Patterns of primary beam non-redundancy in close-packed 21 cm array observations

Radio interferometer arrays such as HERA consist of many close-packed dishes arranged in a regular pattern, giving rise to a large number of `redundant' baselines with the same length and orientation. Since identical baselines should see an identical sky signal, this provides a way of finding a relative gain/bandpass calibration without needing an explicit sky model. In reality, there are many reasons why baselines will not be exactly identical, giving rise to a host of effects that spoil the redundancy of the array and induce spurious structure in the calibration solutions if not accounted for. In this paper, we perform a wide range of simulations for a small HERA-like array to understand how different types of non-redundancy manifest in the observed interferometric visibilities and their resulting frequency (delay-space) power spectra. We focus in particular on differences in the primary beam response between antennas, including variations in the main lobe, sidelobes, ellipticity, and orientation. We find that different types of non-redundancy impart characteristic patterns into the redundant gain solutions, which in turn introduce additional structure into the calibrated visibilities and therefore the delay spectra. We show that the most severe effects of primary beam non-redundancy are induced by the brightest sources passing through the beam, while diffuse emission has a lesser (but non-negligible) effect. We also find that redundant baseline groups with `outlier' antennas (where only one antenna deviates from perfect redundancy) sustain the largest gain errors, while even $\mathcal{O}(1)$ non-redundancies in the sidelobes seem to have a relatively minor impact in comparison.Comment: 19 pages, 14 figures, to be submitted in MNRA

Gravitational Microlensing as a probe of the Electron Scattering Region in Q2237+0305

Recent observations have provided strong evidence for the presence of an Electron Scattering Region (ESR) within the central regions of AGNs. This is responsible for reprocessing emission from the accretion disk into polarised radiation. The geometry of this scattering region is, however, poorly constrained. In this paper, we consider the influence of gravitational microlensing on polarised emission from the ESR in the quadruply imaged quasar, Q2237+0305, demonstrating how correlated features in the resultant light curve variations can determine both the size and orientation of the scattering region. This signal is due to differential magnification between perpendicularly polarised views of the ESR, and is clearest for a small ESR width and a large ESR radius. Cross- and auto-correlation measures appear to be independent of lens image shear and convergence parameters, making it ideal to investigate ESR features. As with many microlensing experiments, the time-scale for variability, being of order decades to centuries, is impractically long. However, with a polarization filter oriented appropriately with respect to the path that the quasar takes across the caustic structure, the ESR diameter and radius can be estimated from the auto- and cross-correlation of polarized light curves on much shorter time-scales.Comment: 11 pages, 12 figures, 1 table, accepted for MNRA

Gravitational Microlensing of a Reverberating Quasar Broad Line Region - I. Method and Qualitative Results

The kinematics and morphology of the broad emission line region (BELR) of quasars are the subject of significant debate. The two leading methods for constraining BELR properties are microlensing and reverberation mapping. Here we combine these two methods with a study of the microlensing behaviour of the BELR in Q2237+0305, as a change in continuum emission (a "flare") passes through it. Beginning with some generic models of the BELR - sphere, bicones, disk - we slice in velocity and time to produce brightness profiles of the BELR over the duration of the flare. These are numerically microlensed to determine whether microlensing of reverberation mapping provides new information about the properties of BELRs. We describe our method and show images of the models as they are flaring, and the unlensed and lensed spectra that are produced. Qualitative results and a discussion of the spectra are given in this paper, highlighting some effects that could be observed. Our conclusion is that the influence of microlensing, while not strong, can produce significant observable effects that will help in differentiating the properties of BELRs.Comment: 17 pages, 14 low resolution figures, 1 table, accepted for MNRAS. v2: Corrected velocities p16, 8 to 0.08, 9 to 0.0

Antenna beam characterisation for the global 21cm experiment LEDA and its impact on signal model parameter reconstruction

Cosmic Dawn, the onset of star formation in the early universe, can in principle be studied via the 21cm transition of neutral hydrogen, for which a sky-averaged absorption signal, redshifted to MHz frequencies, is predicted to be {\it O}(10-100)\,mK. Detection requires separation of the 21cm signal from bright chromatic foreground emission due to Galactic structure, and the characterisation of how it couples to instrumental response. In this work, we present characterisation of antenna gain patterns for the Large-aperture Experiment to detect the Dark Ages (LEDA) via simulations, assessing the effects of the antenna ground-plane geometries used, and measured soil properties. We then investigate the impact of beam pattern uncertainties on the reconstruction of a Gaussian absorption feature. Assuming the pattern is known and correcting for the chromaticity of the instrument, the foregrounds can be modelled with a log-polynomial, and the 21cm signal identified with high accuracy. However, uncertainties on the soil properties lead to \textperthousand\ changes in the chromaticity that can bias the signal recovery. The bias can be up to a factor of two in amplitude and up to few \% in the frequency location. These effects do not appear to be mitigated by larger ground planes, conversely gain patterns with larger ground planes exhibit more complex frequency structure, significantly compromising the parameter reconstruction. Our results, consistent with findings from other antenna design studies, emphasise the importance of chromatic response and suggest caution in assuming log-polynomial foreground models in global signal experiments.Comment: Accepted for publication in MNRA

