{"id":599,"date":"2022-03-02T17:44:02","date_gmt":"2022-03-02T17:44:02","guid":{"rendered":"https:\/\/pressbooks.ccconline.org\/astronomy\/?post_type=chapter&#038;p=599"},"modified":"2022-04-29T18:11:04","modified_gmt":"2022-04-29T18:11:04","slug":"19-4-the-h-r-diagram-and-cosmic-distances","status":"publish","type":"chapter","link":"https:\/\/pressbooks.ccconline.org\/astronomy\/chapter\/19-4-the-h-r-diagram-and-cosmic-distances\/","title":{"raw":"19.4 The H\u2013R Diagram and Cosmic Distances","rendered":"19.4 The H\u2013R Diagram and Cosmic Distances"},"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-id1168583547255\">By the end of this section, you will be able to:<\/p>\r\n\r\n<ul id=\"fs-id1165721065479\">\r\n \t<li>Understand how spectral types are used to estimate stellar luminosities<\/li>\r\n \t<li>Examine how these techniques are used by astronomers today<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1165719745144\">Variable stars are not the only way that we can estimate the luminosity of stars. Another way involves the H\u2013R diagram, which shows that the intrinsic brightness of a star can be estimated if we know its spectral type.<\/p>\r\n\r\n<section id=\"fs-id1165720826367\" data-depth=\"1\">\r\n<h3 data-type=\"title\">Distances from Spectral Types<\/h3>\r\n<p id=\"fs-id1165720769757\">As satisfying and productive as variable stars have been for distance measurement, these stars are rare and are not found near all the objects to which we wish to measure distances. Suppose, for example, we need the distance to a star that is not varying, or to a group of stars, none of which is a variable. In this case, it turns out the\u00a0<span id=\"term1067\" class=\"no-emphasis\" data-type=\"term\">H\u2013R diagram<\/span>\u00a0can come to our rescue.<\/p>\r\n<p id=\"fs-id1165721034203\">If we can observe the spectrum of a star, we can estimate its distance from our understanding of the H\u2013R diagram. As discussed in\u00a0Analyzing Starlight, a detailed examination of a stellar spectrum allows astronomers to classify the star into one of the\u00a0<em data-effect=\"italics\">spectral types<\/em>\u00a0indicating surface temperature. (The types are O, B, A, F, G, K, M, L, T, and Y; each of these can be divided into numbered subgroups.) In general, however, the spectral type alone is not enough to allow us to estimate luminosity. Look again at\u00a0Figure 18.15. A G2 star could be a main-sequence star with a luminosity of [latex]1\\:{{\\rm{L}}_{{\\rm{Sun}}}}[\/latex], or it could be a giant with a luminosity of [latex]100\\:{{\\rm{L}}_{{\\rm{Sun}}}}[\/latex], or even a supergiant with a still higher luminosity.<\/p>\r\n<p id=\"fs-id1165719628963\">We can learn more from a star\u2019s spectrum, however, than just its temperature. Remember, for example, that we can detect pressure differences in stars from the details of the spectrum. This knowledge is very useful because giant stars are larger (and have lower pressures) than main-sequence stars, and supergiants are still larger than giants. If we look in detail at the spectrum of a star, we can determine whether it is a main-sequence star, a giant, or a supergiant.<\/p>\r\n<p id=\"fs-id1165720940719\">Suppose, to start with the simplest example, that the spectrum, color, and other properties of a distant G2 star match those of the Sun exactly. It is then reasonable to conclude that this distant star is likely to be a main-sequence star just like the Sun and to have the same luminosity as the Sun. But if there are subtle differences between the solar spectrum and the spectrum of the distant star, then the distant star may be a giant or even a supergiant.<\/p>\r\n<p id=\"fs-id1165720758460\">The most widely used system of star classification divides stars of a given spectral class into six categories called\u00a0<span id=\"term1068\" data-type=\"term\">luminosity classes<\/span>. These luminosity classes are denoted by Roman numbers as follows:<\/p>\r\n\r\n<ul id=\"fs-id1163975397633\" data-bullet-style=\"bullet\">\r\n \t<li>Ia: Brightest supergiants<\/li>\r\n \t<li>Ib: Less luminous supergiants<\/li>\r\n \t<li>II: Bright giants<\/li>\r\n \t<li>III: Giants<\/li>\r\n \t<li>IV: Subgiants (intermediate between giants and main-sequence stars)<\/li>\r\n \t<li>V: Main-sequence stars<\/li>\r\n<\/ul>\r\n<p id=\"fs-id1165719779481\">The full spectral specification of a star includes its luminosity class. For example, a main-sequence star with spectral class F3 is written as F3 V. The specification for an M2 giant is M2 III.