Revisiting the radio interferometer measurement equation. II. Calibration and direction-dependent effects

Paper I of the series re-derived the radio interferometry measurement equation (RIME) from first principles, and extended the Jones formalism to the full-sky case, incorporating direction-dependent effects (DDEs). This paper aims to describe both classical radio interferometric calibration (selfcal and related methods), and the recent developments in the treatment of DDEs, using the RIME-based mathematical framework developed in Paper I. It also aims to demonstrate the ease with which the various effects can be described and understood. The first section of this paper uses the RIME formalism to describe self-calibration, both with a full RIME, and with the approximate equations of older software packages, and shows how this is affected by DDEs. The second section gives an overview of real-life DDEs and proposed methods of dealing with them. This results in a formal RIME-based description and comparison of existing and proposed approaches to the problem of DDEs.Comment: 11 pages, no figures, accepted by A&

Cygnus A super-resolved via convex optimisation from VLA data

We leverage the Sparsity Averaging Reweighted Analysis (SARA) approach for interferometric imaging, that is based on convex optimisation, for the super-resolution of Cyg A from observations at the frequencies 8.422GHz and 6.678GHz with the Karl G. Jansky Very Large Array (VLA). The associated average sparsity and positivity priors enable image reconstruction beyond instrumental resolution. An adaptive Preconditioned Primal-Dual algorithmic structure is developed for imaging in the presence of unknown noise levels and calibration errors. We demonstrate the superior performance of the algorithm with respect to the conventional CLEAN-based methods, reflected in super-resolved images with high fidelity. The high resolution features of the recovered images are validated by referring to maps of Cyg A at higher frequencies, more precisely 17.324GHz and 14.252GHz. We also confirm the recent discovery of a radio transient in Cyg A, revealed in the recovered images of the investigated data sets. Our matlab code is available online on GitHub.Comment: 14 pages, 7 figures (3/7 animated figures), accepted for publication in MNRA

The Tails of the Crossing Probability

The scaling of the tails of the probability of a system to percolate only in the horizontal direction $\pi_{hs}$ was investigated numerically for correlated site-bond percolation model for $q=1,2,3,4$.We have to demonstrate that the tails of the crossing probability far from the critical point have shape $\pi_{hs}(p) \simeq D \exp(c L[p-p_{c}]^{\nu})$ where $\nu$ is the correlation length index, $p=1-\exp(-\beta)$ is the probability of a bond to be closed. At criticality we observe crossover to another scaling $\pi_{hs}(p) \simeq A \exp (-b {L [p-p_{c}]^{\nu}}^{z})$. Here $z$ is a scaling index describing the central part of the crossing probability.Comment: 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical change

A Multi-Frequency View of the Radio Phoenix in the Abell 85 Cluster

Radio phoenices are complex and filamentary diffuse radio sources found in both merging and relaxed clusters. The formation of these sources was proposed to be adiabatic compression of old Active Galactic Nucleus (AGN) plasma in shock waves. Most of the previous spectral studies of these sources were limited to integrated spectral indices, which were found to be very steep as well as show a curved spectrum. Here, we have performed a multi-frequency investigation of the radio phoenix in the Abell 85 cluster. Owing to the sensitive high-resolution observations, we found some of the finer filamentary structures that were previously undetected. We produced resolved spectral index maps of the radio phoenix between 148, 323, 700, and 1280 MHz. The orientation of the filaments, as well as the gradient across the spectral index maps suggest the possible direction of the shock motion from northeast to southwest. The integrated spectral index of the radio phoenix was found to be very steep with a break at around 700 MHz, indicating the re-energization of fossil electrons being recent. Furthermore, the spectral index of the filaments was found to be less steep compared to the non-filamentary regions, implying greater energy injection in the filaments. The observed features in the radio phoenix in the Abell 85 cluster seem to be in support of the adiabatic shock compression mechanism.Comment: 17 pages, 12 figures, 3 tables, submitted to AAS journa

