{"id":583,"date":"2022-03-02T17:22:18","date_gmt":"2022-03-02T17:22:18","guid":{"rendered":"https:\/\/pressbooks.ccconline.org\/astronomy\/?post_type=chapter&#038;p=583"},"modified":"2022-04-29T17:56:42","modified_gmt":"2022-04-29T17:56:42","slug":"18-4-the-h-r-diagram","status":"publish","type":"chapter","link":"https:\/\/pressbooks.ccconline.org\/astronomy\/chapter\/18-4-the-h-r-diagram\/","title":{"raw":"18.4 The H\u2013R Diagram","rendered":"18.4 The H\u2013R Diagram"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<h3 class=\"textbox__title\">Learning Objectives<\/h3>\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1168583487547\">By the end of this section, you will be able to:<\/p>\r\n\r\n<ul id=\"fs-id1164754873184\">\r\n \t<li>Identify the physical characteristics of stars that are used to create an H\u2013R diagram, and describe how those characteristics vary among groups of stars<\/li>\r\n \t<li>Discuss the physical properties of most stars found at different locations on the H\u2013R diagram, such as radius, and for main sequence stars, mass<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1164755043750\">In this chapter and\u00a0Analyzing Starlight, we described some of the characteristics by which we might classify stars and how those are measured. These ideas are summarized in\u00a0Table 18.2. We have also given an example of a relationship between two of these characteristics in the mass-luminosity relation. When the characteristics of large numbers of stars were measured at the beginning of the twentieth century, astronomers were able to begin a deeper search for patterns and relationships in these data.<\/p>\r\n\r\n<div class=\"os-table os-top-titled-container\">\r\n<table id=\"fs-id1164755038804\" class=\"grid landscape aligncenter\"><caption>Table 18.2 Measuring the Characteristics of Stars<\/caption>\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Characteristic<\/th>\r\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Technique<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Surface temperature<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">\r\n<p id=\"fs-id1164754986804\">1. Determine the color (very rough).<\/p>\r\n<p id=\"fs-id1164754896265\">2. Measure the spectrum and get the spectral type.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Chemical composition<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">Determine which lines are present in the spectrum.<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Luminosity<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">Measure the apparent brightness and compensate for distance.<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Radial velocity<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">Measure the Doppler shift in the spectrum.<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Rotation<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">Measure the width of spectral lines.<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Mass<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">Measure the period and radial velocity curves of spectroscopic binary stars.<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">Diameter<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">\r\n<p id=\"fs-id1164754936599\">1. Measure the way a star\u2019s light is blocked by the Moon.<\/p>\r\n<p id=\"fs-id1164754867630\">2. Measure the light curves and Doppler shifts for eclipsing binary stars.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><span style=\"text-align: initial;font-size: 1em\">To help understand what sorts of relationships might be found, let\u2019s look briefly at a range of data about human beings. If you want to understand humans by comparing and contrasting their characteristics\u2014without assuming any previous knowledge of these strange creatures\u2014you could try to determine which characteristics lead you in a fruitful direction. For example, you might plot the heights of a large sample of humans against their weights (which is a measure of their mass). Such a plot is shown in <\/span>Figure 18.12<span style=\"text-align: initial;font-size: 1em\">\u00a0and it has some interesting features. In the way we have chosen to present our data, height increases upward, whereas weight increases to the left. Notice that humans are not randomly distributed in the graph. Most points fall along a sequence that goes from the upper left to the lower right.<\/span><\/div>\r\n<\/div>\r\n<div id=\"OSC_Astro_18_04_Plot\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_18_04_Plot\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"425\"]<img id=\"2\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/218800a404be404d0251305e0390f1ddaa231ab1\" alt=\"Graph of Height Versus Weight. The vertical axis is labeled \u201cHeight\u201d in arbitrary units. The horizontal axis is labeled \u201cWeight\u201d in arbitrary units. A plot of dots shows a general trend of weight increasing as height increases, with a few outliers above and below.\" width=\"425\" height=\"347\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a018.12<\/strong>\u00a0Height versus Weight.\u00a0The plot of the heights and weights of a representative group of human beings. Most points lie along a \u201cmain sequence\u201d representing most people, but there are a few exceptions.[\/caption]<\/figure>\r\n<\/div>\r\n<p id=\"fs-id1164754908886\">We can conclude from this graph that human height and weight are related. Generally speaking, taller human beings weigh more, whereas shorter ones weigh less. This makes sense if you are familiar with the structure of human beings. Typically, if we have bigger bones, we have more flesh to fill out our larger frame. It\u2019s not mathematically exact\u2014there is a wide range of variation\u2014but it\u2019s not a bad overall rule. And, of course, there are some dramatic exceptions. You occasionally see a short human who is very overweight and would thus be more to the bottom left of our diagram than the average sequence of people. Or you might have a very tall, skinny fashion model with great height but relatively small weight, who would be found near the upper right.<\/p>\r\n<p id=\"fs-id1164754920163\">A similar diagram has been found extremely useful for understanding the lives of stars. In 1913, American astronomer Henry Norris\u00a0<span id=\"term1008\" class=\"no-emphasis\" data-type=\"term\">Russell<\/span>\u00a0plotted the luminosities of stars against their spectral classes (a way of denoting their surface temperatures). This investigation, and a similar independent study in 1911 by Danish astronomer Ejnar\u00a0<span id=\"term1009\" class=\"no-emphasis\" data-type=\"term\">Hertzsprung<\/span>, led to the extremely important discovery that the temperature and luminosity of stars are related (Figure 18.13).<\/p>\r\n\r\n<div id=\"OSC_Astro_18_04_Russell\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_18_04_Russell\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]<img id=\"4\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/e813f96008962b451d884936c8c7c29faee8293d\" alt=\"Photographs of (a) Ejnar Hertzsprung and (b) Henry Norris Russell.\" width=\"487\" height=\"317\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a018.13<\/strong>\u00a0Hertzsprung (1873\u20131967) and Russell (1877\u20131957).\u00a0(a) Ejnar Hertzsprung and (b) Henry Norris Russell independently discovered the relationship between the luminosity and surface temperature of stars that is summarized in what is now called the H\u2013R diagram.[\/caption]<\/figure>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<h3 class=\"textbox__title\">Voyagers in Astronomy<\/h3>\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<h4 id=\"5\" class=\"os-subtitle\" data-type=\"title\"><span class=\"os-subtitle-label\">Henry Norris Russell<\/span><\/h4>\r\n<p id=\"fs-id1164754868000\">When Henry Norris\u00a0<span id=\"term1010\" class=\"no-emphasis\" data-type=\"term\">Russell<\/span>\u00a0graduated from Princeton University, his work had been so brilliant that the faculty decided to create a new level of honors degree beyond \u201csumma cum laude\u201d for him. His students later remembered him as a man whose thinking was three times faster than just about anybody else\u2019s. His memory was so phenomenal, he could correctly quote an enormous number of poems and limericks, the entire Bible, tables of mathematical functions, and almost anything he had learned about astronomy. He was nervous, active, competitive, critical, and very articulate; he tended to dominate every meeting he attended. In outward appearance, he was an old-fashioned product of the nineteenth century who wore high-top black shoes and high starched collars, and carried an umbrella every day of his life. His 264 papers were enormously influential in many areas of astronomy.<\/p>\r\n<p id=\"fs-id1164755015876\">Born in 1877, the son of a Presbyterian minister, Russell showed early promise. When he was 12, his family sent him to live with an aunt in Princeton so he could attend a top preparatory school. He lived in the same house in that town until his death in 1957 (interrupted only by a brief stay in Europe for graduate work). He was fond of recounting that both his mother and his maternal grandmother had won prizes in mathematics, and that he probably inherited his talents in that field from their side of the family.<\/p>\r\n<p id=\"fs-id1164754948440\">Before Russell, American astronomers devoted themselves mainly to surveying the stars and making impressive catalogs of their properties, especially their spectra (as described in\u00a0Analyzing Starlight). Russell began to see that interpreting the spectra of stars required a much more sophisticated understanding of the physics of the atom, a subject that was being developed by European physicists in the 1910s and 1920s. Russell embarked on a lifelong quest to ascertain the physical conditions inside stars from the clues in their spectra; his work inspired, and was continued by, a generation of astronomers, many trained by Russell and his collaborators.