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By the 1820’s, Joseph Fraunhofer, famous for his identification of the elemental lines in the Sun’s spectrum, had built telescopes with such superb pointing accuracy that they were at last capable of making parallax measurements. Using a Fraunhofer 6-inch refractor, the German astronomer Friedrich Bessel is credited with having determined the first definitive parallax. Bessel assuming that a high proper motion indicated that a star was close to Earth, determined the distance to 61 Cygni. In October 1838, he announced a parallax value for 61 Cygni as 0.314 arc seconds based upon hundreds of position measurements from March 1829 to October 1838. He determined this star was some 99 trillion miles distant, equivalent to 10.3 years of travel by light. He thus was the first astronomer to introduce the concept of light years. The modern value for the distance to 61 Cygni is 11.4 light years.

Independently, in 1835 Wilhelm Struve, another German astronomer who was working in Russia using a Fraunhofer 9-½ inch refractor, began measurements of the first magnitude star Vega. In 1837 Struve reported that he had obtained a preliminary parallax value for Vega of 0.261 arc seconds or 12.5 light years. In late 1839, Struve published a greatly improved distance value for Vega of 26 light years (modern value is 25.3 light years), which was about twice as distant as his earlier reported value.


The third astronomer making the earliest successful parallax observations independently was a Scotsman named Thomas Henderson. Henderson also assumed that brighter stars indicated that they were closer and observed Alpha Centauri from the Cape of Good Hope. Henderson obtained a parallax displacement for Alpha Centauri of more than 1 arc second indicating that it was about 3 light years away (modern value is 4.39 light years). Although Henderson made his observations much earlier than Bessel and Struve, he didn’t reduce and publish his results until two months after Bessel did.

For succeeding years, visual trigonometric parallax measurements were considered only accurate for stars out to a distance of 30 light years. Beyond that they became increasingly more uncertain. With the advent of photography in the late 1800’s, the accuracy and ease of parallax measurement was significantly increased. However, even by the 1980’s, the accuracy of these measurements from the Earth’s surface was no better than about 0.008 arc seconds. Distances beyond 100 light years were problematic, though some estimates were made out to approximately 400 light years, which is too small a distance to give us a good picture of our stellar neighborhood. For example, the closest open (galactic) star cluster to the Earth was found to be the Hyades, which was estimated to be 120 light years away (modern value 150 light years). The next closest open star cluster is the Pleiades, which was estimated to be 400 light years away (modern value is 380 light years).

Because of the limitations of ground based parallax measurements to provide an accurate picture of the stars around us, a satellite system was developed to measure parallaxes from space where the distortion of the Earth’s atmosphere would not interfere with the measurements. This would extend an accurate parallax distance scale out much further to more accurately map remote celestial objects. The European Space Agency (ESA) launched the High Precision Parallax Collecting Satellite (Hipparcos) in August 1989, and it ceased functioning in August 1993. Hipparcos was named for Hipparchus (190-120 B.C.) who compiled the first “precise” star catalog in antiquity.

Due to a malfunction in the rocket booster’s final stage, the satellite did not achieve its intended 22,000 mile geostationary circular orbit. Instead it settled in a long elliptical orbit, which greatly increased the effort needed to communicate with the satellite. Nevertheless, it produced an incredible wealth of information (Sky & Telescope June 1999, pages 40-50).

The main Hipparcos catalog has parallaxes and other information for 118,218 stars. Its precision is approximately 0.001 arc seconds. Distances to stars within 30 light years of the Sun are precise to 1% accuracy. The Hyades was found to be 151 light years away and the Pleiades 375 light years away. Distances to stars out to 300 light years away were measured with an error rate of 10% or less. Hipparchos also collected lower precision parallax data on 2.5 million stars, the Tyco Catalog.

Because of the success of Hipparcos, ESA and NASA have several parallax satellites on the drawing board to provide very precise parallax data on millions of stars out to distances of several thousand light years. Recently, G. Fritz Benedict of MacDonald Observatory and eighteen other astronomers used one of the HST’s fine guidance sensors to obtain an even more accurate parallax distance for the classic variable star Delta Cepheus of 3.66 ± 0.15 milliseconds or 890 ± 36 light years (Sky & Telescope December 2002, page 26). The importance of highly accurate variable star measurements for Cepheid Variable Stars is described in detail below.   

