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1.1
date	2002.12.04.11.12.44;	author MarkAllen;	state Exp;
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@Notes on Magnitude-Flux conversions for EIS data
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@Dec 04, notes compiled by Mark Allen.


MAG-Flux conversions and caveats. 
---------------------------------
It has taken quite some time to understand all the issues
pertaining to the photometry of the EIS data and catalogs.
Below, I've listed the main points relevant to flux
conversion in order to plot an SED, and also some
detailed finer points about colour terms. It'd be good
if an EIS team member cast an eye over this. (I've
sent it to S. Arnouts asking for him to check it)

Basic photmetry info relevant to EIS data:

1. The image data are in units of counts/s

2.  The image headers contain a zero point which
    provides a conversion to Vega magnitudes in the
    EIS filters
    m(EIS) = -2.5log10(counts/s) + ZP

3.  The header keywords in the WFI/SOFI/ISAAC images 
    for the zero points are ZP and ZP_ERR for the uncertainty.

4.  In general magnitudes can be converted to fluxes, using
    standard values for the flux F_0 of a zero magnitude star
    in the given filter. 

    m = -2.5log10(Flux/F_0)
    or reaaranged to          Flux =  F_0 * 10^(-0.4*m)

    or sometimes this will be expressed as (yet another) zeropoint
    where  ZP_0= 2.5log10(F_0), so that Flux = 10^(0.4(ZP_0 - m))
                
5.  We've adopted a set of F_0 values for each filter. 
    These are listed below.
 
V=0 flux table for Johnson-Cousins-Glass UBVRIJHKLM system
                               U    B    V    R    I    J    H    K    L    M
------------------------------------------------------------------------------
lambda_eff    (nm)           367  436  545  638  797 1220 1630 2190 3450 4750
delta lambda  (nm)            66   94   85  160  149  213  307  390  472  460  
F_nu(V=0)(10^-30Wcm^-2Hz-1) 1790 4063 3636 3064 2416 1589 1020  640  285  154
------------------------------------------------------------------------------   

One would think these values have solid standardized values, 
but the reality is that there are many tables floating around
with different values, and there are some problems at IR wavelengths
(as noted in HST instrument science report CAL/SCS-008).
Here we've adopted a table from Bessel, where all the values are
at least written down uniformly in the same place (even so, I await
confirmation of a correction to the K value in this table)

6. We use the above table to convert the EIS catalog magnitudes
   into fluxes in Jy.

7. The above dercription is not strictly correct because we are not 
   currently using the colour terms. The EIS catalogs are calibrated
   to the Johnson system (as stated in Arnouts et al 2001), but the
   values in the EIS cross matched colour catalogs are (as far as I'm aware)
   EIS system vega magnitudes. i.e. to convert to Johnson one needs
   to apply the colour terms:
 
   The most recent colour terms were provided by S. Arnouts. (to correct
   errors in the Arnouts et al  2001 paper)

  (Ujc-U'eis) =  0.04 (U'-B)eis
  (Ujc-Ueis)  =  0.03 (U-B)eis
  (Bjc-Beis)  =  0.37 (B-V)eis
  (Vjc-Veis)  = -0.17 (B-V)eis
  (Rjc-Reis)  = -0.03 (V-R)eis
  (Ijc-Ieis)  =  0.19 (R-I)eis

   Note that to apply the colour terms, one needs to operate not just
   with a single catalog column, but with 2 magnitude columns. e.g. the
   Ujc (Johnson U) value depends on the both the U_eis and B_eis value. 

   This has implications for re-extracted catalogs, where if one band was
   re-extracted, then strictly, to re-compute it's flux, then other
   bands must also be re-extracted and colour terms applied.

   Because of this difficulty, and because there are currently no 
   mechanisms for manipulating the columns (in vizier or aladin) in
   this way, we are treating the EIS Vega system magnitudes as if they
   are Johnson magnitudes. Also, I belive there are other colour term 
   subtleties that depend on the type of object (which I think is beyond
   the scope of this exercise for the moment)

   How much difference will it make ?
    --  Estimate offsets using [min,max] colours of EIS catalog:

   (U-B) ~ [-2,2]     =>  Ujc = Ueis +  [-0.06,0.06]    
   (B-V) ~ [-0.5,1.5] =>  Bjc = Beis +  [0.19, 0.55]     
                      =>  Vjc = Veis +  [-0.26, 0.09]
   (V-R) ~ [-1,2]     =>  Rjc = Reis +  [-0.06,0.03]
   (R-I) ~ [-1,2]     =>  Ijc = Ieis +  [-0.19, 0.38]

   
8.  Another "caveat" is that the published single band catalogs have
    been converted further to AB magnitudes (as opposed to Vega magnitudes)
    The AB - Vega conversions are listed in Arnouts et al. 2001.

    U'_eis(AB) = U'_eis + 1.04
    U_eis(AB) = U_eis + 0.80
    B_eis(AB) = B_eis - 0.11
    V_eis(AB) = V_eis
    R_eis(AB) = R_eis + 0.19
    I_eis(AB) = I_eis + 0.50


    So, the published catalogs and the draft cross-matched colour
    catalogs need to be put on the same systems (AB, or Vega) to be
    compared sensibly. These differences of up to a magnitude are
    significant. 

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