<\/p>\r\n<p id=\"fs-id1164754872780\">Russell also made important contributions in the study of binary stars and the measurement of star masses, the origin of the solar system, the atmospheres of planets, and the measurement of distances in astronomy, among other fields. He was an influential teacher and popularizer of astronomy, writing a column on astronomical topics for\u00a0<em data-effect=\"italics\">Scientific American<\/em>\u00a0magazine for more than 40 years. He and two colleagues wrote a textbook for college astronomy classes that helped train astronomers and astronomy enthusiasts over several decades. That book set the scene for the kind of textbook you are now reading, which not only lays out the facts of astronomy but also explains how they fit together. Russell gave lectures around the country, often emphasizing the importance of understanding modern physics in order to grasp what was happening in astronomy.<\/p>\r\n<p id=\"fs-id1164755012180\">Harlow Shapley, director of the Harvard College Observatory, called Russell \u201cthe dean of American astronomers.\u201d Russell was certainly regarded as the leader of the field for many years and was consulted on many astronomical problems by colleagues from around the world. Today, one of the highest recognitions that an astronomer can receive is an award from the American Astronomical Society called the Russell Prize, set up in his memory.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<section id=\"fs-id1164755024160\" data-depth=\"1\">\r\n<h3 data-type=\"title\">Features of the H\u2013R Diagram<\/h3>\r\n<p id=\"fs-id1164754969298\">Following Hertzsprung and Russell, let us plot the temperature (or spectral class) of a selected group of nearby stars against their luminosity and see what we find (Figure 18.14). Such a plot is frequently called the\u00a0<em data-effect=\"italics\">Hertzsprung\u2013Russell diagram<\/em>, abbreviated\u00a0<span id=\"term1011\" data-type=\"term\">H\u2013R diagram<\/span>. It is one of the most important and widely used diagrams in astronomy, with applications that extend far beyond the purposes for which it was originally developed more than a century ago.<\/p>\r\n\r\n<div id=\"OSC_Astro_18_04_Sample\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_18_04_Sample\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"706\"]<img id=\"7\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/dd3b626194347b820b300c0437928fdb31869efd\" alt=\"An H\u2013R Diagram for a Selected Sample of Stars. In this graph the vertical axis is labeled \u201cLuminosity (LSun)\u201d, running from 10-4 to 104 in increments of 102. The horizontal axis is labeled \u201cSpectral class\u201d, and is divided into seven equal length units. From left to right they are labeled \u201cO\u201d, \u201cB\u201d, \u201cA\u201d, \u201cF\u201d, \u201cG\u201d, \u201cK\u201d and \u201cM\u201d. The horizontal axis is also labeled \u201cTemperature (K)\u201d, running from 25,000 on the left to 3,000 on the right. The background of the graph is colored to represent temperature. The O-B section is blue, the A and most of F is green, G is yellow and the K-M section is red. The stars plotted in the diagram fall into four distinct groups. At lower left between spectral types A and F are the \u201cWhite Dwarfs\u201d. Running diagonally across the entire diagram from upper left to lower right is the \u201cMain Sequence\u201d, where most stars lie. The \u201cGiants\u201d lie on a horizontal line at 102 L(Sun) between spectral types G and M. The \u201cSupergiants\u201d are in the upper right. Many well-known stars are plotted in this diagram. The \u201cCompanion of Sirius\u201d is among the white dwarfs. Along the main sequence, from left to right, are \u201dSpica\u201d, \u201cVega\u201d, \u201cSirius\u201d, \u201cProcyon\u201d, \u201cAlpha Centauri A\u201d, \u201cSun\u201d, \u201cTau Ceti\u201d, \u201cBarnard\u2019s Star\u201d and \u201cProxima Centauri\u201d. Along the giant branch from left to right we find \u201cCapella\u201d, \u201cArcturus\u201d and \u201cAldebaran\u201d. Finally, the supergiants from left to right, \u201cRigel\u201d, \u201cCanopus\u201d, \u201cBetelgeuse\u201d and \u201cAntares\u201d.\" width=\"706\" height=\"642\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a018.14<\/strong>\u00a0H\u2013R Diagram for a Selected Sample of Stars.\u00a0In such diagrams, luminosity is plotted along the vertical axis. Along the horizontal axis, we can plot either temperature or spectral type (also sometimes called spectral class). Several of the brightest stars are identified by name. Most stars fall on the main sequence.[\/caption]<\/figure>\r\n<\/div>\r\n<p id=\"fs-id1164754914170\">It is customary to plot H\u2013R diagrams in such a way that temperature increases toward the left and luminosity toward the top. Notice the similarity to our plot of height and weight for people (Figure 18.12). Stars, like people, are not distributed over the diagram at random, as they would be if they exhibited all combinations of luminosity and temperature. Instead, we see that the stars cluster into certain parts of the H\u2013R diagram. The great majority are aligned along a narrow sequence running from the upper left (hot, highly luminous) to the lower right (cool, less luminous). This band of points is called the\u00a0<span id=\"term1012\" data-type=\"term\">main sequence<\/span>. It represents a relationship between\u00a0<em data-effect=\"italics\">temperature<\/em>\u00a0and\u00a0<em data-effect=\"italics\">luminosity<\/em>\u00a0that is followed by most stars. We can summarize this relationship by saying that hotter stars are more luminous than cooler ones.<\/p>\r\n<p id=\"fs-id1164754918619\">A number of stars, however, lie above the main sequence on the H\u2013R diagram, in the upper-right region, where stars have low temperature and high luminosity. How can a star be at once cool, meaning each square meter on the star does not put out all that much energy, and yet very luminous? The only way is for the star to be enormous\u2014to have so many square meters on its surface that the\u00a0<em data-effect=\"italics\">total<\/em>\u00a0energy output is still large. These stars must be\u00a0<em data-effect=\"italics\">giants<\/em>\u00a0or\u00a0<em data-effect=\"italics\">supergiants<\/em>, the stars of huge diameter we discussed earlier.<\/p>\r\n<p id=\"fs-id1164754962482\">There are also some stars in the lower-left corner of the diagram, which have high temperature and low luminosity. If they have high surface temperatures, each square meter on that star puts out a lot of energy. How then can the overall star be dim? It must be that it has a very small total surface area; such stars are known as\u00a0<span id=\"term1013\" data-type=\"term\">white dwarfs<\/span>\u00a0(white because, at these high temperatures, the colors of the electromagnetic radiation that they emit blend together to make them look bluish-white). We will say more about these puzzling objects in a moment.\u00a0Figure 18.15\u00a0is a schematic H\u2013R diagram for a large sample of stars, drawn to make the different types more apparent.<\/p>\r\n\r\n<div id=\"OSC_Astro_18_04_HR\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_18_04_HR\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"475\"]<img id=\"9\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/c2acb4a460838ff7561e020a9b3aae92008c2367\" alt=\"Schematic H\u2013R Diagram for Many Stars. In this graph the vertical axis is labeled \u201cLuminosity (LSun)\u201d, running from 10-4 to 106 in increments of 102. The horizontal axis is labeled \u201cSpectral class\u201d, and is divided into seven equal length units. From left to right they are labeled \u201cO\u201d, \u201cB\u201d, \u201cA\u201d, \u201cF\u201d, \u201cG\u201d, \u201cK\u201d and \u201cM\u201d. The horizontal axis is also labeled \u201cTemperature (K)\u201d, running from 25,000 on the left to 3,000 on the right. The five main classes of stars are plotted. Beginning at lower left is an isolated group of stars labeled \u201cWhite Dwarfs\u201d. The majority of stars lie on the \u201cMain Sequence\u201d, which runs diagonally from upper left to lower right. The lower right part of the main sequence is labeled \u201cRed dwarfs\u201d. Running horizontally from the center of the graph to the right is the narrow band of \u201cRed giants\u201d. Finally, a small number of stars running horizontally across the entire top of the graph are the \u201cSupergiants\u201d.\" width=\"475\" height=\"415\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a018.15<\/strong>\u00a0Schematic H\u2013R Diagram for Many Stars.\u00a0Ninety percent of all stars on such a diagram fall along a narrow band called the main sequence. A minority of stars are found in the upper right; they are both cool (and hence red) and bright, and must be giants. Some stars fall in the lower left of the diagram; they are both hot and dim, and must be white dwarfs.[\/caption]<\/figure>\r\n<\/div>\r\n<p id=\"fs-id1164754874785\">Now, think back to our discussion of star surveys. It is difficult to plot an H\u2013R diagram that is truly representative of all stars because most stars are so faint that we cannot see those outside our immediate neighborhood. The stars plotted in\u00a0Figure 18.14\u00a0were selected because their distances are known. This sample omits many intrinsically faint stars that are nearby but have not had their distances measured, so it shows fewer faint main-sequence stars than a \u201cfair\u201d diagram would. To be truly representative of the stellar population, an H\u2013R diagram should be plotted for all stars within a certain distance. Unfortunately, our knowledge is reasonably complete only for stars within 10 to 20 light-years of the Sun, among which there are no giants or supergiants. Still, from many surveys (and more can now be done with new, more powerful telescopes), we estimate that about 90% of the true stars overall (excluding brown dwarfs) in our part of space are main-sequence stars, about 10% are white dwarfs, and fewer than 1% are giants or supergiants.