G) Photometry Methods
Chris, with the help of Kate, describes aperture photometry and how it is used in calculating magnitude in the 6:49 video below:
A brief description of four types of photometry are defined below. The teacher/leader resource for this Part has more detailed hands-on activities to help with these concepts.
a) Set a ring around the object you are interested in. This ring is called an aperture.
b) Sum up the counts from the pixels inside the ring
c) Place an annulus around the aperture. It should include the nearby background pixels.
– An annulus is a larger ring that has a measurable inner and outer radius. You can think of an annulus as a circle made out of a wide ribbon where you gather information from inside the width of the ribbon, whereas the aperture is a thin ribbon and pixel information is gathered from within the circle the ribbon makes.
d) Find an average of the background pixel counts between the inner and outer radius of the annulus.
e) Subtract the average annulus pixel counts from the aperture counts. This effectively subtracts background light from the source object.
***NOTE: You can use the 3×3 poster grid with a set of rings, one representing the aperture and one representing the annulus, to simulate aperture photometry. This is what Kate and Chris did in the video above. Or adjust the instructions for the smaller version.
2. INSTRUMENTAL PHOTOMETRY (=Instrumental Magnitude)
a) This uses the counts as found in #1 above (aperture photometry). This is converted to “flux”, which has a different unit. (Flux is calculated with a standard algorithm within the image processing program and becomes part of the data that is downloaded).
b) Once the flux is known, it is converted to an instrumental magnitude using the equation below (you used this if you did the optional section on calculating magnitude) – with the additional step of dividing the flux by the exposure length.
m = -2.5log(flux/exposure length), where the ‘m’ stands for apparent magnitude.
****NOTE: This magnitude will not match an accepted magnitude in a star catalog. It is not calibrated. However it can be used in Differential Photometry – see below

3. DIFFERENTIAL PHOTOMETRY (used in asteroid photometry)
This can also be called Differential Magnitude.
This simply uses the difference between the instrumental magnitude (type #2 above) of the object of interest and the instrumental magnitude of a standard star (recall what a standard star is from the beginning of Section 3).
**This allows different observations to be used. This method will agree on magnitude DIFFERENCES even if different instruments, apertures, and exposure times are used, and also, if different seeing conditions exist. YEAH!
a) After finding the instrumental magnitude of your object of interest, find a standard star in that same image. Perform aperture photometry on this standard star. We will soon do this in Afterglow Access.
b) Using the same equation as in #2 above (m=-2.5log(flux/exposure length), calculate the instrumental magnitude of the standard star.
c) Find the difference between the instrumental magnitude of the object of interest and the standard star by subtracting.
OR – Do as Kate and Chris did and use a ratio:
d) Find the ratio of the flux (then you do not have to do the step of dividing by the exposure time) of the standard star to the flux of the object of interest (just divide the two).
e) Then use that ratio in the equation used in method #2 above. Your answer IS the magnitude difference – no need to subtract.
##Let’s try an EXAMPLE of Differential Photometry using the flux ratio method seen in letter d) above. You may use Quorum or a calculator.
Given: flux1
flux1 is found for a standard star in an image to be 8353.9 (this is converted with an algorithm in Afterglow Access – it is from the counts listed below the image on Afterglow Access)
Given: flux2
flux2 is found for the object of interest (our asteroid) to be 5962.148
Find the magnitude difference between the standard star and the asteroid by subtracting. This is delta m.
(answer should be -0.366)
**Note: Afterglow Access uses standard algorithms from a repository of python modules made for astronomers called “astropy”. Google astropy for more information if you are interested.
a) Standard stars have their magnitudes listed in well known catalogs. Each standard star has an accepted magnitude for different filters. Recall, a filter allows only a small, well defined range of light energy through. The sample images we are using were taken with a red filter.
b) Find the difference (subtract!) between the magnitude listed in the catalog and the instrumental magnitude as calculated in #2 above.
c) This difference is called the zero point.
d) This should be done for several standard stars in the same image. Then take the average of all the differences. This average is a better zero point to use.
e) The zero point is then added (or subtracted) from the instrumental magnitude of the object of interest (an asteroid, in our case) to get the CALIBRATED magnitude. Star catalogs will become available on Afterglow Access in the future.

The next part will take you through the method of differential photometry used on Afterglow Access.

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