Explanation of the task SETJY and the incorrect computation of the flux density of 3C286 in 1990-1995

Greg Taylor
20 February 1996

The flux density scale of radio interferometers is often determined by observations of radio sources of known brightness. For interferometric observations, it is important that the standard sources used for this purpose be relatively compact. This is often at odds however with the requirement that the sources have very low variability over long time scales.

For calibration of observations with the VLA, the radio sources 3C48, 3C147 and 3C286 are most commonly used. The standard reference for the flux density of bright radio sources is the paper by Baars, Genzel, Pauliny-Toth, Witzel 1977, Astron., Astrop. volume 61, page 99. The flux density of the standard sources can be modeled as a polynomial expansion over frequency. Polynomial coefficients have also been derived independently by R. Perley and G. Taylor as part of a long-term program to monitor the standard flux density calibrators at the VLA. These flux densities have been tied to 3C295 as it is believed that the bulk of the emission from 3C295 should remain constant over a time scale of thousands of years.

The AIPS task SETJY will calculate the expected flux density of the standard calibrators using the relationship

Log S = A + B * Log(nu) + C * Log(nu)**2 + D * Log(nu)**3

and either the Baars etal. coefficients or those derived from the VLA observations in 1990 or 1995. This option is selected by setting OPCODE to 'CALC'. The coefficient set to be used is selected using APARM(2).

It was recently discovered that the existing 1990 VLA coefficients were rounded incorrectly in SETJY, introducing a positive bias in the calculated flux density of 3C286 at all bands (see tables below for more detail). This systematic error is greater than the intrinsic variability of 3C286 at frequencies below 15 GHz over the last 10 years. A similar rounding was made for 3C48 and 3C147, but by chance introduced a much smaller effect, considerably less than their intrinsic variability. This error affected AIPS versions up to and including 15JAN96. The 1990 coefficients implemented in subsequent versions have been corrected to remove the rounding error.

1990 Coefficients in SETJY

"True" as Derived "Rounded" as in SETJY 15JAN96
Source A B C A B C
3C48 2.08680 0.20889 -0.15498 2.087 0.209 -0.155
3C147 1.92641 0.36072 -0.17389 1.926 0.361 -0.174
3C286 1.35899 0.35990 -0.13338 1.359 0.3599 -0.133

Effect of Rounding Error in 1990 coefficients on 3C286

Frequency "True" "Rounded" Error
(MHz) (Jy) (Jy) (%)
327 26.34 26.49 0.569
1365 15.01 15.14 0.866
4885 7.441 7.530 1.20
8415 5.209 5.280 1.36
14915 3.449 3.502 1.54
22485 2.507 2.549 1.68

For more detailed information regarding the variability of the standard flux density calibrators at the VLA please see the VLA calibrator manual.