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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?


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.

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  • $\begingroup$ Where have you seen “UGRIZ” (that wasn’t just a typo or something like that)? I’m unaware of any such system. $\endgroup$ – Peter Erwin Jul 17 at 0:40
  • $\begingroup$ Oh, so maybe ugriz and UGRIZ are actually the same? $\endgroup$ – Jim421616 Jul 17 at 0:41
  • $\begingroup$ No, I mean there is no “UGRIZ” system as far as I know. (Of course, you go on to mention “U, B, V, R, etc.”, which is a completely different system from ugriz or u'g'r'i'z', so it’s a bit confusing...) $\endgroup$ – Peter Erwin Jul 17 at 0:47
  • $\begingroup$ The UGRIZ seems to be a typo/incorrect capitalization of the standard ugriz. Hopefully you've also found the SDSS photometric transformation details - the first one listed (Jester et al. 2005) is claimed to be suitable for quasars $\endgroup$ – astrosnapper Jul 17 at 1:14
  • $\begingroup$ I hope you don't mind the pedantic edit, feel free to roll back or edit further. $\endgroup$ – uhoh Jul 18 at 2:32
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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.

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