\u00a0Figure 19.15\u00a0illustrates the approximate position of stars of various luminosity classes on the H\u2013R diagram. The dashed portions of the lines represent regions with very few or no stars.<\/p>\r\n\r\n<div id=\"OSC_Astro_19_04_Classes\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_19_04_Classes\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"729\"]<img id=\"2\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/398d5ac1578c7506d87c121935c7f7b5cacc714d\" alt=\"Luminosity Classes. In this graph the vertical axis is labeled \u201cLuminosity (L_Sun),\u201d running from 10^-4 to 10^6 in increments of 10^2. 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. Also labeled on the horizontal axis is \u201cColor Index.\u201d Four values are given, \u201c-0.4\u201d at the beginning of spectral class \u201cO,\u201d \u201c0.0\u201d at the beginning of spectral class \u201cA,\u201d \u201c0.6\u201d at the beginning of spectral class \u201cG,\u201d and \u201c+1.4\u201d at the beginning of spectral class \u201cM.\u201d The five main classes of stars are plotted. Beginning at lower left of the image 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. Running horizontally from the center of the graph to the right is the band of \u201cGiants.\u201d Finally, a small number of stars running horizontally across the top of the graph are the \u201cSupergiants.\u201d Blue curves are plotted indicating the luminosity classes. The first blue curve crosses the entire upper part of the plot at about 10^5 L_Sun and is labeled \u201cIa,\u201d corresponding to the supergiants. Parallel to \u201cIa,\u201d but lower at about 10^4 L_Sun, is the blue curve of \u201cIb,\u201d a subdivision of the supergiants. The next horizontal blue curve at about 10^3 L_Sun is that of luminosity class \u201cII,\u201d corresponding to the bright giants. The next blue curve begins on the main sequence at about spectral type A and goes horizontally to the right at about 10^2 L_Sun. This curve is labeled \u201cIII\u201d for the giants. Another blue curve is drawn between the giants and the main sequence. It is labeled as luminosity class \u201cIV,\u201d corresponding to the subgiants. Finally, the last blue curve traces the entire length of the main sequence and is labeled \u201cV.\u201d\" width=\"729\" height=\"506\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a019.15<\/strong>\u00a0Luminosity Classes.\u00a0Stars of the same temperature (or spectral class) can fall into different luminosity classes on the Hertzsprung-Russell diagram. By studying details of the spectrum for each star, astronomers can determine which luminosity class they fall in (whether they are main-sequence stars, giant stars, or supergiant stars).[\/caption]<\/figure>\r\n<\/div>\r\n<p id=\"fs-id1165720786387\">With both its spectral and luminosity classes known, a star\u2019s position on the H\u2013R diagram is uniquely determined. Since the diagram plots luminosity versus temperature, this means we can now read off the star\u2019s luminosity (once its spectrum has helped us place it on the diagram). As before, if we know how luminous the star really is and see how dim it looks, the difference allows us to calculate its distance. (For historical reasons, astronomers sometimes call this method of distance determination\u00a0<em data-effect=\"italics\">spectroscopic parallax<\/em>, even though the method has nothing to do with parallax.)<\/p>\r\n<p id=\"fs-id1165719708044\">The H\u2013R diagram method allows astronomers to estimate distances to nearby stars, as well as some of the most distant stars in our Galaxy, but it is anchored by measurements of parallax. The distances measured using parallax are the gold standard for distances: they rely on no assumptions, only geometry. Once astronomers take a spectrum of a nearby star for which we also know the parallax, we know the luminosity that corresponds to that spectral type. Nearby stars thus serve as benchmarks for more distant stars because we can assume that two stars with identical spectra have the same intrinsic luminosity.