<\/p>\r\n<p id=\"fs-id1164754898053\">These estimates can be used directly to understand the lives of stars. Permit us another quick analogy with people. Suppose we survey people just like astronomers survey stars, but we want to focus our attention on the location of young people, ages 6 to 18 years. Survey teams fan out and take data about where such youngsters are found at all times during a 24-hour day. Some are found in the local pizza parlor, others are asleep at home, some are at the movies, and many are in school. After surveying a very large number of young people, one of the things that the teams determine is that, averaged over the course of the 24 hours, one-third of all youngsters are found in school.<\/p>\r\n<p id=\"fs-id1164754920602\">How can they interpret this result? Does it mean that two-thirds of students are truants and the remaining one-third spend all their time in school? No, we must bear in mind that the survey teams counted youngsters throughout the full 24-hour day. Some survey teams worked at night, when most youngsters were at home asleep, and others worked in the late afternoon, when most youngsters were on their way home from school (and more likely to be enjoying a pizza). If the survey was truly representative, we\u00a0<em data-effect=\"italics\">can<\/em>\u00a0conclude, however, that if an average of one-third of all youngsters are found in school, then humans ages 6 to 18 years must spend about one-third of\u00a0<em data-effect=\"italics\">their time<\/em>\u00a0in school.<\/p>\r\n<p id=\"fs-id1164755040740\">We can do something similar for stars. We find that, on average, 90% of all stars are located on the main sequence of the H\u2013R diagram. If we can identify some activity or life stage with the main sequence, then it follows that stars must spend 90% of their lives in that activity or life stage.<\/p>\r\n\r\n<\/section><section id=\"fs-id1164754964802\" data-depth=\"1\">\r\n<h3 data-type=\"title\">Understanding the Main Sequence<\/h3>\r\n<p id=\"fs-id1164754963249\">In\u00a0The Sun: A Nuclear Powerhouse, we discussed the Sun as a representative star. We saw that what stars such as the Sun \u201cdo for a living\u201d is to convert protons into helium deep in their interiors via the process of nuclear fusion, thus producing energy. The fusion of protons to helium is an excellent, long-lasting source of energy for a star because the bulk of every star consists of hydrogen atoms, whose nuclei are protons.<\/p>\r\n<p id=\"fs-id1164754973422\">Our computer models of how stars evolve over time show us that a typical star will spend about 90% of its life fusing the abundant hydrogen in its core into helium. This then is a good explanation of why 90% of all stars are found on the main sequence in the H\u2013R diagram. But if all the stars on the\u00a0<span id=\"term1014\" class=\"no-emphasis\" data-type=\"term\">main sequence<\/span>\u00a0are doing the same thing (fusing hydrogen), why are they distributed along a sequence of points? That is, why do they differ in luminosity and surface temperature (which is what we are plotting on the H\u2013R diagram)?<\/p>\r\n<p id=\"fs-id1164754979264\">To help us understand how main-sequence stars differ, we can use one of the most important results from our studies of model stars. Astrophysicists have been able to show that the structure of stars that are in equilibrium and derive all their energy from nuclear fusion is completely and uniquely determined by just two quantities: the\u00a0<em data-effect=\"italics\">total mass<\/em>\u00a0and the\u00a0<em data-effect=\"italics\">composition<\/em>\u00a0of the star. This fact provides an interpretation of many features of the H\u2013R diagram.<\/p>\r\n<p id=\"fs-id1164755031742\">Imagine a cluster of stars forming from a cloud of interstellar \u201craw material\u201d whose chemical composition is similar to the Sun\u2019s. (We\u2019ll describe this process in more detail in\u00a0The Birth of Stars and Discovery of Planets outside the Solar System, but for now, the details will not concern us.) In such a cloud, all the clumps of gas and dust that become stars begin with the same chemical composition and differ from one another only in mass. Now suppose that we compute a model of each of these stars for the time at which it becomes stable and derives its energy from nuclear reactions, but before it has time to alter its composition appreciably as a result of these reactions.<\/p>\r\n<p id=\"fs-id1164754897108\">The models calculated for these stars allow us to determine their luminosities, temperatures, and sizes. If we plot the results from the models\u2014one point for each model star\u2014on the H\u2013R diagram, we get something that looks just like the main sequence we saw for real stars.<\/p>\r\n<p id=\"fs-id1164755024469\">And here is what we find when we do this. The model stars with the largest masses are the hottest and most luminous, and they are located at the upper left of the diagram.<\/p>\r\n<p id=\"fs-id1164754917569\">The least-massive model stars are the coolest and least luminous, and they are placed at the lower right of the plot. The other model stars all lie along a line running diagonally across the diagram. In other words,\u00a0<em data-effect=\"italics\">the main sequence turns out to be a sequence of stellar masses<\/em>.<\/p>\r\n<p id=\"fs-id1164755043934\">This makes sense if you think about it. The most massive stars have the most gravity and can thus compress their centers to the greatest degree. This means they are the hottest inside and the best at generating energy from nuclear reactions deep within. As a result, they shine with the greatest luminosity and have the hottest surface temperatures. The stars with lowest mass, in turn, are the coolest inside and least effective in generating energy. Thus, they are the least luminous and wind up being the coolest on the surface. Our Sun lies somewhere in the middle of these extremes (as you can see in\u00a0Figure 18.14). The characteristics of representative\u00a0<span id=\"term1015\" class=\"no-emphasis\" data-type=\"term\">main-sequence stars<\/span>\u00a0(excluding brown dwarfs, which are not true stars) are listed in\u00a0Table 18.3.<\/p>\r\n\r\n<div class=\"os-table os-top-titled-container\">\r\n<div class=\"os-table-title\"><\/div>\r\n<table id=\"fs-id1164755015460\" class=\"grid landscape aligncenter\"><caption>Table 18.3 Characteristics of Main-Sequence Stars<\/caption>\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Spectral Type<\/th>\r\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Mass (Sun = 1)<\/th>\r\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Luminosity (Sun = 1)<\/th>\r\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Temperature<\/th>\r\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Radius (Sun = 1)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">O5<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">40<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">[latex]7 \\times {10^5}[\/latex]<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">40,000 K<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">18<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">B0<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">16<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">[latex]2.7 \\times {10^5}[\/latex]<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">28,000 K<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">7<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">A0<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">3.3<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">55<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">10,000 K<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">2.5<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">F0<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">1.7<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">5<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">7500 K<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">1.4<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">G0<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">1.1<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">1.4<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">6000 K<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">1.1<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">K0<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">0.8<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">0.35<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">5000 K<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">0.8<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-valign=\"top\" data-align=\"left\">M0<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">0.4<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">0.05<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">3500 K<\/td>\r\n<td data-valign=\"top\" data-align=\"left\">0.6<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><span style=\"text-align: initial;font-size: 1em\">Note that we\u2019ve seen this 90% figure come up before. This is exactly what we found earlier when we examined the mass-luminosity relation (<\/span>Figure 18.9<span style=\"text-align: initial;font-size: 1em\">). We observed that 90% of all stars seem to follow the relationship; these are the 90% of all stars that lie on the main sequence in our H\u2013R diagram. Our models and our observations agree.<\/span><\/div>\r\n<\/div>\r\n<p id=\"fs-id1164755049188\">What about the other stars on the H\u2013R diagram\u2014the giants and supergiants, and the white dwarfs? As we will see in the next few chapters, these are what main-sequence stars turn into as they age: They are the later stages in a star\u2019s life. As a star consumes its nuclear fuel, its source of energy changes, as do its chemical composition and interior structure. These changes cause the star to alter its luminosity and surface temperature so that it no longer lies on the main sequence on our diagram. Because stars spend much less time in these later stages of their lives, we see fewer stars in those regions of the H\u2013R diagram.