Doppler Shifts And Hubbles

With the rise of the Industrial Age in the nineteenth century, rapidly moving trains became a common sight in the countryside of Europe. The sound of a whistle emitted by a train and heard by someone standing by the side of the tracks rises in pitch as the train approaches the person and lowers in pitch as the train recedes. In 1842 the German physicist Christian Doppler (1803—1853) gave an explanation for this phenomenon in terms of the periodic nature of sound. Sound travels in a wave form as a succession of compressions and rarefactions in the air. The pitch or frequency of the sound is a function of the distance between two successive compressions; the shorter the distance, the higher the pitch. If the source of the sound is moving toward the observer, then the wavelength will be shortened since the source moves forward a small distance during the time interval between consecutive emissions of a compression. Similarly, the wavelength will be lengthened if the source is moving away from the observer.

The consolidation of the wave theory of light led, in the nineteenth century, to the investigation of phenomena connected to the periodic nature of light emission. The transmission of light is analogous to the transmission of sound waves. Although light waves vibrate in a direction transverse to the direction of their motion, whereas sound waves vibrate in the direction of their motion, both forms of propagation involve the successive emission of wave crests and troughs from a source. In the case of light, pitch corresponds to frequency, with blue light possessing a higher frequency than red light. Doppler reasoned that if a star was moving away from us, we should see some reddening of its light, whereas if it was moving toward us, we should see some blueing of its light. He advanced this effect as an explanation for the changes in brightness observed in variable stars.

It was later realized that the shifts in light frequency that occur because of the motion of variable stars are much too small to account for their changes in brightness. Nevertheless, the effect Doppler had predicted was a genuine one and would become the basis of an important method in stellar astronomy. With the development of techniques to represent the spectrum of the Sun and stars as a sequence of emission and absorption lines, it became possible to determine very precisely the wavelength of light from these objects and thus to identify very small changes in wavelength that occur as a result of the star's motions. Because these motions are along the radius or line joining the observer to the star, the velocities are known as radial velocities. In 1868 William Huggins obtained a spectrum for the star Sirius in Canis Major and found a radial velocity of 29.4 miles per second (48 kilometers per second). In 1871 Hermann Vogel (1834—1898) examined the spectral lines on the east and west limbs of the Sun and identified a shift in their position resulting from the Sun's rotation.

At the end of the nineteenth century the use of stellar spectra to analyze radial velocities became an active field of research. Velocity shifts turned out to be a key to understanding the behavior of an important class of variable stars known as eclipsing-binary stars, objects which exhibit short-term and highly regular changes in brightness. The best known representative of this class of variables is the star Algol in the constellation of Perseus. Spectral analysis of Algol revealed that it consisted of a pair of stars in rapid rotation about their common center of gravity and that the changes in brightness resulted from one member of the pair being eclipsed by the other. Doppler shifts also proved to be useful in determining the motion of the solar system relative to stars in the solar neighborhood. It was through a statistical study of stellar radial velocities that the rotation of the galaxy was first detected.

The Lowell Observatory in Flagstaff was a major American observatory established in 1894 by Percival Lowell (1855—1916). The clear skies and high-altitude conditions of northern Arizona were well suited to the observation of faint objects. The main instrument at Flagstaff was a 24-inch (60 centimeter) refracting telescope built by the firm of Alvan Clark and Sons. The Lowell Observatory was best known for work in planetary astronomy and, more particularly, for its observations of Mars. Lowell's sensational findings of possible advanced engineering structures on the surface of Mars had attracted worldwide attention. In 1912 the Flagstaff astronomer Vesto Slipher embarked on a project to study the spectra of the white, or spiral nebulae, as they were then called. Some astronomers of the period held that in spiral nebulae we were actually observing the formation of new solar systems in space, so Slipher's study of these nebulae was in keeping with Lowell's emphasis on planetary astronomy. The Clark refractor was fitted with a small dispersion spectroscope and a fast-exposure camera that recorded with precision the absorption lines of the faint extended nebular images.

Much to his surprise, Slipher discovered that the radial velocities of the nebulae were a good order of magnitude larger than any of the velocities observed in stars of the galaxy. He found both positive and negative velocities, indicating that some of the nebulae were approaching the Sun and some were receding from it. He initially interpreted this finding in terms of the nebular hypothesis as an effect resulting from the process of star formation, but he soon abandoned this explanation. He conjectured instead that the Sun was moving through space among the spiral nebulae, and the radial velocities resulted from this motion. Although on a much larger scale, this drift effect was similar to the one observed in stars in the neighborhood of the Sun, indicating the motion of the Sun relative to these nearby stars.

