Designing a Switch Circuit Board for the MIST Calibration Procedure Erika Horneckera,1, H. Cynthia Chianga,2, and Raul A. Monsalvea,2 aDepartment of Physics, McGill University, 3600 Rue Université, Montréeal, QC, H3A 2T8, Canada This manuscript was compiled on April 24, 2020 MIST is a new global 21 cm experiment that aims to independently light that is now present in every cosmological observation. confirm the first detection of the 21cm Cosmic Dawn signal made by When the first stars began appearing, 400 million years after the EDGES group in 2018. Calibration is critical in global 21 cm ex- the beginning of its expansion in what is called the Cosmic periments as the error is dominated by systematics. An important Dawn, the ultraviolet radiation they produced ionised most of subsystem involved in the overall calibration scheme of MIST is a the neutral hydrogen in the universe once again (1). switch network. The purpose of this project is to redesign the ra- dio frequency switch circuit involved in the calibration of MIST, in In order to study and access information from the past, order to incorporate semiconductor switches into the design. This we use the finite property of light propagation, and the fact was done with careful considerations for the sensitivity of radio fre- that the universe is expanding. Indeed, as we study light from quency signals. far away, the original signal gets redshifted, meaning that the oldest emitted light will have its wavelength more stretched 21cm cosmology | Solid-state electronics than light coming from the same phenomenon at a more recent time. Travelling across the electromagnetic spectrum allows ne of the greatest mysteries we face is the question of us to study phenomena from the past by observing a given Ohow this all began, how the universe came to be, and feature at different frequencies. how it got to where it is today. These are the questions that cosmology sets out to explore. As the universe is expanding B. Neutral Hydrogen and the Global Redshifted 21cm Signal. and evolving, so is our understanding of the world and its underlying properties. The 21 cm emission line is a natural redshift marker for This paper explores 21 cm observational cosmology, with a tracing neutral hydrogen in the universe, thus allowing us to focus on globally averaged sky measurements that probe the track the evolution of the properties of the universe through- epoch of Cosmic Dawn, and the experimental implications of out its history. Hydrogen being the most abundant element making globally averaged measurements. In 2018, the EDGES in the universe, this makes 21cm emission a very powerful telescope reported the first detection of the Cosmic Dawn observational tool for cosmologists. signal via global 21 cm observations. However, the detection provided data that was not fully in agreement with our current models for that epoch. The MIST experiment, which sets out to independently confirm the detection made by the EDGES group, will be presented, along with an examination of the workflow and the calibration process, a key part of the experi- ment. We will then explore the re-designing of a switch system involved in the calibration of the telescope. Circuit design challenges that arise when working with radio frequency will Fig. 1. Illustration of 21 cm emission in neutral hydrogen. a) The hydrogen atom with be addressed, and the new design for the MIST switch circuit parallel spins. b) The hydrogen atom after a spin-flip, with anti-parallel spins. A 21 cm will be presented. wavelength photon is emitted. 1. 21cm Cosmology: An Overview Significance Statement A. History and Cosmological Observation. Studying the global 21 cm brightness temperature of neutral hydrogen allows us to trace the thermal history of our universe. 13.8 billion years ago, all the content and energy in the MIST is a radio telescope that aims to measure a dip in the 21 universe, contained at a singularity with infinite density cm brightness temperature, corresponding to the appearance and temperature, experienced very rapid expansion, called of the first stars and galaxies, providing cosmologists with ex- inflation. After inflation, the universe was filled with hot, perimental data to compare with current models of the early dense, ionized gas, and proceeded to continue expanding at universe. The design of MIST is primarily driven by the devel- a slower rate, and cooling. 