Radio Astrophysics

Barbara Manganis  Albert Dvornik

6 December 1993

Abstract Radio-wave emissions at the wavelength of 21 cm in the provide a useful tool in the study of the structure of our galaxy. These emissions result from spin-flip transitions in monotomic hydrogen, and come to us virtually undisturbed from all parts of the galaxy. In this paper, we show that the velocity curve of the galaxy can be determined from observation of the Doppler shift of the 21 cm line. In addition, we determine the effective temperature of the Sun in the 21 cm region to be aprroximately 60,000 K.

1 Introduction

If we could somehow view our galaxy from a distance, we could observe the full beauty of its spiral structure directly. From our vantage point from within one of its sprial arms, however, we must go through more trouble to determine the shape and structure of our galaxy. Optical methods are largely ineffective at large distances. The advent of spectroscopy allowed us greater ability to measure distances and speeds of faraway stars. However, much of the visible light emitted from stars is absorbed by the clouds of dust and gas that make up the interstellular medium. In addition, a lot of the galaxy is too cold to emit visible light.

It was Dutch astronomer H. Van de Hulst who first explored the possibility of observing the universe using the radio spectrum. He theorized that spin-flip transitions in hydrogen would cause emissions at the 21 centemeter wavelength in the radio spectrum. In 1951, these lines were observed by three separate groups: Ewing and Percell at Harvard, Christiansen at Sydney, and Muller and Oort in the Netherlands.

The procedure outlined in the paper published by Van de Hulst, Mueller, and Oort in 1954 proved the basis for the experiment we performed in lab.

Hydrogen is the most abundant element in our galaxy, and conditions in the interstellar medium favor the interactions that produce the 21 cm line. 21 cm radio emissions are not obscured by dust as are emissions in the visible wavelength. We see the entire galaxy at 21 cm, making 21 cm radio observations an important tool in the study of our galaxy.

2 Theoretical foundation

The actual experiment we performed consisted of two parts. In the first part, we calibrated our equipment by finding the effective temperature of the Sun in the frequency region near 21 cm. The second part was the actual measurement of the 21 centimeter hydrogen line spectrum of the galaxy.

A radio telescope dish antenna functions as a circular aperture. Its power response is therefore a Bessel function. The full width at half power of this Bessel function is termed the beam angle of the telescope, θ_{b}, and is a measure of the linear angle subtended by the telescope. Our telescope selects frequencies around 21 centimeters, so we can determine the effective temperature of the Sun at 21 centimeters. We need only measure the antenna power of the telescope when it is aimed at the sun, multiply this power by a conversion factor.

In the second part of the experiment, we measure the radio line at 21 centimeters, produced by spin-flip transitions of monatomic hydrogen. The ground energy state of monatomic hydrogen is affected by the interaction between the electron and proton spins. The energy of the state in which the proton and the electron have anti-parallel spins is a little lower than that of the parallel spin state.

Collisions between atoms, can exite an atom of hydrogen to the parallel spin state. Since this state has a slightly higher energy than the other one, the atom will try to change spin alignment and emitting a photon with energy equal to the difference between the two energy levels. (This corresponds to a frequency of 1420 MHz or wavelength of 21.12 cm.) This transition is commonly known as the spin-flip transition.