{"id":657,"date":"2017-08-08T13:13:24","date_gmt":"2017-08-08T17:13:24","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/22-1-evolution-from-the-main-sequence-to-red-giants\/"},"modified":"2021-05-01T08:40:12","modified_gmt":"2021-05-01T12:40:12","slug":"22-1-evolution-from-the-main-sequence-to-red-giants","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/22-1-evolution-from-the-main-sequence-to-red-giants\/","title":{"raw":"22.1 Evolution from the Main Sequence to Red Giants","rendered":"22.1 Evolution from the Main Sequence to Red Giants"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\n<p id=\"fs-id1168581963707\">By the end of this section, you will be able to:<\/p>\r\n\r\n<ul id=\"fs-id1168047596857\">\r\n \t<li>Explain the zero-age <span class=\"no-emphasis\">main sequence<\/span><\/li>\r\n \t<li>Describe what happens to main-sequence stars of various masses as they exhaust their hydrogen supply<\/li>\r\n<\/ul>\r\n<\/div>\r\nOne of the best ways to get a \u201csnapshot\u201d of a group of stars is by plotting their properties on an <span class=\"no-emphasis\">H\u2013R diagram<\/span>. We have already used the H\u2013R diagram to follow the evolution of protostars up to the time they reach the main sequence. Now we\u2019ll see what happens next.\r\n<p id=\"fs-id1168047141287\">Once a star has reached the main-sequence stage of its life, it derives its energy almost entirely from the conversion of hydrogen to helium via the process of nuclear fusion in its core (see <a class=\"target-chapter\" href=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/16-0-thinking-ahead\/\">The Sun: A Nuclear Powerhouse<\/a>). Since hydrogen is the most abundant element in stars, this process can maintain the star\u2019s equilibrium for a long time. Thus, all stars remain on the main sequence for most of their lives. Some astronomers like to call the main-sequence phase the star\u2019s \u201cprolonged adolescence\u201d or \u201cadulthood\u201d (continuing our analogy to the stages in a human life).<\/p>\r\n<p id=\"fs-id1168047644759\">The left-hand edge of the main-sequence band in the H\u2013R diagram is called the zero-age main sequence (see <a class=\"autogenerated-content\" href=\"#OSC_Astro_18_04_HR\">chapter 18 HR<\/a>). We use the term <em>zero-age<\/em> to mark the time when a star stops contracting, settles onto the main sequence, and begins to fuse hydrogen in its core. The zero-age main sequence is a continuous line in the H\u2013R diagram that shows where stars of different masses but similar chemical composition can be found when they begin to fuse hydrogen.<\/p>\r\n<p id=\"fs-id1168047948993\">Since only 0.7% of the hydrogen used in fusion reactions is converted into energy, fusion does not change the <em>total<\/em> mass of the star appreciably during this long period. It does, however, change the chemical composition in its central regions where nuclear reactions occur: hydrogen is gradually depleted, and helium accumulates. This change of composition changes the luminosity, temperature, size, and interior structure of the star. When a star\u2019s luminosity and temperature begin to change, the point that represents the star on the H\u2013R diagram moves away from the zero-age main sequence.<\/p>\r\n<p id=\"fs-id1168047215933\">Calculations show that the temperature and density in the inner region slowly increase as helium accumulates in the centre of a star. As the temperature gets hotter, each proton acquires more energy of motion on average; this means it is more likely to interact with other protons, and as a result, the rate of fusion also increases. For the proton-proton cycle described in <a class=\"target-chapter\" href=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/16-0-thinking-ahead\/\">The Sun: A Nuclear Powerhouse<\/a>, the rate of fusion goes up roughly as the temperature to the fourth power.<\/p>\r\n<p id=\"fs-id1168047363968\">If the rate of fusion goes up, the rate at which energy is being generated also increases, and the luminosity of the star gradually rises. Initially, however, these changes are small, and stars remain within the main-sequence band on the H\u2013R diagram for most of their lifetimes.