Re: Tech Note 97: Photometric properties of TOM1 data

[Arne Henden <aah@nofs.navy.mil>]

Stupendous Man wrote:
>   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.
>
The way you normally do this is to solve for the color index first
and then substitute that into the magnitude equation.  See the
description in my photometry book.
> 
>>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.
>
yup, but that is on the equator.  you need to handle the general case.

> 
>>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.
> 
There should be random scatter around a mean value, which is not
happening.  I suspect the instrumental color problem is the root
of this.

> 
>>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!  
> 
So then I get confused.  I understand the first two steps (but in step
two, you are transforming to the Tycho2 "BVRI" dataset, right, and
not to Bt/Vt), but don't understand how you are going from there
to the third step.

>   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.
> 

There are several approaches.
   - leave everything instrumental for now, and calculate magnitudes
        differentially with respect to local comparison stars in the
        frame (an ensemble solution, but on Tom's native system).
   - just convert magnitudes to Johnson/Cousins V/Ic by applying
        zeropoints, but with no additional color correction.  This
        is the safest method.
   - do your three-step method, which I think fails since it requires
       the Tycho2 stars be of sufficient V/Ic accuracy.
   - use the LONEOS file to obtain "standards" on about a 5-degree
       grid; that may be sufficient for your calibrations
   - wait for ARNE or another system to obtain reliable photometry
       and reprocess the data (at the starlist level) then.  That
       is the approach I suggest.  As soon as ARNE is ressurected
       I should be able to produce a good photometric catalog.
   - do a global solution.  As long as frames overlap, you should
       be able to transfer calibration across the sky from where
       real standards reside.
Arne