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gaia data release 3 documentation

5.5 Photometric Systems

5.5.1 Photometric 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 DR3 data. Hipparcos (ESA 1997), Tycho-2 (Høg et al. 2000), SDSS12 (Alam et al. 2015), Johnson-Cousins (Stetson 2000), 2MASS (Skrutskie et al. 2006) and GSC2.3 (Lasker et al. 2008) are included here.

Except for the Johnson-Cousins 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 DR3 sources with G<13 mag were considered for the cross-match, 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 we used some Gaia DR3 sources with σG<0.01 and only SDSS12 magnitudes fainter than 15 mag. For the GSC2.3 transformations, two different fittings were done, one using sources with δ0, and the other with sources at δ<0, 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 colour-colour diagrams. Detailed information on the filtering to produce the photometric relationships is given in Table 5.6 and Table 5.7.

The polynomial coefficients obtained with the resulting sources are listed in Table 5.8 and Table 5.9. 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 5.10). The photometric relationships derived between Gaia and Hipparcos, Tycho-2, SDSS12, Johnson-Cousins, 2MASS and GSC2.3 can be seen in Figures 5.34 to 5.43. 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 raw 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 colour-colour 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.

Table 5.6: Filters applied and the resulting number of sources selected to fit the photometric relationships in Table 5.8.
Hipparcos filtering
G<13, e=FBP+FRPFG1.3+0.06(GBP-GRP)2
G-HP=f(B-V) σG<0.01, σHP<0.1, σB-V<0.1, B-V0.0, B-V<2.0 89 460 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-I0.0, V-I<5 98 910 sources
G-HP=f(GBP-GRP) σHP<0.1, σG<0.01, σGBP<0.01, σGRP<0.01 97 800 sources
GBP-HP=f(V-I) σHP<0.1, σGBP<0.01, V-I0.0, V-I<4 97 098 sources
GRP-HP=f(V-I) σHP<0.1, σGRP<0.01, V-I0.0, V-I<5 97 534 sources
GBP-GRP=f(V-I) σGBP<0.1, σGRP<0.01, V-I0.0, 96 771 sources
V-I<4, GBP-GRP>(V-I)-0.5
Tycho-2 filtering
G<13, e=FBP+FRPFG1.3+0.06(GBP-GRP)2
G-VT=f(BT-VT) σG<0.01, σBT<0.05, σVT<0.05 374 697 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<0.01 569 238 sources
G-BT=f(GBP-GRP) σBT<0.05, σG<0.01, σGBP<0.01, σGRP<0.01 393 188 sources
GBP-VT=f(BT-VT) σBT<0.05, σVT<0.05, σGBP<0.01 375 086 sources
GRP-VT=f(BT-VT) σBT<0.05, σVT<0.05, σGRP<0.01 371 974 sources