<\/p>\r\n\r\n<div id=\"fs-id1168047963854\" class=\"example\">\r\n<div class=\"textbox shaded\">\r\n<p id=\"fs-id1168047651163\"><strong>Star Temperature and Rate of Fusion<\/strong>\r\nIf a star\u2019s temperature were to double, by what factor would its rate of fusion increase?<\/p>\r\n<p id=\"fs-id1168047642421\"><strong>Solution<\/strong>\r\nSince the rate of fusion (like temperature) goes up to the fourth power, it would increase by a factor of 2<sup>4<\/sup>, or 16 times.<\/p>\r\n<p id=\"fs-id1168047663003\"><strong>Check Your Learning<\/strong>\r\nIf the rate of fusion of a star increased 256 times, by what factor would the temperature increase?<\/p>\r\n\r\n<div id=\"fs-id1168047690291\" class=\"note\">\r\n<div class=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-id1168047544097\">The temperature would increase by a factor of 256<sup>0.25<\/sup> (that is, the 4<sup>th<\/sup> root of 256), or 4 times.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<section id=\"fs-id1168047996934\">\r\n<h1>Lifetimes on the Main Sequence<\/h1>\r\n<p id=\"fs-id1168047387270\">How many years a star remains in the main-sequence band depends on its mass. You might think that a more massive star, having more fuel, would last longer, but it\u2019s not that simple. The lifetime of a star in a particular stage of evolution depends on how much nuclear fuel it has and on <em>how quickly<\/em> it uses up that fuel. (In the same way, how long people can keep spending money depends not only on how much money they have but also on how quickly they spend it. This is why many lottery winners who go on spending sprees quickly wind up poor again.) In the case of stars, more massive ones use up their fuel much more quickly than stars of low mass.<\/p>\r\n<p id=\"fs-id1168048151186\">The reason massive stars are such spendthrifts is that, as we saw above, the rate of fusion depends <em>very<\/em> strongly on the star\u2019s core temperature. And what determines how hot a star\u2019s central regions get? It is the <em>mass<\/em> of the star\u2014the weight of the overlying layers determines how high the pressure in the core must be: higher mass requires higher pressure to balance it. Higher pressure, in turn, is produced by higher temperature. The higher the temperature in the central regions, the faster the star races through its storehouse of central hydrogen. Although massive stars have more fuel, they burn it so prodigiously that their lifetimes are much shorter than those of their low-mass counterparts. You can also understand now why the most massive main-sequence stars are also the most luminous. Like new rock stars with their first platinum album, they spend their resources at an astounding rate.<\/p>\r\n<p id=\"fs-id1168047642455\">The main-sequence lifetimes of stars of different masses are listed in <a class=\"autogenerated-content\" href=\"#fs-id1168047645207\">Figure 1<\/a>. This table shows that the most massive stars spend only a few million years on the main sequence. A star of 1 solar mass remains there for roughly 10 billion years, while a star of about 0.4 solar mass has a main-sequence lifetime of some 200 billion years, which is longer than the current age of the universe. (Bear in mind, however, that every star spends <em>most<\/em> of its total lifetime on the <span class=\"no-emphasis\">main sequence<\/span>. Stars devote an average of 90% of their lives to peacefully fusing hydrogen into helium.)<\/p>\r\n\r\n<table id=\"fs-id1168047645207\" class=\"span-all aligncenter\" summary=\"This table contains four columns and eight rows. The first row is a header row, and it labels each column, \u201cSpectral Type,\u201d \u201cSurface Temperature (K),\u201d \u201cMass (Mass of Sun = 1),\u201d and \u201cLifetime on Main Sequence (years).\u201d Under the \u201cSpectral Type\u201d column are the values: \u201cO 5,\u201d \u201cB 0,\u201d \u201cA 0,\u201d \u201cF 0,\u201d \u201cG 0,\u201d \u201cK 0,\u201d and \u201cM 0.\u201d Under the \u201cSurface Temperature (K)\u201d column are the values: \u201c54,000,\u201d \u201c29,200,\u201d \u201c9600,\u201d \u201c7350,\u201d \u201c6050,\u201d \u201c5240,\u201d and \u201c3750.