Hertzsprung-Russell diagram

Between 1904 and 1915, Danish astronomer Ejnar Hertzsprung and American astronomer Henry Norris Russell independently discovered significant relationships between the luminosity and surface temperature of stars. The graph or diagram they developed that displays these relationships has become a powerful tool for summarizing many stellar properties and tracing the stages in the “lives” of stars.

Overview

The (or simply H-R diagram) is named for the two astronomers, Ejnar Hertzsprung (1873-1967) and Henry Norris Russell (1877-1957), who independently developed a powerful tool that quickly and easily summarizes many properties of a star.

In an H-R diagram, the ordinate (vertical axis) is used to plot some measures of a star’s intrinsic brightness; these include absolute visual magnitude, absolute bolometric magnitude, and luminosity. The abscissa (horizontal axis) is used to plot some measures of a star’s average photospheric or surface temperature; these include effective temperature, spectral type, and color index. Depending on the particular parameters used to plot stars, the diagram is also known as a color-magnitude diagram or a spectrum-luminosity diagram. However, all variations of the H-R diagram depict the same basic relationships; the slightly different forms of the diagram are due to the specific stellar parameters used in plotting it.

Stars plotted near the top of the H-R diagram are very luminous, while those at the bottom are very dim. Stars plotted on the left side of the diagram have the hottest surfaces and appear bluish, and those on the right side have the coolest surfaces and appear reddish. If spectral type is used, the spectral sequence O B A F G K M is plotted from left to right. The position of a star plotted on an H-R diagram not only indicates the relationship between its luminosity and surface temperature but also provides information about its radius, mass, and stage of development within the stellar life cycle. Updates to stellar classification have added the L, T, and Y spectral types, which represent cool brown dwarfs that do not undergo sustained hydrogen fusion.

The radius is found through the application of the Stefan-Boltzmann law for thermal radiating bodies: the rate of emission of electromagnetic radiation per unit surface area is proportional to the temperature (on an absolute scale) raised to the fourth power. Thus, the luminosity (L) of a star is proportional to its surface area (A) times its surface temperature (T) raised to the fourth power, or L is proportional to A T⁴. Since the surface area of a sphere is proportional to radius squared, another way of stating this relationship is that luminosity (L) is proportional to radius (R) squared times surface temperature (T) raised to the fourth power, or L is proportional to R² T⁴. A star’s position in the H-R diagram gives its luminosity and surface temperature, and that information allows one to calculate its radius.

About 90 percent of all known stars fall along a broad band that extends diagonally across the H-R diagram in a “lazy S” shape, from bright, hot, blue stars at the upper left to faint, cool, red stars at the lower right. This band is known as the “main sequence” and is designated by luminosity class V. The distribution of stars along the main sequence band makes sense intuitively. The stars with the hottest surfaces emit the most light, while those with cooler surfaces emit much less light. Radius does not vary too much along the main sequence, ranging from about five to ten times the Sun’s radius at the upper left (the luminous, hot, blue stars) and diminishing to about one-tenth to one-thirtieth the Sun’s radius at the lower right (the faint, cool, red stars). It has been found that mass also varies along the main sequence, ranging from several tens to perhaps as much as one hundred times the Sun’s mass at the upper left (the luminous, hot, blue stars) and diminishing to about one-tenth to one-fifteenth the Sun’s mass at the lower right (the faint, cool, red stars). A star in this band (referred to as “on the main sequence”) is in the most stable, longest-lasting chapter of its life. It generates energy by fusing hydrogen into helium in its core. Earth’s Sun is a main sequence star with a spectral type and luminosity class of G2 V and an absolute magnitude of about +5, which means it is plotted about midway along the main sequence.

