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Upcoming ground and space-based experiments may have sufficient accuracy to place significant constraints upon high-redshift star formation, Reionization, and dark matter (DM) using the global 21-cm signal of the intergalactic medium. In the early universe, when the relative abundance of low-mass DM halos is important, measuring the global signal would place constraints on the damping of structure formation caused by DM having a higher relic velocity (warm dark matter, or WDM) than in cold dark matter (CDM). Such damping, however, can be mimicked by altering the star formation efficiency (SFE) and difficult to detect because of the presence of Pop III stars with unknown properties. We study these various cases and their degeneracies with the WDM mass parameter $m_X$ using a Fisher matrix analysis. We study the $m_X = 7$ keV case and a star-formation model that parametrizes the SFE as a strong function of halo mass and include several variations of this model along with three different input noise levels for the likelihood; we also use a minimum halo virial temperature for collapse near the molecular cooling threshold. We find that when the likelihood includes only Pop II stars, $m_X$ is constrained to an uncertainty of $\sim 0.4$ keV for all models and noise levels at 68$\%$ CI. When the likelihood includes weak Pop III stars, $m_X \sim 0.3$ keV, and if Pop III star formation is relatively efficient, $m_X \sim 0.1$ keV uncertainty, with tight Pop III star-formation parameter constraints. Our results show that the global 21-cm signal is a promising test-bed for WDM models, even in the presence of strong degeneracies with astrophysical parameters., Comment: 22 pages, 9 figures, updated to version accepted by ApJ

We present an investigation of the horizon and its effect on global 21-cm observations and analysis. We find that the horizon cannot be ignored when modeling low frequency observations. Even if the sky and antenna beam are known exactly, forward models cannot fully describe the beam-weighted foreground component without accurate knowledge of the horizon. When fitting data to extract the 21-cm signal, a single time-averaged spectrum or independent multi-spectrum fits may be able to compensate for the bias imposed by the horizon. However, these types of fits lack constraining power on the 21-cm signal, leading to large uncertainties on the signal extraction, in some cases larger in magnitude than the 21-cm signal itself. A significant decrease in signal uncertainty can be achieved by performing multi-spectrum fits in which the spectra are modeled simultaneously with common parameters. The cost of this greatly increased constraining power, however, is that the time dependence of the horizon's effect, which is more complex than its spectral dependence, must be precisely modeled to achieve a good fit. To aid in modeling the horizon, we present an algorithm and Python package for calculating the horizon profile from a given observation site using elevation data. We also address several practical concerns such as pixelization error, uncertainty in the horizon profile, and foreground obstructions such as surrounding buildings and vegetation. We demonstrate that our training set-based analysis pipeline can account for all of these factors to model the horizon well enough to precisely extract the 21-cm signal from simulated observations., Comment: 19 pages, 11 figures, 1 table

All 21-cm signal experiments rely on electronic receivers that affect the data via both multiplicative and additive biases through the receiver's gain and noise temperature. While experiments attempt to remove these biases, the residuals of their imperfect calibration techniques can still confuse signal extraction algorithms. In this paper, the fourth and final installment of our pipeline series, we present a technique for fitting out receiver effects as efficiently as possible. The fact that the gain and global signal, which are multiplied in the observation equation, must both be modeled implies that the model of the data is nonlinear in its parameters, making numerical sampling the only way to explore the parameter distribution rigorously. However, multi-spectra fits, which are necessary to extract the signal confidently as demonstrated in the third paper of the series, often require large numbers of foreground parameters, increasing the dimension of the posterior distribution that must be explored and therefore causing numerical sampling inefficiencies. Building upon techniques in the second paper of the series, we outline a method to explore the full parameter distribution by numerically sampling a small subset of the parameters and analytically marginalizing over the others. We test this method in simulation using a type-I Chebyshev band-pass filter gain model and a fast signal model based on a spline between local extrema. The method works efficiently, converging quickly to the posterior signal parameter distribution. The final signal uncertainties are of the same order as the noise in the data., Comment: 15 pages, 7 figures, submitted to ApJ

We present a methodology for ensuring the robustness of our analysis pipeline in separating the global 21-cm hydrogen cosmology signal from large systematics based on singular value decomposition (SVD) of training sets. We show how traditional goodness-of-fit metrics such as the $\chi^2$ statistic that assess the fit to the full data may not be able to detect a suboptimal extraction of the 21-cm signal when it is fit alongside one or more additional components due to significant covariance between them. However, we find that comparing the number of SVD eigenmodes for each component chosen by the pipeline for a given fit to the distribution of eigenmodes chosen for synthetic data realizations created from training set curves can detect when one or more of the training sets is insufficient to optimally extract the signal. Furthermore, this test can distinguish which training set (e.g. foreground, 21-cm signal) needs to be modified in order to better describe the data and improve the quality of the 21-cm signal extraction. We also extend this goodness-of-fit testing to cases where a prior distribution derived from the training sets is applied and find that, in this case, the $\chi^2$ statistic as well as the recently introduced $\psi^2$ statistic are able to detect inadequacies in the training sets due to the increased restrictions imposed by the prior. Crucially, the tests described in this paper can be performed when analyzing any type of observations with our pipeline., Comment: 16 pages, 6 figures, 2 tables. Submitted to the Astrophysical Journal

