[Aavso-photometry] Landolt error bars

[Ben Davies]

arne wrote:
> 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
>
Thank you!

Good point about the S/N, but I have to think more about the exposure 
time consideration.  I am doing instrumental magnitudes in adu/sec which 
gives me big negative magnitudes, but it saves  a lot of downstream 
futzing about with exposure time corrections. 

I'm getting a little fuzzy here, but I *think* that since I am plotting 
my instrumental magnitudes as flux rates I wouldn't have to care what 
Landoldt's exposure times were.  And it sure seems like adding, 
squaring, etc logarithms as if they were regular numbers would not be 
the thing to do.  I am probably all wet here but, straighten me out.

Ben