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[1.0] The Discovery Of The Stars

v3.2.1 / chapter 1 of 10 / 01 mar 14 / greg goebel / public domain

* To the ancients, the stars were fixed bright points set into an unchanging heavenly sphere that bounded the Universe. This chapter outlines the history of how astronomers gradually learned the true nature of the stars.

Quintuplet Cluster


[1.1] THE VAULT OF THE HEAVENS
[1.2] THE HUNT FOR DISTANT SUNS / BINARIES & VARIABLE STARS
[1.3] NEBULAS / THE MESSIER OBJECTS
[1.4] DISTANT SUNS CONFIRMED / WHITE DWARFS / NOVAS REDISCOVERED
[1.5] SPECTROSCOPY & PHOTOMETRY / THE HR DIAGRAM
[1.6] THE CEPHEID YARDSTICK / MOVING CLUSTER PARALLAX
[1.7] THE AGE OF THE SUN / FOUNDATIONS OF MODERN ASTROPHYSICS

[1.1] THE VAULT OF THE HEAVENS

* People have been aware of the stars in the sky ever since they were able to look up and understand that there were faint lights over their heads, but it took a long time for them to understand what exactly they were looking at.

The patterns of the stars in the sky are distinctive and in fact beautiful, and by the time of human societies had developed writing and something roughly resembling sciences, these patterns, or "constellations", had been organized and given names. The assigned patterns and names varied between different cultures, but over time one set of assignments won out, and today the most casual amateur astronomer can easily recognize the constellations of the Big Dipper, the Little Dipper, Orion, Cassiopeia, and others.

The stars appeared to be fixed in the sky, in contrast to the moving points of light, the planets, that traveled across it. In the second century BCE the Greek astronomer Hipparchus (190:120 BCE) created the first known detailed map of this heavenly sphere. Hipparchus' work was used by the Alexandrian astronomer Claudius Ptolemaeus, or Ptolemy (~100:170 CE), who published an astronomical treatise titled THE ALMAGEST around 130 CE that was regarded as definitive for over a millennium.

Ptolemy's work established the idea that the planets were objects that moved on sets of transparent heavenly spheres, and that the stars were bright points on the farthest, background sphere. The Earth was at the center of the spheres, though since the planets that moved through the sky in front of the starry sphere tended to backtrack on a regular basis, a system of "spheres carried on spheres" was invented to explain their motion. The idea that stars might be other suns similar to our own was not considered.

* The complexity of the Ptolemaic system was apparent, and as measurements of the sky improved, its complexity grew accordingly to make sure things worked right. Spanish King Alfonso X (1221:1284) commissioned astronomers to come up with modern tables of planetary motions, and in doing so began to wonder about the Ptolemaic system, saying: "If the Lord Almighty had consulted me before embarking on Creation, I should have recommended something simpler."

The Ptolemaic system began to disintegrate in the late 16th and early 17th centuries, with the proposal by Polish astronomer Nikolaus Copernicus (1473:1543) that the Earth actually orbited the Sun in a book that was published, by plan, on the day he died. The idea was not entirely new to Copernicus; the third-century BCE Greek scholar Aristarchus of Samos had come up with the idea almost two millennia earlier, but he had been just too far ahead of his time.

Copernicus' ideas of a "heliocentric" solar system were refined in 1609 by the German astronomer Johannes Kepler (1571:1630), using observations by the great Danish astronomer Tycho Brahe (1546:1601), who had made a new map of the skies to update that created by Hipparchus; Kepler had been his apprentice. Kepler's ideas were championed by the Italian physicist Galileo Galilei (1564:1642). Galileo was one of the first scientists to use the newly-invented telescope to search the sky, where he found the numbers of stars greatly multiplied by his new instrument. The pale stream that ran across the night sky that had been long known as the "Milky Way" turned out to be composed of masses of stars, with our own Sun clearly part of this community, which became known as the "Galaxy".

The Copernican revolution suggested to some that the stars were in fact other suns at great distances away, with worlds of their own. An Englishman named Thomas Digges (1546:1595) promoted this idea in a work published in 1573, and an Italian monk named Giordano Bruno (1548?:1600) proclaimed the plurality of worlds so wildly that he attracted the attention of the Inquisition, who burned him at the stake for heresy when he obstinately refused to recant.

