Transformations between SDSS magnitudes and UBVR_{c}I_{c}
There have been several efforts in calculating transformation equations
between ugriz (or u'g'r'i'z') and UBVR_{c}I_{c}.
Here, we focus on seven of the most current efforts:
 Jester al. (2005),
who derived transformation equations for stars and for z<=2.1 quasars,
 Jordi al. (2006),
who derived general transformation equations for stars, as well
as separate ones for Population I and metalpoor population II stars,
 Kiraali, Bilir, and Tuncel (2005),
who derived transformation equations for stars,
 Bilir, Karaali, and Tuncel (2005),
who derived transformation equations for dwarf stars, and
 West, Walkowicz, and Hawley (2005),
who derived transformation equations for M and L dwarf stars,
 Rodgers et al. (2005),
who derived transformation equations for main sequence stars.
 Lupton (2005),
who derived transformation equations for stars.
There are currently no transformation equations explicitly for
galaxies, but Jester al.'s (2005) and Lupton's (2005) transformation equations for
stars should also provide reasonable results for normal galaxies
(i.e., galaxies without strong emission lines).
Caveat: 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 at this
URL).
At the end of this webpage, we estimate the ugriz colors of Vega and the Sun.
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 z<=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 USNO1.0m u'g'r'i'z' system to the SDSS
2.5m ugriz system via the u'g'r'i'z'tougriz
transformations.
The transformation equations for stars supercede those of
Fukugita et al.(1996) and
Smith et al. (2002).
UBVRcIc > ugriz
================
Quasars at z <= 2.1 (synthetic)
Transformation RMS residual
ug = 1.25*(UB) + 1.02 0.03
gr = 0.93*(BV)  0.06 0.09
ri = 0.90*(RcIc)  0.20 0.07
rz = 1.20*(RcIc)  0.20 0.18
g = V + 0.74*(BV)  0.07 0.02
r = V  0.19*(BV)  0.02 0.08
Stars with RcIc < 1.15 and UB < 0
Transformation RMS residual
ug = 1.28*(UB) + 1.14 0.05
gr = 1.09*(BV)  0.23 0.04
ri = 0.98*(RcIc)  0.22 0.01
rz = 1.69*(RcIc)  0.42 0.03
g = V + 0.64*(BV)  0.13 0.01
r = V  0.46*(BV) + 0.11 0.03
All stars with RcIc < 1.15
Transformation RMS residual
ug = 1.28*(UB) + 1.13 0.06
gr = 1.02*(BV)  0.22 0.04
ri = 0.91*(RcIc)  0.20 0.03
rz = 1.72*(RcIc)  0.41 0.03
g = V + 0.60*(BV)  0.12 0.02
r = V  0.42*(BV) + 0.11 0.03
ugriz > UBVRcIc
================
Quasars at z <= 2.1 (synthetic)
Transformation RMS residual
UB = 0.75*(ug)  0.81 0.03
BV = 0.62*(gr) + 0.15 0.07
VR = 0.38*(ri) + 0.27 0.09
RcIc = 0.72*(ri) + 0.27 0.06
B = g + 0.17*(ug) + 0.11 0.03
V = g  0.52*(gr)  0.03 0.05
Stars with RcIc < 1.15 and UB < 0
Transformation RMS residual
UB = 0.77*(ug)  0.88 0.04
BV = 0.90*(gr) + 0.21 0.03
VR = 0.96*(ri) + 0.21 0.02
RcIc = 1.02*(ri) + 0.21 0.01
B = g + 0.33*(gr) + 0.20 0.02
V = g  0.58*(gr)  0.01 0.02
All stars with RcIc < 1.15
Transformation RMS residual
UB = 0.78*(ug)  0.88 0.05
BV = 0.98*(gr) + 0.22 0.04
VR = 1.09*(ri) + 0.22 0.03
RcIc = 1.00*(ri) + 0.21 0.01
B = g + 0.39*(gr) + 0.21 0.03
V = g  0.59*(gr)  0.01 0.01
Jordi et al. (2006)
The following transformation equations were extracted from Table 3
of Jordi et
al. (2006) and are generally useful for stars. They are derived from comparing Stetson's extension of the Landolt standard stars with the corresponding SDSS DR4 photometry. The equations including the Johnson U band are based on the comparison of Landolt's original standard stars and the SDSS DR4.
