[Aavso-photometry] Landolt error bars

[arne]

Ben Davies wrote:
> 
> arne wrote:
>> 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
>>
> Arne,
> 
> Thanks for the explanation.  I didn't put the question very well.
> 
> The reason I want the Uerr and Berr numbers is that I am using the 
> FITEXY routine in IDL to get a chi-square linear fit to model  color 
> terms like B-b vs (B-V).  FITEXY will use the error bars to get a better 
> fit if you have them.
> 
> I know these error numbers exist for UBRI , because I have them for a 
> few fields.  I just don't know where or how to get others.  Maybe there 
> is a text file somewhere?
> 
> Then, I am trying to figure out how would I construct the error bar for 
> the B-b axis.  This should have been the quadrature question.
> 
If you want Berr, then you do have to derive B from
     B = V + (B-V)
and the error is sqrt (Verr**2 + BVerr**2)
The Berr so derived may be larger than Berr if Landolt had solved
directly for it, since it is now the quadrature sum of two errors.
If you have errors for UBRI for some fields, then I don't think
they came from Landolt himself, but from some researcher who applied
the quadrature sum to derive the errors.  You do not need to convert
to flux units first, and in fact I don't see how you could work in
flux units for this case - the two magnitudes are different filters
with different exposure times and signal/noise, so the flux units
are not directly comparable.
Arne