For some months I’ve been measuring the constant stars niu Aur and NSV 2877. As these were constant stars, and as I was using PEP photometry, I expected the results to be very close to each other. However, I was not so pleased by the results. Or were my expectations and my confidence in PEP photometry too high? I’ve compared my results with the values in the General Catalogue of Photometric Data.
niu Aur (HD 39003)
GCPD: V=3.960±0.007 (248 measurements)
my data: V=3.959±0.006 (13 measurements)
GCPD: (B-V)=1.133±0.007
my data: (B-V)=1.122±0.011
NSV 2877 (HD 43039)
GCPD: V=4.338±0.019 (>41 measurements)
my data: V=4.328±0.010 (13 measurements)
GCPD: (B-V)=1.019±0.011
my data: (B-V)=1.011±0.012
The error margins in the GCPD are similar, so I probably set my expectations too high.
I did BV photometry on niu Aur and NSV 2877, so I calculated ∆(B-V) based on my measurements. For niu Aur, I noticed that the V-magnitude got brighter as the measured ∆(B-V) increased and the B-magnitude got fainter as the measured ∆(B-V) increased.
For NSV 2877 the B-magnitudes showed a similar, but less profound relation, ∆(B-V) vs. V-magnitudes showed no relation at all.
My PEP spreadsheet also calculates the V-only magnitudes, for the observers who do not do B-band photometry. In most cases, the calculated V-magnitudes are the same. If the V-magnitudes are not the same, they differ maximally 0.001 magnitudes. So observers who do BV-photometry get in V-band the same results as observers who do V-photometry. A very reassuring outcome.
My reaction is that if you got these results by measuring the two stars against some group of standards, you did amazingly well in terms of both accuracy and precision. The offsets you see between your data and the GCPD values (which are not necessarily definitive themselves) are quite typical of any system relative to some standard-star network. One has only to look, for instance, at results Arlo Landolt gave in his series of papers for the same stars — things drift around by a percent or so over the many years of his work. His network is very stable to a few millimags in the mean around the sky, but the per-star rms is something like 0.007 mag for V and B-V among stars of ordinary color.
It depends what the procedures are. Does the V-band photometry use an assumed (or previously measured) transformation coefficient? By BV photometry do you mean photometry that determines transformed magnitudes?
Hi Roy, I am talking about Photo Electric Photometry (PEP) with Optec SSP photometers for which the PEP group uses standardized procedures, using transformation and extinction coefficients. Transformations are always measured, but most (but not all) observers use asumend exctinction coefficients.
Hi Erwin, so if both V-band photometry and BV photometry determine transformed magnitudes, it seems to me that you would expect the two sets of results to be similar - which they appear to be.
keep in mind that, even when for most ground-based observers they can be considered as constant, TESS has proven them to be milimagnitude variable stars. They are oscillating red giants (ORG). Yes, most bright stars are variable for TESS!
Hi Roy, you are mostly right. There is one big difference in reducing V-only and BV PEP measurements, and that is ∆(B-V) = (B-V)var - (B-V) comp. In the case of V-only we reduce the measurements using catalogued values (B-V). In the case of the comp, (B-V) is (should be) constant, in the case of variable stars (B-V) can change during the cycle. In the case of BV we reduce the measurements using the actual measured (B-V) of both var and comp.
For instance the catalogued ∆(B-V) for niu Aur an its comp is 0.182 and form my measurements is is 0.171±0.010. Close, but not the same.
The same holds for NSV 2877. The catalogued ∆(B-V)=1.079, my measured ∆(B-V)=1.072±0.012. So they are both very close but they have slight differences. In the reductions this leads at most to minor differences in the reduced magnitudes.
Thank you for sharing these interesting light curves. PEP photometrists can only measure bright stars. There are no red dwarfs bright enough to measure with SSP3’s. So if we measure a red star, they are red giants and they are never constant
Back in 2016, Erwin, Jim Kay, Scott Burgess, and I tried an exercise observing slowly-varying stars with PEP. The goal was to get a bunch of same-night data from at least two observers on the same target in order to evaluate our internal consistency. I attach the JAAVSO paper with the results, in which Table 4 is the most important feature. It shows excellent inter-observer agreement at the 2 sigma level.
The uncertainties we routinely calculate in PEP are likely too small. They are based upon standard deviation of the mean rather than straight standard deviation. Given that our observation sequence typically gathers only three samples, applying a mean is likely not justified (I believe Arne insists on at least five samples for SDOM). More testing is indicated but we need to reconsider our uncertainties.
May I ask you to detail, as applied to the PEP data reduction protocols, the usage of:
Standard Deviation (SD)
Standard Deviation of the Sample (Sample SD)
Standard Deviation of the Mean
Standard Error (SE), please?
Which of these estimates of the dispersion of the measurements due to several factors would be best for the PEP data?
The theory:
Standard Deviation: How much the measurements differ from their mean.
Sample SD: Same thing but adjusted because it’s a sample (So, divide by N-1).
Standard Error: How precisely you know the true mean brightness of the targets, comps, check stars).
Standard Deviation of the Mean: How much someone’s different nightly means vary across nights. Is it the standard deviation of multiple sample means or the same as standard error?
Peter Stetson discusses this topic in regard to photometry here:
Specifically, see the appendix to the paper in regard to finding uncertainties and weights when you have only a few data points. Always keep in mind that means and scatter in data are only estimates based on what data you have, and that you cannot assume a Gaussian distribution, or even that your error distribution has a functional form.
The article you cited, especially its appendix, is quite elucidative, thank you.
Now it is our task to convert these statistical methods into a practical procedure for dealing with our small data samples, usually up to three brightness measurements/estimates per target and observation moment.
I believe that Arne Henden would advise using standard deviation of the sample. PEP currently uses standard error A.K.A. standard deviation of the mean. Before making a change to PEP I want to see more photometry of the constant stars. For the typical 3 sample PEP sequence, changing from SDOM to SD entails multiplying the error by about 1.7.
