arXiv subjects

Emory F. Bunn

Publications and source records attributed to Emory F. Bunn.

At least 19 recordsLinked to original sources

arXiv2025

Simulating Partial Sky Cosmic Microwave Background Maps with 3D Fast Fourier Transforms

Simulated maps of the microwave background (CMB) radiation are generally created using one of two methods: all-sky simulations use the spherical harmonic transform, while maps covering small areas approximate the sky as flat, allowing the use of fast Fourier transforms (FFTs). Current and near-future experiments, particularly ones like CMB S4, will cover areas too large for the flat-sky approximation but significantly less than the full sky. In this regime, it can be more efficient to simulate maps in a 3-D box using FFTs, and then sample onto the observed part of the celestial sphere. We present a method for performing such simulations and show that it can be more efficient than full-sky simulations. We develop the method for scalar maps, but we expect it to be applicable to higher-spin (e.g., polarization) simulations as well.

astro-ph.CO↗

arXiv2024

Circumventing Cosmic Variance via Remote Quadrupole Measurements

A number of important cosmological questions can be addressed only by probing perturbation modes on the largest accessible scales. One promising probe of these modes is the Kamionkowski-Loeb effect, i.e., the polarization induced in the cosmic microwave background (CMB) by Thomson scattering in galaxy clusters, which is proportional to the CMB quadrupole measured at the cluster's location and look-back time. We develop a Fisher formalism for assessing the amount of new information that can be obtained from a future remote quadrupole survey. To demonstrate the constraining power of such a survey, we apply our formalism to a model that suppresses the primordial power spectrum on large scales but is poorly constrained with existing CMB data. We find that the constraints can be improved by over $3\sigma$ for a survey that measures around 100 clusters over $20\%$ of the sky with a signal-to-noise ratio of $3$. In the most optimistic case with a low-noise survey with dense full-sky coverage and only a single degree of freedom in the theory, the constraint improves to over $7\sigma$ beyond local CMB data. Our formalism, which is based in real space rather than harmonic space, can be used to explore a wide range of survey designs, and our results paint an optimistic picture for the utility of remote quadrupole measurements to probe physics on the largest observable scales in the Universe.

astro-ph.CO↗

arXiv2024

Reassessment of the dipole in the distribution of quasars on the sky

We investigate recent claims by Secrest et al. of an anomalously large amplitude of the dipole in the distribution of CatWISE-selected quasars on the sky. Two main issues indicate that the systematic uncertainties in the derived quasar-density dipole are underestimated. Firstly, the spatial distribution of the quasars is not a pure dipole, possessing low-order multipoles of comparable size to the dipole. These multipoles are unexpected and presumably caused by unknown systematic effects; we cannot be confident that the dipole amplitude is not also affected by the same systematics until the origin of these fluctuations is understood. Secondly, the 50 percent sky cut associated with the quasar catalogue strongly couples the multipoles, meaning that the power estimate at ell=1 contains significant contributions from ell>1. In particular, the dominant quadrupole mode in the Galactic mask strongly couples the dipole with the octupole, leading to a large uncertainty in the dipole amplitude. Together these issues mean that the dipole in the quasar catalogue has an uncertainty large enough that consistency with the cosmic microwave background (CMB) dipole cannot be ruled out. More generally, current data sets are insufficiently clean to robustly measure the quasar dipole and future studies will require samples that are larger (preferably covering more of the sky) and free of systematic effects to make strong claims regarding their consistency with the CMB dipole.

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arXiv2024

Cosmological Inflation in N-Dimensional Gaussian Random Fields with Algorithmic Data Compression

There is considerable interest in inflationary models with multiple inflaton fields. The inflaton field $\boldsymbolϕ$ that has been postulated to drive accelerating expansion in the very early universe has a corresponding potential $V$, the details of which are free parameters of the theory. We consider a natural hypothesis that $V$ ought to be maximally random. We realize this idea by defining $V$ as a Gaussian random field in some number $N$ of dimensions. Given a model that statistically determines the shape of $V$, we repeatedly evolve $\boldsymbolϕ$ under random potentials, cataloging a representative sample of trajectories associated with that model. On anthropic grounds, we impose a minimum with $V=0$ and only consider trajectories that reach that minimum. We simulate each path evolution stepwise through $\boldsymbolϕ$-space while simultaneously computing $V$ and its derivatives along the path via a Gaussian random process. When $N$ is large, this method significantly reduces computational load as compared to methods that generate the potential landscape all at once. Even so, the covariance matrix of constraints on $V$ can quickly become large and cumbersome. To solve this problem, we present data compression algorithms to prioritize the necessary information already simulated, then keep an arbitrarily large portion. With these optimizations, we simulate thousands of trajectories, extract matter, tensor, and isocurvature spectra from each, and then assemble statistical predictions of these quantities through repeated trials. We find that the Gaussian random potential is a highly versatile inflationary model with a rich volume of parameter space capable of reproducing modern observations.