UBVRcIc > ugriz
================
Transformation
ug = (0.750 ± 0.050)*(UB) + (0.770 ± 0.070)*(BV) + (0.720 ± 0.040)
gV = (0.630 ± 0.002)*(BV)  (0.124 ± 0.002)
gB = (0.370 ± 0.002)*(BV)  (0.124 ± 0.002)
gr = (1.646 ± 0.008)*(VR)  (0.139 ± 0.004)
gi = (1.481 ± 0.004)*(VI)  (0.536 ± 0.004) if VI <= 1.8
gi = (0.83 ± 0.01)*(VI) + (0.60 ± 0.03) if VI > 1.8
ri = (1.007 ± 0.005)*(RI)  (0.236 ± 0.003)
rz = (1.584 ± 0.008)*(RI)  (0.386 ± 0.005)
rR = (0.267 ± 0.005)*(VR) + (0.088 ± 0.003) if VR <= 0.93
rR = (0.77 ± 0.04)*(VR)  (0.37 ± 0.04) if VR > 0.93
iI = (0.247 ± 0.003)*(RI) + (0.329 ± 0.002)
ugriz > UBVRcIc
================
Transformation
UB = (0.79 ± 0.02)*(ug)  (0.93 ± 0.02)
UB = (0.52 ± 0.06)*(ug) + (0.53 ± 0.09)*(gr)  (0.82 ± 0.04)
Bg = (0.175 ± 0.002)*(ug) + (0.150 ± 0.003)
Bg = (0.313 ± 0.003)*(gr) + (0.219 ± 0.002)
Vg = (0.565 ± 0.001)*(gr)  (0.016 ± 0.001)
VI = (0.675 ± 0.002)*(gi) + (0.364 ± 0.002) if gi <= 2.1
VI = (1.11 ± 0.02)*(gi)  (0.52 ± 0.05) if gi > 2.1
Rr = (0.153 ± 0.003)*(ri)  (0.117 ± 0.003)
RI = (0.930 ± 0.005)*(ri) + (0.259 ± 0.002)
Ii = (0.386 ± 0.004)*(iz)  (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
metalpoor 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 (iz)color is not calculated, because of the small
number of stars.
BVRcIc > griz
================
Transformation for Population I stars:
gV = (0.634 ± 0.002)*(BV)  (0.127 ± 0.002)
gB = (0.366 ± 0.002)*(BV)  (0.126 ± 0.002)
gr = (1.599 ± 0.009)*(VR)  (0.106 ± 0.006)
gi = (1.474 ± 0.004)*(VI)  (0.518 ± 0.005) if VI <= 1.8
gi = (0.83 ± 0.01)*(VI) + (0.62 ± 0.03) if VI > 1.8
ri = (0.988 ± 0.006)*(RI)  (0.221 ± 0.004)
rz = (1.568 ± 0.009)*(RI)  (0.370 ± 0.006)
rR = (0.275 ± 0.006)*(VR) + (0.086 ± 0.004) if VR <= 0.93
rR = (0.71 ± 0.05)*(VR)  (0.31 ± 0.05) if VR > 0.93
iI = (0.251 ± 0.003)*(RI) + (0.325 ± 0.002)
Transformation for metalpoor Population II stars:
gV = (0.596 ± 0.009)*(BV)  (0.148 ± 0.007)
gB = (0.401 ± 0.009)*(BV)  (0.145 ± 0.006)
gr = (1.72 ± 0.02)*(VR)  (0.198 ± 0.007)
gi = (1.48 ± 0.01)*(VI)  (0.57 ± 0.01) if VI <= 1.8
ri = (1.06 ± 0.02)*(RI)  (0.30 ± 0.01)
rz = (1.60 ± 0.06)*(RI)  (0.46 ± 0.03)
rR = (0.34 ± 0.02)*(VR) + (0.015 ± 0.008) if VR <= 0.93
iI = (0.21 ± 0.02)*(RI) + (0.34 ± 0.01)
griz > BVRcIc
================
Transformation for Population I stars:
Bg = (0.163 ± 0.002)*(ug) + (0.170 ± 0.004)
Bg = (0.312 ± 0.003)*(gr) + (0.219 ± 0.002)
Vg = (0.573 ± 0.002)*(gr)  (0.016 ± 0.002)
VI = (0.671 ± 0.002)*(gi) + (0.359 ± 0.002) if gi <= 2.1
VI = (1.12 ± 0.02)*(gi)  (0.53 ± 0.06) if gi > 2.1
Rr = (0.257 ± 0.004)*(ri) + (0.152 ± 0.002)
RI = (0.977 ± 0.006)*(ri) + (0.234 ± 0.003)
Ii = (0.409 ± 0.006)*(iz)  (0.394 ± 0.002)
Transformation for metalpoor Population II stars:
Bg = (0.20 ± 0.01)*(ug) + (0.15 ± 0.01)
Bg = (0.349 ± 0.009)*(gr) + (0.245 ± 0.006)
Vg = (0.569 ± 0.007)*(gr) + (0.021 ± 0.004)
VI = (0.674 ± 0.005)*(gi) + (0.406 ± 0.004) if gi <= 2.1
Rr = (0.25 ± 0.02)*(ri)  (0.119 ± 0.005)
RI = (0.80 ± 0.02)*(ri) + (0.317 ± 0.004)
Karaali, Bilir, and Tuncel (2005)
These transformations appeared in
Karaali, Bilir, and Tuncel (2005). They are based on Landolt
(1992) UBV data for 224 stars in the color range 0.3 < BV < 1.1 with
SDSS ugr photometry from the CASU INT Wide Field
Survey. An improvement over previous SDSS<>UBVR_{c}I_{c}
transformations is the use of two colors in each equation, which is
particularly helpful for the ug transformation.
