Three-point correlations for quantum star graphs

We compute the three point correlation function for the eigenvalues of the Laplacian on quantum star graphs in the limit where the number of edges tends to infinity. This extends a work by Berkolaiko and Keating, where they get the 2-point correlation function and show that it follows neither Poisson, nor random matrix statistics. It makes use of the trace formula and combinatorial analysis.Comment: 10 pages, 2 figure

Detection of Helium in the Atmosphere of the Exo-Neptune HAT-P-11b

The helium absorption triplet at a wavelength of 10,833 \AA\ has been proposed as a way to probe the escaping atmospheres of exoplanets. Recently this feature was detected for the first time using Hubble Space Telescope (HST) WFC3 observations of the hot Jupiter WASP-107b. We use similar HST/WFC3 observations to detect helium in the atmosphere of the hot Neptune HAT-P-11b at the $4\sigma$ confidence level. We compare our observations to a grid of 1D models of hydrodynamic escape to constrain the thermospheric temperatures and mass loss rate. We find that our data are best fit by models with high mass loss rates of $\dot{M} \approx 10^{9}$ - $10^{11}$ g s$^{-1}$. Although we do not detect the planetary wind directly, our data are consistent with the prediction that HAT-P-11b is experiencing hydrodynamic atmospheric escape. Nevertheless, the mass loss rate is low enough that the planet has only lost up to a few percent of its mass over its history, leaving its bulk composition largely unaffected. This matches the expectation from population statistics, which indicate that close-in planets with radii greater than 2 R$_{\oplus}$ form and retain H/He-dominated atmospheres. We also confirm the independent detection of helium in HAT-P-11b obtained with the CARMENES instrument, making this the first exoplanet with the detection of the same signature of photoevaporation from both ground- and space-based facilities.Comment: 12 pages, 9 figures, accepted for publication in ApJ

A comparative study of WASP-67b and HAT-P-38b from WFC3 data

Atmospheric temperature and planetary gravity are thought to be the main parameters affecting cloud formation in giant exoplanet atmospheres. Recent attempts to understand cloud formation have explored wide regions of the equilibrium temperature-gravity parameter space. In this study, we instead compare the case of two giant planets with nearly identical equilibrium temperature ($T_\mathrm{eq}$ $\sim 1050 \, \mathrm{K}$) and gravity ($g \sim 10 \, \mathrm{m \, s}^{-1})$. During $HST$ Cycle 23, we collected WFC3/G141 observations of the two planets, WASP-67 b and HAT-P-38 b. HAT-P-38 b, with mass 0.42 M$_\mathrm{J}$ and radius 1.4 $R_\mathrm{J}$, exhibits a relatively clear atmosphere with a clear detection of water. We refine the orbital period of this planet with new observations, obtaining $P = 4.6403294 \pm 0.0000055 \, \mathrm{d}$. WASP-67 b, with mass 0.27 M$_\mathrm{J}$ and radius 0.83 $R_\mathrm{J}$, shows a more muted water absorption feature than that of HAT-P-38 b, indicating either a higher cloud deck in the atmosphere or a more metal-rich composition. The difference in the spectra supports the hypothesis that giant exoplanet atmospheres carry traces of their formation history. Future observations in the visible and mid-infrared are needed to probe the aerosol properties and constrain the evolutionary scenario of these planets.Comment: 16 pages, 17 figures, 8 tables, accepted for publication in The Astronomical Journa

Gridded and direct Epoch of Reionisation bispectrum estimates using the Murchison Widefield Array

We apply two methods to estimate the 21~cm bispectrum from data taken within the Epoch of Reionisation (EoR) project of the Murchison Widefield Array (MWA). Using data acquired with the Phase II compact array allows a direct bispectrum estimate to be undertaken on the multiple redundantly-spaced triangles of antenna tiles, as well as an estimate based on data gridded to the $uv$-plane. The direct and gridded bispectrum estimators are applied to 21 hours of high-band (167--197~MHz; $z$=6.2--7.5) data from the 2016 and 2017 observing seasons. Analytic predictions for the bispectrum bias and variance for point source foregrounds are derived. We compare the output of these approaches, the foreground contribution to the signal, and future prospects for measuring the bispectra with redundant and non-redundant arrays. We find that some triangle configurations yield bispectrum estimates that are consistent with the expected noise level after 10 hours, while equilateral configurations are strongly foreground-dominated. Careful choice of triangle configurations may be made to reduce foreground bias that hinders power spectrum estimators, and the 21~cm bispectrum may be accessible in less time than the 21~cm power spectrum for some wave modes, with detections in hundreds of hours.Comment: 19 pages, 10 figures, accepted for publication in PAS

Modelling and peeling extended sources with shapelets: a Fornax A case study

To make a power spectrum (PS) detection of the 21 cm signal from the Epoch of Reionisation (EoR), one must avoid/subtract bright foreground sources. Sources such as Fornax A present a modelling challenge due to spatial structures spanning from arc seconds up to a degree. We compare modelling with multi-scale (MS) CLEAN components to 'shapelets', an alternative set of basis functions. We introduce a new image-based shapelet modelling package, SHAMFI. We also introduce a new CUDA simulation code (WODEN) to generate point source, Gaussian, and shapelet components into visibilities. We test performance by modelling a simulation of Fornax A, peeling the model from simulated visibilities, and producing a residual PS. We find the shapelet method consistently subtracts large-angular-scale emission well, even when the angular-resolution of the data is changed. We find that when increasing the angular-resolution of the data, the MS CLEAN model worsens at large angular-scales. When testing on real MWA data, the expected improvement is not seen in real data because of the other dominating systematics still present. Through further simulation we find the expected differences to be lower than obtainable through current processing pipelines. We conclude shapelets are worthwhile for subtracting extended galaxies, and may prove essential for an EoR detection in the future, once other systematics have been addressed.Comment: 17 pages, 11 Figures, accepted for publication in Publications of the Astronomical Society of Australia (18/05/2020). "For the SHAMFI code, see: https://github.com/JLBLine/SHAMFI" . "For the SHAMFI documentation, see: https://shamfi.readthedocs.io/" . "For the WODEN code and documentation see: https://github.com/JLBLine/WODEN