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# 15.12 Distances to Galaxies

Speculation about the nature of galaxies began long before Edwin Hubble’s observations with the giant 100-inch telescope at Mount Wilson Observatory. In the middle of the 18th century, the German philosopher Immanuel Kant and the German mathematician Johann Lambert each considered the possibility that certain fuzzy patches in the night sky might by enormous systems of stars remote from the Milky Way. Kant wrote "If such a world of stars is beheld at such an immense distance from the eye of the spectator situated outside of it, then this world will appear under a small angle as a patch of space whose figure will be circular if its plane is presented directly to the eye, and elliptical if it is seen from the side or obliquely." In other words, Kant realized that a flattened system of stars like the Milky Way might appear to have different shapes depending on its orientation in space. He also realized that a galaxy seen from afar would subtend a small angle on the sky. Finally, he knew that the dimness of the starlight from a galaxy could be explained by the inverse square law of light traveling across a vast distance of space.

For over 150 years, astronomers struggled to understand the nature of the nebulae. Speculation was not the same as evidence. One hypothesis held that they were clouds or whirlpools of gas condensing to form stars. Spectroscopy provided some support for the local hypothesis. The London amateur astronomer William Huggins showed that the spectra of a number of planetary nebulae and unresolved nebulae like that in Orion were due to hot gas and not unresolved stars. The alternative, and much more radical, hypothesis held that the nebulae were distant systems of stars. Spectroscopy of the Andromeda nebula showed the features expected of a composite of stars, demonstrating that not all nebulae were purely gaseous. In addition, the nebulae were distributed all over the sky, showing no preference for the plane of the Milky Way. Nor did they appear to be centered on the center of the galaxy, like the globular clusters. Objects that are very far from Earth will appear isotropic (the same in every direction) in their distribution on the sky.

Part of the confusion about nebulae stemmed from the fact that the catalogs of nebulae created by Herschel and Messier did not consist of a single class of object. Messier’s catalog contains a mixture of star-forming regions like the Orion Nebula (M 42), stellar remnants like the Crab Nebula (M 1), and galaxies like the Milky Way (M 31 and M 51, for example). Also, information on the nebulae was very limited. The technique of spectroscopy had not matured enough to apply to faint objects, so the nebulae were mostly fuzzy patches of light. Very few had spiral features or any particular structure.

Most astronomers were reluctant to subscribe to the "island universe" hypothesis — the idea of the nebulae as giant star systems remote from our own — for the simple reason that they could not conceive of a universe much larger than the Milky Way. This idea occurs repeatedly in the history of astronomy since Copernicus — each major discovery has placed us as minor players in a larger universe. The awareness of insignificance is not a comfortable feeling!

Resolving the controversy over nebulae required a new and reliable indicator of distance. Henrietta Leavitt’s discovery of the relationship between luminosity and period in Cepheid variables provided the tool that was needed. Edwin Hubble finally measured the distance to a spiral nebula in 1924. Using the newly built 2.5-m (100-inch) reflector at the Mount Wilson Observatory, Hubble unambiguously resolved the Andromeda Nebula into myriad individual stars. His crucial observation was to identify and measure the periods of Cepheids in Andromeda. Using the already known relation between period and luminosity, he concluded that the Andromeda nebula was a galaxy of stars about 300 kpc away, far beyond the periphery of the Milky Way. Since then, Hubble’s estimate has been revised upwards by a factor of two, due to an error in the Cepheid distance calibration.

Astronomers use a chain of techniques is used to measure distances. Any property of a star or galaxy that can be used to estimate distance is called a distance indicator. Distances within the solar system are measured in the most direct way possible, by the timing of radar signals bounced off nearby planets. The distances to stars near the Sun are measured by their parallax. Very nearby stars can also show observable proper motions. Some of the stars with distances measured directly by geometry are in clusters, allowing the calibration of the technique of main sequence fitting on an H-R diagram. Then astronomers can plot H-R diagrams for other open clusters, and the amount by which the main sequence has to be shifted in brightness to overlay the cluster of known distance is a measure of the relative distance of the two clusters. This technique takes us to the edge of the Milky Way.

To calibrate distances to nearby galaxies, a more luminous distance indicator is needed than a star like the Sun. Populous clusters include RR Lyrae and Cepheid variable stars. The well-established relationship between the period of variability and the luminosity for these rare stars allows a distance to be calculated, given the apparent brightness. Cepheids, in particular, are up to 20,000 times more luminous than the Sun and so can be seen with large telescopes out to a distance of 10,000 to 20,000 kpc. Finally, it is possible to use supernovae, which can outshine the normal stars of an entire galaxy and can be seen out to distances of hundreds of thousands of kpc. Unfortunately, a supernova is such a fleeting stage of stellar evolution that one is observed only every 40 to 50 years in a galaxy. Therefore, there is no guarantee that we find one in a specific galaxy.

The distance scale is the set of measurements that define distances from the Solar System out to the most remote galaxies. Conceptually, the methods of the distance scale form a pyramid. Nearby methods are more direct and accurate. Moving farther from the Sun requires different techniques. Each technique depends on the reliability of those that work at smaller distances. A range of overlap in distance is required to calibrate each new method. Errors continue to accumulate and grow as we reach toward the galaxies.

Why must astronomers use so many different methods to measure all distances in the universe? Part of the reason is the sheer immensity of empty space. The type of distance indicator found near the Sun must also be found 10,000 times farther away to map out the Milky Way. By the inverse square law, this increase in distance corresponds to a dimming by a factor of 100 million. The type of distance indicator found across the Milky Way must also be discovered a thousand times farther away to be useful in measuring the distances to other galaxies, a dimming by a factor of 1 million. Nearby distance indicators lose their usefulness as the objects become too faint to observe. Distant ones are ineffective in the local universe because luminous stars are very rare. Cepheids can be seen in galaxies up to 20 million parsecs away, but the nearest one to the Sun is about 200 pc, too far for a reliable parallax measurement. Also, it is sheer bad luck that our galaxy has not hosted a supernova since 1604, since we expect a supernova about every 50 years.

The measurement of distance is absolutely fundamental to astronomy. Without knowing an object’s distance, astronomers cannot derive basic parameters such as size, mass, and luminosity. The goal in distance determination is to find objects whose intrinsic brightness or size is well known — distance indicators. Knowing the absolute brightness (from the well-understood physics of the source) and the apparent brightness (measured through a telescope), distance can be easily calculated. It sounds simple, but the long journey to understand the nature of the nebulae shows that accurate distances are very hard to measure.

When astronomers measure distances, they must assume that the laws of physics are constant across the universe. The laws of physics are confirmed only in terrestrial laboratories, and to a more limited degree from our study of Moon rocks and particles in interstellar space. Beyond our galaxy, their application requires a powerful and unifying assumption. Hubble was relieved to find Cepheids and other familiar stars in distant galaxies, because it indicated to him that "the principle of the uniformity of nature thus seems to rule undisturbed in this remote region of space."