Re: color terms

[Robert Creager <Robert_Creager@LogicalChaos.org>]

Thanks Michael,

I was just about to re-send my question, as I missed your response first time
around.

On Mon, 18 Aug 2003 09:54:22 -0400
Stupendous Man <richmond@stupendous.cis.rit.edu> said something like:

> »                                                         2
>                              [  V - (v + a + b*(v - i )) ]
>                2                          j      j   j
>             chi   =   sum  --------------------------------
>                                   2         2          2
>                             sig(V)  + sig(v)   + sig(i)  
> 
>   What is the point of this whole calculation?  Is it "absolute"?  That
> is, is the purpose to estimate the uncertainty in the output magnitude, 
> so that one may attach a "plus/minus" value to the published magnitude?  
> Or is it "relative"?  That is, is the purpose simply to give more weight
> to some stars in a solution than others?

Why not both?  I would presume that in either case, you want to give less weight
to high uncertainty values, and more weight to low uncertainty values.

> 
> > Ignoring them doesn't seem right.  Can sig(V)/(I) somehow be 
> > calculated from the original e_BT and e_VT terms in Tycho2?
>   
>   In _theory_, one could take the e_BT and e_VT terms and turn them
> into sig(V) and sig(I), using the formulae for propagation of errors.
> For example, if
> 
>                        V  =   0.1 +  VT   +  0.1*(BT - VT)
> 
>                           =   0.1 +  0.9*VT  +  0.1*BT
> 
> then formally, one can write something like:
> 
>                  sig(V)   =   sqrt( [0.9*e_VT]^2  +  [0.1*e_BT]^2 )

So, in this theoretical exercise, the constants are simply ignored?  (Thinks
for a moment).  Make sense, as they are just shifting the data.

>                                      
[snip explanation of why practice and theory don't mix]
> 
>   It's quite possible that the a) scatter around the linear fit, and
> b) non-linear deviation from the linear fit, might turn out to be much
> larger than the formal uncertainty.  In that case, ignoring the
> e_VT and e_BT terms would be fine.  In fact, what you would need to
> do in such a case is to figure out yourself what a reasonable
> value for sig(V) would be.  And that would take some work.
> 
>   In the real world, you might just do the following:
> 
>                 - look at the relationship between BT, VT and V
>                 - estimate the scatter from a linear fit for bright stars
>                          call the stdev "s"

Why just bright stars?  Wouldn't you want to do this for all the stars
throughout the magnitude range?  Maybe useing a 1 mag bin (or something)?  The
scatter should increase for dimmer stars, decreasing their contribution to the
solution.  Although only brighter stars are used in calculating the solution, so
you'd just use the same range for calculating the scatter, which would not use
the dimmer stars.  OK.

>                 - calculate the formal uncertainty based on e_BT and e_VT
>                          call that quantity "u"
>                 - calculate
>                          sig(V)  =  sqrt (s*s + u*u)

Hmmm...  So, how do you solve this problem, other than iteratively?  (And to
think I have a math minor :-( )  Your color calculations depend on the
uncertainty, which depends on the color...

Thanks,
Rob

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