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[1.2] THE HUNT FOR DISTANT SUNS / BINARIES & VARIABLE STARS

* The new idea that the stars were distant suns was just that, an idea. As far as anyone could see, the stars were points of light that remained fixed in positions in the sky. Every very rare now and then a "new star" appeared spontaneously out of the heavens, shined for a time, and then disappeared. The Roman encyclopedist Pliny the Elder (23?:79), writing in the 1st century CE, reported a record of one that appeared sometime around 134 BCE. One appeared in June in 1054 CE and was recorded by Chinese and Japanese astronomers, becoming so bright over the two years of its existence that it could be seen during the day and cast shadows at night.

Another appeared in November 1572, becoming brighter than Venus at its peak. It was observed by Tycho Brahe, who wrote a book on it title DE NOVA STELLA, Latin for "of the new star". Such "new stars" became known as "novae" or "novas" as a result. In 1604, Johannes Kepler recorded another such nova, much less spectacular than Tycho's nova. The novas were puzzling, exceptions in a sky that appeared to be immutable and eternal.

In the year 1700, there was still no conclusive evidence to show whether the stars were distant suns, or simply points of light on the remote vault of the heavens. In 1725, the English astronomer James Bradley (1693:1762) discovered that there was a way to determine the distance to the nearer stars, or at least set a minimum bound on that distance, by measuring a "parallax shift" in their position.

A parallax shift is a slight change in position of a star relative to the dimmer, presumably background stars over the six-month period that the Earth moves from one extreme of its orbit to the other. In principle, this allows determination of the distance to these stars through simple triangulation. Unfortunately, if there was any parallax shift in the position of the stars targeted by astronomers as nearby, it was much too small to be measured. The stars were clearly far away. The German-English musician and astronomer Wilhelm or William Herschel (1738:1822), the greatest "amateur" astronomer in history, put his considerable energies to the task. He failed.

* Herschel did, however, perform observations of the sky with incredible patience and thoroughness, meticulously documenting his observations. He was often assisted by his sister Caroline Herschel (1750:1848), who pioneered a tradition of women in astronomy that precedes their work in other scientific fields.

"Double" stars had been known to astronomers before that time, but these were assumed to be two unrelated stars that just happened to lie along almost the same line of sight. The Herschels began a catalog of such double stars in 1782, but as they accumulated entries they began to suspect that double stars were too common to be accidental. William Herschel conducted meticulous observations over several decades of three of the double stars on the list that seemed particularly suspicious, and concluded they were in a common orbit, or were "binary stars". He announced his preliminary findings in 1793. The same test was applied by other astronomers, and a number of other binary star systems were confirmed.

* In the meantime, a 19-year-old British astronomer, John Goodricke (1764:1786), made a parallel discovery that eventually reaffirmed the validity of binary stars. Some stars had been known for a long time to be vary in brightness. The most spectacular of these "variable stars" is "Beta Persei", also known as "Algol", which dims perceptibly for a short time on a very regular schedule of 69 hours.

In 1782, Goodricke suggested that Algol was a binary system, with the plane of orbit between the two stars almost edge-on to our line of sight. Every 69 hours, one of the stars moved in front of the other, causing the light to fall off for the time of its passage. No great attention was paid to Goodricke's theory at the time, but later it would be accepted as the truth, and such variable stars would become known as "eclipsing variables". It was Goodricke's only contribution to astronomy, since he died at age 21.

There were other variable stars that changed in brightness, but did so in a gradual and smoothly cyclical manner. One of these "pulsating" variables was "Omicron Ceti", or "Mira Ceti", which changes from distinctly visible to almost invisible in a variable cycle lasting roughly 11 months. The pulsating variable "Delta Cephei" changes in such a gradual fashion as well, though the period is much shorter and much more predictable, lasting only 5.37 days. Pulsating variable stars with short and predictable periods became known as "Cepheid variables". The best known (and nearest) Cepheid variable is the "North Star", or "Polaris", about 300 light-years away, which changes in brightness by about 2% over a period of four days.

* The stars, then, were obviously not simply points of light on the heavenly sphere, but were objects at vast distances from the Earth and from each other in space. In the absence of any measured parallax, however, their distance remained a mystery. The only thing that was clear was that they were very far away.

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[1.3] NEBULAS / THE MESSIER OBJECTS

* As astronomers surveyed the sky with increasingly powerful telescopes, they discovered extended fuzzy objects that were named "nebulae" or "nebulas". In 1781, Charles Messier (1730:1817), a French comet-hunter, published a meticulous list of 40 of these nebulas so that he and his fellow comet-hunters could stop being misled by the damned things while they were looking for comets. Ultimately, the Messier list was extended to a hundred objects.