In order to characterize and model the beam-weighted foreground for global 21-cm signal experiments, we present a methodology for generating basis eigenvectors that combines analytical and observational models of both the galactic spectral index and sky brightness temperature with simulations of beams having various angular and spectral dependencies and pointings. Each combination creates a unique beam-weighted foreground. By generating eigenvectors to fit each foreground model using Singular Value Decomposition (SVD), we examine the effects of varying the components of the beam-weighted foreground. We find that the eigenvectors for modelling an achromatic, isotropic beam -- the ideal case -- are nearly identical regardless of the unweighted foreground model used, and are practicably indistinguishable from polynomial-based models. When anisotropic, chromatic beams weight the foreground, however, a coupling is introduced between the spatial and spectral structure of the foreground which distorts the eigenvectors away from the polynomial models and induces a dependence of the basis upon the exact features of the beam (chromaticity, pattern, pointing) and foreground (spectral index, sky brightness temperature map). We find that the beam has a greater impact upon the eigenvectors than foreground models. Any model which does not account for its distortion may produce RMS uncertainties on the order of $\sim 10$ - $10^3$ Kelvin for six-parameter, single spectrum fits. If the beam is incorporated directly using SVD and training sets, however, the resultant eigenvectors yield milli-Kelvin level uncertainties. Given a sufficiently detailed description of the sky, our methodology can be applied to any particular experiment with a suitably characterized beam for the purpose of generating accurate beam-weighted foreground models., Comment: 16 pages, 10 figures

The assumptions inherent to global 21-cm signal analyses are rarely delineated. In this paper, we formulate a general list of suppositions underlying a given claimed detection of the global 21-cm signal. Then, we specify the form of these assumptions for two different analyses: 1) the one performed by the EDGES team showing an absorption trough in brightness temperature that they modeled separately from the sky foreground and 2) a new, so-called Minimum Assumption Analysis (MAA), that makes the most conservative assumptions possible for the signal. We show fits using the EDGES analysis on various beam-weighted foreground simulations from the EDGES latitude with no signal added. Depending on the beam used, these simulations produce large false troughs due to the invalidity of the foreground model to describe the combination of beam chromaticity and the shape of the Galactic plane in the sky, the residuals of which are captured by the ad hoc flattened Gaussian signal model. On the other hand, the MAA provides robust fits by including many spectra at different time bins and allowing any possible 21-cm spectrum to be modeled exactly. We present uncertainty levels and example signal reconstructions found with the MAA for different numbers of time bins. With enough time bins, one can determine the true 21-cm signal with the MAA to $<10$ times the noise level., Comment: 19 pages, 4 figures, accepted to ApJ. Since previous version, added frequency correlation structure under MAA analysis and laid out extension of MAA to motion-induced dipole of 21-cm signal

When using valid foreground and signal models, the uncertainties on extracted signals in global 21-cm signal experiments depend principally on the overlap between signal and foreground models. In this paper, we investigate two strategies for decreasing this overlap: (i) utilizing time dependence by fitting multiple drift-scan spectra simultaneously and (ii) measuring all four Stokes parameters instead of only the total power, Stokes I. Although measuring polarization requires different instruments than are used in most existing experiments, all existing experiments can utilize drift-scan measurements merely by averaging their data differently. In order to evaluate the increase in constraining power from using these two techniques, we define a method for connecting Root-Mean-Square (RMS) uncertainties to probabilistic confidence levels. Employing simulations, we find that fitting only one total power spectrum leads to RMS uncertainties at the few K level, while fitting multiple time-binned, drift-scan spectra yields uncertainties at the $\lesssim 10$ mK level. This significant improvement only appears if the spectra are modeled with one set of basis vectors, instead of using multiple sets of basis vectors that independently model each spectrum. Assuming that they are simulated accurately, measuring all four Stokes parameters also leads to lower uncertainties. These two strategies can be employed simultaneously and fitting multiple time bins of all four Stokes parameters yields the best precision measurements of the 21-cm signal, approaching the noise level in the data., Comment: 16 pages, 6 figures, accepted for publication in ApJ

