Grant Foster’s book “Analyzing Light Curves: A Practical Guide” (section 5.5) gives an example of using polynomials to determine critical points of a light curve, in particular: a Mira maximum.
The book addresses the question of how to determine minima/maxima, especially in the presence of scatter in the data. The following figure shows a 7 degree polynomial fit for a Visual JD range around maximum for Mira.
To obtain this plot, load the data from the AAVSO International Database for the JD range shown (2451460.0764 to 2451559.539), select Polynomial Fit from the Analysis menu or toolbar, select the Visual series, then the number of degrees for the polynomial, in his case: 7.
Experiment with the degree value to see the effect upon the least squares polynomial fit. A 5 days-per-bin mean series (again, based upon the Visual series) makes a useful comparison. This can be changed via the View menu’s Plot Control dialog.
Switching to the Model and Means tabs in turn and clicking the Magnitude column to re-order it, allows the maximum value in the series to be easily found. Selecting such a row causes the cross hair in the plot to move also.
Grant’s discussion goes beyond simple polynomial fits, including a discussion of information criteria or “goodness measures” and a consideration of alternatives such as the Lowess smooth, both of which are on the roadmap for VStar. He also spoke about this in more detail at one of the Astro April Citizen Sky talks about uncertainty in determining time of minimum/maximum.
Given that it is currently near maximum, while writing this entry I also created polynomial fits for filtered ranges of R Car, another long period variable. I’ll leave that for another post though.
On a related note, I’ve been asked by a few people recently about when VStar will include a Time of Minimum/Maximum (ToM) capability such as Kwee-van Woerden for use with eclipsing binary light curves. This is working its way higher up the list.