second order extinction

[rrgem]

Dear Karen
we are teaching broad-band photometry (B, V, R, I) to high school students and we would like to use your wonderful software not only for exoplanets but also for pulsating variable stars. We have a couple of question for you. In order to obtain accurate absolute magnitude of the target, what about atmospheric extinction (especially second order extinction)?
The second question relates to overall error estimation. At the end of data processing we obtain something like: Source_AMag_T1 =12.486 ; Source_AMag_Err_T1 = 0.003
but our standard stars have an associated error between 0.018 and 0.055
How we can resolv this problem and producing a final uncertainty measurement with contributions from both the uncertainties of the stellar magnitudes and those of the ADU measurements on the images?
Thank you so much
Marta

[karenacollins]

Hi Marta,

Wow, high school students are given the chance to do some awesome labs these days. Great Job!

I'm not clear on exactly the measurement technique you are planning to use. Are you planning to derive absolute or
apparent magnitude? If apparent magnitude, I think the best you can do is differential photometry using the known
apparent magnitudes of standard/reference stars as near as possible to the target star in the image, which also have a
similar color. This may be the best you can do to deal with second order extinction within AIJ. In that case, you would
enter the known apparent magnitude (in the filter band you are using) of one or more reference stars and AIJ will
calculate the apparent magnitude and uncertainty of the target star in that filter band (I think this is what you have
already done based on your description below). You would then need to combine, in quadrature, the AIJ calculated
magnitude uncertainty with the reference star magnitude uncertainty. As in your provided example, I expect the reference
star apparent magnitude uncertainty will usually dominate the total error. If you use only one reference star, you would
simply square both error uncertainty terms, add the squares together, and take the square root of the sum. If you use
multiple reference stars, you will need to calculate a weighted combined uncertainty from the all of the reference star
uncertainties, and then combine that value in quadrature with the AIJ uncertainty. Finding the weighted average of the
magnitudes may be a bit tricky, and beyond what I can describe here, so you may want to stick with one reference star if
the uncertainty calculation is important to your exercise.

I'm not sure that I have answered the questions you intended. If not, please clarify your planned procedure a bit more,
and I'll try to fine tune my response.

Karen

[rrgem]

Hi Karen
thank you so much for your kindness. You are right. We are are planning to use the measurement technique that you described.
Our goal is to obtain precise and accurate apparent magnitudes in order to be able to send it to the AAVSO database or to be used to support small research projects. Sometimes it's difficult to find comparison stars with the same color index in the ccd frame, so it would be very useful to apply also the second order extinction correction within AIJ to improve photometric accuracy.
Marta