The first publication of Slipher's results took place in 1914. For the next decade Slipher worked virtually alone on the problem of nebular spectra. By 1922 he had accumulated spectral data on 41 spirals, which was sent to Eddington and published in the latter's book General Theory of Relativity. The data showed a preponderance of red shifts (35 red shifts versus 6 blue shifts), indicating a clear pattern of recession. This seemed to refute the explanation for the radial velocities as resulting from solar motion relative to the spirals since according to this hypothesis, one should observe red and blue shifts in approximately equal numbers. Throughout the 1920s, observationalists stuck to a modified version of this hypothesis, holding that the equation for solar motion relative to the spirals needed to be supplemented by a special term to account for the systematic occurrence of red shifts. For a given spiral with outward radial velocity V and coordinates a (right ascension) and 5 (declination) this equation takes the form

* V = X cosa cosS + Y sina cos8 + Z sin8 + K, where the K term represents the additional component of velocity that is needed to produce the observed red shift.

By 1925 Hubble had shown that the white nebulae are objects similar to our own galaxy scattered throughout distant space. With this finding the large-scale structure of the universe was clarified and attention shifted to a more detailed study of the properties of nebulae. The very large radial velocities of these nebulae were certainly consistent with their position in the universe far beyond the gravitational range of the galaxy. Milton Humason (1891-1972) at Mount Wilson took over from Slipher the project of measuring and analyzing nebular spectra. The Hooker 100-inch telescope was perhaps the only instrument in the world with sufficient light-gathering power to allow for a really systematic investigation of this sort. Humason was an expert in the measurement of the size of the shifts, while Hubble concentrated on obtaining reliable distance indicators to the nebulae. The difficult and more theoretical part of the investigation was Hubble's. There is a very considerable degree of variation in the intrinsic brightness of nebulae. It does not follow that a dimmer galaxy is necessarily farther away than a brighter one. One must rely on statistical methods and reasonable supposition. For example, it is evident, given a uniform distribution of galaxies in space, that there will be a correlation between apparent and intrinsic luminosity: on average, the fainter a galaxy is, the farther away it is.

Hubble took the available data and tried to fit them to a group of equations of the form (*). He did so fairly cautiously because there had been earlier attempts to do this for globular clusters that had turned out to be premature and incorrect. The German astronomer Carl Wirtz (1876-1939) had conjectured in 1924 that a relationship between distance and red shift held for spiral nebulae, although the data were too meager to permit any definite conclusion. Hubble mostly worked from Slipher's spectrographic measurements, supplemented by a few observations of Humason's. By 1929 he was confident enough to be able to deduce that the K term in (*) had the form kr, where r was the distance to the spiral nebula. The first term on the right side of (*) resulted from the solar motion, which would become negligible in comparison to kr as r became larger. Neglecting the solar motion, the recessional velocity was given by the positive quantity kr, implying that the nebulae were moving away from the solar system with velocities proportional to their distances from us. In recognition of Hubble's work, later astronomers substituted the constant H for k, and the relationship

(**) v = Hr became known as Hubble's law, giving the red shift as a function of distance. The velocity-distance diagram from Hubble's original paper is presented in figure 8.1. This law is independent of the direction of the nebulae in the sky, thus implying that all nebulae at a given distance have the same red shift. Although Hubble followed convention and expressed these shifts in terms of

Figure 8.1: Hubble's historic red shift—distance graph (1929). The Thomas Fisher Rare Book Library, University of Toronto.

radial velocities, he believed that they might well be due to some cause other than recessional motion and the Doppler effect. In subsequent writings he tended to refer to the velocities in his law as "apparent" radial velocities to emphasize this point.

In the 1929 paper Hubble verified (**) up to a distance of about two mega-parsecs, according to the distance scale for galaxies then in use. (A star one parsec from the sun exhibits an annual parallax of one second of arc; a par-sec is approximately 3.26 light-years. A megaparsec is a million parsecs.) Humason and Hubble continued their work and two years later showed that (**) is valid for galaxies out to 32 megaparsecs. The approximate correctness of Hubble's law has since been established for galaxies at any distance, and Hubble's law is now regarded as the fundamental law of modern cosmology. An immediate and pressing issue facing Hubble was to determine as precisely as possible the value of the constant H. This constant is today given in terms of units of kilometers per second per megaparsec, abbreviated to km s-1 Mpc1. Here, radial velocity is measured in kilometers per second and distance in megaparsecs. Hubble estimated H to be around 520 km s1 Mpc1. Hence for every megaparsec increase in distance, the recessional velocity of a galaxy increases by 520 kilometers per second . As we shall see, the very high value for H derived by Hubble and other researchers created problems for cosmologists for decades to come.

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