Messier himself had no great interest in these objects and many of them had been known long before he was born. In fact, the "Andromeda Nebula", the 31st item in Messier's list or "M31" for short, can be seen with the naked eye on a dark night, and the "Orion Nebula (M42)", can be made out with binoculars. However, he was the first to provide a comprehensive catalog of them and their formal study more or less begins with his work. Messier has been all but forgotten for his work on comets, but immortalized by his catalog.

The Messier list included a variety of forms. There were some objects that were clearly recognized as clusters of stars at the time, not nebulas as such. The most spectacular of these objects is the "Pleiades (M45)". The Pleiades can be seen with the naked eye as a beautiful jewel-like arrangement of stars. Such star clusters were apparently included in the catalog for the sake of thoroughness and because fainter clusters could seem nebular in form.

Other forms were much more mysterious. "M1" was a tangled blob in the constellation Taurus and was known as the "Crab Nebula". There were many nebulas, such as "M2", "M3", "M4", "M5", "M9", and so on, that appeared to be neat spherical fuzzballs. There were objects such as "M51", the "Whirlpool Nebula", that had pretty spiral forms; others such as "M8", the "Lagoon Nebula", that were shapeless dark clouds; and still others, such as "M57", the "Ring Nebula" that looked like faint shining rings.

Messier objects

The astronomers of the time were only able to speculate on what these objects might be. Were the fuzzballs and spiral forms far-away star clusters, maybe even unbelievably distant "island universes"? Or were they nearby clouds of gas? Herschel of course expended considerable effort on inspecting the Messier objects, and believed that objects such as the Ring Nebula, which he named "planetary nebulas" since they could be mistaken for planets by naive astronomers, might actually be stars in the process of being born. In reality, they were stars in the process of dying, but at the time Herschel didn't have the tools to know any different.

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[1.4] DISTANT SUNS CONFIRMED / WHITE DWARFS / NOVAS REDISCOVERED

* In the 19th century, astronomers continued the attempt to determine stellar distances through parallax observations, using improved instruments. A Scottish astronomer named Thomas Henderson (1798:1844), observing from South Africa, carefully plotted the position of the star "Alpha Centauri". Alpha Centauri, visible only from the Southern Hemisphere, is the third brightest star in the sky, and so might be presumed to be nearby. In fact, we now know that it is the closest star to our own Sun, 4.3 light-years away. A "light-year", incidentally, is the distance light travels in a year, or about 9.46 x 10^12 kilometers.

The German-Russian astronomer Friedrich Georg Wilhelm von Struve (1793:1864) was similarly plotting the position of "Vega", the fourth brightest star in the sky. In reality, Vega is 27 light-years away, relatively close as stars go, but it was not the best candidate for parallax observations.

The third effort was conducted by the German astronomer Friedrich Wilhelm Bessel (1784:1846), who was plotting the position of the star "61 Cygni". 61 Cygni is not particularly bright, but it has a fast "proper motion" across the sky, or motion relative to the background stars. This suggested that it was a nearby star, just as an aircraft flying low overhead passes across an observer's field of view much faster than one flying at the same speed at high altitude.

Bessel announced his results first, in 1838, showing that 61 Cygni was about 11 light-years away. Henderson published his findings in 1839, and Struve, with a harder target, followed in 1840. Astronomers now had some idea of the distances to the stars.

* As astronomers further refined their measurement techniques, they made other discoveries. Between the years 1834 and 1844, Bessel performed observations of the bright, nearby star "Sirius", also known as the "Dog Star" because it is found in the constellation "Canis Major (Big Dog)". Bessel found that its motion through the sky undulated, as if it were a binary in orbit around another star. However, no other star was visible.

Bessel speculated that the other star was a "hidden companion" that was invisible to the telescopic technology available to him. This speculation inspired other astronomers to search for the hidden companion of Sirius. In 1862, the American astronomer Alvan Graham Clark (1832:1897) was testing a new telescope when he discovered the hidden companion as a tiny, faint star. The companion became known as "Sirius B", or just the "Pup", while the Dog Star itself became technically known as "Sirius A".

Inspection of this tiny star showed that it had a diameter comparable to that of the Earth, but a mass more on the order of that of our Sun, and so had to be incredibly, some thought preposterously, dense. Bessel also observed the effect of a hidden companion on the nearby star Procyon in 1844, which was even dimmer than the Pup and not detected until 1895. Preposterous they might be, but they existed nonetheless; these and other stars like them became known as "white dwarfs".