\u201d Under the \u201cMass (Mass of Sun = 1)\u201d column are the values: \u201c40,\u201d \u201c16,\u201d \u201c3.3,\u201d \u201c1.7,\u201d \u201c1.1,\u201d \u201c0.8,\u201d and \u201c0.4.\u201d Finally, under the \u201cLifetime on Main Sequence (years)\u201d column are the values: \u201c1 million,\u201d \u201c10 million,\u201d \u201c500 million,\u201d \u201c2.7 billion,\u201d \u201c9 billion,\u201d \u201c14 billion,\u201d and \u201c200 billion.\u201d\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th colspan=\"4\">Figure 1. Lifetimes of Main-Sequence Stars<\/th>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<th>Spectral Type<\/th>\r\n<th>Surface Temperature (K)<\/th>\r\n<th>Mass\r\n<div><\/div>\r\n(Mass of Sun = 1)<\/th>\r\n<th>Lifetime on Main Sequence (years)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>O5<\/td>\r\n<td>54,000<\/td>\r\n<td>40<\/td>\r\n<td>1 million<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>B0<\/td>\r\n<td>29,200<\/td>\r\n<td>16<\/td>\r\n<td>10 million<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>A0<\/td>\r\n<td>9600<\/td>\r\n<td>3.3<\/td>\r\n<td>500 million<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>F0<\/td>\r\n<td>7350<\/td>\r\n<td>1.7<\/td>\r\n<td>2.7 billion<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>G0<\/td>\r\n<td>6050<\/td>\r\n<td>1.1<\/td>\r\n<td>9 billion<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>K0<\/td>\r\n<td>5240<\/td>\r\n<td>0.8<\/td>\r\n<td>14 billion<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>M0<\/td>\r\n<td>3750<\/td>\r\n<td>0.4<\/td>\r\n<td>200 billion<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1168047166304\">These results are not merely of academic interest. Human beings developed on a planet around a G-type star. This means that the Sun\u2019s stable main-sequence lifetime is so long that it afforded life on Earth plenty of time to evolve. When searching for intelligent life like our own on planets around other stars, it would be a pretty big waste of time to search around O- or B-type stars. These stars remain stable for such a short time that the development of creatures complicated enough to take astronomy courses is very unlikely.<\/p>\r\n\r\n<\/section>\r\n<div class=\"textbox shaded\">\r\n\r\n<strong style=\"text-align: initial;font-size: 0.9em\">Calculating the Lifetime of a Star - Mass and Luminosity<\/strong>\r\n<p id=\"fs-id1168047651163\">The lifetime of a star depends on its mass and is inversely proportional to its luminosity.\u00a0 If T = lifetime in solar lifetimes, M = masses in solar mass and L = luminosity in solar luminosities them T = M \/ L.\u00a0 \u00a0 \u00a0If you want it in year, remember that our Sun will live for about 10 billion or 1 x 10 <sup>10<\/sup> years.\u00a0 The equation then becomes.<\/p>\r\nT = M \/ L (1 x 10 <sup>10<\/sup> years )\r\n\r\n<strong>\u00a0<\/strong>If a star has 1\/4 the mass of the Sun and is 1\/8 as luminous, a) how long will it live in solar lifetimes and b) how many years?\r\n<p id=\"fs-id1168047663003\"><strong>Solution<\/strong><\/p>\r\nT = M \/ L = (1\/4 ) \/ (1\/8) = 2.\u00a0 It would live twice as long.\r\n\r\nb) In years that would equal 2 (1 x 10<sup>10<\/sup> year) = 2 x 10<sup>10<\/sup> years.\r\n<div id=\"fs-id1168047690291\" class=\"note\">\r\n<div><\/div>\r\n<div class=\"title\"><strong>Check Your Learning<\/strong><\/div>\r\n<div>If a star has 3 times the mass of the Sun and is 21 times as luminous a) how long will it live in solar lifetimes and b) how many years<\/div>\r\n<div><\/div>\r\n<div class=\"title\"><strong>Answer: <\/strong>a) 7 times b) 7 x 10 <sup>10<\/sup> years<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<p id=\"fs-id1168047651163\"><strong>Calculating the Lifetime of a Star\u00a0 Using Only the Mass\u00a0<\/strong>\r\nIt makes sense that the lifetime of a star depends on its mass ( the amount of fuel) and its luminosity (how quickly it burns that fuel). Remember that the luminosity also depends directly on the mass.