Transformations between SDSS magnitudes and other systems
Introduction
Applicable Objects
- Reference
- Applicable Objects
- Jester et al. (2005)
- Stars and redshift ≤ 2.1 quasars
- Jordi et al. (2006)
- Stars, including for Population I and metal-poor Population II stars
- Karaali, Bilir & Tunçel (2005)
- Stars
- Bilir, Karaali & Tunçel (2005)
- Dwarf Stars
- West, Walkowicz & Hawley (2005)
- M and L dwarf stars
- Rodgers et al. (2006)
- Main Sequence Stars
- Lupton (2005)
- Stars
Caveats
- There are currently no transformation equations explicitly for galaxies, but the Jester et al. (2005) and Lupton (2005) transformation equations for stars should also provide reasonable results for normal galaxies (i.e., galaxies without strong emission lines).
- Note that these transformation equations are for the SDSS ugriz (u′g′r′i′z′) magnitudes as measured, not for SDSS ugriz (u′g′r′i′z′) corrected for AB offsets. If you need AB ugriz magnitudes, please remember to convert from SDSS ugriz to AB ugriz using AB offsets described here).
Jester et al. (2005)
The following transformation equations were extracted from Table 1 of Jester et al. (2005) and are generally useful for stars and for quasars. The transformation equations for redshift ≤ 2.1 quasars is based upon synthetic photometry of an updated version of the quasar composite spectrum of Vanden Berk et al. (2001) using DR1 data as well as the red and reddened quasar composites for Richards et al. (2003). The transformations for stars were derived from the Smith et al. (2002) u′g′r′i′z′ photometry of Landolt stars, suitably transformed from the USNO-1.0m u′g′r′i′z′ system to the SDSS 2.5m ugriz system via the u′g′r′i′z′-to-ugriz transformations. The transformation equations for stars supersede those of Fukugita et al. (1996) and Smith et al. (2002).
UBVRcIc -> ugriz ================ Quasars at z <= 2.1 (synthetic) Transformation RMS residual u-g = 1.25*(U-B) + 1.02 0.03 g-r = 0.93*(B-V) - 0.06 0.09 r-i = 0.90*(Rc-Ic) - 0.20 0.07 r-z = 1.20*(Rc-Ic) - 0.20 0.18 g = V + 0.74*(B-V) - 0.07 0.02 r = V - 0.19*(B-V) - 0.02 0.08 Stars with Rc-Ic < 1.15 and U-B < 0 Transformation RMS residual u-g = 1.28*(U-B) + 1.14 0.05 g-r = 1.09*(B-V) - 0.23 0.04 r-i = 0.98*(Rc-Ic) - 0.22 0.01 r-z = 1.69*(Rc-Ic) - 0.42 0.03 g = V + 0.64*(B-V) - 0.13 0.01 r = V - 0.46*(B-V) + 0.11 0.03 All stars with Rc-Ic < 1.15 Transformation RMS residual u-g = 1.28*(U-B) + 1.13 0.06 g-r = 1.02*(B-V) - 0.22 0.04 r-i = 0.91*(Rc-Ic) - 0.20 0.03 r-z = 1.72*(Rc-Ic) - 0.41 0.03 g = V + 0.60*(B-V) - 0.12 0.02 r = V - 0.42*(B-V) + 0.11 0.03 ugriz -> UBVRcIc ================ Quasars at z <= 2.1 (synthetic) Transformation RMS residual U-B = 0.75*(u-g) - 0.81 0.03 B-V = 0.62*(g-r) + 0.15 0.07 V-R = 0.38*(r-i) + 0.27 0.09 Rc-Ic = 0.72*(r-i) + 0.27 0.06 B = g + 0.17*(u-g) + 0.11 0.03 V = g - 0.52*(g-r) - 0.03 0.05 Stars with Rc-Ic < 1.15 and U-B < 0 Transformation RMS residual U-B = 0.77*(u-g) - 0.88 0.04 B-V = 0.90*(g-r) + 0.21 0.03 V-R = 0.96*(r-i) + 0.21 0.02 Rc-Ic = 1.02*(r-i) + 0.21 0.01 B = g + 0.33*(g-r) + 0.20 0.02 V = g - 0.58*(g-r) - 0.01 0.02 All stars with Rc-Ic < 1.15 Transformation RMS residual U-B = 0.78*(u-g) - 0.88 0.05 B-V = 0.98*(g-r) + 0.22 0.04 V-R = 1.09*(r-i) + 0.22 0.03 Rc-Ic = 1.00*(r-i) + 0.21 0.01 B = g + 0.39*(g-r) + 0.21 0.03 V = g - 0.59*(g-r) - 0.01 0.01