* In the spring of 1848, George Biddell Airy (1801:1892), the British Astronomer Royal, received a letter from an amateur astronomer named John Russell Hind (1823:1895). Hind was an asteroid hunter, and in the course of his search he had found a number of variable stars -- the latest being unusual enough for him to want to contact Airy over it. In fact, calling Hind's discovery a "variable star" was something of an understatement, since it went from obscurity to visible to the naked eye.

Hind had discovered the first nova observed in modern times. His finding later received the designation of "V841 Ophiuchi". As astronomers expanded their sky surveys, they discovered more faint novas, though it would not be until 1918 that a nova, "Nova Aquilae", would be again visible to the naked eye, becoming as bright as Sirius at its peak. It was not until the 1920s that astronomers realized that all novas were not created equal, that their ranks included not only novas but much less dramatic "dwarf novas", and far more energetic "supernovas". The mysterious white dwarfs would prove to be associated with some classes of supernovas, but this is getting ahead of the story and a topic for later.

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[1.5] SPECTROSCOPY & PHOTOMETRY / THE HR DIAGRAM

* Up to the middle of the 18th century, astronomers could only obtain limited information on the distant stars. They could obtain measures of brightness, color, and particularly position with ever improved accuracy, but they had no means of determining other features of the stars, particularly their chemical composition.

Between 1844, when Bessel announced that Sirius had a hidden companion, and 1862, when Clark announced the discovery of that companion, stellar astronomy changed drastically, due to two new discoveries: "spectroscopy" and the related technology of "photometry", and the introduction of photography to astronomy.

In 1814, the German physicist Joseph von Fraunhofer (1787:1826) was observing sunlight passed through a narrow slit and then refracted by precision prisms he had crafted. As any child playing with a piece of crystal knows, a prism breaks up sunlight into a rainbow "spectrum" of colors. It had been known before Fraunhofer's time from comparisons with water waves that the transmission of light through the angled surfaces of a prism caused light of different frequencies to be bent by different amounts, sorting out the low frequency colors, starting with red, at one end of the spectrum from the high frequency colors, ending with violet, at the other. What Fraunhofer observed was that the spectrum created by sunlight passed through the slit featured dark "lines" where the light seemed to absorbed. Others had noticed these dark lines before, but Fraunhofer's prisms were better than any made before, and he was able to map out the dark lines, whose positions relative to the background spectrum did not change.

The exact significance of these lines was not understood until 1859, when the German physicist Robert Kirchoff (1824:1887) and his collaborator, Robert Wilhelm Bunsen (1811:1899), began to study the spectra given off by various vapors in the heat of a "Bunsen burner", a hot gas torch promoted by Bunsen. These hot vapors did not did not generate a rainbow spectrum. Instead, all they produced was a set of bright lines, or "line spectrum". The line spectrum was distinctive for each substance being burned as a vapor. Hydrogen had one recognizable line spectrum, sodium had another, and so on. It was quickly realized that the patterns of dark lines in the solar spectrum matched the patterns of bright lines given off by specific elements studied by Kirchoff and Bunsen. The lines in the solar spectrum were actually providing information on the composition of the Sun, information that astronomers of the previous generation had thought forever beyond their reach.

* Eventually, all these details were sorted out into a few fundamental and simple principles. Hot glowing solid or liquid bodies produce a continuous rainbow spectrum, while hot glowing gases produce a bright "emission" line spectrum characteristic of the substances in the gas. If a hot glowing solid or liquid body shines through a cooler gas, then light is absorbed from the continuous rainbow spectrum in a dark "absorption" line spectrum exactly matching the line spectra patterns of the substances in the gas.

Nobody knew why this was so at the time, and it would take a later revolution in physics to explain it. However, astronomers could use their knowledge of line spectra even without knowing its underlying cause, and were able to use spectroscopy, analysis of the line spectra, to determine details of the composition of the Sun, the stars, and other heavenly objects.

* The continuous spectrum contained information as well, though of a different sort. A continuous rainbow spectrum emitted by a hot solid body such as a glowing cannonball approximated that of what physicists called a "black body", in which the intensity of the light up the spectrum rose in intensity with frequency to a peak, and then fell off quickly at higher frequencies.

As determined by the German physicist Wilhelm Wien (1864:1928) in 1893, the peak frequency corresponded to the temperature of the black body. Incidentally, it was also found that the energy output of the black body increased very strongly with temperature, by about the fourth power. In other words, a doubling of temperature corresponded 16 times the energy output. By determining the shape of the intensity curve using "photometry", astronomers were able to determine the temperature of the Sun and the stars.