<\/p>\r\n\r\n<\/section><section id=\"fs-id1164754997938\" data-depth=\"1\">\r\n<h3 data-type=\"title\">Extremes of Stellar Luminosities, Diameters, and Densities<\/h3>\r\n<p id=\"fs-id1164755012037\">We can use the H\u2013R diagram to explore the extremes in size, luminosity, and density found among the stars. Such extreme stars are not only interesting to fans of the\u00a0<em data-effect=\"italics\">Guinness Book of World Records<\/em>; they can teach us a lot about how stars work. For example, we saw that the most massive main-sequence stars are the most luminous ones. We know of a few extreme stars that are a million times more luminous than the Sun, with masses that exceed 100 times the Sun\u2019s mass. These superluminous stars, which are at the upper left of the H\u2013R diagram, are exceedingly hot, very blue stars of spectral type O. These are the stars that would be the most conspicuous at vast distances in space.<\/p>\r\n<p id=\"fs-id1164755016804\">The cool supergiants in the upper corner of the H\u2013R diagram are as much as 10,000 times as luminous as the Sun. In addition, these stars have diameters very much larger than that of the Sun. As discussed above, some supergiants are so large that if the solar system could be centered in one, the star\u2019s surface would lie beyond the orbit of Mars (see\u00a0Figure 18.16). We will have to ask, in coming chapters, what process can make a star swell up to such an enormous size, and how long these \u201cswollen\u201d stars can last in their distended state.<\/p>\r\n\r\n<div id=\"OSC_Astro_18_04_SizeCompare\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_18_04_SizeCompare\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"975\"]<img id=\"11\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/7f975ced5337d7e283eace0b8e73570cded443fa\" alt=\"Illustration of the Sun and a Supergiant Star. At left, the supergiant star VY Canis Majoris is shown as a large yellow sphere. At the bottom left edge of the supergiant a small rectangle is drawn. This area is enlarged in the inset at right. The Sun is shown as a tiny dot surrounded by a dashed circle representing Earth\u2019s orbit. The surface of the supergiant is drawn running diagonally across the upper right half of the enlargement. The Sun and the orbit of Earth would fit inside VY Canis Majoris many times over.\" width=\"975\" height=\"550\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a018.16<\/strong>\u00a0The Sun and a Supergiant.\u00a0Here you see how small the Sun looks in comparison to one of the largest known stars: VY Canis Majoris, a supergiant.[\/caption]<\/figure>\r\n<\/div>\r\n<p id=\"fs-id1164755007489\">In contrast, the very common red, cool, low-luminosity stars at the lower end of the main sequence are much smaller and more compact than the Sun. An example of such a red dwarf is Ross 614B, with a surface temperature of 2700 K and only 1\/2000 of the Sun\u2019s luminosity. We call such a star a dwarf because its diameter is only 1\/10 that of the Sun. A star with such a low luminosity also has a low mass (about 1\/12 that of the Sun). This combination of mass and diameter means that it is so compressed that the star has an average density about 80 times that of the Sun. Its density must be higher, in fact, than that of any known solid found on the surface of Earth. (Despite this, the star is made of gas throughout because its center is so hot.)<\/p>\r\n<p id=\"fs-id1164755024621\">The faint, red, main-sequence stars are not the stars of the most extreme densities, however. The white dwarfs, at the lower-left corner of the H\u2013R diagram, have densities many times greater still.<\/p>\r\n\r\n<\/section><section id=\"fs-id1164755047022\" data-depth=\"1\">\r\n<h3 data-type=\"title\">The White Dwarfs<\/h3>\r\n<p id=\"fs-id1164755020363\">The first\u00a0<span id=\"term1016\" class=\"no-emphasis\" data-type=\"term\">white dwarf<\/span>\u00a0star was detected in 1862. Called\u00a0<span id=\"term1017\" class=\"no-emphasis\" data-type=\"term\">Sirius<\/span>\u00a0B, it forms a binary system with Sirius A, the brightest-appearing star in the sky. It eluded discovery and analysis for a long time because its faint light tends to be lost in the glare of nearby Sirius A (Figure 18.17). (Since Sirius is often called the Dog Star\u2014being the brightest star in the constellation of Canis Major, the big dog\u2014Sirius B is sometimes nicknamed the Pup.)<\/p>\r\n\r\n<div id=\"OSC_Astro_18_04_Sirius\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_18_04_Sirius\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"731\"]<img id=\"13\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/91d39cd7a7d3556757d4d368de877b06ffdb0ec6\" alt=\"Two Views of Sirius and Its White Dwarf Companion. (a) A visible light image taken by the Hubble Space Telescope. Sirius B is the faint speck in the lower left had quadrant of the image, and nearly lost in the glare of bright Sirius A. (b) X-ray image from the Chandra X-ray telescope. Sirius B is much brighter in X-rays and is the bright object at the center of the image. Above and slightly to the right is Sirius A.\" width=\"731\" height=\"348\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a018.17<\/strong>\u00a0Two Views of Sirius and Its White Dwarf Companion.\u00a0(a) The (visible light) image, taken with the Hubble Space Telescope, shows bright Sirius A, and, below it and off to its left, faint Sirius B. (b) This image of the\u00a0Sirius\u00a0star system was taken with the Chandra X-Ray Telescope. Now, the bright object is the white dwarf companion, Sirius B. Sirius A is the faint object above it; what we are seeing from Sirius is probably not actually X-ray radiation but rather ultraviolet light that has leaked into the detector. Note that the ultraviolet intensities of these two objects are completely reversed from the situation in visible light because Sirius B is hotter and emits more higher-frequency radiation. (credit a: modification of work by NASA, H.E. Bond and E. Nelan (Space Telescope Science Institute), M. Barstow and M. Burleigh (University of Leicester) and J.B. Holberg (University of Arizona); credit b: modification of work by NASA\/SAO\/CXC)[\/caption]<\/figure>\r\n<\/div>\r\n<p id=\"fs-id1164755043950\">We have now found thousands of white dwarfs.\u00a0Table 18.1\u00a0shows that about 7% of the true stars (spectral types O\u2013M) in our local neighborhood are white dwarfs. A good example of a typical white dwarf is the nearby star 40 Eridani B. Its surface temperature is a relatively hot 12,000 K, but its luminosity is only [latex]1\/275\\;{{\\rm{L}}_{{\\rm{Sun}}}}[\/latex]. Calculations show that its radius is only 1.4% of the Sun\u2019s, or about the same as that of Earth, and its volume is [latex]2.5 \\times {10^{-6}}[\/latex]\u00a0that of the Sun. Its mass, however, is 0.57 times the Sun\u2019s mass, just a little more than half. To fit such a substantial mass into so tiny a volume, the star\u2019s density must be about 210,000 times the density of the Sun, or more than [latex]300,000\\:{\\rm{g\/c}}{{\\rm{m}}^3}[\/latex]. A teaspoonful of this material would have a mass of some 1.6 tons! At such enormous densities, matter cannot exist in its usual state; we will examine the particular behavior of this type of matter in\u00a0<a href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/23-thinking-ahead\" data-page-slug=\"23-thinking-ahead\" data-page-uuid=\"8e460daa-be2b-47de-9d38-ab4c21865a8a\" data-page-fragment=\"\">The Death of Stars<\/a>. For now, we just note that white dwarfs are dying stars, reaching the end of their productive lives and ready for their stories to be over.<\/p>\r\n<p id=\"fs-id1164754998767\">The British astrophysicist (and science popularizer) Arthur\u00a0<span id=\"term1019\" class=\"no-emphasis\" data-type=\"term\">Eddington<\/span>\u00a0(1882\u20131944) described the first known white dwarf this way:<\/p>\r\n\r\n<blockquote id=\"fs-id1166568961029\">\r\n<p id=\"fs-id1164754918889\">The message of the companion of\u00a0<span id=\"term1020\" class=\"no-emphasis\" data-type=\"term\">Sirius<\/span>, when decoded, ran: \u201cI am composed of material three thousand times denser than anything you\u2019ve ever come across. A ton of my material would be a little nugget you could put in a matchbox.\u201d What reply could one make to something like that? Well, the reply most of us made in 1914 was, \u201cShut up; don\u2019t talk nonsense.\u201d<\/p>\r\n<\/blockquote>\r\n<p id=\"fs-id1164755031779\">Today, however, astronomers not only accept that stars as dense as white dwarfs exist but (as we will see) have found even denser and stranger objects in their quest to understand the evolution of different types of stars.<\/p>\r\n\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<h3 class=\"textbox__title\">Link to Learning<\/h3>\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nUse this\u00a0<a href=\"https:\/\/openstax.org\/l\/30interhr\" target=\"_blank\" rel=\"noopener nofollow noreferrer\">interactive H-R diagram<\/a> to explore the sizes of stars based on their placement. Overlay the closest stars and the brightest stars, and consider where they lie on the figure. How many stars are among both the closest and brightest stars?\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"textbox\">This book was adapted from the following: Fraknoi, A., Morrison, D., &amp; Wolff, S. C. (2016). 