GRP-VT>-2.1
GBP-GRP=f(BT-VT) σBT<0.05, σVT<0.05, σGBP<0.01, σGRP<0.01 370 974 sources
GBP-GRP<2.1
SDSS12 filtering
G>13 mag, e1.3+0.06(GBP-GRP)2, cl=6 (stars), σG<0.01 mag
G-g=f(g-i) g, i>15 mag, -(g-i)-0.6<G-g<-(g-i)+1 213 563 sources
G-z=f(g-i) 0.45(g-i)-0.6<G-g<0.53(g-i)+0.5 208 282 sources
g, z, i>15 mag, -1<g-i<5 mag
G-r=f(r-i) r, i>15 mag, r-i<4.0, 213 497 sources
-(r-i)-3<G-r<0.7(r-i)+0.12
G-i=f(r-i) r, i>15 mag 212 293 sources
0.7(r-i)-1.0<G-i<1.7(r-i)+0.12
G-z=f(r-i) z, r, i>15 mag 209 682 sources
-0.1(r-i), (r-i)-1.0<G-z
GBP-g=f(g-i) g, i>15 mag, σGBP<0.01 mag, 34 903 sources
-0.1-0.36(g-i)<GBP-g<0.25-0.36(g-i)
GRP-g=f(g-i) g, i>15 mag, σGRP<0.01 mag 65 207 sources
-1.1(g-i)-0.8<GRP-g
GBP-GRP=f(g-i) g, i>15 mag, σGBP, σGRP<0.01 mag 35 111 sources
0.7(g-i)-0.2<GBP-GRP<0.7(g-i)+0.65
G-r=f(GBP-GRP) σGBP, σGRP<0.01 mag, G-r<-0.7(GBP-GRP)+1.37 38 041 sources
r>15 mag, -0.8+0.7(GBP-GRP)-0.3(GBP-GRP)2<G-r
G-i=f(GBP-GRP) i>15 mag, G-i>0.3(GBP-GRP)-0.5 35 253 sources
σGBP, σGRP<0.01 mag
G-g=f(GBP-GRP) g>15 mag, σGBP, σGRP<0.01 mag, 43 112 sources
-1.1(GBP-GRP)-0.2<G-g<-1.4(GBP-GRP)+1.5
G-z=f(GBP-GRP) g,z>15 mag, σGBP, σGRP<0.01 mag, 33 253 sources
G-z<0.7(GBP-GRP)-0.7
Notes. First column: relationship. Second column: criteria applied. Third column: Number of sources selected.
Table 5.7: Filters applied and the resulting number of sources selected to fit the photometric relationships in Table 5.9.
Johnson-Cousins filtering
G-V=f(V-IC) No filter 82 617 sources
G-V=f(V-R) G-V>-0.15-0.5(V-R)-0.32(V-R)2 42 503 sources
G-V=f(B-V) G-V>-0.2+0.03(B-V)-0.32(B-V)2+0.01(B-V)3 85 869 sources
GBP-V=f(V-IC) No filter 82 617 sources
GRP-V=f(V-IC) No filter 82 617 sources
GBP-GRP=f(B-V) GBP-GRP1.15(B-V)+0.4 85 875 sources
GBP-GRP=f(V-IC) No filter 82 617 sources
G-B=f(GBP-GRP) G-B-1.5(GBP-GRP)+0.9 87 362 sources
G-V=f(GBP-GRP) No filter 96 413 sources
G-R=f(GBP-GRP) G-R>-0.15+0.51(GBP-GRP)-0.23(GBP-GRP)2+0.02(GBP-GRP)3 43 384 sources
G-IC=f(GBP-GRP) No filter 83 483 sources
2MASS filtering
G<13, e=FBP+FRPFG1.3+0.06(GBP-GRP)2, Qfl=”AAA”
G-KS=f(H-KS) σG<0.01, σH and σKS<0.03, 1 697 974 sources
H-KS>-0.11, G-KS13(H-KS)-1.5
GBP-KS=f(H-KS) σGBP<0.01, σH and σKS<0.03, H-KS<0.6 1 110 501 sources
GRP-KS=f(H-KS) σGRP<0.01, σH and σKS<0.03 599 005 sources
GBP-GRP=f(H-KS) σGBP and σGRP<0.01, σH, σKS<0.03, -0.1<H-KS<0.55 258 902 sources
G-KS=f(GBP-GRP) σG, σGBP and σGRP<0.01, σKS<0.03 238 171 sources
G-H=f(GBP-GRP) σG, σGBP and σGRP<0.01, σH<0.03 103 388 sources
