Detecting the 21 cm Forest in the 21 cm Power Spectrum

We describe a new technique for constraining the radio loud population of active galactic nuclei at high redshift by measuring the imprint of 21 cm spectral absorption features (the 21 cm forest) on the 21 cm power spectrum. Using semi-numerical simulations of the intergalactic medium and a semi-empirical source population we show that the 21 cm forest dominates a distinctive region of $k$-space, $k \gtrsim 0.5 \text{Mpc}^{-1}$. By simulating foregrounds and noise for current and potential radio arrays, we find that a next generation instrument with a collecting area on the order of $\sim 0.1\text{km}^2$ (such as the Hydrogen Epoch of Reionization Array) may separately constrain the X-ray heating history at large spatial scales and radio loud active galactic nuclei of the model we study at small ones. We extrapolate our detectability predictions for a single radio loud active galactic nuclei population to arbitrary source scenarios by analytically relating the 21 cm forest power spectrum to the optical depth power spectrum and an integral over the radio luminosity function.Comment: 20 pages, 17 figures, accepted for publication in MNRA

The Variational Homoencoder: Learning to learn high capacity generative models from few examples

Hierarchical Bayesian methods can unify many related tasks (e.g. k-shot classification, conditional and unconditional generation) as inference within a single generative model. However, when this generative model is expressed as a powerful neural network such as a PixelCNN, we show that existing learning techniques typically fail to effectively use latent variables. To address this, we develop a modification of the Variational Autoencoder in which encoded observations are decoded to new elements from the same class. This technique, which we call a Variational Homoencoder (VHE), produces a hierarchical latent variable model which better utilises latent variables. We use the VHE framework to learn a hierarchical PixelCNN on the Omniglot dataset, which outperforms all existing models on test set likelihood and achieves strong performance on one-shot generation and classification tasks. We additionally validate the VHE on natural images from the YouTube Faces database. Finally, we develop extensions of the model that apply to richer dataset structures such as factorial and hierarchical categories.Comment: UAI 2018 oral presentatio

Constraining High Redshift X-ray Sources with Next Generation 21 cm Power Spectrum Measurements

We use the Fisher matrix formalism and semi-numerical simulations to derive quantitative predictions of the constraints that power spectrum measurements on next-generation interferometers, such as the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA), will place on the characteristics of the X-ray sources that heated the high redshift intergalactic medium. Incorporating observations between $z=5$ and $z=25$, we find that the proposed 331 element HERA and SKA phase 1 will be capable of placing $\lesssim 10\%$ constraints on the spectral properties of these first X-ray sources, even if one is unable to perform measurements within the foreground contaminated "wedge" or the FM band. When accounting for the enhancement in power spectrum amplitude from spin temperature fluctuations, we find that the observable signatures of reionization extend well beyond the peak in the power spectrum usually associated with it. We also find that lower redshift degeneracies between the signatures of heating and reionization physics lead to errors on reionization parameters that are significantly greater than previously predicted. Observations over the heating epoch are able to break these degeneracies and improve our constraints considerably. For these two reasons, 21\,cm observations during the heating epoch significantly enhance our understanding of reionization as well.Comment: 15 pages, 10 figures, Accepted to MNRA

The impact of modelling errors on interferometer calibration for 21 cm power spectra

We study the impact of sky-based calibration errors from source mismodeling on 21\,cm power spectrum measurements with an interferometer and propose a method for suppressing their effects. While emission from faint sources that are not accounted for in calibration catalogs is believed to be spectrally smooth, deviations of true visibilities from model visibilities are not, due to the inherent chromaticity of the interferometer's sky-response (the "wedge"). Thus, unmodeled foregrounds, below the confusion limit of many instruments, introduce frequency structure into gain solutions on the same line-of-sight scales on which we hope to observe the cosmological signal. We derive analytic expressions describing these errors using linearized approximations of the calibration equations and estimate the impact of this bias on measurements of the 21\,cm power spectrum during the Epoch of Reionization (EoR). Given our current precision in primary beam and foreground modeling, this noise will significantly impact the sensitivity of existing experiments that rely on sky-based calibration. Our formalism describes the scaling of calibration with array and sky-model parameters and can be used to guide future instrument design and calibration strategy. We find that sky-based calibration that down-weights long baselines can eliminate contamination in most of the region outside of the wedge with only a modest increase in instrumental noise.Comment: 24 pages, 8 figures, 1 table, accepted for publication in MNRAS. Matches published versio

A multipole-Taylor expansion for the potential of gravitational lens MG J0414+0534

We employ a multipole-Taylor expansion to investigate how tightly the gravitational potential of the quadruple-image lens MG J0414+0534 is constrained by recent VLBI observations. These observations revealed that each of the four images of the background radio source contains four distinct components, thereby providing more numerous and more precise constraints on the lens potential than were previously available. We expand the two-dimensional lens potential using multipoles for the angular coordinate and a modified Taylor series for the radial coordinate. After discussing the physical significance of each term, we compute models of MG J0414+0534 using only VLBI positions as constraints. The best-fit model has both interior and exterior quadrupole moments as well as exterior m=3 and m=4 multipole moments. The deflector centroid in the models matches the optical galaxy position, and the quadrupoles are aligned with the optical isophotes. The radial distribution of mass could not be well constrained. We discuss the implications of these models for the deflector mass distribution and for the predicted time delays between lensed components.Comment: 44 pages, 5 figures, 11 tables, accepted for publication in Ap