18.4 The H\u2013R Diagram In <i>Astronomy<\/i>. OpenStax. https:\/\/openstax.org\/books\/astronomy\/pages\/18-4-the-h-r-diagram under a <a href=\"http:\/\/creativecommons.org\/licenses\/by\/4.0\/\" target=\"_blank\" rel=\"noopener noreferrer\">Creative Commons Attribution License 4.0<\/a><\/div>\r\n<div>Access the entire book for free at\u00a0<a href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction\">https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction<\/a><\/div>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<h3 class=\"textbox__title\">Learning Objectives<\/h3>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168583487547\">By the end of this section, you will be able to:<\/p>\n<ul id=\"fs-id1164754873184\">\n<li>Identify the physical characteristics of stars that are used to create an H\u2013R diagram, and describe how those characteristics vary among groups of stars<\/li>\n<li>Discuss the physical properties of most stars found at different locations on the H\u2013R diagram, such as radius, and for main sequence stars, mass<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1164755043750\">In this chapter and\u00a0Analyzing Starlight, we described some of the characteristics by which we might classify stars and how those are measured. These ideas are summarized in\u00a0Table 18.2. We have also given an example of a relationship between two of these characteristics in the mass-luminosity relation. When the characteristics of large numbers of stars were measured at the beginning of the twentieth century, astronomers were able to begin a deeper search for patterns and relationships in these data.<\/p>\n<div class=\"os-table os-top-titled-container\">\n<table id=\"fs-id1164755038804\" class=\"grid landscape aligncenter\">\n<caption>Table 18.2 Measuring the Characteristics of Stars<\/caption>\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Characteristic<\/th>\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Technique<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Surface temperature<\/td>\n<td data-valign=\"top\" data-align=\"left\">\n<p id=\"fs-id1164754986804\">1. Determine the color (very rough).<\/p>\n<p id=\"fs-id1164754896265\">2. Measure the spectrum and get the spectral type.<\/p>\n<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Chemical composition<\/td>\n<td data-valign=\"top\" data-align=\"left\">Determine which lines are present in the spectrum.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Luminosity<\/td>\n<td data-valign=\"top\" data-align=\"left\">Measure the apparent brightness and compensate for distance.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Radial velocity<\/td>\n<td data-valign=\"top\" data-align=\"left\">Measure the Doppler shift in the spectrum.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Rotation<\/td>\n<td data-valign=\"top\" data-align=\"left\">Measure the width of spectral lines.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Mass<\/td>\n<td data-valign=\"top\" data-align=\"left\">Measure the period and radial velocity curves of spectroscopic binary stars.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Diameter<\/td>\n<td data-valign=\"top\" data-align=\"left\">\n<p id=\"fs-id1164754936599\">1. Measure the way a star\u2019s light is blocked by the Moon.<\/p>\n<p id=\"fs-id1164754867630\">2. Measure the light curves and Doppler shifts for eclipsing binary stars.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><span style=\"text-align: initial;font-size: 1em\">To help understand what sorts of relationships might be found, let\u2019s look briefly at a range of data about human beings. If you want to understand humans by comparing and contrasting their characteristics\u2014without assuming any previous knowledge of these strange creatures\u2014you could try to determine which characteristics lead you in a fruitful direction. For example, you might plot the heights of a large sample of humans against their weights (which is a measure of their mass). Such a plot is shown in <\/span>Figure 18.12<span style=\"text-align: initial;font-size: 1em\">\u00a0and it has some interesting features. In the way we have chosen to present our data, height increases upward, whereas weight increases to the left. Notice that humans are not randomly distributed in the graph. Most points fall along a sequence that goes from the upper left to the lower right.<\/span><\/div>\n<\/div>\n<div id=\"OSC_Astro_18_04_Plot\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_18_04_Plot\">\n<figure style=\"width: 425px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"2\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/218800a404be404d0251305e0390f1ddaa231ab1\" alt=\"Graph of Height Versus Weight. The vertical axis is labeled \u201cHeight\u201d in arbitrary units. The horizontal axis is labeled \u201cWeight\u201d in arbitrary units. A plot of dots shows a general trend of weight increasing as height increases, with a few outliers above and below.\" width=\"425\" height=\"347\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a018.12<\/strong>\u00a0Height versus Weight.\u00a0The plot of the heights and weights of a representative group of human beings. Most points lie along a \u201cmain sequence\u201d representing most people, but there are a few exceptions.<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<p id=\"fs-id1164754908886\">We can conclude from this graph that human height and weight are related. Generally speaking, taller human beings weigh more, whereas shorter ones weigh less. This makes sense if you are familiar with the structure of human beings. Typically, if we have bigger bones, we have more flesh to fill out our larger frame. It\u2019s not mathematically exact\u2014there is a wide range of variation\u2014but it\u2019s not a bad overall rule. And, of course, there are some dramatic exceptions. You occasionally see a short human who is very overweight and would thus be more to the bottom left of our diagram than the average sequence of people. Or you might have a very tall, skinny fashion model with great height but relatively small weight, who would be found near the upper right.<\/p>\n<p id=\"fs-id1164754920163\">A similar diagram has been found extremely useful for understanding the lives of stars. In 1913, American astronomer Henry Norris\u00a0<span id=\"term1008\" class=\"no-emphasis\" data-type=\"term\">Russell<\/span>\u00a0plotted the luminosities of stars against their spectral classes (a way of denoting their surface temperatures). This investigation, and a similar independent study in 1911 by Danish astronomer Ejnar\u00a0<span id=\"term1009\" class=\"no-emphasis\" data-type=\"term\">Hertzsprung<\/span>, led to the extremely important discovery that the temperature and luminosity of stars are related (Figure 18.13).<\/p>\n<div id=\"OSC_Astro_18_04_Russell\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_18_04_Russell\">\n<figure style=\"width: 487px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"4\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/e813f96008962b451d884936c8c7c29faee8293d\" alt=\"Photographs of (a) Ejnar Hertzsprung and (b) Henry Norris Russell.\" width=\"487\" height=\"317\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a018.13<\/strong>\u00a0Hertzsprung (1873\u20131967) and Russell (1877\u20131957).\u00a0(a) Ejnar Hertzsprung and (b) Henry Norris Russell independently discovered the relationship between the luminosity and surface temperature of stars that is summarized in what is now called the H\u2013R diagram.<\/figcaption><\/figure>\n<\/figure>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<h3 class=\"textbox__title\">Voyagers in Astronomy<\/h3>\n<\/header>\n<div class=\"textbox__content\">\n<h4 id=\"5\" class=\"os-subtitle\" data-type=\"title\"><span class=\"os-subtitle-label\">Henry Norris Russell<\/span><\/h4>\n<p id=\"fs-id1164754868000\">When Henry Norris\u00a0<span id=\"term1010\" class=\"no-emphasis\" data-type=\"term\">Russell<\/span>\u00a0graduated from Princeton University, his work had been so brilliant that the faculty decided to create a new level of honors degree beyond \u201csumma cum laude\u201d for him. His students later remembered him as a man whose thinking was three times faster than just about anybody else\u2019s. His memory was so phenomenal, he could correctly quote an enormous number of poems and limericks, the entire Bible, tables of mathematical functions, and almost anything he had learned about astronomy. He was nervous, active, competitive, critical, and very articulate; he tended to dominate every meeting he attended. In outward appearance, he was an old-fashioned product of the nineteenth century who wore high-top black shoes and high starched collars, and carried an umbrella every day of his life. His 264 papers were enormously influential in many areas of astronomy.<\/p>\n<p id=\"fs-id1164755015876\">Born in 1877, the son of a Presbyterian minister, Russell showed early promise. When he was 12, his family sent him to live with an aunt in Princeton so he could attend a top preparatory school. He lived in the same house in that town until his death in 1957 (interrupted only by a brief stay in Europe for graduate work). He was fond of recounting that both his mother and his maternal grandmother had won prizes in mathematics, and that he probably inherited his talents in that field from their side of the family.<\/p>\n<p id=\"fs-id1164754948440\">Before Russell, American astronomers devoted themselves mainly to surveying the stars and making impressive catalogs of their properties, especially their spectra (as described in\u00a0Analyzing Starlight). Russell began to see that interpreting the spectra of stars required a much more sophisticated understanding of the physics of the atom, a subject that was being developed by European physicists in the 1910s and 1920s. Russell embarked on a lifelong quest to ascertain the physical conditions inside stars from the clues in their spectra; his work inspired, and was continued by, a generation of astronomers, many trained by Russell and his collaborators.<\/p>\n<p id=\"fs-id1164754872780\">Russell also made important contributions in the study of binary stars and the measurement of star masses, the origin of the solar system, the atmospheres of planets, and the measurement of distances in astronomy, among other fields. He was an influential teacher and popularizer of astronomy, writing a column on astronomical topics for\u00a0<em data-effect=\"italics\">Scientific American<\/em>\u00a0magazine for more than 40 years. He and two colleagues wrote a textbook for college astronomy classes that helped train astronomers and astronomy enthusiasts over several decades. That book set the scene for the kind of textbook you are now reading, which not only lays out the facts of astronomy but also explains how they fit together. Russell gave lectures around the country, often emphasizing the importance of understanding modern physics in order to grasp what was happening in astronomy.