G-J=f(GBP-GRP) σG, σGBP and σGRP<0.01, σJ<0.03 93 438 sources
G-KS=f(J-KS) σG<0.01, σJ and σKS<0.03 82 491 sources
GBP-KS=f(J-KS) σGBP<0.01, σJ and σKS<0.03 72 118 sources
GRP-KS=f(J-KS) σGRP<0.01, σJ and σKS<0.03 63 583 sources
GBP-GRP=f(J-KS) σGBP<0.01, σGRP<0.01, σJ and σKS<0.03 55 884 sources
GSC2.3 filtering
G>13, e=FBP+FRPFG1.3+0.06(GBP-GRP)2
J-F=f(GBP-GRP) σGBP and σGRP<0.01, σJ<0.3, σF<0.3, δ0 7049 sources
J-F=f(GBP-GRP) σGBP and σGRP<0.01, σJ<0.3, σF<0.3, δ<0 13 174 sources
G-J=f(GBP-GRP) σG, σGBP and σGRP<0.01, σJ<0.3, δ0, 9537 sources
G-J<-1.1(GBP-GRP)+1
G-J=f(GBP-GRP) σG, σGBP and σGRP<0.01, σJ<0.3, δ<0, 25 973 sources
G-J<-(GBP-GRP)+0.5
G-F=f(GBP-GRP) σG, σGBP and σGRP<0.01, σF<0.3, δ0, G-F<0.6 7921 sources
G-F=f(GBP-GRP) σG, σGBP and σGRP<0.01, σF<0.3, δ<0, G-F<0.6 11 911 sources
G-F=f(J-F) σG<0.01, σJ<0.3, σF<0.3, δ0, J-F>0.4 18 453 sources
G-F=f(J-F) σG<0.01, σJ<0.3, σF<0.3, δ<0, G-F<0.6 24 423 sources
G-J=f(J-F) σG<0.01, σJ<0.3, σF<0.3, δ0, 0.1<J-F<3.0 18 378 sources
G-J=f(J-F) σG<0.01, σJ<0.3, σF<0.3, δ<0, G-F<-(J-F)+1.0 28 208 sources
GBP-GRP=f(J-F) σGBP and σGRP<0.01, σJ<0.3, σF<0.3, δ0, 6851 sources
0.8(J-K)-0.4<GBP-GRP<1.2(J-F)+0.4
GBP-GRP=f(J-F) σGBP and σGRP<0.01, σJ<0.3, σF<0.3, δ<0, 9798 sources
0.8(J-K)-0.2<GBP-GRP<1.2(J-F)+0.4
Notes. First column: relationship. Second column: filtering criteria applied. Third column: Number of sources selected.
Table 5.8: Coefficients of the polynomials derived for sources in common with Hipparcos, Tycho-2 and SDSS12 observed in Gaia DR3.
Hipparcos relationships
𝐁-𝐕 (𝐁-𝐕)𝟐 (𝐁-𝐕)𝟑 σ
G-Hp -0.02392 -0.4069 0.04569 -0.0452 0.02417
𝐕-𝐈 (𝐕-𝐈)𝟐 (𝐕-𝐈)𝟑 σ
G-Hp 0.01546 -0.4308 -0.01872 - 0.08191
GBP-Hp -0.02696 0.1086 -0.009148 0.004715 0.06
GRP-Hp -0.006437 -1.194 0.09962 - 0.1024
GBP-GRP -0.01612 1.274 -0.08143 - 0.082
𝐆BP-𝐆RP (𝐆BP-𝐆RP)𝟐 (𝐆BP-𝐆RP)𝟑 σ
G-Hp -0.01008 -0.2309 -0.1300 0.01894 0.06066
Tycho-2 relationships
𝐁𝐓-𝐕𝐓 (𝐁𝐓-𝐕𝐓)𝟐 (𝐁𝐓-𝐕𝐓)𝟑 σ
G-VT -0.01072 -0.2870 0.05807 -0.06791 0.06084
GBP-VT -0.01868 0.2682 -0.1366 0.01272 0.04127
GRP-VT -0.04424 -1.197 0.4948 -0.1757 0.09359
GBP-GRP 0.02621 1.458 -0.6176 0.1817 0.06834
𝐆BP-𝐆RP (𝐆BP-𝐆RP)𝟐 (𝐆BP-𝐆RP)𝟑 (𝐆BP-𝐆RP)𝟒 (𝐆BP-𝐆RP)𝟓 σ
G-VT -0.01077 -0.0682 -0.2387 0.02342 - - 0.05350
G-BT -0.004288 -0.8547 0.1244 -0.9085 0.4843 -0.06814 0.07063
SDSS12 relationships
𝐠-𝐢 (𝐠-𝐢)𝟐 (𝐠-𝐢)𝟑 (𝐠-𝐢)𝟒 σ
G-z -0.072 0.5872 -0.1021 0.04795 -0.007538 0.1069
G-g -0.1064 -0.4964 -0.09339 0.004444 0.0872
GBP-g 0.06213 -0.2059 -0.06478 0.007264 0.02944
GRP-g -0.3306 -0.9847 -0.02874 0.002112 0.04958
