[Aavso-photometry] Re: Calculating mag errors for filter bands from
color indices
Wolfgang Renz
w_renz at onlinehome.de
Mon Dec 20 23:11:03 EST 2004
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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