\u00a0 The greater the mass of the star, the greater the gravity pressure at the core and the faster the rate of fusion.\u00a0 There must be more outwards pressure due to the fusion to balance the inwards pressure of gravity.\u00a0 This means that the equation shown above can be simplified such that the lifetime of the star T = 1 \/ M <sup>2.5\u00a0\u00a0<\/sup>where T is in solar lifetimes and M is in solar masses.<\/p>\r\nCalculate the lifetime of a star that has a mass that is 1\/2 or 0.5 that of our Sun in a) solar lifetimes and b) years.\r\n<p id=\"fs-id1168047642421\"><strong>Solution<\/strong>\r\nT = 1 \/ (0.5) <sup>2.5<\/sup> = 6 times longer than our Sun<\/p>\r\nOur Sun has a lifetime of about 10 billion years so that equals 6 x 10 <sup>10<\/sup> years.\r\n<p id=\"fs-id1168047663003\"><strong>Check Your Learning<\/strong>\r\nWhat is the lifetime of a star that\u00a0 has a mass that is 16 times greater than that of our Sun?<\/p>\r\n&nbsp;\r\n<div id=\"fs-id1168047690291\" class=\"note\">\r\n<div class=\"title\"><strong>Answer<\/strong><\/div>\r\n<p id=\"fs-id1168047544097\">The lifetime would be 1 \/ (16) <sup>2.5\u00a0<\/sup> = 0.00097 = 9.7 x10<sup>-4<\/sup> times.\u00a0 Our Sun has a lifetime of about 10 billion years or 1 x 10<sup>10<\/sup> years.\u00a0 \u00a0In years this massive star would live 9.7 x10<sup>6<\/sup> years.\u00a0 To one significant figures that is 10 million years which agrees nicely with the table shown above.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<span style=\"font-family: Helvetica, Arial, 'GFS Neohellenic', sans-serif;font-size: 1.2em;font-weight: bold\">Frpm Main-Sequence Star to Red Giant<\/span>\r\n\r\n<section id=\"fs-id1168047784110\">Eventually, all the hydrogen in a star\u2019s core, where it is hot enough for fusion reactions, is used up. The core then contains only helium, \u201ccontaminated\u201d by whatever small percentage of heavier elements the star had to begin with. The helium in the core can be thought of as the accumulated \u201cash\u201d from the nuclear \u201cburning\u201d of hydrogen during the main-sequence stage.\r\n<p id=\"fs-id1168047367284\">Energy can no longer be generated by hydrogen fusion in the stellar core because the hydrogen is all gone and, as we will see, the fusion of helium requires much higher temperatures. Since the central temperature is not yet high enough to fuse helium, there is no nuclear energy source to supply heat to the central region of the star. The long period of stability now ends, gravity again takes over, and the core begins to contract. Once more, the star\u2019s energy is partially supplied by gravitational energy, in the way described by Kelvin and Helmholtz (see <a class=\"target-chapter\" href=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/16-1-sources-of-sunshine-thermal-and-gravitational-energy\/\">Sources of Sunshine: Thermal and Gravitational Energy<\/a>). As the star\u2019s core shrinks, the energy of the inward-falling material is converted to heat.<\/p>\r\n<p id=\"fs-id1168044897935\">The heat generated in this way, like all heat, flows outward to where it is a bit cooler. In the process, the heat raises the temperature of a layer of hydrogen that spent the whole long main-sequence time just outside the core. Like an understudy waiting in the wings of a hit Broadway show for a chance at fame and glory, this hydrogen was almost (but not quite) hot enough to undergo fusion and take part in the main action that sustains the star. Now, the additional heat produced by the shrinking core puts this hydrogen \u201cover the limit,\u201d and a shell of hydrogen nuclei just outside the core becomes hot enough for hydrogen fusion to begin.<\/p>\r\n<p id=\"fs-id1168047201373\">New energy produced by fusion of this hydrogen now pours outward from this shell and begins to heat up layers of the star farther out, causing them to expand. Meanwhile, the helium core continues to contract, producing more heat right around it. This leads to more fusion in the shell of fresh hydrogen outside the core as shown in <a class=\"autogenerated-content\" href=\"#OSC_Astro_22_01_Shell\">Figure 2<\/a>. The additional fusion produces still more energy, which also flows out into the upper layer of the star.