MeerKAT

Abstract:

We propose a flexible method for estimating luminosity functions (LFs) based on kernel density estimation (KDE), the most popular nonparametric density estimation approach developed in modern statistics, to overcome issues surrounding the binning of LFs. One challenge in applying KDE to LFs is how to treat the boundary bias problem, as astronomical surveys usually obtain truncated samples predominantly due to the flux-density limits of surveys. We use two solutions, the transformation KDE method ( ) and the transformation–reflection KDE method ( ) to reduce the boundary bias. We develop a new likelihood cross-validation criterion for selecting optimal bandwidths, based on which the posterior probability distribution of the bandwidth and transformation parameters for and are derived within a Markov Chain Monte Carlo sampling procedure. The simulation result shows that and perform better than the traditional binning method, especially in the sparse data regime around the flux limit of a survey or at the bright end of the LF. To further improve the performance of our KDE methods, we develop the transformation–reflection adaptive KDE approach ( ). Monte Carlo simulations suggest that it has good stability and reliability in performance, and is around an order of magnitude more accurate than using the binning method. By applying our adaptive KDE method to a quasar sample, we find that it achieves estimates comparable to the rigorous determination in a previous work, while making far fewer assumptions about the LF. The KDE method we develop has the advantages of both parametric and nonparametric methods.

Abstract:

Accurate instrumental bandpass corrections are essential for the reliable interpretation of spectral lines from targeted and survey-mode observations with radio interferometers. Bandpass correction is typically performed by comparing measurements of a strong calibrator source to an assumed model, typically an isolated point source. The wide field-of-view and high sensitivity of modern interferometers means that additional sources are often detected in observations of calibrators. This can introduce errors into bandpass corrections and subsequently the target data if not properly accounted for. Focusing on the standard calibrator PKS B1934-638, we perform simulations to asses this effect by constructing a wide-field sky model. The cases of ASKAP (0.7–1.9 GHz), MeerKAT (UHF: 0.58–1.05 GHz; L-band: 0.87–1.67 GHz) and Band 2 (0.95–1.76 GHz) of SKA-MID are examined. The use of a central point source model during bandpass calibration is found to impart amplitude errors into spectra measured by the precursor instruments at the ∼0.2–0.5% level dropping to ∼0.01% in the case of SKA-MID. This manifests itself as ripples in the source spectrum, the behaviour of which is coupled to the distribution of the array baselines, the solution interval, the primary beam size, the hour-angle of the calibration scan, as well as the weights used when imaging the target. Calibration pipelines should routinely employ complete field models for standard calibrators to remove this potentially destructive contaminant from the data, a recommendation we validate by comparing our simulation results to a MeerKAT scan of PKS B1934-638, calibrated with and without our expanded sky model.