* Analysis of the spectra of distant stars provided yet another set of insights. It 1842, the Austrian physicist Christian Johann Doppler (1803:1853) had explained why the sound of a train whistle was high-pitched when the train was approaching, and why it was low-pitched when the train was moving away. When the train was approaching, the wavefronts of the sound waves emitted by the whistle were compressed together proportionally to the speed of the train, and when the train was moving away, the wavefronts were spread apart by the same factor. This phenomenon became logically known as the "Doppler effect".

The Doppler effect also applied to light. The line spectra of a star moving away from the Earth would be shifted down in frequency, or "redshifted". The line spectra of a star moving towards the Earth would be shifted up in frequency, or "blueshifted". Astronomers could now read Doppler shifts to determine the "radial velocity" of a star or other object along the line of sight to Earth. In the case of binary stars, Doppler shifts could be used to get a good value for the velocity of the stars in their orbits around each other. Since the period of the orbits could also be measured, this meant that the actual size of the orbit could be determined by multiplying the orbital velocity by the period. Given the size and period of the orbit, the masses of the stars could be calculated.

In addition, the Doppler shift could be used to determine the rotational period of a star. If a star was spinning with its axis perpendicular to our line of sight from Earth, then the light from one edge of the star that was rotating toward us would be blueshifted, and the light from the other edge of the star that was rotating away from us would be redshifted. The total effect from all parts of the star would be to "smear out" or "broaden" the lines in the star's spectrum, providing an estimate of its rotation rate.

Another revelation provided by spectroscopy was stars whose spectra seemed to "split" on a periodic basis. This indicated that what was seen as a single star was actually a binary, with redshifting and blueshifting of the spectra of the two stellar components causing the lines to move back and forth relative to each other. Such binaries became known as "spectroscopic binaries".

* Photography, which astronomers began to use at roughly the same time, provided another new tool of great value. With photography, astronomers make much more accurate records of images of celestial objects, as well as their spectra.

Given all these tools, by the end of the 19th century astronomers were able to learn many details about the composition of the stars and their behavior. Astronomers were able to organize stars in different categories by their color and spectra, with the first attempt at stellar classification performed by in 1863 Angelo Secchi (1818:1878), a Jesuit priest and astronomer at the Roman College Observatory.

Secchi's scheme was oversimplified and unsatisfactory. An American amateur astronomer named Henry Draper (1837:1882) began investigations on stellar spectra in the 1870s, with the intent of sorting matters out, and on his death Draper's work was bequeathed along with a memorial fund to Harvard University, where it fell into the hands of Harvard astronomy professor Edward Charles Pickering (1846:1919).

Pickering took Draper's work and ran with it, directing a team of up to 15 women to categorize and catalog stars during the late 1880s and the 1890s. Pickering was careful to give credit where it was due, and some of the women, particularly Annie Jump Cannon (1863:1941), became recognized figures in the history of astronomy themselves. The result was the modern scheme of stellar classification, which was in place by 1900. A later result was one of the first modern stellar catalogs, titled the HENRY DRAPER CATALOGUE in honor of the benefactor who had made it possible, and published between 1918 and 1924 by Pickering and Cannon.

Within a few years after the turn of the century, the Danish astronomer Ejnar Hertzsprung (1873:1967) and the American astronomer Henry Norris Russell (1877:1957) independently devised a chart in which the luminosity of stars was plotted against their temperature. The "Hertzsprung-Russell (HR)" diagram seemed to show a definite orderliness in the distribution of stars. An HR diagram is laid out as follows:

HR diagram

Most of the stars in the HR diagram were found in a strip that ran diagonally up the chart, and this strip became known as the "main sequence". Red giants stars occupied one sector of the chart above the main sequence, and white dwarfs occupied another sector of the chart below the main sequence.

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[1.6] THE CEPHEID YARDSTICK / MOVING CLUSTER PARALLAX

* New techniques were developed to measure the distance to the stars. As the decades-long hunt for stellar parallax showed, determining the distance to a point of light in the sky can be very troublesome. In 1908, the American astronomer Henrietta Swan Leavitt (1868:1921) was cataloging stars in the "Small Magellanic Cloud (SMC)", an irregular satellite galaxy of our Milky Way Galaxy that can be seen from the southern hemisphere. The SMC is about 170,000 light-years away, a distance much greater than its size, and so all stars in it can be regarded as being roughly the same distance away.