<\/p>\r\n\r\n<\/section><section id=\"fs-id1165720997828\" data-depth=\"1\">\r\n<h3 data-type=\"title\">A Few Words about the Real World<\/h3>\r\n<p id=\"fs-id1165721118654\">Introductory textbooks such as ours work hard to present the material in a straightforward and simplified way. In doing so, we sometimes do our students a disservice by making scientific techniques seem too clean and painless. In the real world, the techniques we have just described turn out to be messy and difficult, and often give astronomers headaches that last long into the day.<\/p>\r\n<p id=\"fs-id1165720930228\">For example, the relationships we have described such as the period-luminosity relation for certain variable stars aren\u2019t exactly straight lines on a graph. The points representing many stars scatter widely when plotted, and thus, the distances derived from them also have a certain built-in scatter or uncertainty.<\/p>\r\n<p id=\"fs-id1165720715203\">The distances we measure with the methods we have discussed are therefore only accurate to within a certain percentage of error\u2014sometimes 10%, sometimes 25%, sometimes as much as 50% or more. A 25% error for a star estimated to be 10,000 light-years away means it could be anywhere from 7500 to 12,500 light-years away. This would be an unacceptable uncertainty if you were loading fuel into a spaceship for a trip to the star, but it is not a bad first figure to work with if you are an astronomer stuck on planet Earth.<\/p>\r\n<p id=\"fs-id1165720966465\">Nor is the construction of H\u2013R diagrams as easy as you might think at first. To make a good diagram, one needs to measure the characteristics and distances of many stars, which can be a time-consuming task. Since our own solar neighborhood is already well mapped, the stars astronomers most want to study to advance our knowledge are likely to be far away and faint. It may take hours of observing to obtain a single spectrum. Observers may have to spend many nights at the telescope (and many days back home working with their data) before they get their distance measurement. Fortunately, this is changing because surveys like Gaia will study billions of stars, producing public datasets that all astronomers can use.<\/p>\r\n<p id=\"fs-id1165719776259\">Despite these difficulties, the tools we have been discussing allow us to measure a remarkable range of distances\u2014parallaxes for the nearest stars, RR Lyrae variable stars; the H\u2013R diagram for clusters of stars in our own and nearby galaxies; and cepheids out to distances of 60 million light-years.\u00a0Table 19.1\u00a0describes the distance limits and overlap of each method.<\/p>\r\n<p id=\"fs-id1165720686757\">Each technique described in this chapter builds on at least one other method, forming what many call the\u00a0<em data-effect=\"italics\">cosmic distance ladder<\/em>. Parallaxes are the foundation of all stellar distance estimates, spectroscopic methods use nearby stars to calibrate their H\u2013R diagrams, and RR Lyrae and cepheid distance estimates are grounded in H\u2013R diagram distance estimates (and even in a parallax measurement to a nearby cepheid,\u00a0<span id=\"term1069\" class=\"no-emphasis\" data-type=\"term\">Delta Cephei<\/span>).<\/p>\r\n<p id=\"fs-id1165719563181\">This chain of methods allows astronomers to push the limits when looking for even more distant stars. Recent work, for example, has used RR Lyrae stars to identify dim companion galaxies to our own Milky Way out at distances of 300,000 light-years. The H\u2013R diagram method was recently used to identify the two most distant stars in the Galaxy: red giant stars way out in the halo of the Milky Way with distances of almost 1 million light-years.<\/p>\r\n<p id=\"fs-id1165721065002\">We can combine the distances we find for stars with measurements of their composition, luminosity, and temperature\u2014made with the techniques described in\u00a0Analyzing Starlight\u00a0and\u00a0The Stars: A Celestial Census. Together, these make up the arsenal of information we need to trace the evolution of stars from birth to death, the subject to which we turn in the chapters that follow.