GBP-GRP 0.3971 0.777 -0.04164 0.008237 0.03846
𝐫-𝐢 (𝐫-𝐢)𝟐 (𝐫-𝐢)𝟑 σ
G-r -0.01664 0.2662 -0.649 0.08227 0.123
G-i -0.01066 1.298 -0.7595 0.1492 0.07112
G-z -0.0226 1.914 -0.78284 0.14408 0.12349
𝐆BP-𝐆RP (𝐆BP-𝐆RP)𝟐 (𝐆BP-𝐆RP)𝟑 (𝐆BP-𝐆RP)𝟒 σ
G-r -0.09837 0.08592 0.1907 -0.1701 0.02263 0.03776
G-i -0.293 0.6404 -0.09609 -0.002104 0.04092
G-g 0.2199 -0.6365 -0.1548 0.0064 0.0745
G-z -0.4619 0.8992 -0.08271 0.005029 0.041161
Table 5.9: Coefficients of the polynomials derived for sources in common with Johnson-Cousins, 2MASS and GSC2.3 for observed in Gaia DR3.
Johnson-Cousins relationships
𝐕-𝐈𝐂 (𝐕-𝐈𝐂)𝟐 (𝐕-𝐈𝐂)𝟑 (𝐕-𝐈𝐂)𝟒 σ
G-V -0.01597 -0.02809 -0.2483 0.03656 -0.002939 0.0272
GBP-V -0.0143 0.3564 -0.1332 0.01212 0.0371
GRP-V 0.01868 -0.9028 -0.005321 -0.004186 0.03784
GBP-GRP -0.03298 1.259 -0.1279 0.01631 0.04459
𝐕-𝐑 (𝐕-𝐑)𝟐 (𝐕-𝐑)𝟑 σ
G-V -0.03088 -0.04653 -0.8794 0.1733 0.0352
𝐁-𝐕 (𝐁-𝐕)𝟐 (𝐁-𝐕)𝟑 (𝐁-𝐕)𝟒 (𝐁-𝐕)𝟓 σ
GBP-GRP 0.06483 1.575 -0.7815 0.5707 -0.176 0.01916 0.0659
G-V -0.04749 -0.0124 -0.2901 0.02008 0.04772
𝐆BP-𝐆RP (𝐆BP-𝐆RP)𝟐 (𝐆BP-𝐆RP)𝟑 (𝐆BP-𝐆RP)𝟒 σ
G-B 0.01448 -0.6874 -0.3604 0.06718 -0.006061 0.0633
G-R -0.02275 0.3961 -0.1243 -0.01396 0.003775 0.03167
G-V -0.02704 0.01424 -0.2156 0.01426 0.03017
G-IC 0.01753 0.76 -0.0991 0.03765
2MASS relationships
𝐇-𝐊𝐒 (𝐇-𝐊𝐒)𝟐 σ
G-KS 0.5594 11.09 3.040 0.3743
GBP-KS 0.5922 15.36 1.691 0.499
GRP-KS 0.1882 10.3 -3.976 0.2956
GBP-GRP 0.1836 8.456 -3.781 0.2361
𝐆BP-𝐆RP (𝐆BP-𝐆RP)𝟐 σ
G-KS -0.0981 2.089 -0.1579 0.08553
G-H -0.1048 2.011 -0.1758 0.07805
G-J 0.01798 1.389 -0.09338 0.04762
𝐉-𝐊𝐒 (𝐉-𝐊𝐒)2 (𝐉-𝐊𝐒)3 (𝐉-𝐊𝐒)4 σ
GBP-KS 0.1777 5.28 -4.384 4.451 -1.273 0.174
GRP-KS 0.08089 2.655 -1.488 1.618 -0.5068 0.07997
GBP-GRP 0.09396 2.581 -2.782 2.788 -0.8027 0.09668
G-KS 0.1683 3.803 -1.45 0.7867 0.1309
GSC2.3 relationships
𝐆BP-𝐆RP (𝐆BP-𝐆RP)𝟐 σ
J-F (δ0.0) -0.02223 1.225 -0.06094 0.2791
J-F (δ<0.0) -0.03718 1.25 -0.1079 0.6247
G-J (δ0.0) 0.1535 -0.8585 -0.09095 0.2032
G-J (δ<0.0) 0.1819 -0.9921 -0.01864 0.1857
G-F (δ0.0) 0.1601 0.2267 -0.09907 0.1652
G-F (δ<0.0) 0.003457 0.3588 -0.1429 0.2118
𝐉-𝐅 (𝐉-𝐅)2 σ
G-F (δ0.0) 0.006076 0.3817 -0.08016 0.292
G-F (δ<0.0) 0.01069 0.2919 -0.09112 0.1999
G-J (δ0.0) 0.02773 -0.6432 -0.07362 0.2858
G-J (δ<0.0) 0.01615 -0.6868 -0.0654 0.2697
GBP-GRP (δ0.0) 0.42 0.398 0.1181 0.1658
GBP-GRP (δ<0.0) 0.4719 0.4315 0.1111 0.1775
Table 5.10: Range of applicability for the relationships between Gaia DR3 system and other photometric systems.
Hipparcos relationships Tycho-2 relationships