 

SPECTROSCOPIC PARALLAX

In 1902, the American astronomer W. S. Adams, who was the second director of the Mount Wilson Observatory, and a German astronomer A. Kohlschutter discovered the spectral criteria for luminosity, a method by which the distance from the Earth to a star might be estimated by its intrinsic brightness. By examining the ratios of the intensities of the spectral lines of elements such as hydrogen, calcium, strontium and iron, Adams and Kohlschutter noted that the relative intensity of these lines in F, G, K and M spectral class stars differed according to the star’s intrinsic luminosity determined from nearby stars whose trigonometric parallaxes were known Their study of the slight changes in the intensity of these spectral lines resulted in a method where the “absolute” brightness of a star could be estimated and hence its distance computed by just comparing its apparent brightness. This method evolved at Mount Wilson and has been refined over the years to include stars with other spectral types.

The absolute brightness or magnitude of a star is defined as the brightness of the star as if it were seen from a standard distance of 32.6 light years. This distance is known as one parsec, because at this distance the parallax of a star is 0.01 arcsecond. The spectroscopic parallax method is less accurate than the standard parallax method, but it extends our distance scale much further out. It is based on the assumption that stars of a similar mass have the same composition and the same life cycle.

In 1911, the Danish astronomer Enjar Hertzsprung compared the colors and luminosities of stars within several clusters by plotting their magnitudes against their colors. In 1913, the American astronomer Henry Norris Russell undertook a similar investigation of stars in the solar neighborhood by plotting the absolute magnitudes of stars of known distance against their spectral classes. These investigations led to an extremely important discovery concerning the relation between the luminosities and surface temperatures of stars. Today, these findings are exhibited graphically on a diagram known as the Hertzsprung-Russell (HR) diagram, which is a plot of a star’s color (spectral class or surface temperature) versus its intrinsic luminosity.

Extensive work done in the late 1800’s and the early and mid portion of the 1900’s, showed that a star’s position on an HR diagram is also indicative of its approximate mass and its approximate age. If one knows a star’s brightness (its magnitude) and its position on an HR diagram, then one can calculate its distance as well as its size. When stars in an open cluster or globular cluster are measured and plotted on an HR Diagram, it is possible to derive an estimate for the cluster’s age and distance by looking at the distribution of its stars amongst the various spectral classes (Sky & Telescope June 1987, page 482).   

 

CEPHEID VARIABLE STARS- the PERIOD-LUMINOSITY RELATION

Although the spectroscopic parallax method had opened the door to finding our place among more distant stars and nebulae in the early 20th century, it did not show how galaxies fitted into the picture. At this time normal F, G, K and M spectral class stars could not be resolved even in the closest galaxies. Again, some new signpost marker was needed.

In 1912 while studying photographic plates of the Small Magellanic Cloud (SMC), Henrietta Leavitt at the Harvard Observatory found about 100 variable stars, 25 of which were Cepheids [Harvard College Observatory Circular #173, 1912]. Cepheid variable stars are named after Delta Cepheus, the first one of this class of intrinsically pulsating variable stars to be discovered. This type of star goes from a maximum to minimum brightness with a predictable regularity. We now know this change in brightness is due to these stars being in a late phase of their life where radiative and gravitational forces are in an oscillating state. Leavitt noted that the brighter a Cepheid became at its maximum brightness, the longer it took the star to go through its period of change from one maximum to the next. Using this data, she reported her observations concerning the relative period (of brightness change)-luminosity relationship.

Since these SMC Cepheid variable stars were all at about the same distance, Leavitt reasoned that the period must depend upon the absolute magnitude of these stars. If a zero point could be deduced for the relationship between the relative and absolute magnitude of these Cepheids, the distance to the SMC could be determined as well as the distance to the Cepheid variable stars in the Milky Way and its globular star clusters. However, at this time in the early 20th century there were no Cepheid variable stars near enough with a known distance to establish this zero point. The nearest Cepheid star was at an uncertain distance of about 200 light years away.


In 1913, the Danish astronomer Ejnar Hertzprung developed an indirect method to find this zero point. Hertzprung made a determination of the average distance (and from that the average luminosity) of 13 Cepheids in the Milky Way system. Five years after Hertzprung reported his zero point with respect to relative and absolute magnitudes of Cepheid variable stars, Harlow Shapely, later the Director of the Harvard Observatory, recalculated the average distance to several Cepheids. Shapely used his revised figures to map the globular clusters in our Milky Way Galaxy’s halo and determined their distances as being about ten to twenty thousand light years away.

Later work at a number of observatories, such as Harvard, McCormick, and Mount Wilson resulted in further refinement of the relationship between Cepheid period and luminosity. However, Cepheid variable stars could not yet be used as yardsticks to determine the distances to galaxies since such stars still could not be resolved in them. In the early 20th century, it was not yet known what galaxies were, and there was considerable debate among astronomers about their composition. In fact, learned arguments ranged as to whether galaxies were nearby nebulae or remote groups of stars.

 

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