Introduction

The following factors will limit the dynamic range (DR) of a MeerKAT image, more or less in descending order of importance

• Residual phase errors. These can be addressed by regular self calibration.

• Residual delay errors. These can be addressed by incorporating a delay term in the self-calibration (using e.g. the f-slope solver of the CubiCal or QuartiCal packages), or else doing phase self-calibration over e.g. 6 or 8 independent subbands (thus representing the residual delay slope by a stepwise function). The latter approach is prone to errors in the presence of RFI, so users are advised to flag very carefully and apply an aggressive cut to the short baselines.

• Deconvolution artefacts associated with bright, slightly resolved sources will typically limit the DR to ~10,000. No satisfactory practical solution for this problem exists, and it can only be partially mitigated by careful deconvolution with masking. Users are advised to keep such sources as close to the centre of the FoV as possible, to avoid compounding the problem with DDE effects.

• DDE effects (primary beam rotation, pointing errors) become prominent towards the half-power point (the “flanks”) of the primary beam, and will limit the DR to about ~1,000. This is modulated by the apparent flux of the source, therefore faint sources on the flank do not exhibit any artefacts. Therefore, the problem only arises in the presence of bright sources on the flanks. Individual bright point sources can usually be satisfactorily “peeled” using e.g. CubiCal/QuartiCal or DDFacet+killMS; however complex sources can be very troublesome, since the problem is compounded by deconvolution (see point above). See the section below for a pathological example.

• mJy-level sources on the flanks of the beam will exhibit DDE artefacts. There are generally too many of these to be peeled, but they are generally too faint to affect the DR of the overall image. Typically, this population of sources can be improved by applying DD-solutions using killMS+DDFacet, using on the order of 5-10 tassels (solving directions).

• Ionospheric phase effects manifest themselves at the 100,000:1 level in L-band, and presumably at least 50,000:1 in UHF. They can be addressed by the same DD calibration procedures as the primary beam, above.

• Polarization leakage on-axis is on the level of 1%. A 1% polarized source will therefore be DR limited in Stokes I to ~10,000:1, unless polarization calibration (D-Jones), followed by full Stokes deconvolution and selfcal, is done.

• Standard polarization calibration solves for relative not absolute D-Jones terms. In principle, this creates artefacts in Stokes I even on unpolarized sources, at the level of about 50,000-100,000:1. This can be addressed by doing a full complex-2x2 Jones solution in the selfcal loop (using CubiCal/QuartiCal).

DDE example

Conventional first and second-generation calibration techniques are not enough to correct for direction-dependent effects, due to bright sources that fall on highly varying parts of the primary beam. These result in severe radial artefacts that dominate the field (see Figure 1). In principle, these artefacts can be reduced by including the primary beam correction in the data calibration and imaging process, as well as accounting for antenna pointing errors. This means that primary beam corrections have to be supplemented with direction-dependent calibration in order to sufficiently reduce the artefacts. This calibration accounts for imperfections in the primary beam model as well as other effects which have not been accounted for, like antenna pointing errors.

The mean antenna pointing error is currently sigma = 0.6 arcmin. Work is under way to improve this figure.

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Figure 1: Artefacts from a bright source close to the null of the primary beam as a function of frequency. The artefacts are most prominent at the low-end of the band and become less severe at the high-end as the bright “problematic” source is pushed further into the null.

The effect of the bright source in the figure above can be mitigated by changing the central pointing position to move it away from the null, for continuum imaging; or by placing it in the primary beam null at the frequency of interest for spectral line imaging.

Identifying interfering sources

The user is advised to check existing surveys such as NVSS, SUMSS or RACS for any bright (>1 Jy) sources within a 1° radius of their requested pointing centre for L-band (2° for UHF).

The L- and UHF band demerit maps were constructed using the method described in Section 3 of Mauch et al. (2020); the “demerit” score (D) at any position in the images is derived from Equations 6 through 13 there. D gives an indication at any potential pointing position what the contribution of pointing errors and gain errors induced by sources in the MeerKAT primary beam will be and therefore indicates the potential likelihood that the given pointing will be dominated by direction-dependent calibration errors. 

The demerit maps were constructed by searching the SUMSS catalog south of δ = −35° and the NVSS catalog from δ ≥ −35° to δ = +10° over a fine grid of potential pointings in the ~24000 degree area defined by δ < 10°. At each grid position we computed D from flux densities shifted to 1.28 GHz assuming S ∝ ν^−0.7 and with parameters conservatively appropriate to MeerKAT: Primary Beam FWHM θ_b = 68' (L-band), θ_b = 107' (UHF), rms pointing error σ_p = 30'', and rms receiver gain fluctuation σ_g = 0.01. At each position in the grid we included SUMSS and NVSS sources out to radius ρ = 3° in L-band and ρ = 5° in UHF-band, extending beyond the second sidelobe of the MeerKAT primary beam. Figures 4-5 plot the cumulative percentage of the sky area with demerit scores < D. If the demerit score at the proposed position is in the top 80-100% of sky shown in Figures 4 or 5 , it is recommended that the proposer simulate their potential pointing using sources from SUMSS/NVSS to determine what impact direction dependent errors will have.

The ‘critical’ (i.e. 80%) cumulative Demerit score for each bandsis:

UHF: 17.2 mJy/beam

L: 9.8 mJy/beam

S: 4.4 mJy/beam

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Figure 2: Radial sky plot of the MeerKAT L-band demerit map for declinations less than +10°. The fits file can be downloaded here for closer inspection.

Mitigation

The effect of such bright sources can be modelled using CASA and MeqTrees. A quickstart guide is available here. In some cases, the worst effects of a bright source could be mitigated by adjusting the pointing centre in such a way as to move the bright source away from regions of rapidly changing beam response. See the page on the primary beam for more information.

Implementing direction dependent self-calibration

After transfering gain solutions from the primary and secondary calibrators, it may be necessary to apply direction-dependent calibration, targeting problematic sources.

A detailed discussion of this method is beyond the scope of this forum. Please see the help documentation for DDFacet (Tasse et al. 2017) and Cubical (Kenyon et al. 2018).

Further information can be found on the pages of the The Rhodes Centre for Radio Astronomy Techniques & Technologies (RATT)