However, not all stars have luminosities and surface temperatures that place them on or near the main sequence. Stars plotted away from the main sequence represent other stages of the stellar life cycle. Some stars are located above and to the right of the main sequence. They are brighter than main sequence stars with the same surface temperature, so by the , they must have much larger surface areas from which to radiate, and this means larger radii. Hence, these stars are referred to as giants and supergiants. Giants (luminosity class III) typically have about one hundred to ten thousand times the surface area and thus about ten to one hundred times the radius of the Sun. Supergiants (luminosity classes Ia, Iab, and Ib) are even larger, typically having surface areas ten thousand to one million times that of the Sun and radii one hundred to one thousand times that of the Sun. The very largest giants and supergiants are those with the coolest surfaces and, hence, are red in color. Giants and supergiants have masses ranging from several tens of times the Sun’s mass down to about the Sun’s mass. They represent stars that have left the main sequence because they exhausted the hydrogen in their cores. An easily seen orange giant (not quite as large or cool as a red giant) is Aldebaran (Alpha Tauri), with spectral type and luminosity class K5 III and absolute magnitude about minus one, located in the of Taurus the bull; if placed at the center of our solar system, it would fill more than half of Mercury’s orbit around the Sun. An easily seen red supergiant is Betelgeuse (Alpha Orionis), spectral type and luminosity class M2 Iab, absolute magnitude about minus five, located in the constellation of Orion the hunter; if placed at the center of our solar system, it would be about twice as big as the orbit of Mars and extend out into the asteroid belt.

Other stars are plotted below and to the left of the main sequence. They are quite hot but very faint, meaning they must have small surface areas and radii. They are called white dwarfs and have about the mass of the Sun (about 300,000 Earth masses) packed into a volume about the size of the Earth. They are stars near the end of their lives, having exhausted all their ways of generating energy and shining only because they are still hot.

Applications

The Hertzsprung-Russell diagram illustrates the evolutionary stages of a star’s life, and it has played a significant role in stellar astrophysics. A star is “born” with a certain mass and chemical composition (typically about 75 percent hydrogen and 25 percent helium by mass, with traces of heavier elements). During most of its life, its mass remains nearly constant; only in the last stages of its life does it undergo significant mass loss. On the other hand, its chemical composition changes, at least in its central region, as the star generates energy through a series of nuclear fusion reactions, converting light atomic nuclei into heavier nuclei. A star is in a constant tug-of-war between its tendency to collapse under its gravity and its tendency to expand due to its pressure. As the star evolves, tapping one energy source after another, its structure changes, affecting its luminosity, surface temperature, and hence its position in the H-R diagram. By utilizing the H-R diagram, astronomers can easily depict these changes and trace a star's evolutionary development as a path followed on the H-R diagram.

Stars are born in interstellar clouds of gas and dust (nebulae) by gravitational contraction. The contraction may be triggered by shock waves from nearby supernova explosions or by an encounter with a galactic spiral arm density wave that compresses the density. As a part of the nebula contracts, it heats up and starts to shine as a protostar. A protostar first appears in the H-R diagram at the extreme right-hand (cool) side. As the protostar continues to contract, it gets hotter and, therefore, brighter, and it moves diagonally up and to the left in the H-R diagram. When the star’s central temperature reaches several million kelvins, hydrogen fusion ignites in the star’s core, converting hydrogen to helium. The star stops shrinking, and it stabilizes, landing on the main sequence. For a star with the Sun’s mass, the protostar stage lasts about thirty million years. More massive stars have stronger self-gravity and contract more rapidly, while low-mass stars have weaker self-gravity and contract more slowly.

A star’s location on the main sequence depends on its mass: higher masses toward the upper left and lower masses toward the lower right. The main sequence is the longest, most stable period in a star’s energy-producing life. As long as it has hydrogen in its core to fuse into helium, it stays near the main sequence. The length of a star’s main sequence stage depends on its mass. Massive stars have more fuel, but they consume it much more rapidly; that is why they are so luminous. Consequently, they have very short main sequence lifetimes, no more than a few million years for stars with several tens of solar masses. Earth’s Sun is about halfway through its ten-billion-year-long main sequence stage. Low-mass stars have less fuel, but they consume it very slowly; that is why they are so faint. Consequently, they have long main sequence lifetimes, much longer than the Sun’s and longer even than the present age of the universe; every low-mass main sequence star that ever formed is still a low-mass main sequence star. As a star consumes the hydrogen in its core, it becomes slightly hotter and brighter, and on the H-R diagram, it rises slightly above the zero-age main sequence.