Probing planetary mass dark matter in galaxies: gravitational nanolensing of multiply imaged quasars

Gravitational microlensing of planetary-mass objects (or "nanolensing", as it has been termed) can be used to probe the distribution of mass in a galaxy that is acting as a gravitational lens. Microlensing and nanolensing light curve fluctuations are indicative of the mass of the compact objects within the lens, but the size of the source is important, as large sources will smooth out a light curve. Numerical studies have been made in the past that investigate a range of sources sizes and masses in the lens. We extend that work in two ways - by generating high quality maps with over a billion small objects down to a mass of 2.5\times10-5M\odot, and by investigating the temporal properties and observability of the nanolensing events. The system studied is a mock quasar system similar to MG 0414+0534. We find that if variability of 0.1 mag in amplitude can be observed, a source size of ~ 0.1 Einstein Radius (ER) would be needed to see the effect of 2.5\times10-5M\odot masses, and larger, in the microlensing light curve. Our investigation into the temporal properties of nanolensing events finds that there are two scales of nanolensing that can be observed - one due to the crossing of nanolensing caustic bands, the other due to the crossing of nanolensing caustics themselves. The latter are very small, having crossing times of a few days, and requiring sources of size ~ 0.0001 ER to resolve. For sources of the size of an accretion disk, the nanolensing caustics are slightly smoothed-out, but can be observed on time scales of a few days. The crossing of caustic bands can be observed on times scales of about 3 months.Comment: 14 pages, 9 figures, 1 table, low-quality image

Computational advances in gravitational microlensing: a comparison of CPU, GPU, and parallel, large data codes

To assess how future progress in gravitational microlensing computation at high optical depth will rely on both hardware and software solutions, we compare a direct inverse ray-shooting code implemented on a graphics processing unit (GPU) with both a widely-used hierarchical tree code on a single-core CPU, and a recent implementation of a parallel tree code suitable for a CPU-based cluster supercomputer. We examine the accuracy of the tree codes through comparison with a direct code over a much wider range of parameter space than has been feasible before. We demonstrate that all three codes present comparable accuracy, and choice of approach depends on considerations relating to the scale and nature of the microlensing problem under investigation. On current hardware, there is little difference in the processing speed of the single-core CPU tree code and the GPU direct code, however the recent plateau in single-core CPU speeds means the existing tree code is no longer able to take advantage of Moore's law-like increases in processing speed. Instead, we anticipate a rapid increase in GPU capabilities in the next few years, which is advantageous to the direct code. We suggest that progress in other areas of astrophysical computation may benefit from a transition to GPUs through the use of "brute force" algorithms, rather than attempting to port the current best solution directly to a GPU language -- for certain classes of problems, the simple implementation on GPUs may already be no worse than an optimised single-core CPU version.Comment: 11 pages, 4 figures, accepted for publication in New Astronom

LOFAR sparse image reconstruction

The LOw Frequency ARray (LOFAR) radio telescope is a giant digital phased array interferometer with multiple antennas distributed in Europe. It provides discrete sets of Fourier components of the sky brightness. Recovering the original brightness distribution with aperture synthesis forms an inverse problem that can be solved by various deconvolution and minimization methods Aims. Recent papers have established a clear link between the discrete nature of radio interferometry measurement and the "compressed sensing" (CS) theory, which supports sparse reconstruction methods to form an image from the measured visibilities. Empowered by proximal theory, CS offers a sound framework for efficient global minimization and sparse data representation using fast algorithms. Combined with instrumental direction-dependent effects (DDE) in the scope of a real instrument, we developed and validated a new method based on this framework Methods. We implemented a sparse reconstruction method in the standard LOFAR imaging tool and compared the photometric and resolution performance of this new imager with that of CLEAN-based methods (CLEAN and MS-CLEAN) with simulated and real LOFAR data Results. We show that i) sparse reconstruction performs as well as CLEAN in recovering the flux of point sources; ii) performs much better on extended objects (the root mean square error is reduced by a factor of up to 10); and iii) provides a solution with an effective angular resolution 2-3 times better than the CLEAN images. Conclusions. Sparse recovery gives a correct photometry on high dynamic and wide-field images and improved realistic structures of extended sources (of simulated and real LOFAR datasets). This sparse reconstruction method is compatible with modern interferometric imagers that handle DDE corrections (A- and W-projections) required for current and future instruments such as LOFAR and SK

PySE: Software for Extracting Sources from Radio Images

PySE is a Python software package for finding and measuring sources in radio telescope images. The software was designed to detect sources in the LOFAR telescope images, but can be used with images from other radio telescopes as well. We introduce the LOFAR Telescope, the context within which PySE was developed, the design of PySE, and describe how it is used. Detailed experiments on the validation and testing of PySE are then presented, along with results of performance testing. We discuss some of the current issues with the algorithms implemented in PySE and their inter- action with LOFAR images, concluding with the current status of PySE and its future development.Comment: 26 pages, 6 figure