380,000 years later, electrons opment of rigorous built-in calibration to precisely quantify the began to combine with hydrogen nuclei in what is called instrumental systematic errors that dominate the uncertainty in "recombination". This marks the appearance of the first global 21 cm measurements. neutral hydrogen atoms. At this stage, light can now propagate freely as it is no longer being scattered by the dense cloud of free electrons, and this represents the formation of the Cosmic Microwave Background (CMB) which is the first 2To whom correspondence should be addressed. E-mail: [email protected] PNAS | April 24, 2020 | vol. XXX | no. XX | 1–5 This emission arises from the spin-spin coupling of the of this feature in the signal, and although the feature was hydrogen atom’s electron and proton. Neutral hydrogen is overall in accordance with the predictions based on current made up of one proton and one electron, each having either models, the intensity of the dip was greater than estimated (5). spin up or spin down. The combination of spin states, in the This suggests that in its earlier stages, our universe was much ground state of hydrogen, gives different energy levels. Indeed, cooler than what we have predicted, or that there was more the interaction of the magnetic moments of the electron and radiation present than previously thought. Because global proton lead to this hyperfine splitting, each spin state will 21 cm experiments observe total power, they are limited by thus have slightly different magnetic energy (2). The hyperfine systematic errors from the measurement device and its calibra- splitting from the spin-spin coupling is expressed as tion. Meaning that in order to build confidence in the EDGES detection we would have to be able to observe it again using a 2 µ0gpe different telescope. Ehf = 3 hSp · Sei, [1] 3πmpmea To understand the significance of systematic errors on the with µ0 the vacuum permeability, gp the proton’s gyromagnetic measurement, let’s run through an estimate of the integra- ratio, mp the mass of a proton, me the mass of an electron, a tion time with statistical considerations alone, meaning how the Bohr radius, Sp the spin of the proton, and Se the spin long the instrument would need to operate before we have of the electron (3). Notice from the dot product of the spins enough signal-to-noise ratio on the absorption feature, without that the state with higher energy is the state where the spins considering systematics. are parallel (as opposed to anti-parallel). In transitioning The system’s noise temperature (statistical error) is gov- between these two states, the electron moves slightly closer to erned by the radiometer equation, the proton and releases energy as 1420 MHz radiation (21cm Tsyst wavelength). This spin flip being highly forbidden, the excited ∆T = √ , [3] state (parallel spins) has a mean lifetime of approximately B · t 20 million years (4). This would suggest that measuring this where ∆T is the residual uncertainty in a noise temperature emission line is quite difficult, but as there is a large amount measurement, Tsyst is the system temperature, B is the band- of hydrogen in the universe, and the measurement is averaged width over which a single measurement is made, and t is over the sky, the long lifetime of the excited state is not an the integration time (6). The system temperature Tsyst is issue. dominated by the Galaxy, which is approximately 1000K. In order to get enough frequency bins to resolve the absorption feature we are trying to measure we can choose a bin width of B ≈ 1MHz. Note that this value can be adjusted based on how much detail we want to observe in the feature. In standard models, models that do not account for the EDGES enhancement, the amplitude of the absorption feature is about 100mK as seen in Figure2. If we want an approximate signal to noise ratio of 10, meaning the level of the statistical noise Fig. 2. Projection of the globally averaged 21 cm brightness temperature over frequency, based on current cosmological models. The absorption feature cen- is roughly 10 times smaller than the amplitude of the feature, tered around 70 MHz corresponds to the Cosmic Dawn, the epoch during which allowing us to distinguish the signal from the noise, then we the first stars, galaxies, and black holes began to appear. (Borrowed from should have ∆T ≈ 10mK. Rearranging Equation3 to solve for http://pritchardjr.github.io/research.html) t we get T When making a measurement with a telescope, the quantity t = ( )2 · B−1, [4] that is measured is the sky averaged redshifted 21 cm bright- ∆T ness temperature, as seen in Figure2. Brightness temperature and plugging the values we estimated into Equation4, we get is defined by the proportionality relation an approximate integration time of 3 hours. If we take into account the approximations we made and the fact that the 1/2 (TS − TCMB ) δTb ∝ [xHI (1 + z) · ] [2] bandwidth can be changed, we can estimate the integration TS time to 1 day. This integration time is very short compared to Tb is the brightness temperature, xHI is the ratio of neutral the time it takes to account for systematic errors.