Characterization of the primary beams
In order to provide information on the reliability of the measured primary beam images, we undertake an empirical comparison to the NVSS catalog over the full data release. While similar in philosophy to the Gaussian process regression used to derive the primary beam images, this comparison provides information about overall systematics in the flux scale, in addition to quantifying the scatter in the accuracy of derived fluxes using the provided primary beam images. It also allows a direct comparison between the reliability and accuracy of primary beam images derived from different measurement techniques.
Briefly, in order to provide a comparison over the full data release, the following steps are taken for every continuum image in the data release:
- Convolve the Apertif continuum image to 45″ resolution
- Regrid the primary beam image to the Apertif continuum image
- Primary beam correct the Apertif image (mask below 10% response)
- Create an Apertif source catalog by running pybdsf; identify sources with S/N > 5
- Cross-match to the NVSS catalog
The cross-matches are recorded and later combined to build a global picture of a compound beam over the full data release.
The key value examined to understand and characterize the primary beam response images is the ratio of the Apertif integrated flux over the NVSS integrated flux. The first check was to look for systematics in this value as a function of position, since this could point to biases in the derivation of the primary beam responses. The primary beam images constructed from drift scans resulted in systematically higher flux ratios at the outskirts of the primary beam response in a consistent (south-west) direction for all compound beams. This points to an issue with source confusion around Cyg A which is under active investigation. This systematic was not seen in the primary beam images derived with the Gaussian process regression.
The key characterization of the primary beam images is to understand the impact they have on the flux scale. Flux validation of continuum images takes an initial look at this using a single medium-deep field to look at the internal consistency of the flux scale and compare to NVSS. With the full primary beam characterization, this can be examined for each compound beam in aggregate over the full data release. While the originally returned primary beam images from the Gaussian process regression match the NVSS flux scale by construction, it is informative to undertake the comparison for the normalized primary beam images as this provides information about any overall differences in the flux scale between Apertif and NVSS (which would also be seen in primary beam images derived from the drift scan approach). Cross-matched sources were filtered to have a deconvolved major axis in the NVSS catalog < 45” and to have a measurement error on the ratio of integrated fluxes between Apertif and NVSS <0.1. Table 1 provides (as a csv file) the median ratio between the integrated fluxes, along with the standard deviation of the flux ratios and the median measurement error on the flux ratio. Table 2 provides (as a csv file) these same values but limited to the inner part of the primary beam images where the response level is ≤50%. The typical value is 1.11 in both regimes, indicating the Apertif fluxes are systematically ~10% higher than those from the NVSS catalog. The Apertif fluxes are expected to be ~2% higher based on a typical spectral index of -0.7 and the difference in center frequency in between Apertif and NVSS. In addition, the NVSS integrated fluxes are catalog flux values, corrected for various biases, while the Apertif integrated fluxes are measured directly from the images and may include calibration and clean biases. This will be examined in more detail in the forthcoming data release paper (Adams et al., in prep).
Table 1 and 2 also include the standard deviation of the flux ratios for each compound beam. These values are rather large, typically ~16-17%. This does not indicate an uncertainty in the primary beam measurement at this level as there are several contributing factors. The typical measurement uncertainty is ~5%, and intrinsic source variability is on the order of ~10% (e.g., Hovatta 2009). The data release paper will undertake an accounting of all sources of scatter to quantify what the uncertainty on the flux scale from primary beam variability might be. In addition, the internal consistency of flux measurements for all medium-deep observations in the data release will be undertaken to provide an additional handle on the accuracy of the flux scale within the Apertif datasets.
Table 1: Median ratio of Apertif/NVSS integrated flux, standard deviation of flux ratio, and median measurement error of flux ratio over the full Apertif primary beam (to 10% level)
Table 2: Median ratio of Apertif/NVSS integrated flux, standard deviation of flux ratio, and median measurement error of flux ratio over the inner Apertif primary beam (≥50% level)