Summary. Smith et al. standard stars observed from 2003 to July 20 2005 are used to derive transformation equations to put MegaCam observations on the (i) USNO and (ii) SDSS systems. Colour term coefficients can be found in Section 4 , and zeropoints can be found in Section 5. It's best to transform to the USNO system, and use the zeropoints to define a natural MegaCam system that matches the USNO system at zero colour.
where c_g,c_r,c_i,c_z are colour coefficients, k_g,k_r,k_i,k_z are atmospheric extinction coefficients, and the zp_g,zp_r,zp_i,zp_z are the zeropoints. Some notes:
|Type of transform||Stars||Comments|| g
Transformations to USNO (Smith et al.)
|Mega to USNO||Smith stds to 2005Jul20||analstds: pairs of stars, same night (Theil/lsq)||0.090/0.085||0.016/0.007||0.051/0.038||-0.058/-0.054|
|Mega to USNO||Smith stds to 2005Jul20||analstds: pairs of stars, same exp (Theil/lsq)||0.092/0.086||0.017/0.008||0.052/0.039||-0.044/-0.043|
|Mega to USNO||Smith stds to 2005Jul20||analstds: single stars, Q-run corrected (Theil/lsq)||0.096/0.088||0.021/0.008||0.060/0.048||-0.039/-0.060|
Transformations to SDSS
|Mega to SDSS||Smith stds to 2005Jul20||analstds: pairs of stars, same night (Theil/lsq)||0.144/0.139||0.032/0.022||0.094/0.081||-0.077/-0.078|
|Mega to SDSS||Smith stds to 2005Jul20||analstds: pairs of stars, same exp (Theil/lsq)||0.146/0.140||0.033/0.023||0.095/0.082||-0.063/-0.067|
|Mega to SDSS||Smith stds to 2005Jul20||analstds: single stars, Q-run corrected (Theil/lsq)||0.147/0.140||0.036/0.022||0.097/0.083||-0.061/-0.081|
|Mega to SDSS||SDSS DR5||D2 [from Don]||0.143/0.144||0.000/0.002||0.072/0.078||-0.075/-0.078|
|Mega to SDSS||SDSS DR5||D3 [from Don]||0.161/0.160||0.006/0.012||0.085/0.088||-0.064/-0.073|
|Mega to SDSS||synthetic (all)||[from Mark May 24]||0.143||0.020||0.085||-0.035|
Transformations to SDSS, with colour cut
|Mega to SDSS||Smith stds to 2005Jul20 (col cut)||analstds: pairs of stars, same night (Theil/lsq)||0.152/0.146||0.031/0.021||0.092/0.081||-0.077/-0.078|
|Mega to SDSS||Smith stds to 2005Jul20 (col cut)||analstds: pairs of stars, same exp (Theil/lsq)||0.156/0.149||0.031/0.022||0.092/0.080||-0.063/-0.067|
|Mega to SDSS||Smith stds to 2005Jul20 (col cut)||analstds: single stars, Q-run corrected (Theil/lsq)||0.155/0.145||0.034/0.020||0.098/0.087||-0.062/-0.083|
|Mega to SDSS||SDSS DR5 (col cut)||D2 [from Don]||0.140/0.147||0.011/0.007||0.068/0.067||-0.082/-0.089|
|Mega to SDSS||SDSS DR5 (col cut)||D3 [from Don]||0.160/0.160||0.015/0.016||0.073/0.074||-0.085/-0.014!|
|Mega to SDSS||French (col cut)||0.156||0.000||0.094||-0.050|
|Mega to SDSS||synthetic (col cut)||[from Mark May 24]||0.158||0.019||0.086||-0.038|
Transformations to SDSS, with colour cut (limited time interval 2004Dec to 2005Jul)
|Mega to SDSS||Smith stds 2004Dec-2005Jul20 (col cut)||analstds: pairs of stars, same night (Theil/lsq)||0.154/0.150||0.045/0.030||0.087/0.070||-0.109/-0.098|
|Mega to SDSS||Smith stds 2004Dec-2005Jul20 (col cut)||analstds: pairs of stars, same exp (Theil/lsq)||0.158/0.153||0.046/0.036||0.092/0.079||-0.114/-0.010|
|Mega to SDSS||Smith stds 2004Dec-2005Jul20 (col cut)||analstds: single stars, Q-run corrected (Theil/lsq)||0.150/0.147||0.038/0.026||0.086/0.072||-0.104/-0.112|
|Filt||Comments||SDSS transform mean slope||extreme range||Smith transform mean slope|
|g'||Do a straight mean of the 5 determinations (analstds and Don's D2/D3 analysis). Use only Theil slope estimator. Just average over the difference between D2 and D3. Result is 0.153, with an extreme range +0.007 - 0.013. This agrees well with the French 0.156 and synthetic 0.158. It also agrees very well with the direct MegaCam to Smith et al transform (0.093 + 0.060 = 0.153, where the last term is the quoted colour transform going from Smith to SDSS)||0.153*(g-r)|| +0.007 |
