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Re: Tech Note 97: Photometric properties of TOM1 data




  Arne wrote:

> TN97 indicates the equation is
> 
>   calibrated mag  =   raw mag  +  a   +   b * (raw color)  +  k * airmass
>   
> You should be using "standard color" in here.  If the zeropoint for
> each filter changes, then you get
>
>           b * [(mag1 + z1) - (mag2 + z2)]
>           b * [mag1-mag2] + b*[z1-z2]
>                   
> This second term will influence your calibrated magnitudes unless
> I don't understand what you mean by "raw color".

  This is true.  Let me go over this in some detail.  I'll use 
upper-case letters "V" and "I" to represent the "true" values
of magnitudes (known from some other source, for example),
and lower-case letters "v" and "i" to represent the observed,
instrumental values.  Let's leave extinction out of the
discussion for a moment.

  I've read several times that one ought to use these equations:
picking stars of known magnitude -- standards -- one writes

          V   =   v  +  av  +  bv*(V - I)          (1)
          I   =   i  +  ai  +  bi*(V - I)          (2)

Solve for the zeropoints av and ai, and the color terms bv and bi,
by the method of least squares.  Fine.

  Now, for all the stars which do NOT have known magnitudes, 
we want to calibrate the instrumental magnitudes; that is, we
wish to turn v and i into V and I.  We _must_ have some formula
for doing so in terms of the quantities we know: the instrumental magnitudes,
the zero points, and the color terms:

          V   =  f(v, i, av, bv, ai, bi)
          I   =  f(v, i, av, bv, ai, bi)

The references I have found state at this point: "one must invert
the equations (1) and (2) to solve for the standard magnitudes
in terms of the instrumental ones."  Presumably, one ends up
with something like this:

          V   =   v  +  av' +  bv'*(v - i)          (1a)
          I   =   i  +  ai' +  bi'*(v - i)          (2a)

where the values av', ai', bv' and bi' are related algebraically
to their counterparts av, ai, bv and bi.  

  So, what I have done is to skip directly to equations (1a) and (2a),
rather than going through (1) and (2) and inverting.  I understand that
this is less desireable, because one knows the true V,I magnitudes
of standard stars to a high accuracy, and so can derive 
_accurate_ values of the primed coefficients.

  Do I have to modify the photometric calibration step of the 
pipeline?  Hmmmmm.  Maybe I do.
  
> kv = 0.2 is too low for ground-level sites.  Values of 0.3 would be closer.

  That's easy to change: it's the "fixk" parameter in the 
photom.param file.  How big a difference does this make?  A typical
airmass for stars on the equator is about 1.4.  Only differential 
extinction across a frame is required, and the difference in airmass 
is about 0.1 at most from the top to bottom of a Mark IV image.
So the difference between a star at the top and a star at the
bottom would be

            currently, in V:     (0.1 airmass)*(0.2 mag/airmass) = 0.02 mag
            Arne's suggestion    (0.1 airmass)*(0.3 mag/airmass) = 0.03 mag

A difference of 0.01 mag at most.  This might show up as a small systematic
error, indeed.  It would be smaller than the spatial errors I mention
in TN 97, which are of order 0.05 mag in amplitude.

> Why are you calculating the color term on each night?  Mean values
> should be better since the color coefficient is *very* slowly changing
> (like, years).

  Because that's all the information there is.  Tom reduces one night
of images at a time.  We didn't know what the average color term was
over many night until now. 

> What are the values for the two color terms?

  This bothers me.  The terms are small, but they are NOT the same 
from one night to the next.  I indeed looked at this during my 
recent work, hoping that I could derive good mean values that
could then be fixed and used for all nights.  But look at my 
results:

         based on all data on disk (good and bad sections of nights),
         derived one night at a time
                  bv   ranges   -0.02 to -0.15
                  bi   ranges   +0.03 to -0.13

         based only on a set of 10 good nights,
         derived one night at a time
                  bv   ranges   -0.02 to -0.10
                  bi   ranges   -0.07 to -0.13

         based on good night 606, 2745 stars total
                  bv   =  -0.021
                  bi   =  +0.076

         based on good nights 606 + 608, 3644 stars total,
         derived simultaneously 
                  bv   =  -0.049
                  bi   =  +0.007

         based on good nights 606 + 608 + 609, 10821 stars total
         derived simultaneously 
                  bv   =  -0.044
                  bi   =  +0.062

         based on good nights 606 + 608 + 609 + 614, 26650 stars total
         derived simultaneously 
                  bv   =  -0.032
                  bi   =  +0.074
    
  You see?  I was hoping that the values would converge, but it's not
clear to me that they do.

> You should *not* use the Tycho2 transformations to determine color
> terms.  The Ic values are nowhere near close enough to Landolt.
> You should only use those Landolt standards that fall within scans
> for that determination.  So set zeropoints perhaps with Tycho2,
> but determine coefficients separately.

  Perhaps you don't understand what's happening here.  The procedure
I followed is:

        - start with raw instrumental magnitudes
        - transform to Tycho2 magnitudes  
        - transform AGAIN to Johnson-Cousins magnitudes
          
I'd love to skip the intermediate step, but it's not possible:
there is no guarantee that a Landolt standard will appear in
every image.  In fact, there is no guarantee that a Landolt
standard will appear in an entire night!  

  If the Mark IV units were run like so:

         a) only on clear nights
         b) moving to fields with Landolt standards once per hour or so

then one could reduce their data in the usual fashion, following several
of the criticisms you have raised.  I'd love to do that, of course.
However, given that Tom collects data

         a) on all nights, clear or otherwise
         b) with no plan to acquired fields with Landolt standards

I don't see a way to reduce his data in any other way.  One could argue
that the proper thing to do is to discard it, or perform only
differential measurements within a single field.  One might be correct.
I'm trying to do the best job possible to place Tom's measurements
onto the standard scale, so that they might be of use to others.

  I will think about using the standard color (V-I) in the photometric
reductions -- thanks for reminding me about it.
    
                                     Michael Richmond