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In 21-cm experimental cosmology, accurate characterization of a radio telescope's antenna beam response is essential to measure the 21-cm signal. Computational electromagnetic (CEM) simulations estimate the antenna beam pattern and frequency response by subjecting the EM model to different dependencies, or beam hyper-parameters, such as soil dielectric constant or orientation with the environment. However, it is computationally expensive to search all possible parameter spaces to optimize the antenna design or accurately represent the beam to the level required for use as a systematic model in 21-cm cosmology. We therefore present $\texttt{MEDEA}$, an emulator which rapidly and accurately generates farfield radiation patterns over a large hyper-parameter space. $\texttt{MEDEA}$ takes a subset of beams simulated by CEM software, spatially decomposes them into coefficients in a complete, linear basis, and then interpolates them to form new beams at arbitrary hyper-parameters. We test $\texttt{MEDEA}$ on an analytical dipole and two numerical beams motivated by upcoming lunar lander missions, and then employ $\texttt{MEDEA}$ as a model to fit mock radio spectrometer data to extract covariances on the input beam hyper-parameters. We find that the interpolated beams have RMS relative errors of at most $10^{-2}$ using 20 input beams or less, and that fits to mock data are able to recover the input beam hyper-parameters when the model and mock derive from the same set of beams. When a systematic bias is introduced into the mock data, extracted beam hyper-parameters exhibit bias, as expected. We propose several future extensions to $\texttt{MEDEA}$ to potentially account for such bias., Comment: 23 pages, 12 figures, accepted for publication in ApJ

Accurate detection of the cosmological 21-cm global signal requires galactic foreground models which can remove power over ~$10^6$. Although foreground and global signal models unavoidably exhibit overlap in their vector-spaces inducing bias error in the extracted signal, a second source of bias and error arises from inadequate foreground models, i.e. models which cannot fit spectra down to the noise level of the signal. We therefore test the level to which seven commonly employed foreground models -- including nonlinear and linear forward-models, polynomials, and maximally-smooth polynomials -- fit realistic simulated mock foreground spectra, as well as their dependence upon model inputs. The mock spectra are synthesized for an EDGES-like experiment and we compare all models' goodness-of-fit and preference using a Kolomogorov-Smirnov test of the noise-normalized residuals in order to compare models with differing, and sometimes indeterminable, degrees of freedom. For a single LST bin spectrum and p-value threshold of $p=0.05$, the nonlinear-forward model with 4 parameters is preferred ($p=0.99$), while the linear forward-model fits well with 6-7 parameters ($p=0.94,0.97$ respectively). The polynomials and maximally-smooth polynomials, like those employed by the EDGES and SARAS3 experiments, cannot produce good fits with 5 parameters for the experimental simulations in this work ($p<10^{-6}$). However, we find that polynomials with 6 parameters pass the KS-test ($p=0.4$), although a 9 parameter fit produces the highest p-value ($p\sim0.67$). When fitting multiple LST bins simultaneously, we find that the linear forward-model outperforms (a higher p-value) the nonlinear for 2, 5 and 10 LST bins. Importantly, the KS-test consistently identifies best-fit \textit{and} preferred models., Comment: 26 pages, 12 figures, accepted for publication by ApJ, minor revisions and edits from previous version

The Lunar Surface Electromagnetics Explorer 'LuSEE Night' is a low frequency radio astronomy experiment that will be delivered to the farside of the Moon by the NASA Commercial Lunar Payload Services (CLPS) program in late 2025 or early 2026. The payload system is being developed jointly by NASA and the US Department of Energy (DOE) and consists of a 4 channel, 50 MHz Nyquist baseband receiver system and 2 orthogonal $\sim$6m tip-to-tip electric dipole antennas. LuSEE Night will enjoy standalone operations through the lunar night, without the electromagnetic interference (EMI) of an operating lander system and antipodal to our noisy home planet., Comment: summary paper submitted to URSI GASS 2023

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