When the hydrogen in the star’s core is transformed into helium, the changes accelerate. The helium core contracts and heats up, and hydrogen fusion is transferred to a shell surrounding the core, where it proceeds at a faster rate. The star leaves the main sequence as it becomes more luminous, and its outer layers expand and cool. A star like the Sun becomes a red giant. (When that happens to the Sun, in about five billion years, it will become about one thousand times brighter than it is now. Earth’s oceans will boil away, its atmosphere will escape into space, the rocks of its surface will at least partly melt, and all life on the planet will be extinguished.) Eventually, the core of a red giant gets hot enough to fuse helium into carbon. With a nuclear fusion reaction generating energy in the star’s core, once again, it enters a stable stage, but this phase is brief. A star like the Sun quickly consumes the helium in its core in no more than one billion years (compared to ten billion years for hydrogen fusion in its core while on the main sequence), but it is not massive enough to shrink sufficiently to get hot enough to start any more nuclear fusion reactions.

Instead, it puffs off its bloated atmosphere, losing as much as half of its mass. The ejected outer layers are called planetary nebulae. (A planetary nebula has nothing to do with planets; the term developed in the nineteenth century, when these expanding bubbles of gas were seen as round, like planets, and fuzzy, like nebulae, through the telescopes then in use.) from the hot core often ionizes these gases, making them shine. Examples of planetary nebulae are the Helix nebula in the constellation Aquarius and the Ring nebula in the constellation Lyra. A star’s own stellar wind, along with thermal pulses, will drive these outer shells away as expanding bubbles of gas, leaving an exposed hot core as the central star of the planetary nebula.

Such stars exist in a hook-shaped region at the extreme left side of the H-R diagram. The remaining core contracts as much as it can and enters the white dwarf stage. A white dwarf shines because it is hot, but as it shines, it radiates its heat away and becomes cooler and fainter, ending as a cooled-off black dwarf.

A very massive star (more than several times the mass of the Sun) becomes a red supergiant when it leaves the main sequence. It is massive enough for its core to shrink enough to get hot enough to initiate fusion reactions that form elements up to iron. Iron is the heaviest nucleus that can form in fusion reactions that release energy; heavier nuclei require the input of energy to form via fusion. The iron core collapses, sending shock waves through the star, which explodes as a supernova. The outer part of the star is blown away, leaving a collapsed core that becomes a neutron star or, in some cases, a black hole.

The position of the main sequence in the H-R diagram is affected slightly by the chemical composition of the stars that reach it. As supernovae explode and enrich the interstellar material with elements heavier than helium, new generations of stars will be born with slightly increased abundances of heavier elements, and this shifts the main sequence slightly farther to the right in the H-R diagram.

Context

Ejnar Hertzsprung’s interest in astronomy was fostered by his father, who, although educated as an astronomer at the University of Copenhagen, worked for the Danish Department of Finance. He encouraged his son’s interest in astronomy as an avocation, not a vocation, believing that it was impossible to make a living studying the stars. Hertzsprung graduated with a degree in chemical engineering in 1898 from the Polytechnical Institute in Copenhagen and began work in St. Petersburg, Russia. In 1901, Hertzsprung went to Leipzig and spent a year studying photochemistry in Friedrich Wilhelm Ostwald’s laboratory. Photography was developing as a serious scientific tool, and Hertzsprung realized its inherent advantages in astronomy, particularly in studying the spectra of stars.

In 1902, Hertzsprung returned to Denmark, where he corresponded regularly with astronomer Karl Schwarzschild. In 1905 and 1907, he published two papers on stellar spectra and magnitudes. In these papers, he pointed out the distinction between red stars that were very luminous and those that were not. He realized that this indicated a significant difference in the size of the stars, and he named them giants and dwarfs, respectively. Hertzsprung did not include a diagram with either his 1905 or 1907 paper. Still, in 1911, he published graphs of the relationship of color to magnitude based on the stars in several star clusters, including the Pleiades. Hertzsprung noted that stars in the diagrams could be divided into two groups: a more populous one, later known as the main sequence, and a smaller group recognized as giants and supergiants.