astro-ph.CO↗

arXiv2023

Optimal method for reconstructing polychromatic maps from broadband observations with an asymmetric antenna pattern

Broadband time-ordered data obtained from telescopes with a wavelength-dependent, asymmetric beam pattern can be used to extract maps at multiple wavelengths from a single scan. This technique is especially useful when collecting data on cosmic phenomena such as the Cosmic Microwave Background (CMB) radiation, as it provides the ability to separate the CMB signal from foreground contaminants. We develop a method to determine the optimal linear combinations of wavelengths (``colors'') that can be reconstructed for a given telescope design and the number of colors that are measurable with high signal-to-noise ratio. The optimal colors are found as eigenvectors of a matrix derived from the inverse noise covariance matrix. When the telescope is able to scan the sky isotropically, it is useful to transform to a spherical harmonic basis, in which this matrix has a particularly simple form. We propose using the optimal colors determined from the isotropic case even when the actual scanning pattern is not isotropic (e.g., covers only part of the sky). We perform simulations showing that maps in multiple colors can be reconstructed accurately from both full-sky and partial-sky scans. Although the original motivation for this research comes from mapping the CMB, this method of polychromatic map-making will have broader applications throughout astrophysics.

astro-ph.IM↗

arXiv2023

Constraining H0 Via Extragalactic Parallax

We examine the prospects for measurement of the Hubble parameter $H_0$ via observation of the secular parallax of other galaxies due to our own motion relative to the cosmic microwave background rest frame. Peculiar velocities make distance measurements to individual galaxies highly uncertain, but a survey sampling many galaxies can still yield a precise $H_0$ measurement. We use both a Fisher information formalism and simulations to forecast errors in $H_0$ from such surveys, marginalizing over the unknown peculiar velocities. The optimum survey observes $\sim 10^2$ galaxies within a redshift $z_\mathrm{max}=0.06$. The required errors on proper motion are comparable to those that can be achieved by Gaia and future astrometric instruments. A measurement of $H_0$ via parallax has the potential to shed light on the tension between different measurements of $H_0$.

astro-ph.CO↗

arXiv2019

Testing for directionality in the Planck polarization and lensing data

In order to better analyse the polarization of the cosmic microwave background (CMB), which is dominated by emission from our Galaxy, we need tools that can detect residual foregrounds in cleaned CMB maps. Galactic foregrounds introduce statistical anisotropy and directionality to the polarization pseudo-vectors of the CMB, which can be investigated by using the D statistic of Bunn and Scott. This statistic is rapidly computable and capable of investigating a broad range of data products for directionality. We demonstrate the application of this statistic to detecting foregrounds in polarization maps by analysing the uncleaned Planck 2018 frequency maps. For the Planck 2018 CMB maps, we find no evidence for residual foreground contamination. In order to examine the sensitivity of the D statistic, we add a varying fraction of the polarized thermal dust and synchrotron foreground maps to the CMB maps and show the percent-level foreground contamination that would be detected with 95 percent confidence. We also demonstrate application of the D statistic to another data product by analysing the gradient of the minimum-variance CMB lensing potential map (i.e., the deflection angle) for directionality. We find no excess directionality in the lensing potential map when compared to the simulations provided by the Planck Collaboration.

astro-ph.CO↗

arXiv2019

Taller in the saddle: constraining CMB physics using saddle points

The statistics of extremal points in the cosmic microwave background (CMB) temperature (hot and cold spots) have been well explored in the literature, and have been used to constrain models of the early Universe. Here, we extend the study of critical points in the CMB to the set that remains after removing extrema, namely the saddle points. We perform stacks of temperature and polarization about temperature saddle points in simulations of the CMB, as well as in data from the Planck satellite. We then compute the theoretical profile of saddle-point stacks, given the underlying power spectra of the CMB. As an example of the utility of such stacks, we constrain models of cosmic birefringence, and compare the constraining power of the saddle points with that of extremal points. We find that, in the specific example of birefringence, we can place tighter constraints using saddle points in our analysis than using extrema. In fact, we find our saddle-point analysis yields close to optimal constraints, as seen by comparing to a power spectrum analysis. We, therefore, suggest that stacking on saddle points may, in general, be a useful way of testing for non-standard physics effects that change the CMB power spectra.