Low radio frequency experiments performed on Earth are contaminated by both ionospheric effects and radio frequency interference (RFI) from Earth-based sources. The lunar farside provides a unique environment above the ionosphere where RFI is heavily attenuated by the presence of the Moon. We present electrodynamics simulations of the propagation of radio waves around and through the Moon in order to characterize the level of attenuation on the farside. The simulations are performed for a range of frequencies up to 100 kHz, assuming a spherical lunar shape with an average, constant density. Additionally, we investigate the role of the topography and density profile of the Moon in the propagation of radio waves and find only small effects on the intensity of RFI. Due to the computational demands of performing simulations at higher frequencies, we propose a model for extrapolating the width of the quiet region above 100 kHz that also takes into account height above the lunar surface as well as the intensity threshold chosen to define the quiet region. This model, which we make publicly available through a Python package, allows the size of the radio quiet region to be easily calculated both in orbit or on the surface, making it directly applicable for lunar satellites as well as surface missions., Comment: 14 pages, 8 figures, accepted to Advances in Space Research. Additional physical insight such as the skin depth of the lunar material added since previous version. Inset of figure 5 revised to be more legible. Results unchanged

We present the completion of a data analysis pipeline that self-consistently separates global 21-cm signals from large systematics using a pattern recognition technique. In the first paper of this series, we obtain optimal basis vectors from signal and foreground training sets to linearly fit both components with the minimal number of terms that best extracts the signal given its overlap with the foreground. In this second paper, we utilize the spectral constraints derived in the first paper to calculate the full posterior probability distribution of any signal parameter space of choice. The spectral fit provides the starting point for a Markov Chain Monte Carlo (MCMC) engine that samples the signal without traversing the foreground parameter space. At each MCMC step, we marginalize over the weights of all linear foreground modes and suppress those with unimportant variations by applying priors gleaned from the training set. This method drastically reduces the number of MCMC parameters, augmenting the efficiency of exploration, circumvents the need for selecting a minimal number of foreground modes, and allows the complexity of the foreground model to be greatly increased to simultaneously describe many observed spectra without requiring extra MCMC parameters. Using two nonlinear signal models, one based on EDGES observations and the other on phenomenological frequencies and temperatures of theoretically expected extrema, we demonstrate the success of this methodology by recovering the input parameters from multiple randomly simulated signals at low radio frequencies (10-200 MHz), while rigorously accounting for realistically modeled beam-weighted foregrounds., Comment: 19 pages, 11 figures, 5 tables. Submitted to ApJ. Code available at https://bitbucket.org/ktausch/pylinex

Detecting the cosmological sky-averaged (global) 21 cm signal as a function of observed frequency will provide a powerful tool to study the ionization and thermal history of the intergalactic medium (IGM) in the early Universe ($\sim$ 400 million years after the Big Bang). The greatest challenge in conventional total-power global 21 cm experiments is the removal of the foreground synchrotron emission ($\sim 10^3$-$10^4$ K) to uncover the weak cosmological signal (tens to hundreds of mK), especially since the intrinsic smoothness of the foreground spectrum is corrupted by instrumental effects. Although the EDGES team has recently reported an absorption profile at 78 MHz in the sky-averaged spectrum, it is necessary to confirm this detection with an independent approach. The projection effect from observing anisotropic foreground source emission with a wide-view antenna pointing at the North Celestial Pole (NCP) can induce a net polarization, referred as the Projection-Induced Polarization Effect (PIPE). Due to Earth's rotation, observation centered at the circumpolar region will impose a dynamic sky modulation on the net polarization's waveforms which is unique to the foreground component. In this study, we review the implementation practicality and underlying instrumental effects of this new polarimetry-based technique with detailed numerical simulation and a testbed instrument, the Cosmic Twilight Polarimeter (CTP). In addition, we explore an SVD-based analysis approach for separating the foreground and instrumental effects from the background global 21 cm signal using the sky-modulated PIPE., Comment: 19 pages, 24 figures, 1 table, accepted by ApJ

Most of the current Global 21-cm experiments include ground screens that help moderate effects from the Earth. In this paper, we report on a possible systematic artifact within the ground plane that may produce broad absorption features in the spectra observed by these experiments. Using analytical approximations and numerical modeling, the origin of the artifact and its impact on the sky-averaged spectrum are described. The publicly released EDGES dataset, from which a 78 MHz absorption feature was recently suggested, is used to probe for the potential presence of ground plane resonances. While the lack of a noise level for the EDGES spectrum makes traditional goodness-of-fit statistics unattainable, the rms residual can be used to assess the relative goodness of fits performed under similar circumstances. The fit to the EDGES spectrum using a model with a simple 2-term foreground and three cavity-mode resonances is compared to a fit to the same spectrum with a model used by the EDGES team consisting of a 5-term foreground and a flattened Gaussian signal. The fits with the physically motivated resonance and empirical flattened Gaussian models have rms residuals of 20.8 mK (11 parameters) and 24.5 mK (9 parameters), respectively, allowing us to conclude that ground plane resonances constitute another plausible explanation for the EDGES data., Comment: 12 pages, 9 figures, accepted to ApJ