<\/p>\r\n\r\n<figure id=\"OSC_Astro_22_01_Shell\">\r\n<div class=\"title\" style=\"text-align: center\"><strong>Star Layers during and after the Main Sequence.<\/strong><\/div>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"975\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-content\/uploads\/sites\/235\/2017\/08\/OSC_Astro_22_01_Shell-1.jpg\" alt=\"Stellar Structure During and After the Main Sequence. In (a), on the left, the \u201cHydrogen burning core\u201d is shown as a small disk within a larger, yellow disk depicting the non-fusion \u201cStellar envelope.\u201d In (b), on the right, the \u201cHelium core\u201d is drawn as a smaller disk within a larger disk labeled, \u201cHydrogen burning shell.\u201d These are within a larger \u201cStellar envelope,\u201d which is drawn in yellow.\" width=\"975\" height=\"262\" \/> <strong>Figure 2.<\/strong> (a) During the main sequence, a star has a core where fusion takes place and a much larger envelope that is too cold for fusion. (b) When the hydrogen in the core is exhausted (made of helium, not hydrogen), the core is compressed by gravity and heats up. The additional heat starts hydrogen fusion in a layer just outside the core. Note that these parts of the Sun are not drawn to scale.[\/caption]<\/figure>\r\n<p id=\"fs-id1168047129383\">Most stars actually generate more energy each second when they are fusing hydrogen in the shell surrounding the helium core than they did when hydrogen fusion was confined to the central part of the star; thus, they increase in luminosity. With all the new energy pouring outward, the outer layers of the star begin to expand, and the star eventually grows and grows until it reaches enormous proportions as illustrated in <a class=\"autogenerated-content\" href=\"#OSC_Astro_22_01_Delta\">Figure 3<\/a>.<\/p>\r\n\r\n<figure id=\"OSC_Astro_22_01_Delta\">\r\n<div class=\"title\" style=\"text-align: center\"><strong>Relative Sizes of Stars.<\/strong><\/div>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"731\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-content\/uploads\/sites\/235\/2017\/08\/OSC_Astro_22_01_Delta-1.jpg\" alt=\"Relative Sizes of Stars Compared to the Sun. In this illustration the Sun is represented at center-left with a yellow disk labeled \u201cSun.\u201d The giant star labeled \u201cDelta Bo\u00f6tis\u201d is drawn at right with an orange disk about 10 times the size of the Sun\u2019s disk. At the top of this image, covering the entire upper portion of the figure, a small part of the supergiant labeled \u201cXi Cygni\u201d is shown in red.\" width=\"731\" height=\"360\" \/> <strong>Figure 3.<\/strong> This image compares the size of the Sun to that of Delta Bo\u00f6tis, a giant star, and Xi Cygni, a supergiant. Note that Xi Cygni is so large in comparison to the other two stars that only a small portion of it is visible at the top of the frame.[\/caption]<\/figure>\r\n<p id=\"fs-id1168047969818\">When you take the lid off a pot of boiling water, the steam can expand and it cools down. In the same way, the expansion of a star\u2019s outer layers causes the temperature at the surface to decrease. As it cools, the star\u2019s overall colour becomes redder. (We saw in <a class=\"target-chapter\" href=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/5-0-thinking-ahead\/\">Radiation and Spectra<\/a> that a red colour corresponds to cooler temperature.)<\/p>\r\n<p id=\"fs-id1168047124729\">So the star becomes simultaneously more luminous and cooler. On the H\u2013R diagram, the star therefore leaves the main-sequence band and moves upward (brighter) and to the right (cooler surface temperature). Over time, massive stars become red supergiants, and lower-mass stars like the Sun become red giants. (We first discussed such giant stars in <a class=\"target-chapter\" href=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/18-0-thinking-ahead\/\">The Stars: A Celestial Census<\/a><em>;<\/em> here we see how such \u201cswollen\u201d stars originate.) You might also say that these stars have \u201csplit personalities\u201d: their cores are contracting while their outer layers are expanding. (Note that red giant stars do not actually look deep red; their colors are more like orange or orange-red.)