[Aavso-photometry] Re: Calculating mag errors for filter bands
fromcolor indices
Richard Miles
rmiles.btee at btinternet.com
Tue Dec 21 06:04:56 EST 2004
Wolfgang,
I agree with your analysis.
Your formulae, (VI) for rms i', (XV) for rms z', (XVII) for rms g', and
(XIX) for rms u' should be robust estimates of the derived errors in the
SDSS mags.
You have only one small error (maybe a typo) in your analysis, that is where
you write:
>> While (VI) leads to an alternative value of rms i' <= 0.0049 rounded up
>> 0.005.
This should read:
>> While (VI) leads to an alternative value of rms i' <= 0.0045 rounded up
>> 0.005.
This typo has no bearing on the outcome of your analysis.
Otherwise you're spot on.
Now it's just a matter of making sure that everyone adopts the procedure you
outline for error analysis.
Cheers,
Richard Miles
----- Original Message -----
From: "Wolfgang Renz" <w_renz at onlinehome.de>
To: "AAVSO-PHOTOMETRY" <aavso-photometry at mira.aavso.org>
Sent: Tuesday, December 21, 2004 4:11 AM
Subject: [Aavso-photometry] Re: Calculating mag errors for filter bands
fromcolor indices
> Hello
>
> Not a single comment on this subject ?
>
> I know that the non-photometry astronomers prefere color indices
> to ease their work.
> Calculating a color index and a rms of a color index is a pretty simple
> task But keeping combined error estimates as small as possible is
> not.
>
> Shouldn't the photometrists use the original values with the smaller
> error estimates instead of color indices with already combined error
> estimates ?
>
> Clear skies
> Wolfgang
>
> --
> Wolfgang Renz, Karlsruhe, Germany
> Rz.BAV = WRe.vsnet = RWG.AAVSO
>
>
>
> ----- Original Message -----
> From: "Wolfgang Renz" <w_renz at onlinehome.de>
> To: "AAVSO-PHOTOMETRY" <aavso-photometry at mira.aavso.org>
> Sent: Friday, December 10, 2004 7:16 PM
> Subject: [Aavso-photometry] Calculating mag errors for filter bands from
> color indices
>
>
>> Hello
>>
>> Whats the accepted standard in calculating mag errors for filter bands
>> from color indices ?
>> Just the usual error propagation that will overestimate the error ?
>>
>> Taking G158-100 of "The u'g'r'i'z' Standard Star System" as an example of
>> the
>> reference below :
>>
>> Calculating i' via
>> (I) i' = r' - (r'-i')
>> gives a value of i' = 14.469.
>>
>> Calculating rms i' with usual error propagation via
>> (II) rms i' = SQRT( SQR(rms r') + SQR(rms r'-i') )
>>
>> But as nobody can measured a color index directly the rms r'-i' must have
>> come from subtracing the color mags and the rms r'-i' probably from
>> (III) rms r'-i' = SQRT( SQR(rms r') + SQR(rms i') )
>>
>> Inserting (III) into (II) shows that the rms r' is counted twice using
>> usual
>> error propagation
>> (IV) rms i' = SQRT( SQR(rms r') + SQR(rms r') + SQR(rms i') )
>> leading to a too big error estimate.
>>
>> Converting (III) to rms i' gives
>> (V) rms i' = SQRT( SQR(rms r'-i') - SQR(rms r') )
>> numerically
>> (VI) rms i' <= SQRT( SQR(rms r'-i'[rounded up]) - SQR(rms
>> r'[rounded down]) )
>> assuming all given rms were rounded up and
>> (VII) rms r'[rounded down] = rms r' - 1 in the least
>> significant digit
>>
>> Usual error propagation (II) gives in the example a value of rms i' =
>> 0.0092 rounded up 0.010.
>> While (VI) leads to an alternative value of rms i' <= 0.0049 rounded up
>> 0.005.
>> Checking this value via (III) gives rms r'-i' = 0.0078 (>= 0.007 as
>> listed in the ref).
>>
>>
>> Calculating z' via
>> (VIII) z' = r' - (r'-i') - (i'-z')
>> gives a value of z' = 14,377.