Jordi et al. (2005)
UBVRcIc -> ugriz ================ Transformation u-g = (0.750 ± 0.050)*(U-B) + (0.770 ± 0.070)*(B-V) + (0.720 ± 0.040) g-V = (0.630 ± 0.002)*(B-V) - (0.124 ± 0.002) g-B = (-0.370 ± 0.002)*(B-V) - (0.124 ± 0.002) g-r = (1.646 ± 0.008)*(V-R) - (0.139 ± 0.004) g-i = (1.481 ± 0.004)*(V-I) - (0.536 ± 0.004) if V-I <= 1.8 g-i = (0.83 ± 0.01)*(V-I) + (0.60 ± 0.03) if V-I > 1.8 r-i = (1.007 ± 0.005)*(R-I) - (0.236 ± 0.003) r-z = (1.584 ± 0.008)*(R-I) - (0.386 ± 0.005) r-R = (0.267 ± 0.005)*(V-R) + (0.088 ± 0.003) if V-R <= 0.93 r-R = (0.77 ± 0.04)*(V-R) - (0.37 ± 0.04) if V-R > 0.93 i-I = (0.247 ± 0.003)*(R-I) + (0.329 ± 0.002) ugriz -> UBVRcIc ================ Transformation U-B = (0.79 ± 0.02)*(u-g) - (0.93 ± 0.02) U-B = (0.52 ± 0.06)*(u-g) + (0.53 ± 0.09)*(g-r) - (0.82 ± 0.04) B-g = (0.175 ± 0.002)*(u-g) + (0.150 ± 0.003) B-g = (0.313 ± 0.003)*(g-r) + (0.219 ± 0.002) V-g = (-0.565 ± 0.001)*(g-r) - (0.016 ± 0.001) V-I = (0.675 ± 0.002)*(g-i) + (0.364 ± 0.002) if g-i <= 2.1 V-I = (1.11 ± 0.02)*(g-i) - (0.52 ± 0.05) if g-i > 2.1 R-r = (-0.153 ± 0.003)*(r-i) - (0.117 ± 0.003) R-I = (0.930 ± 0.005)*(r-i) + (0.259 ± 0.002) I-i = (-0.386 ± 0.004)*(i-z) - (0.397 ± 0.001)
The following transformation equations were extracted from Table 4 of Jordi et al. (2006) and are generally useful for Population I and metal-poor Population II stars, respectively. The transformations for the Population II stars are derived from comparing Stetson fields around Draco, NGC 2419 and NGC 7078 with their SDSS DR4 photometry. The transformations for the Population I stars are derived from the Stetson extension of Landolt's equatorial fields compared with the SDSS DR4 photometry. The transformation equation for Population II stars including the SDSS (i-z)-color is not calculated, because of the small number of stars.
BVRcIc -> griz ============== Transformation for Population I stars: g-V = (0.634 ± 0.002)*(B-V) - (0.127 ± 0.002) g-B = (-0.366 ± 0.002)*(B-V) - (0.126 ± 0.002) g-r = (1.599 ± 0.009)*(V-R) - (0.106 ± 0.006) g-i = (1.474 ± 0.004)*(V-I) - (0.518 ± 0.005) if V-I <= 1.8 g-i = (0.83 ± 0.01)*(V-I) + (0.62 ± 0.03) if V-I > 1.8 r-i = (0.988 ± 0.006)*(R-I) - (0.221 ± 0.004) r-z = (1.568 ± 0.009)*(R-I) - (0.370 ± 0.006) r-R = (0.275 ± 0.006)*(V-R) + (0.086 ± 0.004) if V-R <= 0.93 r-R = (0.71 ± 0.05)*(V-R) - (0.31 ± 0.05) if V-R > 0.93 i-I = (0.251 ± 0.003)*(R-I) + (0.325 ± 0.002) Transformation for metal-poor Population II stars: g-V = (0.596 ± 0.009)*(B-V) - (0.148 ± 0.007) g-B = (-0.401 ± 0.009)*(B-V) - (0.145 ± 0.006) g-r = (1.72 ± 0.02)*(V-R) - (0.198 ± 0.007) g-i = (1.48 ± 0.01)*(V-I) - (0.57 ± 0.01) if V-I <= 1.8 r-i = (1.06 ± 0.02)*(R-I) - (0.30 ± 0.01) r-z = (1.60 ± 0.06)*(R-I) - (0.46 ± 0.03) r-R = (0.34 ± 0.02)*(V-R) + (0.015 ± 0.008) if V-R <= 0.93 i-I = (0.21 ± 0.02)*(R-I) + (0.34 ± 0.01) griz -> BVRcIc ============== Transformation