[Aavso-photometry] Landolt error bars

[arne]

Ben Davies wrote:
> I want to get the U and  B error numbers for some of Arlo Landolt's 
> standard fields and am wondering if the color error magnitudes given in 
> his paper 
> <http://articles.adsabs.harvard.edu//full/1983AJ.....88..439L/0000444.000.html> 
> are just quadrature sums of the individual UBV errors.
> 
> If they are, and I want to back out the U and B errors, do I need to 
> first convert them to flux-like values (ie not logarithmic), do the 
> subtraction and then reconvert to magnitudes?
> 
> Also, in the paper, I notice that in numerous instances the (for 
> example) reported (B-V) errors are smaller than the V errors.  How can 
> that be?
> 
> Can anyone get me pointed me in the right direction here?
> 
Not quite sure what you mean, but I'll take a stab at it.
The normal method of all-sky data reduction is to use transformation
equations that give the V magnitude, plus a number of color indices.
These color indices are of course formed by taking two instrumental
magnitudes and subtracting them.  The formal error for an individual
measurement set does depend on the Poisson error of each measure,
plus lots of other terms like how well extinction was determined on
a night, how well the transformation fits the standard stars observed
on that night, etc.

So the all-sky calibration is *not* done as U, B, V, R, I and then
forming (U-B), (B-V) for the tables.  Instead, each color index has
its own equation and transformation coefficient.  The error in the
tables represents the error in the color indices themselves.  The
reported color indices are the means from several nights, and the
errors are the standard deviations from the mean across those nights.
Once you do this, the Poisson error, etc. of the individual measure
goes away since you are creating an empirical error across many
nights of individual measures.

You can have smaller error in a color index than in a magnitude
because, to first order, the extinction and any transparency
variations cancel out when you take the difference of two magnitudes,
much like differential photometry between two stars.
Arne