>>
>> Calculating rms z' with usual error propagation via
>> (IX) rms z' = SQRT( SQR(rms r') + SQR(rms r'-i') + SQR(rms
>> i'-z') )
>>
>> But as again nobody can measured a color index directly the rms i'-z'
>> must have
>> come from subtracing the color mags and the rms i'-z' probably from
>> (X) rms i'-z' = SQRT( SQR(rms i') + SQR(rms z') )
>>
>> Inserting (III) into (IX) shows again that the rms r' is counted twice
>> using usual
>> error propagation although r' wasn't probably used at all to calc z'
>> (XI) rms z' = SQRT( SQR(rms r') + SQR(rms r') + SQR(rms i') +
>> SQR(rms i'-z') )
>> leading to a too big error estimate.
>> ...
>>
>> Converting (X) to rms z' gives
>> (XII) rms z' = SQRT( SQR(rms i'-z') - SQR(rms i') )
>> numerically
>> (XIII) rms z' <= SQRT( SQR(rms i'-z'[rounded up]) - SQR(rms
>> i'[rounded down]) )
>> Inserting (V) into (XIII) gives
>> (XIV) rms z' <= SQRT( SQR(rms i'-z'[rounded up]) - ( SQR(rms
>> r'-i') - SQR(rms r') )[rounded down] )
>> or simpler
>> (XV) rms z' <= SQRT( SQR(rms i'-z'[rounded up]) - SQR(rms
>> r'-i'[rounded down]) + SQR(rms r'[rounded up]) )
>> assuming all given rms were rounded up and
>> (XVI) rms r'-i'[rounded down] = rms r'-i' - 1 in the least
>> significant digit
>>
>> Usual error propagation (IX) gives in the example a value of rms z' =
>> 0.0136 rounded up 0.014.
>> While (XV) leads to a value of rms z' <= 0.0100 rounded up 0.010.
>> Checking this alternative value and the alternative rms i' via (X) gives
>> rms i'-z' = 0.0111 (>= 0.010 as listed in the ref).
>>
>>
>> Simillarly would be
>> (XVII) rms g' <= SQRT( SQR(rms g'-r'[rounded up]) - SQR(rms
>> r'[rounded down]) )
>> assuming all given rms were rounded up and
>> (XVIII) rms r'[rounded down] = rms r' - 1 in the least
>> significant digit
>>
>> Simillarly would be
>> (XIX) rms u' <= SQRT( SQR(rms u'-g'[rounded up]) - SQR(rms
>> g'-r'[rounded down]) + SQR(rms r'[rounded up]) )
>> assuming all given rms were rounded up and
>> (XX) rms g'-r'[rounded down] = rms g'-r' - 1 in the least
>> significant digit
>>
>>
>> Is it allowed to use the smaller error estimates (VI) for rms i', (XV)
>> for rms z', (XVII) for
>> rms g', and (XIX) for rms u' for consistent data as long as the
>> conditions
>> 0 < rms r' <= rms r'-i' <= rms i'-z'
>> and
>> 0 < r' <= rms g'-r' <= rms u'-g'
>> are fullfilled ?
>> These conditions are true for all SDSS standard stars in the reference
>> below !
>>
>>
>> Clear skies
>> Wolfgang
>>
>> --
>> Wolfgang Renz, Karlsruhe, Germany
>> Rz.BAV = WRe.vsnet = RWG.AAVSO
>>
>>
>>
>> Reference:
>>
>> The u'g'r'i'z' Standard Star System:
>> Main Page
>> http://home.fnal.gov/~dtucker/ugriz/tab08.dat
>> The u'g'r'i'z' standard star network: calibrated magnitudes and colors
>> (Table 8 of Smith et al. 2002, AJ, 123, 2121)
>> ====================================================================================================================
>> A machine-readable version of this table is also available at
>> www.journals.uchicago.edu/AJ/journal/issues/v123n4/201445/datafile8.txt
>> StarName RA (J2000.0) DEC (J2000.0) r' u'-g' g'-r' r'-i' i'-z' rms r' rms
>> u'-g' rms g'-r' rms r'-i' rms i'-z' n u' n g' n r' n i' n z'
>> -------- ------------ ------------- -- ----- ----- ----- ----- ------ ---------
>> --------- --------- --------- ---- ---- ---- ---- ----
>> ...
>> G 158-100 00:33:54.60 -12:07:58.9 14.691 1.101 0.510 0.222 0.092 0.006
>> 0.019 0.008 0.007 0.010 6 7 8 6 6
>> ...
>>
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