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# Calculating Zero Points

What the Photutils have given so far is the instrumental magnitude of an object, which is different across all telescopes due to differences in the equipment. To calculate the apparent magnitude of an object, then, requires us to add in the “zero point” to the instrumental magnitude. In other words, the apparent magnitude of an astronomical object is calculated by:

$$m = -2.5 \times log (\frac{ADU}{t}) + ZPs$$

Where refers to the apparent magnitude, ADU the analog-to-digital unit, t the exposure time, and ZPs the zero points of the telescope. The setting of the zero point allows us to calibrate the telescope to a standard photometric system, such as Johnson BV and Cousins RI.

The easiest way to calculate the zero points of an instrument is through using the published magnitudes of standard stars—that is, carefully observed non-variable stars in various photometric bandpass filters—and subtracting these literature magnitudes with the instrumental magnitudes that you have. This method requires you to take images of a field of standard stars on photometric nights.

Well-established photometric standards:

1. For Johnson-Cousins BVRI: Landolt Standards
2. For Sloan ugriz: Smith Standards
3. For CTIO JHK: Persson Standards
4. For CTIO Y: Check out Krisciunas et al. (2017)

## Step One

As mentioned, we will have to take images of the standard stars in order to calculate our zero points. Say that our telescope is using the Sloan ugriz photometric system, we will have to use the Smith standards. […]

## Step Two

Now that we have a few images of the standards, we need to identify these stars. We will first have to astrometer them as we are relying on Photutil’s aperture photometry tool which relies on astrometric data. To find out the coordinates of the objects that you wish to photometer, open up your DS9 and match the objects to the standards provided in the literature. In our case, we have four stars in our field, and we are going to use all of them.

[image: comparison-matching]

## Step Three

After you’re done, create aperture objects in your Jupyter notebook. Photometer the standards.

## Step Four

All that is left then is a simple calculation:

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