | 6 434 513 sources |
G-H=f(GBP-GRP) | σG, σGBP and σGRP<0.01, σH<0.03 | 5 225 045 sources |
G-J=f(GBP-GRP) | σG, σGBP and σGRP<0.01, σJ<0.03 | 6 386 215 sources |
G-K=f(J-K) | σG<0.01, σJ and σK<0.03, Qfl=”AAA” | 6 329 333 sources |
GBP-K=f(J-K) | σG<0.01, σJ and σK<0.03, Qfl=”AAA” | 6 196 909 sources |
GRP-K=f(J-K) | σG<0.01, σJ and σK<0.03, Qfl=”AAA” | 6 196 909 sources |
GBP-GRP=f(J-K) | σG<0.01, σJ and σK<0.03, Qfl=”AAA” | 6 191 425 sources |
GSC2.3 FILTERING | ||
Non-variable sources, G<13, e≤1.3+0.06(GBP-GRP)2 | ||
J-F=f(GBP-GRP) diagram | σGBP and σGRP<0.01, σJ<0.3, σF<0.3 | |
G-J=f(GBP-GRP) diagram | σG, σGBP and σGRP<0.01, σJ<0.3, σF<0.3 | |
G-F=f(GBP-GRP) diagram | σG, σGBP and σGRP<0.01, σJ<0.3, σF<0.3 | |
G-F=f(J-F) diagram | σG<0.01, σJ<0.3, σF<0.3 | |
G-J=f(J-F) diagram | σG<0.01, σJ<0.3, σF<0.3, 0.1<J-F<3.0 | |
GBP-GRP=f(J-F) diagram | σGBP and σGRP<0.01, σJ<0.3, σF<0.3 | |
0.8(J-K)-0.4<GBP-GRP<1.2(J-F)+0.4 |
Hipparcos relationships | |||||
𝐁-𝐕 | (𝐁-𝐕)𝟐 | (𝐁-𝐕)𝟑 | σ | ||
G-Hp | -0.03704 | -0.3915 | 0.01855 | -0.03239 | 0.02502 |
𝐕-𝐈 | (𝐕-𝐈)𝟐 | (𝐕-𝐈)𝟑 | σ | ||
G-Hp | -0.01259 | -0.3336 | -0.1171 | 0.02244 | 0.09610 |
GBP-Hp | -0.01205 | 0.1105 | 0.06624 | ||
GSC GRP-Hp | -0.00055 | -1.203 | 0.1078 | 0.1089 | |
GBP-GRP | -0.01146 | 1.315 | -0.1103 | 0.09390 | |
𝐆BP-𝐆RP | (𝐆BP-𝐆RP)𝟐 | (𝐆BP-𝐆RP)𝟑 | σ | ||
G-Hp | -0.01968 | -0.2344 | -0.1200 | 0.01490 | 0.06875 |
Tycho-2 relationships | |||||
𝐁𝐓-𝐕𝐓 | (𝐁𝐓-𝐕𝐓)𝟐 | (𝐁𝐓-𝐕𝐓)𝟑 | σ | ||
G-VT | -0.02051 | -0.2706 | 0.03394 | -0.05937 | 0.06373 |
GBP-VT | -0.006739 | 0.2758 | -0.1350 | 0.01098 | 0.04415 |
GRP-VT | -0.03757 | -1.188 | 0.4871 | -0.1729 | 0.09637 |
GBP-GRP | 0.03147 | 1.456 | -0.6043 | 0.1750 | 0.07024 |
𝐆BP-𝐆RP | (𝐆BP-𝐆RP)𝟐 | (𝐆BP-𝐆RP)𝟑 | σ | ||
G-VT | -0.01842 | -0.06629 | -0.2346 | 0.02157 | 0.05501 |
G-BT | -0.02441 | -0.4899 | -0.9740 | 0.2496 | 0.07293 |
SDSS12 relationships | |||||
𝐠-𝐢 | (𝐠-𝐢)𝟐 | (𝐠-𝐢)𝟑 | σ | ||
G-g | -0.074189 | -0.51409 | -0.080607 | 0.0016001 | 0.046848 |
𝐠-𝐫 | (𝐠-𝐫)𝟐 | (𝐠-𝐫)𝟑 | σ | ||
G-g | -0.038025 | -0.76988 | -0.1931 | 0.0060376 | 0.065837 |
𝐫-𝐢 | (𝐫-𝐢)𝟐 | (𝐫-𝐢)𝟑 | σ | ||
G-r | 0.0014891 | 0.36291 | -0.81282 | 0.14711 | 0.043634 |
G-i | -0.007407 | 1.4337 | -0.95312 | 0.22049 | 0.041165 |