G-HP=f(B-V) -0.25<B-V<1.9a G-VT=f(BT-VT) -0.2<BT-VT<2.0b
G-HP=f(V-I) -0.25<V-I<5.0 G-VT=f(GBP-GRP) -0.35<GBP-GRP<4.0
G-HP=f(GBP-GRP) -0.5<GBP-GRP<4.0 G-BT=f(GBP-GRP) -0.3<GBP-GRP<3.0
GBP-HP=f(V-I) -0.2<V-I<3.0 GBP-VT=f(BT-VT) -0.2<BT-VT<2.5
GRP-HP=f(V-I) -0.4<V-I<3.5 GRP-VT=f(BT-VT) -0.3<BT-VT<2.0c
GBP-GRP=f(V-I) -0.5<V-I<3.5 GBP-GRP=f(BT-VT) -0.3<BT-VT<2.0d
SDSS12 relationships Johnson-Cousins relationships
G-g=f(g-i) -1.0<g-i<9.0 G-V=f(V-IC) -0.4<V-IC<5.0
G-r=f(r-i) -0.5<r-i<2.0 G-V=f(V-R) -0.15<V-R<2.3h
G-i=f(r-i) -0.35<r-i<2.0 G-V=f(B-V) -0.4<B-V<3.3i
GBP-g=f(g-i) -0.6<g-i<3.5 GBP-V=f(V-IC) 0.0<V-IC<4.0
GRP-r=f(r-i) -0.9<g-i<8.0 GRP-V=f(V-IC) -0.4<V-IC<5.0
GBP-GRP=f(g-i) -0.5<g-i<3.5e GBP-GRP=f(V-IC) -0.4<V-IC<5.0
G-r=f(GBP-GRP) 0.0<GBP-GRP<3.0f G-V=f(GBP-GRP) -0.5<GBP-GRP<5.0
G-i=f(GBP-GRP) 0.5<GBP-GRP<2.0 G-R=f(GBP-GRP) 0.0<GBP-GRP<4.0j
G-g=f(GBP-GRP) 0.3<GBP-GRP<3.0g G-IC=f(GBP-GRP) -0.5<GBP-GRP<4.5
G-z=f(g-i) 0.0<g-i<4.0 G-B=f(GBP-GRP) -0.5<GBP-GRP<4.0k
G-z=f(r-i) 0.0<r-i<2.0 GBP-GRP=f(B-V) -0.5<B-V<3.5
G-z=f(GBP-GRP) -0.5<GBP-GRP<4.5
GSC2.3 relationships 2MASS relationships
J-F=f(GBP-GRP), δ0 0.5<GBP-GRP<3.0 G-KS=f(H-KS) -0.1<H-KS<0.4
J-F=f(GBP-GRP), δ<0 0.5<GBP-GRP<2.5 GBP-KS=f(H-KS) -0.1<H-KS<0.4
G-J=f(GBP-GRP), δ0 0.5<GBP-GRP<3.0 GRP-KS=f(H-KS) -0.1<H-KS<0.4
G-J=f(GBP-GRP), δ<0 0.1<GBP-GRP<2.7 GBP-GRP=f(H-KS) -0.1<H-KS<0.4
G-J=f(GBP-GRP), δ0 0.7<GBP-GRP<2.0 G-KS=f(GBP-GRP) -0.5<GBP-GRP<2.5
G-J=f(GBP-GRP), δ<0 0.6<GBP-GRP<2.2 G-H=f(GBP-GRP) -0.5<GBP-GRP<2.5
G-F=f(J-F), δ0 0.5<J-F<2.6 G-J=f(GBP-GRP) -0.5<GBP-GRP<2.5
G-F=f(J-F), δ<0 -1.5<J-F<2.6 G-KS=f(J-KS) -0.2<H-KS<1.1
G-J=f(J-F), δ0 0.1<J-F<3.0 GBP-KS=f(J-KS) -0.2<H-KS<1.1
G-J=f(J-F), δ<0 -1.6<J-F<3.0 GRP-KS=f(J-KS) -0.2<H-KS<1.1
GBP-GRP=f(J-F) , δ0 0.5<J-F<2.5 GBP-GRP=f(J-KS) -0.1<H-KS<1.1
GBP-GRP=f(J-F) , δ<0 0.3<J-F<2.5
a G-HP=f(B-V) is only valid for M giants when B-V>1.4 b G-VT=f(BT-VT) is only valid for M giants when BT-VT>1.7.
c GRP-VT=f(BT-VT) is only valid for M giants when BT-VT>1.7. d GBP-GRP=f(BT-VT) is only valid for M giants when BT-VT>1.7.
e GBP-GRP=f(g-i) is only valid for M giants when GBP-GRP>2.25. f G-r=f(GBP-GRP) is only valid for M giants when GBP-GRP>2.0.
g G-g=f(GBP-GRP) is only valid for M giants when GBP-GRP>2.0. h G-V=f(V-R) is only valid for M giants when V-R>0.9.
i G-V=f(B-V) is only valid for M giants when B-V>1.3. j G-R=f(GBP-GRP) is only valid for M giants when GBP-GRP>2.0.
k G-B=f(GBP-GRP) is only valid for M giants when GBP-GRP>1.75.