for Population I stars: B-g = (0.163 ± 0.002)*(u-g) + (0.170 ± 0.004) B-g = (0.312 ± 0.003)*(g-r) + (0.219 ± 0.002) V-g = (-0.573 ± 0.002)*(g-r) - (0.016 ± 0.002) V-I = (0.671 ± 0.002)*(g-i) + (0.359 ± 0.002) if g-i <= 2.1 V-I = (1.12 ± 0.02)*(g-i) - (0.53 ± 0.06) if g-i > 2.1 R-r = (-0.257 ± 0.004)*(r-i) + (0.152 ± 0.002) R-I = (0.977 ± 0.006)*(r-i) + (0.234 ± 0.003) I-i = (-0.409 ± 0.006)*(i-z) - (0.394 ± 0.002) Transformation for metal-poor Population II stars: B-g = (0.20 ± 0.01)*(u-g) + (0.15 ± 0.01) B-g = (0.349 ± 0.009)*(g-r) + (0.245 ± 0.006) V-g = (-0.569 ± 0.007)*(g-r) + (0.021 ± 0.004) V-I = (0.674 ± 0.005)*(g-i) + (0.406 ± 0.004) if g-i <= 2.1 R-r = (-0.25 ± 0.02)*(r-i) - (0.119 ± 0.005) R-I = (0.80 ± 0.02)*(r-i) + (0.317 ± 0.004)
Karaali, Bilir & Tunçel (2005)
UBVRcIc -> ugriz ================ Stars with 0.3 < B-V < 1.1 u-g = 0.779*(U-B) + 0.755*(B-V) + 0.801 g-r = 1.023*(B-V) + 0.016*(U-B) - 0.187 ugriz -> UBVRcIc ================ Stars with 0.3 < B-V < 1.1 B-V = 0.992*(g-r) - 0.0199*(u-g) + 0.202
Bilir, Karaali & Tunçel (2005)
UBVRcIc -> ugriz ================ Dwarf (Main Sequence) Stars g-r = 1.124*(B-V) - 0.252 r-i = 1.040*(R-I) - 0.224 g = V + 0.634*(B-V) - 0.108
West, Walkowicz & Hawley (2005)
UBVRcIc -> ugriz ================ M0-L0 Dwarfs, 0.67 <= r-i <= 2.01 Transformation RMS residual r-i = -2.69 + 2.29*(V-Ic) 0.05 - 0.28*(V-Ic)**2 M0-L0 Dwarfs, 0.37 <= i-z <= 1.84 Transformation RMS residual i-z = -20.6 + 26.0*(Ic-Ks) 0.10 - 11.7*(Ic-Ks)**2 - 2.30*(Ic-Ks)**3 - 0.17*(Ic-Ks)**4
Rodgers et al. (2006)
UBVRcIc -> u'g'r'i'z' ===================== Main Sequence Stars u'-g' = (1.101 ± 0.004)*(U-B) + (0.358 ± 0.004)*(B-V) + 0.971 g'-r' = (0.278 ± 0.016)*(B-V) + (1.321 ± 0.030)*(V-Rc) - 0.219 r'-i' = (1.000 ± 0.006)*(Rc-Ic) - 0.212 r'-z' = (1.567 ± 0.020)*(Rc-Ic) - 0.365
Lupton (2005)
Stars B = u - 0.8116*(u - g) + 0.1313; sigma = 0.0095 B = g + 0.3130*(g - r) + 0.2271; sigma = 0.0107 V = g - 0.2906*(u - g) + 0.0885; sigma = 0.0129 V = g - 0.5784*(g - r) - 0.0038; sigma = 0.0054 R = r - 0.1837*(g - r) - 0.0971; sigma = 0.0106 R = r - 0.2936*(r - i) - 0.1439; sigma = 0.0072 I = r - 1.2444*(r - i) - 0.3820; sigma = 0.0078 I = i - 0.3780*(i - z) -0.3974; sigma = 0.0063
Here is the CAS SQL query Robert used to perform the matchup of DR4 photometry with Stetson's:
SELECT dbo.fSDSS(P.objId) AS ID, name, S.B, S.Berr, S.V, S.Verr , S.R, S.Rerr, S.I, S.Ierr, psfMag_u, psfMagErr_u, psfMag_g, psfMagErr_g, psfMag_r, psfMagErr_r, psfMag_i, psfMagErr_i, psfMag_z, psfMagErr_z, (CASE WHEN 0 = (flags_u & 0x800d00000000000) AND status_u = 0 THEN 1 ELSE 0 END) AS good_u, (CASE WHEN 0 = (flags_g & 0x800d00000000000) AND status_g = 0 THEN 1 ELSE 0 END) AS good_g, (CASE WHEN 0 = (flags_r & 0x800d00000000000) AND status_r = 0 THEN 1 ELSE 0 END) AS good_r, (CASE WHEN 0 = (flags_i & 0x800d00000000000) AND status_i = 0 THEN 1 ELSE 0 END) AS good_i, (CASE WHEN 0 = (flags_z & 0x800d00000000000) AND status_z = 0 THEN 1 ELSE 0 END) AS good_z FROM stetson AS S JOIN star AS P ON S.objId = P.objId JOIN field AS F ON P.fieldId = F.fieldId WHERE 0 = (flags & 0x40006);