<\/p>\r\n\r\n<div class=\"os-table os-top-titled-container\">\r\n<table id=\"fs-id1165720742736\" class=\"grid landscape aligncenter\" style=\"height: 75px\"><caption>Table 19.1 Distance Range of Celestial Measurement Methods<\/caption>\r\n<thead>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<th style=\"height: 15px;width: 282.344px\" scope=\"col\" data-valign=\"top\" data-align=\"center\">Method<\/th>\r\n<th style=\"height: 15px;width: 379.266px\" scope=\"col\" data-valign=\"top\" data-align=\"center\">Distance Range<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 282.344px\" data-valign=\"top\" data-align=\"left\">Trigonometric parallax<\/td>\r\n<td style=\"height: 15px;width: 379.266px\" data-valign=\"top\" data-align=\"left\">4\u201330,000 light-years when the Gaia mission is complete<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 282.344px\" data-valign=\"top\" data-align=\"left\">RR Lyrae stars<\/td>\r\n<td style=\"height: 15px;width: 379.266px\" data-valign=\"top\" data-align=\"left\">Out to 300,000 light-years<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 282.344px\" data-valign=\"top\" data-align=\"left\">H\u2013R diagram and spectroscopic distances<\/td>\r\n<td style=\"height: 15px;width: 379.266px\" data-valign=\"top\" data-align=\"left\">Out to 1,200,000 light-years<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\" valign=\"top\">\r\n<td style=\"height: 15px;width: 282.344px\" data-valign=\"top\" data-align=\"left\">Cepheid stars<\/td>\r\n<td style=\"height: 15px;width: 379.266px\" data-valign=\"top\" data-align=\"left\">Out to 60,000,000 light-years<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/section>\r\n<div class=\"textbox\">This book was adapted from the following: Fraknoi, A., Morrison, D., &amp; Wolff, S. C. (2016). 19.4 The H\u2013R Diagram and Cosmic Distances In <i>Astronomy<\/i>. OpenStax. https:\/\/openstax.org\/books\/astronomy\/pages\/19-4-the-h-r-diagram-and-cosmic-distances 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-id1168583547255\">By the end of this section, you will be able to:<\/p>\n<ul id=\"fs-id1165721065479\">\n<li>Understand how spectral types are used to estimate stellar luminosities<\/li>\n<li>Examine how these techniques are used by astronomers today<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1165719745144\">Variable stars are not the only way that we can estimate the luminosity of stars. Another way involves the H\u2013R diagram, which shows that the intrinsic brightness of a star can be estimated if we know its spectral type.<\/p>\n<section id=\"fs-id1165720826367\" data-depth=\"1\">\n<h3 data-type=\"title\">Distances from Spectral Types<\/h3>\n<p id=\"fs-id1165720769757\">As satisfying and productive as variable stars have been for distance measurement, these stars are rare and are not found near all the objects to which we wish to measure distances. Suppose, for example, we need the distance to a star that is not varying, or to a group of stars, none of which is a variable. In this case, it turns out the\u00a0<span id=\"term1067\" class=\"no-emphasis\" data-type=\"term\">H\u2013R diagram<\/span>\u00a0can come to our rescue.<\/p>\n<p id=\"fs-id1165721034203\">If we can observe the spectrum of a star, we can estimate its distance from our understanding of the H\u2013R diagram. As discussed in\u00a0Analyzing Starlight, a detailed examination of a stellar spectrum allows astronomers to classify the star into one of the\u00a0<em data-effect=\"italics\">spectral types<\/em>\u00a0indicating surface temperature. (The types are O, B, A, F, G, K, M, L, T, and Y; each of these can be divided into numbered subgroups.) In general, however, the spectral type alone is not enough to allow us to estimate luminosity. Look again at\u00a0Figure 18.15. A G2 star could be a main-sequence star with a luminosity of [latex]1\\:{{\\rm{L}}_{{\\rm{Sun}}}}[\/latex], or it could be a giant with a luminosity of [latex]100\\:{{\\rm{L}}_{{\\rm{Sun}}}}[\/latex], or even a supergiant with a still higher luminosity.