Figure 5.34: Photometric relationships obtained using Gaia DR3 data with G<13 cross-matched with Hipparcos data.

Figure 5.35: Photometric relationships obtained using Gaia DR3 data with G<13 mag cross-matched with Tycho-2 data.

Figure 5.36: Photometric relationships obtained using Gaia DR3 data cross-matched with SDSS12 data. Other relationships between the two photometric systems are shown in Figure 5.37.

Figure 5.37: Photometric relationships obtained using Gaia DR3 data cross-matched with SDSS12 data. Other relationships between the two photometric systems are shown in Figure 5.36.

Figure 5.38: Photometric relationships obtained using Gaia DR3 data cross-matched with Johnson-Cousins standard stars in Stetson (2000) included in Gaia DR3. More relationships between the two photometric systems are shown in Figure 5.39.

Figure 5.39: Photometric relationships obtained using Gaia DR3 data cross-matched with Johnson-Cousins standard stars in Stetson (2000) included in Gaia DR3. More relationships between the two photometric systems are shown in Figure 5.38.

Figure 5.40: Photometric relationships obtained using Gaia DR3 data with G<13 mag cross-matched with 2MASS data. Other relationships between the two photometric systems are shown in Figure 5.41.

Figure 5.41: Photometric relationships obtained using Gaia DR3 data with G<13 mag cross-matched with 2MASS data. Other relationships between the two photometric systems are shown in Figure 5.40.

Figure 5.42: Photometric relationships obtained using Gaia DR3 data with G<13 mag cross-matched with GSC2.3 data having positive declination. Relationships for sources with negative declination can be found in Figure 5.43.

Figure 5.43: Photometric relationships obtained using Gaia DR3 data with G<13 mag cross-matched with GSC2.3 data having negative declination. Relationships for sources with positive declination can be found in Figure 5.42.