<\/p>\n<p id=\"fs-id1164755012180\">Harlow Shapley, director of the Harvard College Observatory, called Russell \u201cthe dean of American astronomers.\u201d Russell was certainly regarded as the leader of the field for many years and was consulted on many astronomical problems by colleagues from around the world. Today, one of the highest recognitions that an astronomer can receive is an award from the American Astronomical Society called the Russell Prize, set up in his memory.<\/p>\n<\/div>\n<\/div>\n<section id=\"fs-id1164755024160\" data-depth=\"1\">\n<h3 data-type=\"title\">Features of the H\u2013R Diagram<\/h3>\n<p id=\"fs-id1164754969298\">Following Hertzsprung and Russell, let us plot the temperature (or spectral class) of a selected group of nearby stars against their luminosity and see what we find (Figure 18.14). Such a plot is frequently called the\u00a0<em data-effect=\"italics\">Hertzsprung\u2013Russell diagram<\/em>, abbreviated\u00a0<span id=\"term1011\" data-type=\"term\">H\u2013R diagram<\/span>. It is one of the most important and widely used diagrams in astronomy, with applications that extend far beyond the purposes for which it was originally developed more than a century ago.<\/p>\n<div id=\"OSC_Astro_18_04_Sample\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_18_04_Sample\">\n<figure style=\"width: 706px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"7\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/dd3b626194347b820b300c0437928fdb31869efd\" alt=\"An H\u2013R Diagram for a Selected Sample of Stars. In this graph the vertical axis is labeled \u201cLuminosity (LSun)\u201d, running from 10-4 to 104 in increments of 102. The horizontal axis is labeled \u201cSpectral class\u201d, and is divided into seven equal length units. From left to right they are labeled \u201cO\u201d, \u201cB\u201d, \u201cA\u201d, \u201cF\u201d, \u201cG\u201d, \u201cK\u201d and \u201cM\u201d. The horizontal axis is also labeled \u201cTemperature (K)\u201d, running from 25,000 on the left to 3,000 on the right. The background of the graph is colored to represent temperature. The O-B section is blue, the A and most of F is green, G is yellow and the K-M section is red. The stars plotted in the diagram fall into four distinct groups. At lower left between spectral types A and F are the \u201cWhite Dwarfs\u201d. Running diagonally across the entire diagram from upper left to lower right is the \u201cMain Sequence\u201d, where most stars lie. The \u201cGiants\u201d lie on a horizontal line at 102 L(Sun) between spectral types G and M. The \u201cSupergiants\u201d are in the upper right. Many well-known stars are plotted in this diagram. The \u201cCompanion of Sirius\u201d is among the white dwarfs. Along the main sequence, from left to right, are \u201dSpica\u201d, \u201cVega\u201d, \u201cSirius\u201d, \u201cProcyon\u201d, \u201cAlpha Centauri A\u201d, \u201cSun\u201d, \u201cTau Ceti\u201d, \u201cBarnard\u2019s Star\u201d and \u201cProxima Centauri\u201d. Along the giant branch from left to right we find \u201cCapella\u201d, \u201cArcturus\u201d and \u201cAldebaran\u201d. Finally, the supergiants from left to right, \u201cRigel\u201d, \u201cCanopus\u201d, \u201cBetelgeuse\u201d and \u201cAntares\u201d.\" width=\"706\" height=\"642\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a018.14<\/strong>\u00a0H\u2013R Diagram for a Selected Sample of Stars.\u00a0In such diagrams, luminosity is plotted along the vertical axis. Along the horizontal axis, we can plot either temperature or spectral type (also sometimes called spectral class). Several of the brightest stars are identified by name. Most stars fall on the main sequence.<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<p id=\"fs-id1164754914170\">It is customary to plot H\u2013R diagrams in such a way that temperature increases toward the left and luminosity toward the top. Notice the similarity to our plot of height and weight for people (Figure 18.12). Stars, like people, are not distributed over the diagram at random, as they would be if they exhibited all combinations of luminosity and temperature. Instead, we see that the stars cluster into certain parts of the H\u2013R diagram. The great majority are aligned along a narrow sequence running from the upper left (hot, highly luminous) to the lower right (cool, less luminous). This band of points is called the\u00a0<span id=\"term1012\" data-type=\"term\">main sequence<\/span>. It represents a relationship between\u00a0<em data-effect=\"italics\">temperature<\/em>\u00a0and\u00a0<em data-effect=\"italics\">luminosity<\/em>\u00a0that is followed by most stars. We can summarize this relationship by saying that hotter stars are more luminous than cooler ones.<\/p>\n<p id=\"fs-id1164754918619\">A number of stars, however, lie above the main sequence on the H\u2013R diagram, in the upper-right region, where stars have low temperature and high luminosity. How can a star be at once cool, meaning each square meter on the star does not put out all that much energy, and yet very luminous? The only way is for the star to be enormous\u2014to have so many square meters on its surface that the\u00a0<em data-effect=\"italics\">total<\/em>\u00a0energy output is still large. These stars must be\u00a0<em data-effect=\"italics\">giants<\/em>\u00a0or\u00a0<em data-effect=\"italics\">supergiants<\/em>, the stars of huge diameter we discussed earlier.<\/p>\n<p id=\"fs-id1164754962482\">There are also some stars in the lower-left corner of the diagram, which have high temperature and low luminosity. If they have high surface temperatures, each square meter on that star puts out a lot of energy. How then can the overall star be dim? It must be that it has a very small total surface area; such stars are known as\u00a0<span id=\"term1013\" data-type=\"term\">white dwarfs<\/span>\u00a0(white because, at these high temperatures, the colors of the electromagnetic radiation that they emit blend together to make them look bluish-white). We will say more about these puzzling objects in a moment.\u00a0Figure 18.15\u00a0is a schematic H\u2013R diagram for a large sample of stars, drawn to make the different types more apparent.<\/p>\n<div id=\"OSC_Astro_18_04_HR\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_18_04_HR\">\n<figure style=\"width: 475px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"9\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/c2acb4a460838ff7561e020a9b3aae92008c2367\" alt=\"Schematic H\u2013R Diagram for Many Stars. In this graph the vertical axis is labeled \u201cLuminosity (LSun)\u201d, running from 10-4 to 106 in increments of 102. The horizontal axis is labeled \u201cSpectral class\u201d, and is divided into seven equal length units. From left to right they are labeled \u201cO\u201d, \u201cB\u201d, \u201cA\u201d, \u201cF\u201d, \u201cG\u201d, \u201cK\u201d and \u201cM\u201d. The horizontal axis is also labeled \u201cTemperature (K)\u201d, running from 25,000 on the left to 3,000 on the right. The five main classes of stars are plotted. Beginning at lower left is an isolated group of stars labeled \u201cWhite Dwarfs\u201d. The majority of stars lie on the \u201cMain Sequence\u201d, which runs diagonally from upper left to lower right. The lower right part of the main sequence is labeled \u201cRed dwarfs\u201d. Running horizontally from the center of the graph to the right is the narrow band of \u201cRed giants\u201d. Finally, a small number of stars running horizontally across the entire top of the graph are the \u201cSupergiants\u201d.\" width=\"475\" height=\"415\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a018.15<\/strong>\u00a0Schematic H\u2013R Diagram for Many Stars.\u00a0Ninety percent of all stars on such a diagram fall along a narrow band called the main sequence. A minority of stars are found in the upper right; they are both cool (and hence red) and bright, and must be giants. Some stars fall in the lower left of the diagram; they are both hot and dim, and must be white dwarfs.<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<p id=\"fs-id1164754874785\">Now, think back to our discussion of star surveys. It is difficult to plot an H\u2013R diagram that is truly representative of all stars because most stars are so faint that we cannot see those outside our immediate neighborhood. The stars plotted in\u00a0Figure 18.14\u00a0were selected because their distances are known. This sample omits many intrinsically faint stars that are nearby but have not had their distances measured, so it shows fewer faint main-sequence stars than a \u201cfair\u201d diagram would. To be truly representative of the stellar population, an H\u2013R diagram should be plotted for all stars within a certain distance. Unfortunately, our knowledge is reasonably complete only for stars within 10 to 20 light-years of the Sun, among which there are no giants or supergiants. Still, from many surveys (and more can now be done with new, more powerful telescopes), we estimate that about 90% of the true stars overall (excluding brown dwarfs) in our part of space are main-sequence stars, about 10% are white dwarfs, and fewer than 1% are giants or supergiants.<\/p>\n<p id=\"fs-id1164754898053\">These estimates can be used directly to understand the lives of stars. Permit us another quick analogy with people. Suppose we survey people just like astronomers survey stars, but we want to focus our attention on the location of young people, ages 6 to 18 years. Survey teams fan out and take data about where such youngsters are found at all times during a 24-hour day. Some are found in the local pizza parlor, others are asleep at home, some are at the movies, and many are in school. After surveying a very large number of young people, one of the things that the teams determine is that, averaged over the course of the 24 hours, one-third of all youngsters are found in school.