For practice, I have obtained BVRI photometry on CN And for a primary eclipse and a secondary eclipse. I am writing a program to fit the photometry near the minima to a parabola to determine the ToMs. I do this separately for all for bands. I also compute the errors on the parabola parameters and can thus compute the error on the ToM. For the secondary I get:
B: 2459561.1043 +/- 0006 (HJD)
V: 2459561.1027 +/- 0.004 (HJD)
R: 2459561.1033 +/- 0.003 (HJD)
I: 2459561.1028 +/- 0.005 (HJD)
The average of these is 2459561.1033 +/- 0.0007 (standard deviation).
So, the errors on each ToM are from the errors on the fit parameters of the parabola. (I have limited the fit close to the minima, but still had ~ 55 data points to fit). The chi-squared for a typical fit is ~ 63 with 52 degrees of freedom so the fits are okay.
My question is, is it better to quote the average of the 4 ToMs +/- the standard deviation or to quote the 4 ToM separately? Is there any physics that says the minima will be different for the different bands? Obviously, mine here are all statistically the same.
(I am trying to include a screenshot of a fit, but the "File Upload" below, doesn't seem to work. I can paste an image into the text, but it doesn't show up in the preview).
Thanks for any help/info. Tony...
Just for clarification, please confirm that the HJD_errors are 0.0006, 0.0004, 0.0003 and 0.0005, not those that were posted. There are two ways to evaluate the variability in this case. One is to determine the variability within a sample (standard deviation) or the variability across samples of a population (standard error). The standard deviation of the four times of minimum is ± 0.0007, as you have calculated. However since you have also provided the uncertainty in measuring each value, my preference would be to report the standard error calculated as follows:
SE= SQRT((0.0006^2+0.0004^2+0.0003^2+0.0005^2)/4^2) = ±0.0002
Having digressed, I would still recommend reporting the individual ToMs for each passband and not calculate the average. Nine seconds out of a day (9/86400) is 0.0001 day. It is very likely that the total exposure time from the first filter to the last is significantly greater than 0.0001 day. Therefore, there is a realistic expectation that ToMs could be biased by the fixed order of filters generally used throughout the night. I suppose you could examine whether the ToM values followed a rank order corresponding to each filter and only average the results if the data failed the rank order test. Perhaps most importantly there are phenomenological reasons why a ToM value may be bandpass sensitive. In the case of eclipsing binary stars, ToM values can be affected by the presence of star spots which can deform a light curve during eclipses. Star spots can be hotter or cooler than the surrounding surface temperature and therefore have a different bandpass profile. This bandpass differentiation extends to measuring times-of-maximum from pulsating stars which can significantly change temperature during each pulsation cycle. The bottom line is that reporting moments of extrema separately for each filter is probably the safest practice.
Thanks for the…
Thanks for the reply. My errors were correct (except I forgot the decimal place on the first error: 0.006). I will take your advice and report my ToMs for various bands separately. One thing I am trying to understand is that my uncertainties for the individual ToMs are much larger than the standard deviation of the group of ToMs. That doesn't make sense to me. They should be comparable.
Also, I have varied the fitting procedure (order of polynomial & fitted range) and the variations in ToMs I get are much smaller than my estimated uncertainties from the polynomial fit parameter uncertainties. I will continue to explore this.
BTW, do you (or anyone else) know how to upload/attach an image to a forum post?
Here is a link to a screenshot from one of my fits: https://buckeyemailosu-my.sharepoint.com/:i:/g/personal/shoup_31_osu_edu/EdwERuLxk6FOulcpeAo8hjgBk-XbFpYVdBH9j1Pzca0h0g?e=6Aa1O8
Thanks again, Tony...
I suspect that your HJD uncertainty is being overestimated but I would need to evaluate the raw HJD, magnitude and mag_err data. Have you tried to use Bob Nelson's "Minima" program or MAVKA ((https://arxiv.org/ftp/arxiv/papers/1812/1812.06949.pdf) to compare to your results. If you are willing to send me your data (DropBox) I can provide you with comparison values using Peranso 3 and MAVKA.
Sorry for the long delay for a reply. I have used Minima27 on my laptop windows system, using all the methods available. The mean of all the ToMs from Minima27 is consistent with my ToM (all are HJD):
1. Parabolic Fit: 2459561.10277 +/- 0.00008
2. Tracing Paper: 2459561.10296 +/- 0.0001
3. Bisectors of Cords: 2459561.10241 +/- 00161
4. Kwee and vanWoerden: 2459561.10267 +/- 0.00016
5. Fourier Fit: 2459561.10274 +/- 0.00034
6. Sliding Integrations: 2459561.10283 +/- 0.00009
7. Mean: 2459561.10273 +/- 0.00018 (std dev)
Mine: 2459561.1027 +/- 0.004
Perhaps the reason my uncertainties are larger is that my parabolic fitting uses a weighted method so the photometry errors are included in the determination of the uncertainty of the location of the minima. Although if that were the case, then the standard deviation between my bands would be comparable to my uncertainty estimates. The standard deviation of my bands is 0.0007.
At least there is good agreement on the central value between my method and Minima27. I will perhaps try the other two programs you suggested. Do they use the photometric uncertainties?
BTW, this ToM is for a secondary minima. The ToM for the primary is: 2459557.165 +/- 0.002 HJD. Again this is for CN And.
Gary, is there any way to check to see if this ToM is consistent with current database of ToMs for CN And? If so, how can I do it?
Thank, many thanks to all for all your help. Tony...
p.s. How can I include a file upload in my posts? Screen shots would be good to include.
I haven't previously been part of this thread... but a site that I use a lot for "checking" ToMs is:
Just type in the id of your star. If it is a numeric GCVS, make sure the number is 4 digits, e.g. V0541 And
That site is implying your ToMs are early by about 0.04 d -- very close to an hour. Possibly a "daylight savings time" problem somewhere?
Where is your observing site? I am wondering because your ToMs of 245nnnn.1 day would not be possible from my location (Mountain time zone). I think you'd have to be west of me... but AAVSO says your home is Ohio? Or am I going the wrong way in my head ! ?
Hi Gary (and all),
I finally figured out my problem. To plot my photometry (light curves, ToMs) I was plotting MJD (JD-2400000.5) to save space on time axis. Then when my code reported the results of a ToM fit, it added back in the 2400000, but not the 0.5! My photometry has the correct times, but my routine reporting the fit results was off by 0.5 days. I have fixed this and now my ToM for CN And agrees very well with the O-C gateway data on CN And:
O-C was -0.003 d which is consistent with the O-C trend at that time.
Many, many thanks for all the help from everyone. Now, hopefully and can start reporting ToMs correctly. Tony...
p.s. Can someone let me know if the link above is accessible and the correct way to show a screen shot on this forum?