Image-plane self-calibration in interferometry.

We develop a process of image-plane self-calibration for interferometric imaging data. The process is based on shape-orientation-size (SOS) conservation for the principal triangle in an image generated from the three fringes made from a triad of receiving elements, in situations where interferometric phase errors can be factorized into element-based terms. The basis of the SOS conservation principle is that, for a three-element array, the only possible image corruption due to an element-based phase screen is a tilt of the aperture plane, leading to a shift in the image plane. Thus, an image made from any three-element interferometer represents a true image of the source brightness, modulo an unknown translation. Image-plane self-calibration entails deriving the unknown translations for each triad image via cross-correlation of the observed triad image with a model image of the source brightness. After correcting for these independent shifts, and summing the aligned triad images, a good image of the source brightness is generated from the full array, recovering source structure at diffraction-limited resolution. The process is iterative, using improved source models based on previous iterations. We demonstrate the technique in a high signal-to-noise context, and include a configuration based on radio astronomical facilities, and simple models of double sources. We show that the process converges for the simple models considered, although convergence is slower than for aperture-plane self-calibration for large-N arrays. As currently implemented, the process is most relevant for arrays with a small number of elements. More generally, the technique provides geometric insight into closure phase and the self-calibration process. The technique is generalizable to non-astronomical interferometric imaging applications across the electromagnetic spectrum.

Invariants in Polarimetric Interferometry: A Non-Abelian Gauge Theory.

The discovery of magnetic fields close to the M87 black hole using very long baseline interferometry by the Event Horizon Telescope collaboration utilized the novel concept of "closure traces," that are immune to element-based aberrations. We take a fundamentally new approach to this promising tool of polarimetric very long baseline interferometry, using ideas from the geometric phase and gauge theories. The multiplicative distortion of polarized signals at the individual elements are represented as gauge transformations by general 2×2 complex matrices, so the closure traces now appear as gauge-invariant quantities. We apply this formalism to polarimetric interferometry and generalize it to any number of interferometer elements. Our approach goes beyond existing studies in the following respects: (1) we use triangular combinations of correlations as basic building blocks of invariants, (2) we use well-known symmetry properties of the Lorentz group to transparently identify a complete and independent set of invariants, and (3) we do not need autocorrelations, which are susceptible to large systematic biases, and therefore unreliable. This set contains all the information, immune to corruption, available in the interferometer measurements, thus providing important robust constraints for interferometric studies.

Constraining Cosmological Phase Transitions with the Parkes Pulsar Timing Array.

A cosmological first-order phase transition is expected to produce a stochastic gravitational wave background. If the phase transition temperature is on the MeV scale, the power spectrum of the induced stochastic gravitational waves peaks around nanohertz frequencies, and can thus be probed with high-precision pulsar timing observations. We search for such a stochastic gravitational wave background with the latest data set of the Parkes Pulsar Timing Array. We find no evidence for a Hellings-Downs spatial correlation as expected for a stochastic gravitational wave background. Therefore, we present constraints on first-order phase transition model parameters. Our analysis shows that pulsar timing is particularly sensitive to the low-temperature (T∼1-100 MeV) phase transition with a duration (ß/H_{*})^{-1}∼10^{-2}-10^{-1} and therefore can be used to constrain the dark and QCD phase transitions.

Detecting Cosmic Reionization Using the Bispectrum Phase.

Detecting neutral hydrogen (H i) via the 21 cm line emission from the intergalactic medium at z≳6 has been identified as one of the most promising probes of the epoch of cosmic reionization-a major phase transition of the Universe. However, these studies face severe challenges imposed by the bright foreground emission from cosmic objects. Current techniques require precise instrumental calibration to separate the weak H i line signal from the foreground continuum emission. We propose to mitigate this calibration requirement by using measurements of the interferometric bispectrum phase. The bispectrum phase is unaffected by antenna-based direction-independent calibration errors and hence for a compact array it depends on the sky brightness distribution only (subject to the usual thermal-like noise). We show that the bispectrum phase of the foreground synchrotron continuum has a characteristically smooth spectrum relative to the cosmological line signal. The two can be separated effectively by exploiting this spectral difference using Fourier techniques, while eliminating the need for precise antenna-based calibration of phases introduced by the instrument, and the ionosphere, inherent in existing approaches. Using fiducial models for continuum foregrounds, and for the cosmological H i signal, we show the latter should be detectable in bispectrum phase spectra, with reasonable significance at |k_{∥}|≳0.5h Mpc^{-1}, using existing instruments. Our approach will also benefit other H i intensity mapping experiments that face similar challenges, such as those measuring baryon acoustic oscillations (BAO).