Leavitt was logging the periods of 25 pulsating variable stars, with properties similar to Delta Cephei, and so categorized as "Cepheid variables". Leavitt noticed that the longer the period of these Cepheid variables, the brighter they were, and a simple linear relationship could be derived between the period and the luminosity. This meant that if the period of a Cepheid variable could be measured, its brightness could be known as well. Cepheids could potentially be used as a "standard candle" to measure interstellar distances.

However, we now know that the nearest Cepheid variable is about 300 light-years away. Although the distances of stars up to 500 light-years away can now can now be accurately determined through parallax measurements by satellites precision-designed for the task, before the age of spaceflight parallax measurements were limited to about 100 light-years.

At that time, nobody knew the actual distance to any Cepheid variable. Although the relative luminosity of different Cepheid variables could be determined, until the actual distance to at least one was found, their absolute luminosity could not be "calibrated" and remained unknown. Leavitt's discovery of the "period-luminosity" relationship was two steps forward, and somehow the missing step had to be found.

* In 1913, Hertzsprung came up with a means of determining the distance to the nearer Cepheid variables, known loosely as "moving-cluster parallax". The idea is subtle and requires an extended explanation.

The basic idea is that if we know the proper motion of a star across the sky in terms of degrees of arc per some unit time, and we know the actual velocity in, say, kilometers per second, we can then determine how far it is away. As an analogy, if we know a jetliner is flying directly overhead at, say, 800 kilometers per hour, then if we measure how long it takes to fly through a few degrees of sky, then it's simple trigonometry to figure out how far away the jetliner is. If we know that the jetliner is traveling at 250 meters a second and it covers three degrees of angle in three seconds, then we know that this angle corresponds to an actual distance of 3 * 250 = 750 meters. This forms the end of what can be approximated as a right triangle with an angle of 3 degrees, allowing the base of the triangle, the distance to the jetliner, to be calculated.

However, this assumes the jetliner is flying directly overhead, with its direction of flight at a right angle, or "tangential", to our line of sight. This is not likely to happen very often, but the trick still works if we also know the actual direction of the jetliner's flight. If we know it's traveling away from us at, say, an angle of 45 degrees, and still covers three degrees of angle in three seconds, then we know its motion across our line of sight amounts to 750/SQRT(2) = 530 meters even though its actual motion is 750 meters, and the trick still works.

With stars, this gets even trickier because we don't know a star's actual velocity and we don't know its true direction in space. We can determine its "radial velocity" along the line of sight to the Earth using spectroscopy to measure its Doppler shift, and we can measure its proper motion, or tangential velocity, across our line of sight. This gives two sides of a right triangle, but unfortunately the radial velocity is in kilometers per second, while the proper motion is in degrees per second, or some appropriately microscaled variation thereof.

If we knew the actual direction, or "true space direction", of the star, we could relate the radial velocity to the proper motion, obtain the actual tangential velocity of the star using trigonometry, and then use that to obtain the distance to the star with another application of trigonometry. But how do we obtain the true space direction of the star?

That would be impossible for an individual star, but Hertzsprung realized that all the stars in a star cluster are moving in parallel in the same direction through the sky, except for minor "peculiar motions" of individual stars. Due to the rules of perspective, they all appear to be either diverging from a "vanishing point" in the sky, if the cluster is moving towards the Sun, or converging towards that vanishing point.

Consider a star cluster in the shape of a perfect, fixed ring of stars that are moving in parallel directly towards us. If we take multiple snapshots of the ring as it moves toward us, all the stars seem to be moving outward from a central point at the same rate. Similarly, if the ring is moving directly away from us, all the stars seem to be moving towards a central point at the same rate. If the ring is moving across our line of sight, at the left far horizon it appears as a circle that grows bigger and more elliptical as it approaches. When it passes directly in front of us, the ellipse momentarily flattens into a straight line of stars, and as it passes away from us the ring grows smaller and less elliptical, until it is a circle again at the right far horizon. The stars nearer to us in the ring move across the sky slightly faster than those farther away.

This scenario could be implemented on a computer graphics workstation, with a program using the rules of perspective and "projective geometry" to show how the appearance of the ring changes from our point of view, given any specified distance and direction of motion. Similarly, if we were to take snapshots of such a moving ring in the real Universe, we would be able to reverse the math to determine its direction of motion. No star cluster has such a neat appearance, of course, but the same principles apply to a disorderly cluster of stars all moving in the same direction and allow determination of its direction of motion -- though the analysis is more troublesome. There is also the confounding influence of the peculiar motions of the stars in the cluster, but this error can be reduced with some statistical adjustments.

