# Colours and Transformations

## Transformations Between Filter Systems

Using WFS observations of Landolt Standard fields (Landolt 1992, AJ 104, 340), we provide relations for tranforming between the natural WFC system (filter+detector, Vega-like) and this other common observing systems.

Provisional Colour Terms
Filter CombinationLandolt TransformNotes
URGO-ULan-0.084(U-B)Lan+0.106
BKPNO-BLan-0.129(B-V)Lan
VHarris-VLan-0.009(V-R)Lan
VHarris-VLan-0.005(V-I)Lan
RHarris-RLan-0.010(V-R)Lan
IHarris-ILan-0.062(R-I)Lan
IHarris-ILan-0.009(V-I)Lan
ZRGO-ILan-0.381(R-I)Lan
gCCD-BLan-0.531(B-V)Lan+0.053
rCCD-RLan+0.245(V-R)Lan+0.01923/9/03: previous value (-0.245) wrong
rCCD-RLan+0.275(R-I)Lan+0.008 minor (<1%) change
iCCD-ILan+0.211(R-I)Lan
iCCD-ILan+0.101(V-I)Lan

Some examples for using these terms in conjuction with the zeropoints are here:

1. BCCD = ZPB - 2.5 log10(counts/s) = BLan - 0.129 (B-V)Lan
2. gCCD = ZPg - 2.5 log10(counts/s) = BLan - 0.521 (B-V)Lan
3. ZCCD = ZPZ - 2.5 log10(counts/s) = ILan - 0.381 (R-I)Lan

Note that the Z-band Landolt zero-point is in the natural WFC filter + CCD passband and has been approximately normalised to the Vega system using an extrapolated colour correction for the Landolt photometry.

## Transforming between WFS magnitudes and SLOAN AB

The following equations were derived using stellar objects with good photometry in both SLOAN and WFS in the ELAIS N1 area:

 uAB = u + 0.845 gAB = g - 0.10 + 0.12 * (g - r) rAB = r + 0.10 - 0.02 * (g - r) iAB = i + 0.26 + 0.09 * (r - i) zAB = z + 0.43 + 0.01 * (i - z)

where uAB,...,zAB are the magnitudes in the SLOAN system and u,...,z are the magnitudes in the WFS system (Vega), i.e.,

u = ZPu - 2.5*log10(counts/s)

## Transforming Colours

Using standards measured over five runs with good conditions in Jul 1999, Sep1999, Oct1999, Jun2000 and Sep2000 we find the following colour-equations to transform between the Landolt (Johnson-Cousin's) and WFS natural filter+ccd (Vega) systems.

Please exercise caution when using these relations, they have not been thoroughly tested, and do not yet include error analysis. For example the offsets in the relations should be equal to zero (i.e the case for an A0 star with colour defined to be zero between all passbands). I'm not yet sure whether these values are within error.

(g-r)CCD=0.908(B-V)Lan+0.048

(r-i)CCD=1.052(R-I)Lan+0.004

(i-Z)CCD=0.715(R-I)Lan-0.056

(URGO-BKPNO)CCD=1.022(U-B)Lan+0.156

(BKPNO-VHarris)CCD=0.904(B-V)Lan+0.004

I've saved the U-g colour till last as it's the most complicated given there is a degeneracy in U-B (and U-g) around the balmer jump. The following prescriptions seem to work reasonably well and are in reasonable agreement with data where there are sufficient blue stars (see colour-colour plot at bottom of page).

 (U-g)CCD=1.271(U-B)Lan+0.37 (for B-V>0.5) (U-g)CCD=1.271(U-B)Lan (for 0.5>=B-V>0) (U-g)CCD=(U-B)Lan (for 0.0>B-V)

The following data are from WFC imaging of the Ursa Minor dwarf galaxy which shows a nice horizontal branch. This isochrone is from the Hyades UBV data and converted to Ugr using the relations above.