<\/p>\n<p id=\"fs-id1164754920602\">How can they interpret this result? Does it mean that two-thirds of students are truants and the remaining one-third spend all their time in school? No, we must bear in mind that the survey teams counted youngsters throughout the full 24-hour day. Some survey teams worked at night, when most youngsters were at home asleep, and others worked in the late afternoon, when most youngsters were on their way home from school (and more likely to be enjoying a pizza). If the survey was truly representative, we\u00a0<em data-effect=\"italics\">can<\/em>\u00a0conclude, however, that if an average of one-third of all youngsters are found in school, then humans ages 6 to 18 years must spend about one-third of\u00a0<em data-effect=\"italics\">their time<\/em>\u00a0in school.<\/p>\n<p id=\"fs-id1164755040740\">We can do something similar for stars. We find that, on average, 90% of all stars are located on the main sequence of the H\u2013R diagram. If we can identify some activity or life stage with the main sequence, then it follows that stars must spend 90% of their lives in that activity or life stage.<\/p>\n<\/section>\n<section id=\"fs-id1164754964802\" data-depth=\"1\">\n<h3 data-type=\"title\">Understanding the Main Sequence<\/h3>\n<p id=\"fs-id1164754963249\">In\u00a0The Sun: A Nuclear Powerhouse, we discussed the Sun as a representative star. We saw that what stars such as the Sun \u201cdo for a living\u201d is to convert protons into helium deep in their interiors via the process of nuclear fusion, thus producing energy. The fusion of protons to helium is an excellent, long-lasting source of energy for a star because the bulk of every star consists of hydrogen atoms, whose nuclei are protons.<\/p>\n<p id=\"fs-id1164754973422\">Our computer models of how stars evolve over time show us that a typical star will spend about 90% of its life fusing the abundant hydrogen in its core into helium. This then is a good explanation of why 90% of all stars are found on the main sequence in the H\u2013R diagram. But if all the stars on the\u00a0<span id=\"term1014\" class=\"no-emphasis\" data-type=\"term\">main sequence<\/span>\u00a0are doing the same thing (fusing hydrogen), why are they distributed along a sequence of points? That is, why do they differ in luminosity and surface temperature (which is what we are plotting on the H\u2013R diagram)?<\/p>\n<p id=\"fs-id1164754979264\">To help us understand how main-sequence stars differ, we can use one of the most important results from our studies of model stars. Astrophysicists have been able to show that the structure of stars that are in equilibrium and derive all their energy from nuclear fusion is completely and uniquely determined by just two quantities: the\u00a0<em data-effect=\"italics\">total mass<\/em>\u00a0and the\u00a0<em data-effect=\"italics\">composition<\/em>\u00a0of the star. This fact provides an interpretation of many features of the H\u2013R diagram.<\/p>\n<p id=\"fs-id1164755031742\">Imagine a cluster of stars forming from a cloud of interstellar \u201craw material\u201d whose chemical composition is similar to the Sun\u2019s. (We\u2019ll describe this process in more detail in\u00a0The Birth of Stars and Discovery of Planets outside the Solar System, but for now, the details will not concern us.) In such a cloud, all the clumps of gas and dust that become stars begin with the same chemical composition and differ from one another only in mass. Now suppose that we compute a model of each of these stars for the time at which it becomes stable and derives its energy from nuclear reactions, but before it has time to alter its composition appreciably as a result of these reactions.<\/p>\n<p id=\"fs-id1164754897108\">The models calculated for these stars allow us to determine their luminosities, temperatures, and sizes. If we plot the results from the models\u2014one point for each model star\u2014on the H\u2013R diagram, we get something that looks just like the main sequence we saw for real stars.<\/p>\n<p id=\"fs-id1164755024469\">And here is what we find when we do this. The model stars with the largest masses are the hottest and most luminous, and they are located at the upper left of the diagram.<\/p>\n<p id=\"fs-id1164754917569\">The least-massive model stars are the coolest and least luminous, and they are placed at the lower right of the plot. The other model stars all lie along a line running diagonally across the diagram. In other words,\u00a0<em data-effect=\"italics\">the main sequence turns out to be a sequence of stellar masses<\/em>.<\/p>\n<p id=\"fs-id1164755043934\">This makes sense if you think about it. The most massive stars have the most gravity and can thus compress their centers to the greatest degree. This means they are the hottest inside and the best at generating energy from nuclear reactions deep within. As a result, they shine with the greatest luminosity and have the hottest surface temperatures. The stars with lowest mass, in turn, are the coolest inside and least effective in generating energy. Thus, they are the least luminous and wind up being the coolest on the surface. Our Sun lies somewhere in the middle of these extremes (as you can see in\u00a0Figure 18.14). The characteristics of representative\u00a0<span id=\"term1015\" class=\"no-emphasis\" data-type=\"term\">main-sequence stars<\/span>\u00a0(excluding brown dwarfs, which are not true stars) are listed in\u00a0Table 18.3.<\/p>\n<div class=\"os-table os-top-titled-container\">\n<div class=\"os-table-title\"><\/div>\n<table id=\"fs-id1164755015460\" class=\"grid landscape aligncenter\">\n<caption>Table 18.3 Characteristics of Main-Sequence Stars<\/caption>\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Spectral Type<\/th>\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Mass (Sun = 1)<\/th>\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Luminosity (Sun = 1)<\/th>\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Temperature<\/th>\n<th scope=\"col\" data-valign=\"top\" data-align=\"center\">Radius (Sun = 1)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">O5<\/td>\n<td data-valign=\"top\" data-align=\"left\">40<\/td>\n<td data-valign=\"top\" data-align=\"left\">[latex]7 \\times {10^5}[\/latex]<\/td>\n<td data-valign=\"top\" data-align=\"left\">40,000 K<\/td>\n<td data-valign=\"top\" data-align=\"left\">18<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">B0<\/td>\n<td data-valign=\"top\" data-align=\"left\">16<\/td>\n<td data-valign=\"top\" data-align=\"left\">[latex]2.7 \\times {10^5}[\/latex]<\/td>\n<td data-valign=\"top\" data-align=\"left\">28,000 K<\/td>\n<td data-valign=\"top\" data-align=\"left\">7<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">A0<\/td>\n<td data-valign=\"top\" data-align=\"left\">3.3<\/td>\n<td data-valign=\"top\" data-align=\"left\">55<\/td>\n<td data-valign=\"top\" data-align=\"left\">10,000 K<\/td>\n<td data-valign=\"top\" data-align=\"left\">2.5<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">F0<\/td>\n<td data-valign=\"top\" data-align=\"left\">1.7<\/td>\n<td data-valign=\"top\" data-align=\"left\">5<\/td>\n<td data-valign=\"top\" data-align=\"left\">7500 K<\/td>\n<td data-valign=\"top\" data-align=\"left\">1.4<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">G0<\/td>\n<td data-valign=\"top\" data-align=\"left\">1.1<\/td>\n<td data-valign=\"top\" data-align=\"left\">1.4<\/td>\n<td data-valign=\"top\" data-align=\"left\">6000 K<\/td>\n<td data-valign=\"top\" data-align=\"left\">1.1<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">K0<\/td>\n<td data-valign=\"top\" data-align=\"left\">0.8<\/td>\n<td data-valign=\"top\" data-align=\"left\">0.35<\/td>\n<td data-valign=\"top\" data-align=\"left\">5000 K<\/td>\n<td data-valign=\"top\" data-align=\"left\">0.8<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">M0<\/td>\n<td data-valign=\"top\" data-align=\"left\">0.4<\/td>\n<td data-valign=\"top\" data-align=\"left\">0.05<\/td>\n<td data-valign=\"top\" data-align=\"left\">3500 K<\/td>\n<td data-valign=\"top\" data-align=\"left\">0.6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><span style=\"text-align: initial;font-size: 1em\">Note that we\u2019ve seen this 90% figure come up before. This is exactly what we found earlier when we examined the mass-luminosity relation (<\/span>Figure 18.9<span style=\"text-align: initial;font-size: 1em\">). We observed that 90% of all stars seem to follow the relationship; these are the 90% of all stars that lie on the main sequence in our H\u2013R diagram. Our models and our observations agree.<\/span><\/div>\n<\/div>\n<p id=\"fs-id1164755049188\">What about the other stars on the H\u2013R diagram\u2014the giants and supergiants, and the white dwarfs? As we will see in the next few chapters, these are what main-sequence stars turn into as they age: They are the later stages in a star\u2019s life. As a star consumes its nuclear fuel, its source of energy changes, as do its chemical composition and interior structure. These changes cause the star to alter its luminosity and surface temperature so that it no longer lies on the main sequence on our diagram. Because stars spend much less time in these later stages of their lives, we see fewer stars in those regions of the H\u2013R diagram.<\/p>\n<\/section>\n<section id=\"fs-id1164754997938\" data-depth=\"1\">\n<h3 data-type=\"title\">Extremes of Stellar Luminosities, Diameters, and Densities<\/h3>\n<p id=\"fs-id1164755012037\">We can use the H\u2013R diagram to explore the extremes in size, luminosity, and density found among the stars. Such extreme stars are not only interesting to fans of the\u00a0<em data-effect=\"italics\">Guinness Book of World Records<\/em>; they can teach us a lot about how stars work. For example, we saw that the most massive main-sequence stars are the most luminous ones. We know of a few extreme stars that are a million times more luminous than the Sun, with masses that exceed 100 times the Sun\u2019s mass. These superluminous stars, which are at the upper left of the H\u2013R diagram, are exceedingly hot, very blue stars of spectral type O. These are the stars that would be the most conspicuous at vast distances in space.