<\/p>\n<p id=\"fs-id1165719628963\">We can learn more from a star\u2019s spectrum, however, than just its temperature. Remember, for example, that we can detect pressure differences in stars from the details of the spectrum. This knowledge is very useful because giant stars are larger (and have lower pressures) than main-sequence stars, and supergiants are still larger than giants. If we look in detail at the spectrum of a star, we can determine whether it is a main-sequence star, a giant, or a supergiant.<\/p>\n<p id=\"fs-id1165720940719\">Suppose, to start with the simplest example, that the spectrum, color, and other properties of a distant G2 star match those of the Sun exactly. It is then reasonable to conclude that this distant star is likely to be a main-sequence star just like the Sun and to have the same luminosity as the Sun. But if there are subtle differences between the solar spectrum and the spectrum of the distant star, then the distant star may be a giant or even a supergiant.<\/p>\n<p id=\"fs-id1165720758460\">The most widely used system of star classification divides stars of a given spectral class into six categories called\u00a0<span id=\"term1068\" data-type=\"term\">luminosity classes<\/span>. These luminosity classes are denoted by Roman numbers as follows:<\/p>\n<ul id=\"fs-id1163975397633\" data-bullet-style=\"bullet\">\n<li>Ia: Brightest supergiants<\/li>\n<li>Ib: Less luminous supergiants<\/li>\n<li>II: Bright giants<\/li>\n<li>III: Giants<\/li>\n<li>IV: Subgiants (intermediate between giants and main-sequence stars)<\/li>\n<li>V: Main-sequence stars<\/li>\n<\/ul>\n<p id=\"fs-id1165719779481\">The full spectral specification of a star includes its luminosity class. For example, a main-sequence star with spectral class F3 is written as F3 V. The specification for an M2 giant is M2 III.\u00a0Figure 19.15\u00a0illustrates the approximate position of stars of various luminosity classes on the H\u2013R diagram. The dashed portions of the lines represent regions with very few or no stars.<\/p>\n<div id=\"OSC_Astro_19_04_Classes\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_19_04_Classes\">\n<figure style=\"width: 729px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"2\" src=\"https:\/\/openstax.org\/apps\/archive\/20220118.185250\/resources\/398d5ac1578c7506d87c121935c7f7b5cacc714d\" alt=\"Luminosity Classes. In this graph the vertical axis is labeled \u201cLuminosity (L_Sun),\u201d running from 10^-4 to 10^6 in increments of 10^2. 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. Also labeled on the horizontal axis is \u201cColor Index.\u201d Four values are given, \u201c-0.4\u201d at the beginning of spectral class \u201cO,\u201d \u201c0.0\u201d at the beginning of spectral class \u201cA,\u201d \u201c0.6\u201d at the beginning of spectral class \u201cG,\u201d and \u201c+1.4\u201d at the beginning of spectral class \u201cM.\u201d The five main classes of stars are plotted. Beginning at lower left of the image 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. Running horizontally from the center of the graph to the right is the band of \u201cGiants.\u201d Finally, a small number of stars running horizontally across the top of the graph are the \u201cSupergiants.\u201d Blue curves are plotted indicating the luminosity classes. The first blue curve crosses the entire upper part of the plot at about 10^5 L_Sun and is labeled \u201cIa,\u201d corresponding to the supergiants. Parallel to \u201cIa,\u201d but lower at about 10^4 L_Sun, is the blue curve of \u201cIb,\u201d a subdivision of the supergiants. The next horizontal blue curve at about 10^3 L_Sun is that of luminosity class \u201cII,\u201d corresponding to the bright giants. The next blue curve begins on the main sequence at about spectral type A and goes horizontally to the right at about 10^2 L_Sun. This curve is labeled \u201cIII\u201d for the giants. Another blue curve is drawn between the giants and the main sequence. It is labeled as luminosity class \u201cIV,\u201d corresponding to the subgiants. Finally, the last blue curve traces the entire length of the main sequence and is labeled \u201cV.\u201d\" width=\"729\" height=\"506\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a019.15<\/strong>\u00a0Luminosity Classes.\u00a0Stars of the same temperature (or spectral class) can fall into different luminosity classes on the Hertzsprung-Russell diagram. By studying details of the spectrum for each star, astronomers can determine which luminosity class they fall in (whether they are main-sequence stars, giant stars, or supergiant stars).