astro-ph.CO↗

arXiv2019

QUBIC: Exploring the primordial Universe with the Q\&U Bolometric Interferometer

In this paper we describe QUBIC, an experiment that will observe the polarized microwave sky with a novel approach, which combines the sensitivity of state-of-the art bolometric detectors with the systematic effects control typical of interferometers. QUBIC unique features are the so-called "self-calibration", a technique that allows us to clean the measured data from instrumental effects, and its spectral imaging power, i.e. the ability to separate the signal in various sub-bands within each frequency band. QUBIC will observe the sky in two main frequency bands: 150 GHz and 220 GHz. A technological demonstrator is currently under testing and will be deployed in Argentina during 2019, while the final instrument is expected to be installed during 2020.

astro-ph.IM↗

arXiv2017

Measuring Polarized Emission in Clusters in the CMB S4 Era

The next generation of CMB experiments (CMB Stage-4) will produce a Sunyaev-Zel'dovich (SZ) cluster catalog containing $\sim10^{5}$ objects, two orders of magnitudes more than currently available. In this paper, we discuss the detectability of the polarized signal generated by scattering of the CMB quadrupole on the cluster electron gas using this catalog. We discuss the possibility of using this signal to measure the relationship between cluster optical depth and mass. We find that the area of observation of S4 maximizes the signal-to-noise (S/N) on the polarized signal but that this S/N is extremely small for an individual cluster, of order 0.5% for a typical cluster in our catalog, the main source of noise being the residual primordial E-mode signal. However, we find that the signal could be detected using the full cluster catalog and that the significance of the result will increase linearly with the size of the CMB S4 telescope mirror.

astro-ph.CO↗

arXiv2017

Pure E and B polarization maps via Wiener filtering

In order to draw scientific conclusions from observations of cosmic microwave background (CMB) polarization, it is necessary to separate the contributions of the E and B components of the data. For data with incomplete sky coverage, there are ambiguous modes, which can be sourced by either E or B signals. Techniques exist for producing "pure" E and B maps, which are guaranteed to be free of cross-contamination, although the standard method, which involves constructing an eigenbasis, has a high computational cost. We show that such pure maps can be thought of as resulting from the application of a Wiener filter to the data. This perspective leads to far more efficient methods of producing pure maps. Moreover, by expressing the idea of purification in the general framework of Wiener filtering (i.e., maximization of a posterior probability), it leads to a variety of generalizations of the notion of pure E and B maps, e.g., accounting for noise or other contaminants in the data as well as correlations with temperature anisotropy.

astro-ph.CO↗

arXiv2016

Testing cosmological models with large-scale power modulation using microwave background polarization observations

We examine the degree to which observations of large-scale cosmic microwave background (CMB) polarization can shed light on the puzzling large-scale power modulation in maps of CMB anisotropy. We consider a phenomenological model in which the observed anomaly is caused by modulation of large-scale primordial curvature perturbations, and calculate Fisher information and error forecasts for future polarization data, constrained by the existing CMB anisotropy data. Because a significant fraction of the available information is contained in correlations with the anomalous temperature data, it is essential to account for these constraints. We also present a systematic approach to finding a set of normal modes that maximize the available information, generalizing the well-known Karhunen-Loeve transformation to take account of the constraints from the temperature data. A polarization map covering at least $\sim 60\%$ of the sky should be able to provide a $3σ$ detection of modulation at the level favored by the temperature data. A significant fraction of the information in such a data set is contained in the single mode that optimally encapsulates the signal due to temperature-polarization correlation.

astro-ph.CO↗

arXiv2016

Fisher Matrix Optimization of Cosmic Microwave Background Interferometers

We describe a method for forecasting errors in interferometric measurements of polarization of the cosmic microwave background (CMB) radiation, based on the use of the Fisher matrix calculated from the visibility covariance and relation matrices. In addition to noise and sample variance, the method can account for many kinds of systematic error by calculating an augmented Fisher matrix, including parameters that characterize the instrument along with the cosmological parameters to be estimated. The method is illustrated with examples of gain errors and errors in polarizer orientation. The augmented Fisher matrix approach is applicable to a much wider range of problems beyond CMB interferometry.

astro-ph.CO↗

arXiv2016

Bayesian semi-blind component separation for foreground removal in interferometric 21-cm observations

