On 'Relative Flux'

[pmohan336]

I’m phasing into retirement after a long career in remote sensing R&D and devoting more time to amateur astronomy pursuits. This includes delving deeper into AIJ with its rigorous feature set for differential photometry. In reading documents, watching Webinars and working some image analysis, a persistent question nags me about the definition of Relative Flux. It has no doubt come up before, but I’ve not been able to track down in the AIJ forum.
As well-detailed in the AIJ (Expanded Edition) journal article by K.Collins et al , Jan 19 2017, the term Relative Flux is defined as a ratio of single star flux (net integrated counts of a target star or a comparison star) to the sum of fluxes from a set of (N) or (N-1) comparison stars. My rather fundamental question is why is the denominator term not a flux average versus a flux summation? Using a flux average would, i) allow relative flux values for a given target star to be independent of how many comparison stars are used (across different observer(s) trials for example), ii) allow the direct comparison of relative flux values between a target star (Rel_flux_T1) and the associated set of comparison stars (Rel_flux_Cn) .
Perhaps my question is academic, since ultimately what we’re really after is the normalized flux variations over time, which are flexibly specified, computed and available within the multi-plot tool.

Cheers, Paul

[karenacollins]

Hi Paul, I agree that it is more of an academic question since relative flux is typically normalized for modeling, especially in the field of transiting exoplanets. I don't think that the average flux would stay the same either. For example, if a s brighter star is added or removed from the to the ensemble (brighter compared to the other stars in the ensemble), then the average will drop. Granted it will drop less than with the technique of adding all fluxes in the ensemble, but it would still bump up or down depending on the brightness of the star added or removed (compared to the average brightness). Regarding your point (ii), you can define multiple target stars and could compare those fluxes directly, even with the current approach. If you are instead wanting to move stars in and out of the ensemble to compare to T1, the average will still move up and down unless the star(s) you are working with have the same flux as the ensemble's average flux. --Karen

[pmohan336]

Thanks Karen and appreciate your feedback.
Yes, the average flux certainly reflects the variations in the Cn ensemble, but its mean does not carry the (1/N) weighting of the summation. A quick simulation provided some plots, for academic interest :-)
Regards,
Paul