|r'||r' is more difficult than g'; there is quite a difference between SDSS D2/D3 determinations on the one hand, and Smith et al stds on the other. But there definitely seems to be a postive slope, contrary to the French (and CFHT) determination of slope=0. A straight average of the 5 methods gives 0.024, with an extreme range of +0.010 and -0.013. The transform to the Smith et al system has a slope 0.018, and correcting to SDSS (0.018 + 0.035*0.6 = 0.039, where the 0.035 is the Smith->SDSS coefficient in r-i, and the 0.6 is the rough slope d(g-r)/d(r-i) [since our colour term is in terms of g-r]), the agreement is not too bad. The agreement with the synthetic term, 0.019, is OK too.||0.024*(g-r)|| +0.010 |
|i'||Again, an offset between Smith et al stars (slope around 0.095) and SDSS stars (0.07). Straight mean give 0.085, with a range +0.013 -0.017 (better than May 30 results). Good agreement with synthetic and French values, and also transform to Smith, corrected to SDSS (0.054 + 0.041 = 0.095).||0.085*(r-i)|| +0.013 |
|z'||Large range, straight mean of 5 methods gives -0.074. Much better consistency with the 5 methods than for May 30 results. Agreement with French (-0.05) and synthetic (-0.038) is not so good however. The MegaCam to Smith et al transform coeff (-0.047) coupled with Smith to SDSS ( -0.03) gives -0.077 - spectacular agreement!||-0.074*(i-z)|| +0.013 |
|Transform to USNO||Transform to SDSS|
|g'||Q run averages||Individual stars||Q run averages||Individual stars|
|r'||Q run averages||Individual stars||Q run averages||Individual stars|
|i'||Q run averages||Individual stars||Q run averages||Individual stars|
|z'||Q run averages||Individual stars||Q run averages||Individual stars|
The columns marked "Q run averages" give zeropoints averaged over a queue run: The data in these files is:
The columns marked Individual stars give zeropoints for each star observation. Note that generally there's more than on star per exposure. The data in these files is:
Basically d(zp) = d(slope) * colmn, where colmn is the mean colour of the stars being analyzed (the "centre of gravity" of the slope fit). Typical mean colours are less than or around 0.5, so a mean slope error of +-0.01 gives a zeropoint uncertainty of +-0.005 - which is tolerable!
In more detail, I've tried jiggling the assumed colour coefficients by +-0.01 to see what the effect is on the derived zeropoints. Here are the results:
So the effects are pretty small.
What the table means - Column 3 gives my best estimate of the colour term for transforming MegaCam mags to the SDSS system. Column 5 gives my best estimate for transforming MegaCam mags to the Smith et al USNO system.
Calibration Procedure - Probably the best procedure is to keep all magnitudes in the MegaCam natural system, and derive the zeropoints using Smith et al stds, without ever going to the SDSS system. In that case we use the MegaCam-to-Smith colour term (column 5), and determine the zeropoint at colour=0 (as this web page explains). The SDSS system is nevertheless useful for consistency checks.
SDSS - Smith et al differences - For use of the SDSS system, the question does arise whether it's better to use the grand average colour terms of column 3 (which average together SDSS DR5 estimates and Smith et al std star estimates), or just stick with the SDSS DR5 estimates. This needs to be discussed. Personally I think that there are systematics affecting all of the determinations of the colour term slopes, and it's better to use the grand average.