GBP-r | 0.1463 | 1.7244 | -1.1912 | 0.22004 | 0.059674 |
GRP-r | -0.29869 | -1.1303 | 0.039156 | ||
GBP-GRP | 0.47108 | 2.7001 | -0.97174 | 0.14601 | 0.067573 |
𝐆BP-𝐆RP | (𝐆BP-𝐆RP)𝟐 | (𝐆BP-𝐆RP)𝟑 | σ | ||
G-r | -0.12879 | 0.24662 | -0.027464 | -0.049465 | 0.066739 |
G-i | -0.29676 | 0.64728 | -0.10141 | 0.098957 | |
G-g | 0.13518 | -0.46245 | -0.25171 | 0.021349 | 0.16497 |
Johnson-Cousins relationships | ||||||
𝐕-𝐈 | (𝐕-𝐈)𝟐 | (𝐕-𝐈)𝟑 | σ | |||
G-V | -0.01746 | 0.008092 | -0.2810 | 0.03655 | 0.04670 | |
GBP-V | -0.05204 | 0.4830 | -0.2001 | 0.02186 | 0.04483 | |
GRP-V | 0.0002428 | -0.8675 | -0.02866 | 0.04474 | ||
GBP-GRP | -0.04212 | 1.286 | -0.09494 | 0.02366 | ||
𝐕-𝐑 | (𝐕-𝐑)𝟐 | (𝐕-𝐑)𝟑 | σ | |||
G-V | -0.02269 | 0.01784 | -1.016 | 0.2225 | 0.04895 | |
𝐁-𝐕 | (𝐁-𝐕)𝟐 | (𝐁-𝐕)𝟑 | σ | |||
G-V | -0.02907 | -0.02385 | -0.2297 | -0.001768 | 0.06285 | |
𝐆BP-𝐆RP | (𝐆BP-𝐆RP)𝟐 | σ | ||||
G-V | -0.01760 | -0.006860 | -0.1732 | 0.045858 | ||
G-R | -0.003226 | 0.3833 | -0.1345 | 0.04840 | ||
G-I | 0.02085 | 0.7419 | -0.09631 | 0.04956 | ||
2MASS relationships | ||||||
𝐇-𝐊𝐒 | (𝐇-𝐊𝐒)𝟐 | σ | ||||
G-KS | 0.6613 | 12.073 | -1.359 | 0.3692 | ||
GBP-KS | 0.8174 | 14.66 | 2.711 | 0.4839 | ||
GRP-KS | 0.3560 | 9.287 | -1.721 | 0.2744 | ||
GBP-GRP | 0.4238 | 6.098 | 1.991 | 0.2144 | ||
𝐆BP-𝐆RP | (𝐆BP-𝐆RP)𝟐 | σ | ||||
G-KS | -0.1885 | 2.092 | -0.1345 | 0.08281 | ||
G-H | -0.1621 | 1.968 | -0.1328 | 0.07103 | ||
G-J | -0.01883 | 1.394 | -0.07893 | 0.05246 | ||
𝐉-𝐊 | (𝐉-𝐊)2 | (𝐉-𝐊)3 | (𝐉-𝐊)4 | σ | ||
G-KS | 0.23587 | 4.0548 | -2.5608 | 2.2228 | -0.54944 | 0.14274 |
GBP-KS | 0.26216 | 5.1917 | -3.6237 | 3.4095 | -0.85956 | 0.18957 |
GBP-KS | 0.14624 | 2.4329 | -0.83901 | 0.96813 | -0.26534 | 0.089368 |
GBP-GRP | 0.20215 | 1.9561 | -0.69629 | 0.47633 | 0.11034 | |
GSC2.3 relationships | ||||||
GBP-GRP | (GBP-GRP)2 | σ | ||||
J-F (δ≥0.0) | -0.10948 | 1.4553 | -0.14375 | 0.32231 | ||
J-F (δ<0.0) | -0.1621 | 1.4348 | -0.16587 | 0.40361 | ||
G-J (δ≥0.0) | 0.092602 | -0.87175 | -0.061304 | 0.3658 | ||
G-J (δ<0.0) | 0.12609 | -0.89624 | -0.04906 | 0.24571 | ||
G-F (δ≥0.0) | 0.11082 | 0.40808 | -0.15175 | 0.29104 | ||
G-F (δ<0.0) | -0.0031867 | 0.54324 | -0.19188 | 0.32779 | ||
J-F | (J-F)2 | σ | ||||