Once the direction of a star cluster's true motion is known, then the true space direction of each star in the cluster is known. Its radial velocity can then be related to its proper motion, giving a baseline for distance measurement by triangulation. In pre-spaceflight days, this trick allowed estimates of the distances of stars up to 500 light-years away. Hertzsprung's work allowed the calibration of the Cepheid standard candle. It was a major step forward in galactic and intergalactic astronomy.

* Within a few years, a slight flaw in the scheme was uncovered and led to some recalibration of the yardstick. In 1930, the Swiss-American astronomer Robert Julius Trumpler (1886:1956) showed that distant clusters of stars were dimmer than expected, and this dimming increased with distance.

Interstellar space is filled with thin dust and gas, and it causes a slight dimming and reddening of light that increases with distance and the total amount of dust and gas in the line of sight. The reddening is caused by the fact that shorter wavelengths towards the blue end of the visible light spectrum are scattered more easily by dust than the longer wavelengths towards the red end -- incidentally, this is why the Sun sets blood-red after wildfires have taken place in a vicinity, since the smoke particles scatter the shorter bluish wavelengths of light. It was the unusually red color of objects whose color was known that was the tipoff that something was wrong.

The Cepheid yardstick was based on the simple principle of observing the period of a variable star, obtaining its absolute luminosity from the period, and then comparing its absolute luminosity to its measured luminosity to get the distance. The dimming of stars due to the interstellar medium reduced their measured luminosity and made stars look farther away than they were, and so a corrective factor needed to be applied. There was a more fundamental problem with the use of Cepheid variables as a yardstick, but that was discovered later and is discussed below.

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[1.7] THE AGE OF THE SUN / FOUNDATIONS OF MODERN ASTROPHYSICS

* The birth, life, and death of stars was still largely a mystery at the beginning of the 20th century, though some progress had been made on the problem.

The central problem was the mechanisms by which stars produced their heat and light. In 1853, the German scientist Hermann Ludwig Ferdinand von Helmholtz (1821:1894) suggested that our Sun might obtain its power from the gravitational energy released from its formation. Helmholtz's calculations based on this premise established the age of the Sun as 18 million years, which only decades earlier would have seemed like an immense period of time. However, in the 1830s, the Scots geologist Charles Lyell (1797:1875) had published an influential book, THE PRINCIPLES OF GEOLOGY, that built on previous thinking with thorough research to convincingly argue that the Earth's features were the product of at least hundreds of millions of years of slow, gradual changes. Astronomers were therefore claiming that the Sun, and by association the Earth, was far younger than geologists believed it to be.

The dispute wasn't reconciled until the next century. In 1896, the French physicist Henri Becquerel (1852:1908) discovered that uranium ore emitted a mysterious radiation, leading other physicists to discover that atoms were not indivisible entities. This led to the understanding of the internal organization of the atom, with a nucleus consisting of positively charged "protons" and neutral "neutrons", surrounded by orbiting negatively charged "electrons". It was apparent that there might be great energies locked into the structure of the atom. In 1905, Albert Einstein (1879:1955) had published his Special Theory of Relativity, which as one of its implications established that mass was equivalent to energy by the famous formula E = MC^2. Since C is the speed of light, which is 300,000,000 meters per second, that meant that a small amount of mass could be converted into a great deal of energy.

As understanding of the internal structure of the atom improved, physicists were able to obtain an understanding of "nuclear reactions" such as the breakdown, or "fission", of nuclei, or the merger, or "fusion" of nuclei, which could result in the conversion of a small fraction of their mass into energy. Nuclear reactions were obviously the powerhouses of the stars.

* In the 1920s, the British physicist Sir Arthur Stanley Eddington (1882:1944) began to perform the first practical analyses of the Sun and the stars, establishing the science of astrophysics. In 1926, Eddington published THE INTERNAL CONSTITUTION OF THE STARS, which gave the first detailed description of the mechanics of stars. Eddington calculated the temperature required at the core of the Sun required to keep it from collapsing in on itself as the value of 15 million degrees Kelvin. That was beyond all experience, but with nuclear reactions it was possible, and in fact the high temperature was clearly needed to initiate those reactions. Eddington established one of the most fundamental principles for the behavior of stars, that it involved a balance between the tendency of the star to collapse under its own gravity and its generation of energy.

Eddington realized that the balance between gravity and energy production resulted in a "mass-luminosity curve" that set limits on the mass of a star. At a lower limit, which we now know to be about 75 times the mass of the planet Jupiter, the core of the star can never reach temperatures high enough to initiate sustained nuclear reactions. At an upper limit, the temperatures would be so great that they would disrupt the star. Eddington calculated this limit as 65 times the mass of our Sun, or 65 Suns for short, and no star has been observed with much more than half that mass.