<\/p>\r\n<p id=\"fs-id1168047194984\">Just how different are these red giants and supergiants from a main-sequence star? <a class=\"autogenerated-content\" href=\"#fs-id1168048147581\">Figure 4<\/a> compares the <span class=\"no-emphasis\">Sun<\/span> with the red supergiant <span class=\"no-emphasis\">Betelgeuse<\/span>, which is visible above Orion\u2019s belt as the bright red star that marks the hunter\u2019s armpit. Relative to the Sun, this supergiant has a much larger radius, a much lower average density, a cooler surface, and a much hotter core.<\/p>\r\n\r\n<table id=\"fs-id1168048147581\" class=\"span-all aligncenter\" summary=\"This table contains three columns and eight rows. The first row is a header row, and it labels each column, \u201cProperty,\u201d \u201cSun,\u201d and \u201cBetelgeuse.\u201d Under the \u201cProperty\u201d column are the values: \u201cMass (2 \u00d7 1033 g),\u201d \u201cRadius (k m),\u201d \u201cSurface temperature (K),\u201d \u201cCore temperature (K),\u201d \u201cLuminosity (4 \u00d7 1026 W),\u201d \u201cAverage density (g\/c m3),\u201d and \u201cAge (million years).\u201d Under the \u201cSun\u201d column are the values: \u201c1,\u201d \u201c700,000,\u201d \u201c5,800,\u201d \u201c15,000,000,\u201d \u201c1,\u201d \u201c1.4,\u201d and \u201c4,500.\u201d Finally, under the \u201cBetelgeuse\u201d column are the values: \u201c16,\u201d \u201c500,000,000,\u201d \u201c3,600,\u201d \u201c160,000,000,\u201d \u201c46,000,\u201d \u201c1.3 \u00d7 10\u20137,\u201d and \u201c10.\u201d\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th colspan=\"3\">Figure 4. Comparing a Supergiant with the Sun<\/th>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<th>Property<\/th>\r\n<th>Sun<\/th>\r\n<th>Betelgeuse<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>Mass (2 \u00d7 10<sup>33<\/sup> g)<\/td>\r\n<td>1<\/td>\r\n<td>16<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>Radius (km)<\/td>\r\n<td>700,000<\/td>\r\n<td>500,000,000<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>Surface temperature (K)<\/td>\r\n<td>5,800<\/td>\r\n<td>3,600<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>Core temperature (K)<\/td>\r\n<td>15,000,000<\/td>\r\n<td>160,000,000<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>Luminosity (4 \u00d7 10<sup>26<\/sup> W)<\/td>\r\n<td>1<\/td>\r\n<td>46,000<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>Average density (g\/cm<sup>3<\/sup>)<\/td>\r\n<td>1.4<\/td>\r\n<td>1.3 \u00d7 10<sup>\u20137<\/sup><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>Age (millions of years)<\/td>\r\n<td>4,500<\/td>\r\n<td>10<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1168047355141\">Red giants can become so large that if we were to replace the Sun with one of them, its outer atmosphere would extend to the orbit of Mars or even beyond as shown in <a class=\"autogenerated-content\" href=\"#OSC_Astro_22_01_Orion\">Figure 3<\/a>. This is the next stage in the life of a star as it moves (to continue our analogy to human lives) from its long period of \u201cyouth\u201d and \u201cadulthood\u201d to \u201cold age.\u201d (After all, many human beings today also see their outer layers expand a bit as they get older.) By considering the relative ages of the Sun and Betelgeuse, we can also see that the idea that \u201cbigger stars die faster\u201d is indeed true here. Betelgeuse is a mere 10 million years old, which is relatively young compared with our Sun\u2019s 4.5 billion years, but it is already nearing its death throes as a red supergiant.<\/p>\r\n\r\n<figure id=\"OSC_Astro_22_01_Orion\">\r\n<div class=\"title\" style=\"text-align: center\"><strong>Betelgeuse.