UBVRcIc > ugriz
================
Stars with 0.3 < BV < 1.1
ug = 0.779*(UB) + 0.755*(BV) + 0.801
gr = 1.023*(BV) + 0.016*(UB)  0.187
ugriz > UBVRcIc
================
Stars with 0.3 < BV < 1.1
BV = 0.992*(gr)  0.0199*(ug) + 0.202
Bilir, Karaali, and Tuncel (2005)
These transformation equations appeared in
Bilir, Karaali, and Tuncel (2005, AN 326, 321). They are based
upon 195 dwarf stars that have both ugriz photometry and Landolt UBV
photometry.
UBVRcIc > ugriz
================
Dwarf (Main Sequence) Stars
gr = 1.124*(BV)  0.252
ri = 1.040*(RI)  0.224
g = V + 0.634*(BV)  0.108
West, Walkowicz, and Hawley (2005)
These transformation equations appeared in
West, Walkowicz, and Hawley (2005, PASP 117, 706). They are based
upon photometry of M and L dwarf stars from SDSS Data Release 3.
UBVRcIc > ugriz
================
M0L0 Dwarfs, 0.67 <= ri <= 2.01
Transformation RMS residual
ri = 2.69 + 2.29*(VIc) 0.05
 0.28*(VIc)**2
M0L0 Dwarfs, 0.37 <= iz <= 1.84
Transformation RMS residual
iz = 20.6 + 26.0*(IcKs) 0.10
 11.7*(IcKs)**2
 2.30*(IcKs)**3
 0.17*(IcKs)**4
Rodgers et al. (2005)
These equations are from Rodgers et al. (2005, AJ, submitted). They
are based upon a set of main sequence stars from the
Smith et al. (2002) u'g'r'i'z' standard star network that also
have Landolt UBVR_{c}I_{c} photometry. Note that
these equations, strictly speaking, transform from
UBVR_{c}I_{c} to u'g'r'i'z' and not to ugriz. The transformation from
u'g'r'i'z' to ugriz, however, is rather small. Note also, as with
the Karaali, Bilir, and Tuncel (2005)
transformations listed above, two colors are used in the u'g' and
g'r' equations to improve the fits. The use of two colors in the
fits is especially useful for u'g', which is strongly affected by the
Balmer discontinuity.
UBVRcIc > u'g'r'i'z'
=====================
Main Sequence Stars
u'g' = 1.101(+/0.004)*(UB) + 0.358(+/0.004)*(BV) + 0.971
g'r' = 0.278(+/0.016)*(BV) + 1.321(+/0.030)*(VRc)  0.219
r'i' = 1.070(+/0.009)*(RcIc)  0.228
r'z' = 1.607(+/0.012)*(RcIc)  0.371
Lupton (2005)
These equations that Robert Lupton derived by matching DR4
photometry to Peter Stetson's published photometry for stars.
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)
Estimates for the ugriz Colors of Vega and the Sun
Assuming V=+0.03 and UB = BV = VR_{c} =
R_{c}I_{c} = 0.00, we find for the A0V star Vega the
following:
g = 0.08 (+/0.03)
ug = +1.02 (+/0.08)
gr = 0.25 (+/0.03)
ri = 0.23 (+/0.02)
iz = 0.17 (+/0.02)
where we used the Bilir, Karaali, and Tuncel
(2005) transformation for g and the Rodgers et
al. (2005) transformations (plus the u'g'r'i'z'tougriz
transformations) for the ug, gr, ri, and iz colors.
The error bars in parentheses are rough estimates
of the systematic errors based upon the different values
that different sets of transformation equations yield.
Assuming M(V)=+4.82, UB=+0.195, BV=+0.650,
VR_{c}=+0.36, and R_{c}I_{c}=+0.32,
we find for the Sun the following:
M(g)= +5.12 (+/0.02)
ug = +1.43 (+/0.05)
gr = +0.44 (+/0.02)
ri = +0.11 (+/0.02)
iz = +0.03 (+/0.02)
where, again, we used the Bilir, Karaali, and
Tuncel (2005) transformation for g and the Rodgers et al. (2005) transformations (plus
the u'g'r'i'z'tougriz
transformations) for the ug, gr, ri, and iz colors. As above,
the error bars in parentheses are rough estimates of the systematic
errors based upon the different values that different sets of
transformation equations yield.
This page was last modified on $Date: 2008/10/24 11:20:48 $ (UT).
