2.3. Accurate Flux Density Bootstrapping

      Because of source variability, it is impossible to compile an
accurate listing of flux densities for most VLA calibrators.  The
values given in Chapter 4 of this manual are only approximate.  We
strongly recommend bootstrapping the flux density of a calibrator by
comparing the calibrator observations with one or several observations
of 3C286, 3C48 or 3C147. Careful observations have allowed the
following set of rules to be established for accurate bootstrapping of
flux densities using 3C286, 3C48 or 3C147.

      3C286 is partially resolved to most combinations of configuration and
band.  Its resolution occurs on two different scales - there is a weak
secondary located 2.5" from the core, and the core itself is partially
resolved on longer baselines.  Nevertheless, 3C286 can be used as a flux
calibrator for all VLA observations providing the rules laid down below are

3C48 and 3C147 are heavily resolved to some combinations of
configuration and frequency and exhibit some variability on timescales
of months to years (see section 2.2), but nevertheless may be
preferable as a flux calibrator over 3C286 since they contain no
extended structure on scales greater than 1".  


      The following combinations of array configuration and band have no
restrictions in number of antennas or UV range:

               3C48/3C147     90cm     All configurations
                              20cm     C and D configurations
                              6cm      D configuration
                              3.6cm    D configuration

               3C286          90cm     B,C,D configurations
                              20cm     C and D configurations
                              6cm      D configuration
                              2cm      D configuration
                              1.3cm    D configuration


      The following combinations of configuration and band should not be
calibrated with 3C48 or 3C147 without supplying a good model.

                              2cm      A configuration
                              1.3cm    A configuration
                              0.7cm    A, B configurations

Some FITS format images, along with clean component models for 3C48
and 3C286 can be found at:
(look for the latest links therein).
If a model 
is used then no (u,v) restrictions or limitations on the number of
antennas are needed.  Note that it is still necessary to run SETJY on
the primary flux density calibrator even when supplying a model
to CALIB.  


      The following rules must be carefully followed to ensure proper
flux bootstrapping in the combinations of array scale and band noted
below.  For the hybrid configurations (BnA, CnB, DnC) the rule for the
more compact configuration should be adopted (i.e. follow B config
rules for BnA).  When specifying inner antennas to be used for the
calibration solution, no antenna on the North arm further out than on
the East or West arms should be used.  Finally, it is a good idea to
set WTUV = 0.1 in CALIB to ensure a stable solution.

                                            NUMBER OF
            (cm)      (Kl)                  (per arm)
3C48/3C147   90       0-40       All           All        

3C48/3C147   20       0-40        A             7
                       "        B,C,D          All

3C48/3C147    6       0-40        A             3
                       "        B,C,D          All

3C48/3C147   3.6      0-40        A             2
                       "          B             6
                       "         C,D           All

3C48/3C147    2       0-60        A             1            Not recommended
                       "          B             5
                       "         C,D           All

3C48/3C147   1.3      0-80        A             1            Not recommended
                       "          B             5
                       "         C,D           All

3C48/3C147   0.7      0-100       A             1,*          Not recommended
                       "          B             3,*          see note below
                       "         C,D           All,*         see note below

                                               NUMBER OF
          (cm)      (Kl)                       (per arm)
3C286      90       0-18            A              7
                     "            B,C,D           All

3C286      20       0-18            A              4
                     "            B,C,D           All
                   90-180           A             All     Reduce flux by 6%

3C286       6       0-25            A              1      Not recommended
                     "              B              4
                     "             C,D            All
                  150-300           A             All     Reduce flux by 2%

3C286      3.6     50-300           A              3      Reduce flux by 1%
                   50-300           B              7      Reduce flux by 1%
                   50-300           C             All     Reduce flux by 1%
                    0-15            D             All

3C286       2       0-150           A              3
                     "            B,C,D           All

3C286      1.3      0-185           A              2
                     "              B              7
                     "             C,D            All

3C286      0.7      0-300           A              2,*    See note below
                     "              B              6,*    See note below
                     "             C,D             All

* NOTE: We are also investigating additional
sources that may be suitable as primary flux density calibrators 1.3
and 0.7 cm.  The latest information concerning absolute flux calibration
at 0.7 cm can be found in the High Frequency Observing Guide under Absolute
gain calibration:  
Due to its (u,v) restrictions, low flux density,
and evidence suggesting that 3C48 is variable at
this wavelength, it is not recommended for flux calibration at 0.7 cm.

      If one were to ignore the guidelines, and blindly calibrate the
data on the basis of the available data, the flux error obtained would
vary according roughly to how much resolution occurs but would not
exceed 5% for 3C286.  Bear in mind that there will occur a
differential error as well, as the antennas at the ends of the array
will be overcalibrated with respect to those at the center.

If these guidelines are followed, the bootstrap accuracy should be 1
or 2 percent at 20, 6, and 3.6 cm, and perhaps 3 to 5 percent at 2,
1.3 and 0.7 cm.  At 2cm and 1.3cm bands, other effects, such as dish
efficiency, pointing and atmospheric absorption (1.3cm and 0.7cm) are
probably more important.

Elevation-dependent gain corrections:

  At frequencies of 15 GHz and above, there are appreciable changes in
the antenna gains as a function of elevation.  Atmospheric opacity,
especially at 22 GHz, also introduces an elevation-dependence on the
observed visibility amplitudes.  By calibrating the target source with
a nearby calibrator, much of these variations can be removed.
However, if the primary flux calibrator (e.g. 3C286) is observed at a
different elevation from the secondary gain and phase calibrator, then
the flux bootstrapping will be in error.  Proper calibration of the
flux densities at high frequencies requires knowledge of a gain curve
for the antennas, and the atmospheric opacity as well.  Software has
been developed in AIPS to address these issues (see the task ELINT).
If you don't have enough data to make your own gain curve, you can
find gain curves at  

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