The mass-luminosity curve also defined the rate of energy production for a star with a given mass. A more massive star has a higher temperature, resulting in greater luminosity and a much greater rate of energy production. The increase in energy production was much greater than the increase in mass, and so large stars squandered their fuel and led short lives. Small stars lived an eternity, big stars burned themselves out in a short period of time.

stellar temperature-luminosity plot

* When Eddington published his pioneering work on astrophysics, physicists had general concepts of nuclear reactions and it seemed plausible that stars were powered by the fusion of hydrogen into helium. However, the details of such processes were not understood, and some critics doubted that even the cores of stars were hot enough to initiate fusion. Eddington, irritated, suggested that they could go to someplace hotter.

The details of stellar fusion reactions began to emerge through the work of the Ukrainian-American physicist George Gamow (1904:1968), followed by the research of the German astrophysicist Carl von Weizsaecker (1912:2007) and the German-American physicist Hans Bethe (1906:2005), work which incidentally led to the development of the hydrogen bomb in the 1950s.

The Indian astrophysicist Subrahmanyan Chandrasekhar (1910:1995) also performed studies of white dwarfs in 1930. Observations and Eddington's work had made it clear that white dwarfs were "stellar fossils", the cinders of stars that had expended their nuclear fuel and collapsed in on themselves, but their extreme densities were difficult to understand. Chandrasekhar used the new principles of quantum mechanics to explain these densities. His work also hinted that massive stars enter into a state of unending collapse, but this idea was too radical at the time to be taken very seriously.

* With this work, most of the essential elements of stellar mechanics and evolution became clear, though one matter required some serious rethinking. Cepheid variables had been used to measure the distances to star clusters and to confirm that large numbers of nebulas whose nature had long been mysterious were actually independent galaxies far beyond the Milky Way. However, in the 1940s, astronomers using Cepheid variables to investigate such external galaxies began to realize they were getting strange results. The measurements seemed to show that the relatively nearby Andromeda galaxy was not only smaller than our own, but had smaller star clusters and dimmer stars. It was of course plausible that the Andromeda galaxy was smaller than our own, but it seemed hard to believe that everything in the Andromeda galaxy was on a smaller scale. It was like observing a distant city through a telescope and observing that not only was the city itself smaller, the people, the plants, and the animals all were, too.

The problem turned out to be the assumption was that all Cepheid variable stars fell on the same period-luminosity curve. In other words, very small and dim stars with short periods were on the low end of a curve, while very big and bright stars with long periods were on the high end of the same curve. It actually turned out that the small and dim stars were on a different curve. In 1944, the German-American astronomer Walter Baade (1893:1960) discovered that the larger Cepheid variables used to the calibrate the cosmic distance scale did not follow the same period-luminosity relationship as the smaller Cepheid variable stars that were found in globular clusters.

In other words, there were two distinct populations of Cepheids. The larger Cepheid variables became known as "Population I" Cepheids or "classical Cepheids"; while the smaller became known as "Population II" Cepheids or "RR Lyrae" variables, after the first and brightest of the type to be studied. The classical Cepheids had periods from days to weeks, and turned out to be bright young stars. The RR Lyrae stars were very old stars -- as discussed later, big stars have short lifetimes, and only small stars live to ripe old ages -- and had periods of less than a day. They had different period-luminosity curves, and as a result the cosmic distance scale was in need of recalibration.

variable star period-luminosity relationships

* In the postwar period, the theoretical understanding of stellar mechanics and evolution continued to be refined, particularly with the help of simulations performed on increasingly cheap and powerful computers. Observations took an even greater leap forward, with astronomers making use of new types of telescopes and space satellites to probe the low-energy radio and infrared and high-energy ultraviolet, X-ray, and gamma-ray regions of the electromagnetic spectrum.

White dwarfs were joined by other stellar fossils, the even more massive and much denser neutron stars, and the "black holes" in space created by the endless collapse of the most massive stars into infinitely tiny "singularities" that warped space around them. At the other end of the scale, astronomers also found "substars" named "brown dwarfs" that were not massive enough to become true stars.

By this time, astronomers had realized that the Milky Way Galaxy was only one of a vast number of galaxies, which seemed to be expanding outward in space from an explosive event billions of years ago that became known as the "Big Bang". These discoveries are discussed in detail in following chapters.

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