Updated alternative to the Kwee van Warden method

Hi Andy, I've been using, or at least experimenting, with this for a while.  I just coded the function in R (one line of code for their eq'n (3), plus a few lines of function wrapper), and solve it using "nls".  No GUI or anything, I just run it from an R console after having input my time series data to a data frame.

One thing I like about the Brat+ method, is that it uses the photometric time-series as given.  KvW interpolates the time series to get regular sampling, symmetric about the trial ToM.  If you use linear interpolation (as the paper describes) across a gap in observations when the true lightcurve was not straight, i.e. where it has curvature, the interpolated magnitudes will be biased away from the curve, and so the resulting ToM will be biased away from the true value.  If you use "smarter" interpolation you can avoid that bias, but then I don't think you can strictly say your are using the KvW algorithm.  The Brat+ method just fits an interesting functional form to the magnitude time-series, without resampling / interpolating.

As an aside, I've also coded KvW in R, and have been testing it against KvW as implemented in AVE  -- which is an ancient implementation that has to be installed on Win XP (I run it on a Virtual PC on Win7).  It would be nice to be working with open-source implementations of these codes.  I am not averse to the idea of making my KvW code available, but haven't thought about how to do that, nor created suitable documentation etc.  There are a few tricky / interpretive elements re first last points, the interpolation, etc.

I haven't made a study of the errors reported by the Brat+ method.

Gary Billings

Hi Gary, Good to know you are doing & have done the same using R. I have started writing a Python routine to accomplish pretty much the same. I don't recall whether KvW uses least-squares optimization, but I do agree that linear interpolation between points would be a source of inaccuracy. Visually, I noticed a discrepancy between KvW and Brat+ in my recent light curve of BU Vul. I believe that the former's ToM result is biased. To get a handle on this alternative method's estimate of time error, I plan to incorporate resampling of the observational data, more or less as the Brat+ paper explains. A possible drawback is that the objective function in the Brat+ model assumes symmetry around the time of minimum. However, the paper points out at the very end that a linear term in time (c₂t_i is how the paper references it) could be included in the objective function. This might accommodate time trends caused by factors such as changing air mass. I look forward to comparing our results soon.

Hi Andy, Your comments remind me of another reason I like the Brat+ method:  it is trivial to fit the additional linear term, which I think is a useful way to examine one aspect of the quality of the time-series.

Re assuming symmetry:  that is at the core of the KvW algorithm too.  And I think we want it to be so:  in the absence of systematic time-dependent errors in the photometry, noise, and spots, the lightcurve through an eclipse should be symmetric. And the time of the min of that symmetric LC is the time of the conjunction of the two stars, and it is the time of conjunction that we are actually seeking.  When we analyze ToMs looking for 3rd body light-time effects, apsidal rotation etc, we actually want times of conjunctions.  We say we want the time of the min of the LC, and we are hoping that is the same as time of conjunction, i.e. that the ToM we have determined hasn't been perturbed away from the "ToConjunction" by some other effect.

So, another useful thing to do, which is trivial to do, is look at how much the actual LC deviates from the assumed (fitted) symmetric one.  I.e. compute and plot the residuals of the fitted LC.  With the Brat+ method, it might have systematic mis-fits (but they should be symmetric!), and random noise.

It would be great to discuss this further:  there are probably further nuances and exceptions than I have not acknowledged...

Gary 

Hi, Andy:

I started experimenting with Brat+ earlier this year. I put together a little Python implementation. One of my hesitations with it is that I don't know how "universal" the underlying model is. I used it on V1463 Her, a semi-detached EB with a slightly asymmetric primary eclipse (due to an accretion hotspot??). Brat+ ignored the asymmetry, but gave an otherwise very good match for the overall shape of the eclipse. It left me wondering if there are any EB geometries that the Brat+ model doesn't match well. (I don't have much EB experience, but this seemed more "bulletproof" than KvW.)

- Mark

Hi Andy,

Thanks for having made available your data - I really appreciate. I have been able to calculate the KvW ToM both with Peranso 2 and Peranso 3. See my PM.

Best regards
Tonny