[Aavso-photometry] Ensemble photometry - revised

[Ron Baker]

I too am interested in using an ensemble of comparison stars for making
variable star estimates.  I've just started to make photometric measurements
and would like to make sure that the method I'm using to calculate
instrumental magnitude and error is reasonable.

Here is a  typical example of what I've tried so far:  5 individual images
(with a V filter) are taken one right after the other, and the instrumental
magnitude of the variable (V) and 3 comparison stars (C1, C2, C3) is
measured.  The differential instrumental magnitudes (V-C1, C2-C1, and V-Ens)
are determined.  The mean and the standard deviation for each of these
values are calculated.  To get the instrumental magnitude of the variable,
the mean of V-Ens is added to the "calculated" instrumental magnitude of a
so-called "master comparison star".  The value for the master comparison
star is determined by first converting the known standard magnitudes of each
of the 3 selected comparison stars (most likely from the AAVSO database) to
flux.  Then the flux is added up and converted back to magnitude.

To calculate error, the standard deviation of C2-C1 is added to the error
component contributed by the 3 comparison stars (also from the AAVSO
database), in quadrature.  Referring to Arne's post from January 2006
(Subject: Ensemble photometry question), this error component is calculated
by adding the known standard errors of the 3 individual comparison stars, in
quadrature.  But as part of that calculation, and before the square root is
taken, the sum is divided by N (the number of comparison stars) times N-1.
I hope I've interpreted this correctly.

In this example, only 3 stars make up the comparison star ensemble.
Possibly more (or many more) could be used.  But I don't know if adding more
stars to the ensemble would help with the precision if they are much fainter
and/or would not normally qualify as good comparison star candidates.  Also,
in order to use this "master comparison star" method, it seems like the
known standard magnitudes (with errors) would be needed for all the stars
making up the ensemble.

I know that estimates based on an ensemble of comparison stars are not yet
being submitted to the AAVSO.  But I'm curious as to whether the method I've
outlined appears to be reasonable?

This is all still very new to me and it's quite possible that I'm way off
base.  Thank you in advance for helping me to understand these photometric
calculations.  I will surely appreciate comments. 

Ron Baker (BFX)
Kirtland, Ohio

> -----Original Message-----
> From: aavso-photometry-bounces at mira.aavso.org [mailto:aavso-photometry-
> bounces at mira.aavso.org] On Behalf Of arne
> Sent: Friday, November 23, 2007 11:23 AM
> To: Jim Roe
> Cc: Aavso-Photometry
> Subject: Re: [Aavso-photometry] Ensemble photometry - revised
> 
> Jim Roe wrote:
> > I'm trying to understand and learn how to do "ensemble photometry"
> > because I have come to believe that it will produce more accurate and
> > precise results.  Right?  I have re-visited threads on the list,
> > Googled, read several papers but I have yet to find a clear, concise
> > definition of the technique.  E.g.,
> >
> > Honeycutt (PASP 104:435-440, June 1992) states: "A simple (and often
> > quite adequate) technique for CCD ensemble photometry is to calculate
> > the difference between the instrumental magnitude for the program star
> > and a comparison magnitude obtained from the sum of the intensities of
> > perhaps a dozen of the brighter stars which appear in each exposure of
> > the series."  This doesn't seem right to me, perhaps it is a typo that
> > was mentioned in an earlier post.
> >
> > In another paper on the web by Hayes-Gehrke
> > <http://www.astro.umd.edu/~avondale/extra/Variability.html>
> > it is stated "Ensemble averages make this technique even more reliable.
> > Given at least a few dozen stars in the image, the assumption is made
> > that the average magnitude of these stars would remain constant from
> > frame to frame, regardless of the type or behavior of the individual
> > stars. "  This makes more sense to me.
> >
> > Finally, The MaximDl manual says: "If you tag more than one reference
> > star, you must set the magnitude for each; the results will be
> > averaged."  Does this, then, constitute "ensemble photometry?"
> >
> > If so, and I would just as soon continue using Maxim given my $400
> > investment therein, several questions arise.
> >
> > Which extra reference stars should I include?  Presumably only from
> > those for which photometry exists, but sometimes (often) there are
> > photometry stars that are much fainter than the program star and, unless
> > I expose for good S/N on them, their measurement errors will be greater
> > and it would seem adding them to the "ensemble" will degrade the whole
> > system.
> >
> > Would I consider all of the individual reference stars to be check stars
> > to be compared to the ensemble average?
> >
> Dang - one *important* word got left out.  Here is a revised reply.
> ------------------------------
> We are not recommending ensemble photometry submission until the
> new upload formats are announced (shortly; how shortly depends on
> the conclusion of our beta testing period, so I can't give a
> definitive date).
> 
> The basic concept is that you have multiple comparison stars in your
> image, so why not use all of them to derive a magnitude for the
> target object?  You can think of it as (V-C1), (V-C2), etc., where you
> average these values together.  That reduces the effect of some bad
> measurement of any comparison star, variability of the comparison stars,
> systematic effects like transformation, etc.  So it is good, right?
> The devil lies in the details.  There are multiple methods of
> creating such an ensemble solution, from using flux space or magnitude
> space, averaging (V-C) or forming a master comparison star, how
> many stars form the ensemble, how do you weight the individual
> measurements, etc.  In addition, what magnitudes you use for the
> comparison stars impacts the final solution, and we cannot deconvolve
> this effect sometime later like we can if you use just a single
> comparison star.
> 
> The new format gives a method for submitting ensemble results, and
> includes
> a way in which we can adjust the photometry later.  I hope it works!  In
> addition, the new comparison star database photometry is precise enough
> that choice of ensemble stars should not affect solutions dramatically.
> So
> we are getting closer to accepting ensemble results.
> Arne
> _______________________________________________
> 
> Aavso-photometry mailing list
> Aavso-photometry at mira.aavso.org
> http://www.aavso.org/mailman/listinfo/aavso-photometry