Photometry systems

Question

I know there's a difference between the ugriz and u'g'r'i'z' systems of photometric magnitude, but I also sometimes see UGRIZ written. Is there a difference between a UGRIZ magnitude and a ugriz magnitude?

I'm trying to apply the method from the paper Photometric Redshifts of Quasars (Richards et al. 2001, ApJ 122, 1151-1162, Equation 1) to my data, which contain data in U, B, V, R, etc. Do I need to do any transformations to my data in order to apply their equation?

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First, we construct an empirical color-redshift $\chi^2$ (for each redshiftÈ indicated by the subscript z) is computed as

$$\chi_z^2 = {\left((u'-g')-(u'-g')_z \right)^2 \over \sigma^2_{u'-g'} - \sigma^2_{(u'-g')_z}} + C_{gr} + C_{ri} + C_{iz} \tag{1}\label{eq1}$$

where $(u'-g')$ is the measured $u'-g'$ color of the object, $(u'-g')_z$ is the color from the median color-redshift relation at a given redshift, $\sigma_{u'-g'}$ is the photometric error in the $u'-g'$ color, which is given by $(\sigma_{u'}^2+\sigma_{g'}^2)^{1/2}$, and $\sigma_{(u'-g')_z}$ is the 1 $\sigma$ error width of the median color-redshift relation as a function of redshift.

Answer 1

Doing photometric reduction (from image to brightness) includes the following steps:

• image cleaning (bias + dark + flat + etc.)

• identify/measure brightness of the object of interests from the cleaned image (using e.g. sextractor). Let's say the image was taken in U filter with the brightness (mA_U_image) in any arbitrary magnitude given any arbitrary zeropoint (ZP).

• identify/measure brightness of standard objects (which are objects that we know their brightness) using U filter and the same ZP. Let's say the brightness is mB_U_image.

• Find transformation: mB_U_real(AB) = mB_U_image(arbitrary with zeropoint = ZP) + correction where mB_U_real(AB) = magnitude of B in U filter in AB system (or in other magnitude system as identified by the database of B given U filter).

• Apply the transformation: mA_U_real(AB) = mA_U_image(arbitrary with zeropoint = ZP) + correction

Note: this method is simplified because both science objects and standards were assumed to be taken from the same U filter.

So, to answer your question:

• Typically, there are two frequently used magnitude systems: Vega and AB. You might need to get the Vega to AB correction if the transformation involve changing from one system to another.

• UGRIZ and ugriz: I found that sometimes UGRIZ is used to notify that the magnitude is expressed in Vega system and ugriz is in AB system, or vice versa. For an example, https://arxiv.org/abs/1605.01054

• U and u and u' are slightly different (check their response curves from the telescope handbooks). So, transforming from one filter to another might need to include more terms in the transformation.

• If standards and science objects were taken from different filter/telescope/setting (even in the case of U and u), you might need to also include a color correction term in the transformation.

• Eq. 1 is for calculating chi-sq to be used in the optimization problem. I believe that the equation is expressed in u-g color index as an example. You should be able to use any color index pair. If you really want to use u-g index, but you have UBVR, here is what I think you should do: find u = U + correction, and g = B + correction.