What is the correct mathematical or physically method of determining the maximum of Delta-Scuti-Stars or HADS?
If I take the wohle lightcurve I get other results as I only take half of the lightcurve. Some collegues told me, only to take half of the LC, but is that only an opinion, or is there a physically proof somewhere?
- Does one take the whole LC, from the plateou (blue lines)?
- Does one take the whole LC, but only from ascent to descent?
- Does one take oly half of the LC (green line)
(How can I upload an image?)
There is no "correct" way to do this. Some methods are more reliably or consistent, others may be more appropriate under the circumstances. Basically the reason why one wants to derive the time of maximum comes down to choosing a point in the light curve that can be compared to that point in other cycles, without having to compare the full light curve each time. But that means that calculation is best left to the people who want to do that comparison, so that it is done in a consistent way, whatever method they choose.
I agree with Patrick that, in studies such as period change studies, it is best to treat all of the data in a consistent manner. That doesn't mean that studies are impossible if only times of maximum are available, but in those cases one has to be aware of the possibility of systematic errors in comparing maxima from different researchers.
Perhaps I should add that some of these stars have had period changes large enough that differences in the method of determining the time of maximum won't significantly affect the pattern of change. Still, if I wanted to engage in a period study, I would try to look at as many of the original photometric observations as was feasible.
My method for time of maximum involves fitting polynomials to the data. I do not use the lower inflection points since these make the polynomial more complex than required. I typically fit a half dozen or more polynomials that cover a wide range of orders. I toss out any outliers and choose from the maxima that cluster together. I also do a visual inspection to make sure the result looks right.
This works well for Delta Sct stars and RRab stars. RRc stars can be a challenge because the maxima can be broad and have multiple humps.