<\/p>\n<p id=\"fs-id1164755016804\">The cool supergiants in the upper corner of the H\u2013R diagram are as much as 10,000 times as luminous as the Sun. In addition, these stars have diameters very much larger than that of the Sun. As discussed above, some supergiants are so large that if the solar system could be centered in one, the star\u2019s surface would lie beyond the orbit of Mars (see\u00a0Figure 18.16). We will have to ask, in coming chapters, what process can make a star swell up to such an enormous size, and how long these \u201cswollen\u201d stars can last in their distended state.<\/p>\n<div id=\"OSC_Astro_18_04_SizeCompare\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_18_04_SizeCompare\">\n<figure style=\"width: 975px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"11\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/7f975ced5337d7e283eace0b8e73570cded443fa\" alt=\"Illustration of the Sun and a Supergiant Star. At left, the supergiant star VY Canis Majoris is shown as a large yellow sphere. At the bottom left edge of the supergiant a small rectangle is drawn. This area is enlarged in the inset at right. The Sun is shown as a tiny dot surrounded by a dashed circle representing Earth\u2019s orbit. The surface of the supergiant is drawn running diagonally across the upper right half of the enlargement. The Sun and the orbit of Earth would fit inside VY Canis Majoris many times over.\" width=\"975\" height=\"550\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a018.16<\/strong>\u00a0The Sun and a Supergiant.\u00a0Here you see how small the Sun looks in comparison to one of the largest known stars: VY Canis Majoris, a supergiant.<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<p id=\"fs-id1164755007489\">In contrast, the very common red, cool, low-luminosity stars at the lower end of the main sequence are much smaller and more compact than the Sun. An example of such a red dwarf is Ross 614B, with a surface temperature of 2700 K and only 1\/2000 of the Sun\u2019s luminosity. We call such a star a dwarf because its diameter is only 1\/10 that of the Sun. A star with such a low luminosity also has a low mass (about 1\/12 that of the Sun). This combination of mass and diameter means that it is so compressed that the star has an average density about 80 times that of the Sun. Its density must be higher, in fact, than that of any known solid found on the surface of Earth. (Despite this, the star is made of gas throughout because its center is so hot.)<\/p>\n<p id=\"fs-id1164755024621\">The faint, red, main-sequence stars are not the stars of the most extreme densities, however. The white dwarfs, at the lower-left corner of the H\u2013R diagram, have densities many times greater still.<\/p>\n<\/section>\n<section id=\"fs-id1164755047022\" data-depth=\"1\">\n<h3 data-type=\"title\">The White Dwarfs<\/h3>\n<p id=\"fs-id1164755020363\">The first\u00a0<span id=\"term1016\" class=\"no-emphasis\" data-type=\"term\">white dwarf<\/span>\u00a0star was detected in 1862. Called\u00a0<span id=\"term1017\" class=\"no-emphasis\" data-type=\"term\">Sirius<\/span>\u00a0B, it forms a binary system with Sirius A, the brightest-appearing star in the sky. It eluded discovery and analysis for a long time because its faint light tends to be lost in the glare of nearby Sirius A (Figure 18.17). (Since Sirius is often called the Dog Star\u2014being the brightest star in the constellation of Canis Major, the big dog\u2014Sirius B is sometimes nicknamed the Pup.)<\/p>\n<div id=\"OSC_Astro_18_04_Sirius\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_18_04_Sirius\">\n<figure style=\"width: 731px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"13\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/91d39cd7a7d3556757d4d368de877b06ffdb0ec6\" alt=\"Two Views of Sirius and Its White Dwarf Companion. (a) A visible light image taken by the Hubble Space Telescope. Sirius B is the faint speck in the lower left had quadrant of the image, and nearly lost in the glare of bright Sirius A. (b) X-ray image from the Chandra X-ray telescope. Sirius B is much brighter in X-rays and is the bright object at the center of the image. Above and slightly to the right is Sirius A.\" width=\"731\" height=\"348\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a018.17<\/strong>\u00a0Two Views of Sirius and Its White Dwarf Companion.\u00a0(a) The (visible light) image, taken with the Hubble Space Telescope, shows bright Sirius A, and, below it and off to its left, faint Sirius B. (b) This image of the\u00a0Sirius\u00a0star system was taken with the Chandra X-Ray Telescope. Now, the bright object is the white dwarf companion, Sirius B. Sirius A is the faint object above it; what we are seeing from Sirius is probably not actually X-ray radiation but rather ultraviolet light that has leaked into the detector. Note that the ultraviolet intensities of these two objects are completely reversed from the situation in visible light because Sirius B is hotter and emits more higher-frequency radiation. (credit a: modification of work by NASA, H.E. Bond and E. Nelan (Space Telescope Science Institute), M. Barstow and M. Burleigh (University of Leicester) and J.B. Holberg (University of Arizona); credit b: modification of work by NASA\/SAO\/CXC)<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<p id=\"fs-id1164755043950\">We have now found thousands of white dwarfs.\u00a0Table 18.1\u00a0shows that about 7% of the true stars (spectral types O\u2013M) in our local neighborhood are white dwarfs. A good example of a typical white dwarf is the nearby star 40 Eridani B. Its surface temperature is a relatively hot 12,000 K, but its luminosity is only [latex]1\/275\\;{{\\rm{L}}_{{\\rm{Sun}}}}[\/latex]. Calculations show that its radius is only 1.4% of the Sun\u2019s, or about the same as that of Earth, and its volume is [latex]2.5 \\times {10^{-6}}[\/latex]\u00a0that of the Sun. Its mass, however, is 0.57 times the Sun\u2019s mass, just a little more than half. To fit such a substantial mass into so tiny a volume, the star\u2019s density must be about 210,000 times the density of the Sun, or more than [latex]300,000\\:{\\rm{g\/c}}{{\\rm{m}}^3}[\/latex]. A teaspoonful of this material would have a mass of some 1.6 tons! At such enormous densities, matter cannot exist in its usual state; we will examine the particular behavior of this type of matter in\u00a0<a href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/23-thinking-ahead\" data-page-slug=\"23-thinking-ahead\" data-page-uuid=\"8e460daa-be2b-47de-9d38-ab4c21865a8a\" data-page-fragment=\"\">The Death of Stars<\/a>. For now, we just note that white dwarfs are dying stars, reaching the end of their productive lives and ready for their stories to be over.<\/p>\n<p id=\"fs-id1164754998767\">The British astrophysicist (and science popularizer) Arthur\u00a0<span id=\"term1019\" class=\"no-emphasis\" data-type=\"term\">Eddington<\/span>\u00a0(1882\u20131944) described the first known white dwarf this way:<\/p>\n<blockquote id=\"fs-id1166568961029\">\n<p id=\"fs-id1164754918889\">The message of the companion of\u00a0<span id=\"term1020\" class=\"no-emphasis\" data-type=\"term\">Sirius<\/span>, when decoded, ran: \u201cI am composed of material three thousand times denser than anything you\u2019ve ever come across. A ton of my material would be a little nugget you could put in a matchbox.\u201d What reply could one make to something like that? Well, the reply most of us made in 1914 was, \u201cShut up; don\u2019t talk nonsense.\u201d<\/p>\n<\/blockquote>\n<p id=\"fs-id1164755031779\">Today, however, astronomers not only accept that stars as dense as white dwarfs exist but (as we will see) have found even denser and stranger objects in their quest to understand the evolution of different types of stars.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<h3 class=\"textbox__title\">Link to Learning<\/h3>\n<\/header>\n<div class=\"textbox__content\">\n<p>Use this\u00a0<a href=\"https:\/\/openstax.org\/l\/30interhr\" target=\"_blank\" rel=\"noopener nofollow noreferrer\">interactive H-R diagram<\/a> to explore the sizes of stars based on their placement. Overlay the closest stars and the brightest stars, and consider where they lie on the figure. How many stars are among both the closest and brightest stars?<\/p>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"textbox\">This book was adapted from the following: Fraknoi, A., Morrison, D., &amp; Wolff, S. C. (2016). 18.4 The H\u2013R Diagram In <i>Astronomy<\/i>. OpenStax. https:\/\/openstax.org\/books\/astronomy\/pages\/18-4-the-h-r-diagram under a <a href=\"http:\/\/creativecommons.org\/licenses\/by\/4.0\/\" target=\"_blank\" rel=\"noopener noreferrer\">Creative Commons Attribution License 4.0<\/a><\/div>\n<div>Access the entire book for free at\u00a0<a href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction\">https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction<\/a><\/div>\n","protected":false},"author":33,"menu_order":11,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-583","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":572,"_links":{"self":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/583","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/users\/33"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/583\/revisions"}],"predecessor-version":[{"id":1049,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/583\/revisions\/1049"}],"part":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/parts\/572"}],"metadata":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/583\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/media?parent=583"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapter-type?post=583"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/contributor?post=583"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/license?post=583"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}