Calibrating the Flux Density Scale

by Stephan W. Witz last modified Sep 07, 2018 by Tony Perreault

Normal calibration of the flux density scale for VLA observations is effected by including a scan on a source of presumed known flux density in each Scheduling Block (SB). Using that known flux density source, the flux density of the complex gain calibrator(s) can be determined and then transferred to your target source(s). Historically, 3C48 and 3C286 have been the standard sources for which NRAO has assumed flux densities are known as a function of frequency, and which have been recommended as flux density scale calibrator sources for the VLA. Restrictions on baseline length as a function of VLA configuration and observing band were supplied which, if followed, allowed relatively accurate flux density scale calibration. We have recently improved the ability to calibrate the flux density scale by providing sky brightness models for these sources in CASA and AIPS, which loosens the restrictions on configurations and bands. We have also added the sources 3C138 and 3C147 to the list of calibrators that have models. However, 3C48*, 3C138, and 3C147 have spectral flux densities that vary with time (3C286, along with 3C295 and 3C196, are constant), so some care should be taken if the most accurate flux density scale calibration is desired.

A single observation of a few minutes of one of the above-mentioned flux density scale calibrators will suffice for most observers. If possible, the flux density scale calibrator should be observed at a time when it is nearly at the same elevation as the complex gain calibrator, especially for the highest four bands (Ku-, K-, Ka-, and Q-band). This is not always possible because of timing and geometry of sources, and that it is not typically known when an SB will be executed (so elevations versus time are uncertain). Flux density scale calibration accuracy in this case should be of order 10% at 4- and P-bands, 5% at L- through Ku-bands, and 10-15% for the three higher bands. If more accuracy is needed, a more careful strategy should be adopted, potentially using multiple flux density scale calibrators. The fundamental accuracy of the scale is ~5% at 4- and P-bands, 3% at L- through Ku-bands, increasing to 5% at Q-band. See Perley and Butler (2017) for more details on how the spectral flux densities of 3C48*, 3C138, 3C147, and 3C286 (and many other sources) have been determined across the frequency range from 50 MHz to 50 GHz and how they vary versus time, along with information on the fundamental accuracy of the flux density scale when using these sources.

If less accuracy is needed in the flux density scale calibration, an observation of one of these standard sources need not necessarily be included in an SB. As an example, for a short triggered observation where a simple detection is desired, the time spent slewing back and forth to the flux density scale calibrator can make the SB significantly longer than it could otherwise be. In this scenario, the switched power measurement can be used to calibrate the flux density scale; see EVLA Memo 120 for some background. This technique is not a standard path of calibration, and is not easily supported in CASA or AIPS, but it is possible. The flux density scale accuracy in this case is ~10% for L- through Ku-bands, increasing to ~20% at Q-band; not nearly as good as using the "standard" method of flux density scale calibration, but it may be sufficient for some observers.

For reference, the polynomial expression for the spectral flux density for 3C286 determined in Perley and Butler (2017) is: [display]\log(S) = 1.2481 - 0.4507 \log(f) - 0.1798 \log^2(f) + 0.0357 \log^3(f)[/display] where S is the flux density in Jy, and f is the frequency in GHz. The table below shows flux densities determined using the polynomial coefficients in Perley and Butler (2017) for a few sources at a single frequency within each of the VLA bands. Since several of these sources are variable with time, these values are appropriate for January 2016.

Flux densities (Jy) of Standard Calibrators for January 2016
Source75 MHz350 MHz1500 MHz3000 MHz6000 MHz10000 MHz15000 MHz22000 MHz33000 MHz45000 MHz
3C48* = J0137+3309 72.8 42.2 15.4 8.44 4.42 2.68 1.79 1.22 0.815 0.601
3C138 = J0521+1638 26.5 16.1 8.25 5.44 3.39 2.33 1.72 1.28 0.949 0.761
3C147 = J0542+4951 58.0 52.3 21.0 12.0 6.45 3.99 2.73 1.93 1.39 1.13
3C196 = J0813+4813 129 44.4 13.6 6.98 3.38 1.91 1.20 0.763 0.473 0.329
3C286 = J1331+3030 30.0 25.9 14.6 9.91 6.39 4.50 3.37 2.54 1.88 1.49
3C295 = J1411+5212 124 58.4 21.2 11.0 5.06 2.70 1.60 0.970 0.571 0.385

* The flux density scale calibrator 3C48 has been undergoing a flare since January 2018 or so.  While we have not fully characterized this with the VLA, other instruments have measured it at some frequencies. At Ku-band the magnitude of the flare is of order 10%.  The effect will be smaller at lower frequencies (of order 5% at L-band), and might be larger at higher frequencies (of order 20% at Q-band).  If you care about the flux density scale of your observations at that level, you may want to re-calibrate your data once new time-variable values have been put into CASA and AIPS.