5.3.7 Photometric relationships with other photometric systems

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).

Table 5.5: Filters applied and the resulting number of sources used to fit the photometric relationships in Table 5.7.
Tycho-2 filtering
Non-variable sources, G<13, e1.5+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, e1.5+0.03(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 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-I0.0 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-I0.0 76 428 sources
GRP-HP=f(V-I) σHP<0.1, σGRP<0.01, V-I0.0 76 660 sources
GBP-GRP=f(V-I) σGBP<0.1, σGRP<0.01, V-I0.0 76 037 sources
SDSS12 filtering
Non-variable sources, e1.3+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
Notes. First column: relationship. Second column: criteria applied. Third column: Number of sources used.
Table 5.6: Filters applied and the resulting number of sources used to fit the photometric relationships in Table 5.8.
Johnson-Cousins filtering
Non-variable sources, G<13, e1.5+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, e1.5+0.03(GBP-GRP)2
G-K=f(H-K) σG<0.01, σH and σK<0.03, G-K13(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, e1.3+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
Notes. First column: relationship. Second column: filtering criteria applied. Third column: Number of sources used.
Table 5.7: Coefficients of the polynomials for sources in common with Hipparcos, Tycho-2, SDSS12 and Johnson-Cousins observed in Gaia DR2.
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
Table 5.8: Coefficients of the polynomials in common with 2MASS and GSC2.3 for sources observed in Gaia DR2.
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 (δ0.0) -0.10948 1.4553 -0.14375 0.32231
J-F (δ<0.0) -0.1621 1.4348 -0.16587 0.40361
G-J (δ0.0) 0.092602 -0.87175 -0.061304 0.3658
G-J (δ<0.0) 0.12609 -0.89624 -0.04906 0.24571
G-F (δ0.0) 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 (δ0.0) -0.031048 0.48358 -0.14923 0.2302
G-F (δ<0.0) -0.076434 0.52101 -0.14503 0.28117
G-J (δ0.0) -0.11371 -0.35619 -0.20973 0.19187
G-J (δ<0.0) -0.096134 -0.39097 -0.18957 0.25026
GBP-GRP (δ0.0) 0.23021 0.54188 0.10319 0.15494
GBP-GRP (δ<0.0) 0.25408 0.62881 0.066154 0.2028
Table 5.9: Range of applicability for the relationships found here between Gaia passbands and other photometric systems.
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.

Figure 5.11: Photometric relationships obtained using Gaia DR2 data with G<13 cross-matched with Hipparcos data.

Figure 5.12: Photometric relationships obtained using Gaia DR2 data with G<13 mag cross-matched with Tycho-2 data.

Figure 5.13: Photometric relationships obtained using Gaia DR2 data cross-matched with SDSS12 data. More relationships between the two photometric systems are shown in Figure 5.14.

Figure 5.14: Photometric relationships obtained using Gaia DR2 data cross-matched with SDSS12 data. More relationships between the two photometric systems are shown in Figure 5.13.

Figure 5.15: Johnson-Cousins relationships using Landolt standard stars observed with Gaia. More relationships between the two photometric systems are shown in Figure 5.16

Figure 5.16: Johnson-Cousins relationships using Landolt standard stars observed with Gaia. More relationships between the two photometric systems are shown in Figure 5.15

Figure 5.17: Photometric relationships obtained using Gaia DR2 data with G<13 mag cross-matched with 2MASS data. More relationships between the two photometric systems are shown in Figure 5.18 and Figure 5.19.

Figure 5.18: Photometric relationships obtained using Gaia DR2 data with G<13 mag cross-matched with 2MASS data. More relationships between the two photometric systems are shown in Figure 5.17 and Figure 5.19 .

Figure 5.19: Photometric relationships obtained using Gaia DR2 data with G<13 mag cross-matched with 2MASS data. More relationships between the two photometric systems are shown in Figure 5.17 and Figure 5.18.

Figure 5.20: Photometric relationships obtained using Gaia DR2 data with G<13 mag cross-matched with GSC2.3 data having positive declination. Relationships for sources with negative declination can be found in Fig. 5.21.

Figure 5.21: Photometric relationships obtained using Gaia DR2 data with G<13 mag cross-matched with GSC2.3 data having negative declination. Relationships for sources with positive declination can be found in Fig. 5.20.