<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<p id=\"fs-id1165720786387\">With both its spectral and luminosity classes known, a star\u2019s position on the H\u2013R diagram is uniquely determined. Since the diagram plots luminosity versus temperature, this means we can now read off the star\u2019s luminosity (once its spectrum has helped us place it on the diagram). As before, if we know how luminous the star really is and see how dim it looks, the difference allows us to calculate its distance. (For historical reasons, astronomers sometimes call this method of distance determination\u00a0<em data-effect=\"italics\">spectroscopic parallax<\/em>, even though the method has nothing to do with parallax.)<\/p>\n<p id=\"fs-id1165719708044\">The H\u2013R diagram method allows astronomers to estimate distances to nearby stars, as well as some of the most distant stars in our Galaxy, but it is anchored by measurements of parallax. The distances measured using parallax are the gold standard for distances: they rely on no assumptions, only geometry. Once astronomers take a spectrum of a nearby star for which we also know the parallax, we know the luminosity that corresponds to that spectral type. Nearby stars thus serve as benchmarks for more distant stars because we can assume that two stars with identical spectra have the same intrinsic luminosity.<\/p>\n<\/section>\n<section id=\"fs-id1165720997828\" data-depth=\"1\">\n<h3 data-type=\"title\">A Few Words about the Real World<\/h3>\n<p id=\"fs-id1165721118654\">Introductory textbooks such as ours work hard to present the material in a straightforward and simplified way. In doing so, we sometimes do our students a disservice by making scientific techniques seem too clean and painless. In the real world, the techniques we have just described turn out to be messy and difficult, and often give astronomers headaches that last long into the day.<\/p>\n<p id=\"fs-id1165720930228\">For example, the relationships we have described such as the period-luminosity relation for certain variable stars aren\u2019t exactly straight lines on a graph. The points representing many stars scatter widely when plotted, and thus, the distances derived from them also have a certain built-in scatter or uncertainty.<\/p>\n<p id=\"fs-id1165720715203\">The distances we measure with the methods we have discussed are therefore only accurate to within a certain percentage of error\u2014sometimes 10%, sometimes 25%, sometimes as much as 50% or more. A 25% error for a star estimated to be 10,000 light-years away means it could be anywhere from 7500 to 12,500 light-years away. This would be an unacceptable uncertainty if you were loading fuel into a spaceship for a trip to the star, but it is not a bad first figure to work with if you are an astronomer stuck on planet Earth.<\/p>\n<p id=\"fs-id1165720966465\">Nor is the construction of H\u2013R diagrams as easy as you might think at first. To make a good diagram, one needs to measure the characteristics and distances of many stars, which can be a time-consuming task. Since our own solar neighborhood is already well mapped, the stars astronomers most want to study to advance our knowledge are likely to be far away and faint. It may take hours of observing to obtain a single spectrum. Observers may have to spend many nights at the telescope (and many days back home working with their data) before they get their distance measurement. Fortunately, this is changing because surveys like Gaia will study billions of stars, producing public datasets that all astronomers can use.<\/p>\n<p id=\"fs-id1165719776259\">Despite these difficulties, the tools we have been discussing allow us to measure a remarkable range of distances\u2014parallaxes for the nearest stars, RR Lyrae variable stars; the H\u2013R diagram for clusters of stars in our own and nearby galaxies; and cepheids out to distances of 60 million light-years.\u00a0Table 19.1\u00a0describes the distance limits and overlap of each method.