Algorithm Descriptions

## Transformations between SDSS magnitudes and UBVR |

There have been several efforts in calculating transformation equations
between ugriz (or u'g'r'i'z') and UBVR - Jester al. (2005), who derived transformation equations for stars and for z<=2.1 quasars,
- 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 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 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 supercede 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 ## 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 < B-V < 1.1 with
SDSS ugr photometry from the CASU INT Wide Field
Survey. An improvement over previous SDSS<->UBVR 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, 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 g-r = 1.124*(B-V) - 0.252 r-i = 1.040*(B-V) - 0.224 g = V + 0.634*(B-V) - 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 ================ 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. (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 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' = 1.070(+/-0.009)*(Rc-Ic) - 0.228 r'-z' = 1.607(+/-0.012)*(Rc-Ic) - 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 SunAssuming V=+0.03 and U-B = B-V = V-R g = -0.08 (+/-0.03) u-g = +1.02 (+/-0.08) g-r = -0.25 (+/-0.03) r-i = -0.23 (+/-0.02) i-z = -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'-to-ugriz transformations) for the u-g, g-r, r-i, and i-z 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, U-B=+0.195, B-V=+0.650,
V-R M(g)= +5.12 (+/-0.02) u-g = +1.43 (+/-0.05) g-r = +0.44 (+/-0.02) r-i = +0.11 (+/-0.02) i-z = +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'-to-ugriz transformations) for the u-g, g-r, r-i, and i-z 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. Last modified: Mon Apr 10 21:30:06 BST 2006 |