G-F (δ≥0.0) | -0.031048 | 0.48358 | -0.14923 | 0.2302 | ||
G-F (δ<0.0) | -0.076434 | 0.52101 | -0.14503 | 0.28117 | ||
G-J (δ≥0.0) | -0.11371 | -0.35619 | -0.20973 | 0.19187 | ||
G-J (δ<0.0) | -0.096134 | -0.39097 | -0.18957 | 0.25026 | ||
GBP-GRP (δ≥0.0) | 0.23021 | 0.54188 | 0.10319 | 0.15494 | ||
GBP-GRP (δ<0.0) | 0.25408 | 0.62881 | 0.066154 | 0.2028 |
Hipparcos relationships | |
G-HP=f(B-V) | -0.2<B-V<1.5 |
G-HP=f(V-I) | -0.3<V-I<3.0 |
G-HP=f(GBP-GRP) | -0.5<GBP-GRP<4.0 |
GBP-HP=f(V-I) | 0.0<V-I<2.5 |
GRP-HP=f(V-I) | -0.3<V-I<2.5 |
GBP-GRP=f(V-I) | -0.4<V-I<2.5 |
Tycho-2 relationships | |
G-VT=f(BT-VT) | -0.1<BT-VT<2.0 |
G-VT=f(GBP-GRP) | -0.3<GBP-GRP<4.0 |
G-BT=f(GBP-GRP) | 0.0<GBP-GRP<2.5 |
GBP-VT=f(BT-VT) | -0.2<BT-VT<2.5 |
GRP-VT=f(BT-VT) | -0.2<BT-VT<2.0 |
GBP-GRP=f(BT-VT) | -0.2<BT-VT<2.0 |
SDSS12 relationships | |
G-g=f(g-i) | -1.0<g-i<4.0 |
G-g=f(g-r) | -0.6<g-r<1.5 |
G-r=f(r-i) | -0.5<r-i<2.0 |
G-i=f(r-i) | -0.2<r-i<1.8 |
GBP-r=f(r-i) | -0.1<r-i<0.9 |
GRP-r=f(r-i) | -0.4<r-i<1.0 |
GBP-GRP=f(r-i) | -0.4<r-i<0.8 |
G-r=f(GBP-GRP) | 0.2<GBP-GRP<2.7 |
G-i=f(GBP-GRP) | 0.0<GBP-GRP<4.5 |
G-g=f(GBP-GRP) | -0.5<GBP-GRP<2.0 |
Johnson-Cousins relationships | |
G-V=f(V-I) | -0.3<V-I<2.7 |
GBP-V=f(V-I) | -0.3<V-I<2.7 |
GRP-V=f(V-I) | -0.3<V-I<2.7 |
GBP-GRP=f(V-I) | -0.3<V-I<2.7 |
G-V=f(V-R) | -0.15<V-R<1.4 |
G-V=f(B-V) | -0.3<B-V<2.4 |
G-V=f(GBP-GRP) | -0.5<GBP-GRP<2.75 |
G-R=f(GBP-GRP) | -0.5<GBP-GRP<2.75 |
G-I=f(GBP-GRP) | -0.5<GBP-GRP<2.75 |
2MASS relationships | |
G-K=f(H-K) | -0.1<H-K<0.7 |
GBP-K=f(H-K) | -0.1<H-K<0.6 |
GRP-K=f(H-K) | -0.1<H-K<0.7 |
GBP-GRP=f(H-K) | -0.1<H-K<0.55 |
G-K=f(GBP-GRP) | 0.25<GBP-GRP<5.5 |
G-H=f(GBP-GRP) | 0.25<GBP-GRP<5.0 |
G-J=f(GBP-GRP) | -0.5<GBP-GRP<5.5 |
G-K=f(J-K) | -0.3<H-K<2.2 |
GBP-K=f(J-K) | -0.25<H-K<2.0 |
GRP-K=f(J-K) | -0.3<H-K<2.1 |
GBP-GRP=f(J-K) | -0.2<H-K<1.9 |
GSC2.3 RELATIONSHIPS | |
J-F=f(GBP-GRP) | 0.1<GBP-GRP<3.0 |
G-J=f(GBP-GRP) | 0.1<GBP-GRP<3.0 |
G-F=f(GBP-GRP) | 0.2<GBP-GRP<3.0 |
G-F=f(J-F) | 0.3<J-F<2.8 |
G-J=f(J-F) | 0.1<J-F<3.0 |
GBP-GRP=f(J-F) | 0.2<J-F<3.0 |
Photometric relationships derived between Gaia and Hipparcos, Tycho-2, SDSS12, Johnson, 2MASS and GSC2.3 can be seen in Figures from 5.11 to 5.21.