<\/p>\n<p id=\"fs-id1165720686757\">Each technique described in this chapter builds on at least one other method, forming what many call the\u00a0<em data-effect=\"italics\">cosmic distance ladder<\/em>. Parallaxes are the foundation of all stellar distance estimates, spectroscopic methods use nearby stars to calibrate their H\u2013R diagrams, and RR Lyrae and cepheid distance estimates are grounded in H\u2013R diagram distance estimates (and even in a parallax measurement to a nearby cepheid,\u00a0<span id=\"term1069\" class=\"no-emphasis\" data-type=\"term\">Delta Cephei<\/span>).<\/p>\n<p id=\"fs-id1165719563181\">This chain of methods allows astronomers to push the limits when looking for even more distant stars. Recent work, for example, has used RR Lyrae stars to identify dim companion galaxies to our own Milky Way out at distances of 300,000 light-years. The H\u2013R diagram method was recently used to identify the two most distant stars in the Galaxy: red giant stars way out in the halo of the Milky Way with distances of almost 1 million light-years.<\/p>\n<p id=\"fs-id1165721065002\">We can combine the distances we find for stars with measurements of their composition, luminosity, and temperature\u2014made with the techniques described in\u00a0Analyzing Starlight\u00a0and\u00a0The Stars: A Celestial Census. Together, these make up the arsenal of information we need to trace the evolution of stars from birth to death, the subject to which we turn in the chapters that follow.<\/p>\n<div class=\"os-table os-top-titled-container\">\n<table id=\"fs-id1165720742736\" class=\"grid landscape aligncenter\" style=\"height: 75px\">\n<caption>Table 19.1 Distance Range of Celestial Measurement Methods<\/caption>\n<thead>\n<tr style=\"height: 15px\" valign=\"top\">\n<th style=\"height: 15px;width: 282.344px\" scope=\"col\" data-valign=\"top\" data-align=\"center\">Method<\/th>\n<th style=\"height: 15px;width: 379.266px\" scope=\"col\" data-valign=\"top\" data-align=\"center\">Distance Range<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 282.344px\" data-valign=\"top\" data-align=\"left\">Trigonometric parallax<\/td>\n<td style=\"height: 15px;width: 379.266px\" data-valign=\"top\" data-align=\"left\">4\u201330,000 light-years when the Gaia mission is complete<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 282.344px\" data-valign=\"top\" data-align=\"left\">RR Lyrae stars<\/td>\n<td style=\"height: 15px;width: 379.266px\" data-valign=\"top\" data-align=\"left\">Out to 300,000 light-years<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 282.344px\" data-valign=\"top\" data-align=\"left\">H\u2013R diagram and spectroscopic distances<\/td>\n<td style=\"height: 15px;width: 379.266px\" data-valign=\"top\" data-align=\"left\">Out to 1,200,000 light-years<\/td>\n<\/tr>\n<tr style=\"height: 15px\" valign=\"top\">\n<td style=\"height: 15px;width: 282.344px\" data-valign=\"top\" data-align=\"left\">Cepheid stars<\/td>\n<td style=\"height: 15px;width: 379.266px\" data-valign=\"top\" data-align=\"left\">Out to 60,000,000 light-years<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/section>\n<div class=\"textbox\">This book was adapted from the following: Fraknoi, A., Morrison, D., &amp; Wolff, S. C. (2016). 19.4 The H\u2013R Diagram and Cosmic Distances In <i>Astronomy<\/i>. OpenStax. https:\/\/openstax.org\/books\/astronomy\/pages\/19-4-the-h-r-diagram-and-cosmic-distances 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-599","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":591,"_links":{"self":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/599","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":3,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/599\/revisions"}],"predecessor-version":[{"id":1056,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/599\/revisions\/1056"}],"part":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/parts\/591"}],"metadata":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/599\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/media?parent=599"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapter-type?post=599"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/contributor?post=599"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/license?post=599"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}