A radio bridge connecting the minihalo and phoenix in the Abell 85 cluster

Galaxy clusters are located at the nodes of cosmic filaments and therefore host a lot of hydrodynamical activity. However, cool core clusters are considered to be relatively relaxed systems without much merging activity. The Abell 85 cluster is a unique example where the cluster hosts both a cool core and multiple ongoing merging processes. In this work, we used 700 MHz uGMRT as well as MeerKAT L-band observations, carried out as part of the MGCLS, of the Abell 85. We reconfirm the presence of a minihalo in the cluster centre at 700MHz that was recently discovered in MGCLS. Furthermore, we discovered a radio bridge connecting the central minihalo and the peripheral radio phoenix. The mean surface brightness, size and flux density of the bridge at 700 MHz is found to be $\sim 0.14\ \mu$Jy/arcsec$^2$, $\sim 220$ kpc and $\sim 4.88$ mJy, respectively, with a spectral index of $\alpha_{700}^{1.28} = -0.92$. Although the origin of the seed relativistic electrons is still unknown, turbulent re-acceleration caused by both the spiralling sloshing gas in the intracluster medium (ICM) and the post-shock turbulence from the outgoing merging shock associated with the phoenix formation may be responsible for the bridge.Comment: 7 pages, 6 Figures, 2 Tables. Accepted for publication in MNRAS-

Modeling of celiac disease immune response and the therapeutic effect of potential drugs

BACKGROUND: Celiac disease (CD) is an autoimmune disorder that occurs in genetically predisposed people and is caused by a reaction to the gluten protein found in wheat, which leads to intestinal villous atrophy. Currently there is no drug for treatment of CD. The only known treatment is lifelong gluten-free diet. The main aim of this work is to develop a mathematical model of the immune response in CD patients and to predict the efficacy of a transglutaminase-2 (TG-2) inhibitor as a potential drug for treatment of CD. RESULTS: A thorough analysis of the developed model provided the following results: 1. TG-2 inhibitor treatment leads to insignificant decrease in antibody levels, and hence remains higher than in healthy individuals. 2. TG-2 inhibitor treatment does not lead to any significant increase in villous area. 3. The model predicts that the most effective treatment of CD would be the use of gluten peptide analogs that antagonize the binding of immunogenic gluten peptides to APC. The model predicts that the treatment of CD by such gluten peptide analogs can lead to a decrease in antibody levels to those of normal healthy people, and to a significant increase in villous area. CONCLUSIONS: The developed mathematical model of immune response in CD allows prediction of the efficacy of TG-2 inhibitors and other possible drugs for the treatment of CD: their influence on the intestinal villous area and on the antibody levels. The model also allows to understand what processes in the immune response have the strongest influence on the efficacy of different drugs. This model could be applied in the pharmaceutical R&D arena for the design of drugs against autoimmune small intestine disorders and on the design of their corresponding clinical trials

A Wideband Polarization Study of Cygnus A with the JVLA. I: The Observations and Data

We present results from deep, wideband, high spatial and spectral resolution observations of the nearby luminous radio galaxy Cygnus A with the Jansky Very Large Array. The high surface brightness of this source enables detailed polarimetric imaging, providing images at 0.75\arcsec, spanning 2 - 18 GHz, and at 0.30\arcsec (6 - 18 GHz). The fractional polarization from 2000 independent lines of sight across the lobes decreases strongly with decreasing frequency, with the eastern lobe depolarizing at higher frequencies than the western lobe. The depolarization shows considerable structure, varying from monotonic to strongly oscillatory. The fractional polarization in general increases with increasing resolution at a given frequency, as expected. However, there are numerous lines of sight with more complicated behavior. We have fitted the 0.3\arcsec images with a simple model incorporating random, unresolved fluctuations in the cluster magnetic field to determine the high resolution, high-frequency properties of the source and the cluster. From these derived properties, we generate predicted polarization images of the source at lower frequencies, convolved to 0.75\arcsec. These predictions are remarkably consistent with the observed emission. The observations are consistent with the lower-frequency depolarization being due to unresolved fluctuations on scales $\gtrsim$ 300 - 700 pc in the magnetic field and/or electron density superposed on a partially ordered field component. There is no indication in our data of the location of the depolarizing screen or the large-scale field, either, or both of which could be located throughout the cluster, or in a boundary region between the lobes and the cluster.Comment: 24 pages, 13 figures. The manuscript has been accepted for publication in The Astrophysical Journa