Henry Norris Russell, an American astronomer, began measuring stellar parallaxes using photographic techniques in 1903 in Cambridge, England. By 1910, he had accumulated hundreds of photographic plates. Russell’s graphical analysis of the absolute magnitude and spectral type of different stars revealed an interesting correlation. The stars were not scattered randomly over the graph. For most stars, as the magnitude of their luminosity decreased, so did the surface temperature, as determined by the spectral type. In December 1913, Russell presented a graph of the relationship (later known as the H-R diagram) to the American Astronomical Society. In his address, he also identified giant and white dwarf stars, for which he had laid the theoretical foundations in his papers of 1910 and 1912.

Through the filter of history, the priority for the idea for the diagram goes to Hertzsprung. However, Russell was unaware of Hertzsprung’s work when he presented his diagram in 1913, based on hundreds of stars he studied from 1903 to 1910, and began to relate the graph to theories of stellar evolution. The origin of identifying the graph as the “Hertzsprung-Russell diagram” is unclear. Hertzsprung often remarked that it should be called a color-magnitude diagram for clarification purposes. Calling it the Hertzsprung-Russell (or H-R) diagram seems to have evolved gradually, helped along in its use by the English astronomer Sir Arthur Stanley Eddington, who, in 1924, discovered the mass-luminosity relation of main sequence stars. The H-R diagram was included in the articles and lectures of the Danish astronomer Bengt Strömgren during the 1930s, in which he provided an explanation of what the main sequence represents.

The early 1900s was a time of great advances in astronomy. The development of the H-R diagram was one of the more important. The recognition of a correlation between luminosity and surface temperature resulted in a domino effect for stellar research. The H-R diagram has proved to be a versatile astronomical tool. It provides a simple way to represent the structure and depict the evolution of stars. The H-R diagram continues to evolve into the twenty-first century, with astronomers integrating multi-wavelength data from X-ray, infrared, and radio observations into H-R diagrams to gain a more comprehensive understanding of stellar properties.

Bibliography:

“Astronomy - 17.3 The Spectra of Stars (and Brown Dwarfs).” University of Central Florida, 2017, pressbooks.online.ucf.edu/astronomybc/chapter/17-3-the-spectra-of-stars-and-brown-dwarfs/. Accessed 10 Feb. 2025.

Chaisson, Eric, and Steve McMillan. Astronomy Today. 6th ed., Addison-Wesley, 2008.

Fraknoi, Andrew, David Morrison, and Sidney Wolff. Voyages to the Stars and Galaxies. Brooks/Cole-Thomson Learning, 2006.

Freedman, Roger A., and William J. Kaufmann III. Universe. 6th ed., W. H. Freeman, 2019.

"The Hertzsprung-Russell Diagram." Cesar, www.cosmos.esa.int/web/cesar/the-hertzsprung-russell-diagram. Accessed 10 Feb. 2025.

Korn, Katherine G. "Henry Norris Russell (1877-1957)." Vistas in Astronomy, vol. 12, 1970, pp. 3-6.

Leuschner, A. O. "The Award of the Bruce Gold Medal to Professor Ejnar Hertzsprung." Publications of the Astronomical Society of the Pacific, vol. 49, 1937, pp. 65-81.

Nielsen, Axel V. "Ejnar Hertzsprung: Measurer of Stars." Sky and Telescope, vol. 35, Jan. 1968, pp. 4-6.

Philip, D. A. G., and L. C. Green. "The H-R Diagram as an Astronomical Tool." Sky and Telescope, May 1978, pp. 395-400.

Russell, Henry Norris. "Relations Between the Spectra and Other Characteristics of the Stars." Nature, vol. 93, 1914, pp. 227-230, 252-258, 281-286.

Schneider, Stephen E., and Thomas T. Arny. Pathways to Astronomy. 2nd ed., McGraw-Hill, 2008.

Struve, Otto. "The Two Fundamental Relations of Stellar Astronomy." Sky and Telescope, Aug. 1949, pp. 250-252, 262.