We present in this paper a new Bayesian semi-blind approach for foreground removal in observations of the 21-cm signal with interferometers. The technique, which we call HIEMICA (HI Expectation-Maximization Independent Component Analysis), is an extension of the Independent Component Analysis (ICA) technique developed for two-dimensional (2D) CMB maps to three-dimensional (3D) 21-cm cosmological signals measured by interferometers. This technique provides a fully Bayesian inference of power spectra and maps and separates the foregrounds from signal based on the diversity of their power spectra. Only relying on the statistical independence of the components, this approach can jointly estimate the 3D power spectrum of the 21-cm signal and, the 2D angular power spectrum and the frequency dependence of each foreground component, without any prior assumptions about foregrounds. This approach has been tested extensively by applying it to mock data from interferometric 21-cm intensity mapping observations under idealized assumptions of instrumental effects. We also discuss the impact when the noise properties are not known completely. As a first step toward solving the 21 cm power spectrum analysis problem we compare the semi-blind HIEMICA technique with the commonly used Principal Component Analysis (PCA). Under the same idealized circumstances the proposed technique provides significantly improved recovery of the power spectrum. This technique can be applied straightforwardly to all 21-cm interferometric observations, including epoch of reionization measurements, and can be extended to single-dish observations as well.

astro-ph.CO↗

arXiv2015

The Meaning of Einstein's Equation

This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic equation of the theory: Einstein's equation. Here we give a simple formulation of this equation in terms of the motion of freely falling test particles. We also sketch some of its consequences, and explain how the formulation given here is equivalent to the usual one in terms of tensors. Finally, we include an annotated bibliography of books, articles and websites suitable for the student of relativity.

gr-qc↗

arXiv2014

Simulation of the analysis of interferometric microwave background polarization data

We present results from an end-to-end simulation pipeline interferometric observations of cosmic microwave background polarization. We use both maximum-likelihood and Gibbs sampling techniques to estimate the power spectrum. In addition, we use Gibbs sampling for image reconstruction from interferometric visibilities. The results indicate the level to which various systematic errors (e.g., pointing errors, gain errors, beam shape errors, cross- polarization) must be controlled in order to successfully detect and characterize primordial B modes as well as other scientific goals. In addition, we show that Gibbs sampling is an effective method of image reconstruction for interferometric data in other astrophysical contexts.

astro-ph.CO↗

arXiv2013

Probabilistic image reconstruction for radio interferometers

We present a novel, general-purpose method for deconvolving and denoising images from gridded radio interferometric visibilities using Bayesian inference based on a Gaussian process model. The method automatically takes into account incomplete coverage of the uv-plane, signal mode coupling due to the primary beam, and noise mode coupling due to uv sampling. Our method uses Gibbs sampling to efficiently explore the full posterior distribution of the underlying signal image given the data. We use a set of widely diverse mock images with a realistic interferometer setup and level of noise to assess the method. Compared to results from a proxy for point source- based CLEAN method we find that in terms of RMS error and signal-to-noise ratio our approach performs better than traditional deconvolution techniques, regardless of the structure of the source image in our test suite. Our implementation scales as O(np log np), provides full statistical and uncertainty information of the reconstructed image, requires no supervision, and provides a robust, consistent framework for incorporating noise and parameter marginalizations and foreground removal.

astro-ph.IM↗

arXiv2013

Maximum likelihood analysis of systematic errors in interferometric observations of the cosmic microwave background

We investigate the impact of instrumental systematic errors in interferometric measurements of the cosmic microwave background (CMB) temperature and polarization power spectra. We simulate interferometric CMB observations to generate mock visibilities and estimate power spectra using the statistically optimal maximum likelihood technique. We define a quadratic error measure to determine allowable levels of systematic error that do not induce power spectrum errors beyond a given tolerance. As an example, in this study we focus on differential pointing errors. The effects of other systematics can be simulated by this pipeline in a straightforward manner. We find that, in order to accurately recover the underlying B-modes for r=0.01 at 28<l<384, Gaussian-distributed pointing errors must be controlled to 0.7^\circ rms for an interferometer with an antenna configuration similar to QUBIC, in agreement with analytical estimates. Only the statistical uncertainty for 28<l<88 would be changed at ~10% level. With the same instrumental configuration, we find the pointing errors would slightly bias the 2-σupper limit of the tensor-to-scalar ratio r by ~10%. We also show that the impact of pointing errors on the TB and EB measurements is negligibly small.

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