Calibration of the EDGES High-Band Receiver to Observe the Global 21-cm Signature from the Epoch of Reionization

The EDGES High-Band experiment aims to detect the sky-average brightness temperature of the $21$-cm signal from the Epoch of Reionization (EoR) in the redshift range $14.8 \gtrsim z \gtrsim 6.5$. To probe this redshifted signal, EDGES High-Band conducts single-antenna measurements in the frequency range $90-190$ MHz from the Murchison Radio-astronomy Observatory in Western Australia. In this paper, we describe the current strategy for calibration of the EDGES High-Band receiver and report calibration results for the instrument used in the $2015-2016$ observational campaign. We propagate uncertainties in the receiver calibration measurements to the antenna temperature using a Monte Carlo approach. We define a performance objective of $1$~mK residual RMS after modeling foreground subtraction from a fiducial temperature spectrum using a five-term polynomial. Most of the calibration uncertainties yield residuals of $1$~mK or less at $95\%$ confidence. However, current uncertainties in the antenna and receiver reflection coefficients can lead to residuals of up to $20$ mK even in low-foreground sky regions. These dominant residuals could be reduced by 1) improving the accuracy in reflection measurements, especially their phase 2) improving the impedance match at the antenna-receiver interface, and 3) decreasing the changes with frequency of the antenna reflection phase.Comment: Updated to match version accepted by Ap

Difference score correlations in relationship research: A conceptual primer

The practice of computing correlations between “difference” or “discrepancy” scores and an outcome variable is common in many areas of social science. Relationship researchers most commonly use difference scores to index the (dis)similarity of members of two-person relationships. Using an intuitive, graphical approach—and avoiding formulas and pointing fingers—we illustrate problems with using difference score correlations in relationship research, suggest ways to ensure that difference score correlations are maximally informative, and briefly review alternatives to difference score correlations in studying similarity, accuracy, and related constructs.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73008/1/j.1475-6811.1999.tb00206.x.pd

Quantum reflection of ultracold atoms from thin films, graphene, and semiconductor heterostructures

We show that thin dielectric films can be used to enhance the performance of passive atomic mirrors by enabling quantum reflection probabilities of over 90% for atoms incident at velocities ~1 mm/s, achieved in recent experiments. This enhancement is brought about by weakening the Casimir-Polder attraction between the atom and the surface, which induces the quantum reflection. We show that suspended graphene membranes also produce higher quantum reflection probabilities than bulk matter. Temporal changes in the electrical resistance of such membranes, produced as atoms stick to the surface, can be used to monitor the reflection process, non-invasively and in real time. The resistance change allows the reflection probability to be determined purely from electrical measurements without needing to image the reflected atom cloud optically. Finally, we show how perfect atom mirrors may be manufactured from semiconductor heterostructures, which employ an embedded two-dimensional electron gas to tailor the atom-surface interaction and so enhance the reflection by classical means.Comment: 8 pages, 4 figure

Toward Empirical Constraints on the Global Redshifted 21 cm Brightness Temperature During the Epoch of Reionization

Preliminary results are presented from a simple, single-antenna experiment designed to measure the all-sky radio spectrum between 100 and 200 MHz. The system used an internal comparison-switching scheme to reduce non-smooth instrumental contaminants in the measured spectrum to 75 mK. From the observations, we place an initial upper limit of 450 mK on the relative brightness temperature of the redshifted 21 cm contribution to the spectrum due to neutral hydrogen in the intergalactic medium (IGM) during the epoch of reionization, assuming a rapid transition to a fully ionized IGM at a redshift of 8. With refinement, this technique should be able to distinguish between slow and fast reionization scenarios. To constrain the duration of reionization to dz > 2, the systematic residuals in the measured spectrum must be reduced to 3 mK.Comment: Submitted to ApJ. 9 pages including 6 figure

Geometric scaling in the spectrum of an electron captured by a stationary finite dipole

We examine the energy spectrum of a charged particle in the presence of a {\it non-rotating} finite electric dipole. For {\emph{any}} value of the dipole moment $p$ above a certain critical value p_{\mathrm{c}}$ an infinite series of bound states arises of which the energy eigenvalues obey an Efimov-like geometric scaling law with an accumulation point at zero energy. These properties are largely destroyed in a realistic situation when rotations are included. Nevertheless, our analysis of the idealised case is of interest because it may possibly be realised using quantum dots as artificial atoms.Comment: 5 figures; references added, outlook section reduce

Addition theorems for spin spherical harmonics. II Results

Based on the results of part I, we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-$s'$ and one spin-$s$ spherical harmonics with $s',s=1/2$, 1, 3/2, and $|s'-s|=0$, 1. We obtain also a fully general addition theorem for one scalar and one tensor spherical harmonic of arbitrary rank. A variety of bilocal sums of ordinary and spin spherical harmonics are given in explicit form, including a general explicit expression for bilocal spherical harmonics