The reduced chi-squared statistic is a commonly used goodness-of-fit measure, but it cannot easily detect features near the noise level, even when a large amount of data is available. In this paper, we introduce a new goodness-of-fit measure that we name the reduced psi-squared statistic. It probes the two-point correlations in the residuals of a fit, whereas chi-squared accounts for only the absolute values of each residual point, not considering the relationship between these points. The new statistic maintains sensitivity to individual outliers, but is superior to chi-squared in detecting wide, low level features in the presence of a large number of noisy data points. After presenting this new statistic, we show an instance of its use in the context of analyzing radio spectroscopic data for 21-cm cosmology experiments. We perform fits to simulated data with four components: foreground emission, the global 21-cm signal, an idealized instrument systematic, and noise. This example is particularly timely given the ongoing efforts to confirm the first observational result for this signal, where this work found its original motivation. In addition, we release a Python script dubbed $\texttt{psipy}$ which allows for quick, efficient calculation of the reduced psi-squared statistic on arbitrary data arrays, to be applied in any field of study., Comment: 22 pages, 10 figures, submitted to JCAP, psipy code to calculate new statistic available at https://bitbucket.org/ktausch/psipy

The sky-averaged (global) highly redshifted 21-cm spectrum from neutral hydrogen is expected to appear in the VHF range of $\sim20-200$ MHz and its spectral shape and strength are determined by the heating properties of the first stars and black holes, by the nature and duration of reionization, and by the presence or absence of exotic physics. Measurements of the global signal would therefore provide us with a wealth of astrophysical and cosmological knowledge. However, the signal has not yet been detected because it must be seen through strong foregrounds weighted by a large beam, instrumental calibration errors, and ionospheric, ground and radio-frequency-interference effects, which we collectively refer to as "systematics". Here, we present a signal extraction method for global signal experiments which uses Singular Value Decomposition (SVD) of "training sets" to produce systematics basis functions specifically suited to each observation. Instead of requiring precise absolute knowledge of the systematics, our method effectively requires precise knowledge of how the systematics can vary. After calculating eigenmodes for the signal and systematics, we perform a weighted least square fit of the corresponding coefficients and select the number of modes to include by minimizing an information criterion. We compare the performance of the signal extraction when minimizing various information criteria and find that minimizing the Deviance Information Criterion (DIC) most consistently yields unbiased fits. The methods used here are built into our widely applicable, publicly available Python package, $\texttt{pylinex}$, which analytically calculates constraints on signals and systematics from given data, errors, and training sets., Comment: 10 pages, 7 figures, submitted to ApJ, code available at https://bitbucket.org/ktausch/pylinex

The redshifted 21-cm monopole is expected to be a powerful probe of the epoch of the first stars and galaxies ($10

Synthetic antiferromagnets with strong perpendicular anisotropy can be modeled by layered Ising antiferromagnets. Accounting for the fact that in the experimental systems the ferromagnetic layers, coupled antiferromagnetically via spacers, are multilayers, we propose a description through Ising films where ferromagnetic stacks composed of multiple layers are coupled antiferromagnetically. We study the equilibrium and non-equilibrium properties of these systems where we vary the number of layers in each stack. Using numerical simulations, we construct equilibrium temperature$-$magnetic field phase diagrams for a variety of cases. We find the same dominant features (three stable phases, where one phase boundary ends in a critical end point, whereas the other phase boundary shows a tricritical point at which the transition changes from first to second order) for all studied cases. Using time-dependent quantities, we also study the ordering processes that take place after a temperature quench. The nature of long-lived metastable states are discussed for thin films, whereas for thick films we compute the surface autocorrelation exponent., Comment: 23 pages, 10 figures, accepted for publication in the Physical Review B

We study the surface phase diagram of the three-dimensional kinetic Ising model below the equilibrium critical point subjected to a periodically oscillating magnetic field. Changing the surface interaction strength as well as the period of the external field, we obtain a non-equilibrium surface phase diagram that in parts strongly resembles the corresponding equilibrium phase diagram, with an ordinary transition, an extraordinary transition and a surface transition. These three lines meet at a special transition point. For weak surface couplings, however, the surface does not order. These results are found to remain qualitatively unchanged when using different single-spin flip dynamics., Comment: 11 pages, 5 figures, accepted for publication in Physical Review E