Accurate Flux Density Bootstrapping

Introduction

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 followed.

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".

When 3C48, 3C147 and 3C286 can be used directly

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

When 3C48 and 3C147 require a model

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

Some FITS format images, along with clean component models for 3C48 and 3C286 can be found at

http://www.aoc.nrao.edu/~cchandle/cal/cal.html.

or

http://www.aoc.nrao.edu/~smyers/calibration/

(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.

When special restrictions are necessary for flux calibration

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.

* 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 relevant section of the VLA Guide to Observing.

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 over-calibrated 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 http://www.aoc.nrao.edu/~smyers/calibration/.