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Figure 2.2 Schematic illustration
of the compression and/or stretching of light waves from a
moving source. Observer A would see a redshift while
Observer B would see a blueshift. The amount of shift depends
upon the velocity of the source.
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A galaxy with Vr (its radial velocity) of 3000 km/s will show a shift of 1%, as the speed of light is 300,000 km/s. Thus, a spectral line which has a rest wavelength of 6562 Angstroms would be shifted by 65 Angstroms to the red and be observed at a wavelength of 6627 Angstroms. Following up on Slipher's original work, Edwin Hubble and Milton Humason began a systematic spectroscopic survey of galaxies and again found that most galaxies exhibited a redshift, indicating radial motion away from the observer.
Now we have a fundamental observation that most galaxies around us are moving away from us. What does that imply? For one thing, Hubble noticed that not all galaxies exhibited the same redshift as might be expected if galaxies were fixed on some spherical shell (e.g. a crystalline sphere) which was moving away from us. This difference in observed redshift must indicate that the amplitude of the redshift depends on some other property. However, at the time galaxy redshifts were first being measured, there was also a debate about the overall nature of these nebulae (galaxies). There existed two possibilities, either a) these nebulae were part of our own Galaxy and their redshifts were due to motion within the Galaxy, or b) these nebulae were actually separate galaxies that lay at distances far beyond the dimensions of the Milky Way. Until there was a way to determine the distances to these nebulae, this debate did not have a satisfactory resolution.
This dilemma culminated in the Shapley-Curtis debate in 1920. The title of this debate was Scale of the Universe and like our ancient ancestors it represented humanity once again struggling to find its proper place in the Cosmos. At issue was the overall size of the Universe. Shapley argued that the spiral nebulae Hubble and others were measuring were just gas or dust clouds in our own Galaxy and that, therefore, the Milky Way was the Universe. Curtis, however, advanced the idea that these spiral nebulae were galaxies just like our own which indicated that the Universe consisted of a sea of individual galaxies. Each point of view had its merits and could be supported by the data on hand at the time. Inadequate or ambiguous data often is the reason for scientific debate and this is part of the scientific process. The debate usually ends when sufficiently good data arises to declare one side the winner.
This good data came in the form of Hubble's discovery of Cepheid variables in the Andromeda Nebula (M31) in 1923. Using the 100-inch Telescope at Mt. Wilson, Hubble took many photographic plates of M31 and observed some of the brighter stars to vary in brightness over time. By 1925, Hubble had sufficient data to show that these variable stars were just like the Cepheid variables seen previously in the Large Magellanic Cloud (LMC). The only difference was that, on average, the Cepheids in M31 were 200-300 times fainter than those in the LMC. This indicated that M31 had to be approximately 15 times farther away than the LMC and therefore must be a large galaxy located millions of light years from our own Galaxy.
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Figure 4.4 Schematic representation of
the relation between the period of pulsation and the luminosity
of a Cepheid. The most luminous Cepheids have physically larger
radii and correspondingly longer pulsational periods than the
lower luminosity Cepheids.
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Cepheid Variable:. These variable stars show a strong relationship between their intrinsic luminosity and their period of variation. This relationship is shown in Figure 4.4 and is known as the period-luminosity (PL) relation. When the PL is calibrated, the intrinsic luminosity of a Cepheid variable detected in another galaxy can be determined by just measuring its period of variation. As shown in Figure 4.4, the typical Cepheid has a period of 10-100 days with the longer period variables being the brightest. Hubble made use of this PL relation to determine the distance to M31 relative to the Large Magellanic Cloud (LMC). However, before we can use the PL relation to derive absolute distances, we must find a calibration for it. As a first attempt we can try to determine the distances to stellar clusters in our Galaxy that contain Cepheid variables.
Having now demonstrated that the spiral nebulae were indeed other galaxies, then their observed redshifts reflected some form of relative motion between the galaxies. But what could drive this relative motion? Over time, Hubble acquired spectra of fainter and smaller galaxies. He noticed that, in general, their observed redshifts were significantly larger than were observed for bigger and brighter galaxies. By assuming that all galaxies had the same physical size or were of the same physical brightness, Hubble concluded that the smaller and fainter galaxies appeared that way because they were farther away. Hence, Hubble used the apparent size or apparent brightness of a galaxy as a distance indicator.
| Figure 2.3 Hubble's original data plot which shows the correlation between redshift and distance for his sample of galaxies. Although the data is quite noisy, the overall trend is adequately represented by a linear law which redshift is directly proportional to distance. That law is depicted by the solid line. |
When Hubble then plotted the observed redshift versus the indicated distance he saw a correlation. Although the original data is quite noisy (see Figure 2.3), there is a tendency for the smaller, fainter galaxies to have larger redshifts than the bigger, brighter galaxies. Thus, the farther away a galaxy is, the greater its redshift will be. So this means that distant galaxies are moving away from us at a faster rate than nearby galaxies.
While Hubble did help resolve the distances to galaxies, this was a point of considerable debate in the early part of the 20th century. The key debate was between Shapely and Curtis