<\/strong><\/div>\r\n<figcaption><\/figcaption>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"731\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-content\/uploads\/sites\/235\/2017\/08\/OSC_Astro_22_01_Orion-1.jpg\" alt=\"Direct Image of the Star Betelgeuse. In this figure the H S T image of Betelgeuse is presented in the inset in the upper left of this image where the reddish, extended atmosphere surrounds the brighter, yellow core. Below the inset is a list of relative scales based on the image. At the top the \u201cSize of Star\u201d is indicated with a bar the width of Betelgeuse in the image. At the center the \u201cSize of Earth\u2019s Orbit\u201d is shown with a much smaller bar. Finally, at the bottom, the \u201cSize of Jupiter\u2019s Orbit\u201d is also shown with a bar. Both the orbits of Earth and Jupiter fit comfortably within the size of Betelgeuse. The right hand panel shows the full constellation of Orion, with Betelgeuse indicated at the upper left of the image.\" width=\"731\" height=\"457\" \/> <strong>Figure 3.<\/strong> Betelgeuse is in the constellation Orion, the hunter; in the right image, it is marked with a yellow \u201cX\u201d near the top left. In the left image, we see it in ultraviolet with the Hubble Space Telescope, in the first direct image ever made of the surface of another star. As shown by the scale at the bottom, Betelgeuse has an extended atmosphere so large that, if it were at the center of our solar system, it would stretch past the orbit of Jupiter. (credit: Modification of work by Andrea Dupree (Harvard-Smithsonian CfA), Ronald Gilliland (STScI), NASA and ESA)[\/caption]<\/figure>\r\n<\/section><section id=\"fs-id1168047149982\">\r\n<h1>Models for Evolution to the Giant Stage<\/h1>\r\nAs we discussed earlier, astronomers can construct computer models of stars with different masses and compositions to see how stars change throughout their lives. <a class=\"autogenerated-content\" href=\"#OSC_Astro_22_01_Mass\">Figure 4<\/a>, which is based on theoretical calculations by University of Illinois astronomer Icko Iben, shows an H\u2013R diagram with several tracks of evolution from the main sequence to the giant stage. Tracks are shown for stars with different masses (from 0.5 to 15 times the mass of our Sun) and with chemical compositions similar to that of the Sun. The red line is the initial or zero-age main sequence. The numbers along the tracks indicate the time, in years, required for each star to reach those points in their evolution after leaving the main sequence. Once again, you can see that the more massive a star is, the more quickly it goes through each stage in its life.\r\n<figure id=\"OSC_Astro_22_01_Mass\">\r\n<div class=\"title\" style=\"text-align: center\"><strong>Evolutionary Tracks of Stars of Different Masses.<\/strong><\/div>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"710\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-content\/uploads\/sites\/235\/2017\/08\/OSC_Astro_22_01_Mass-1.jpg\" alt=\"Evolutionary Tracks of Stars of Different Masses. In this plot the vertical axis is labeled \u201cLuminosity (LSun)\u201d and goes from 10-2 at the bottom to over 104 at the top. The horizontal axis is labeled \u201cSurface Temperature (K)\u201d and goes from 25,000 on the left to 4,000 on the right. The \u201cZero-age main sequence\u201d is drawn as a diagonal red line beginning above L = 104 at the upper left of the image down to T ~ 4000 at the lower right. Six evolutionary tracks are drawn. Beginning at the top, a star of \u201c15 solar masses\u201d is plotted. It leaves the main sequence above L ~ 104 and T ~ 25,000. The track moves rightward across the top of the plot. The star maintains a relatively constant luminosity, but its surface temperature decreases with time. At \u201c1.01 \u00d7 107\u201d years its temperature is about 20,000 K. At \u201c1.11 \u00d7 107\u201d years it has fallen to about 15,000 K. At \u201c1.19 \u00d7 107\u201d years T is about 9000 K, and the track ends at \u201c1.2 \u00d7 107\u201d years near 4000 K. Next, a star of \u201c5 solar masses\u201d is plotted beginning near L ~ 103, where it leaves the main sequence. The star maintains a relatively constant luminosity, but its surface temperature decreases with time. At \u201c6.55 \u00d7 107\u201d years its temperature is about 12,000 K. but its surface temperature decreases with time. At \u201c2.39 \u00d7 107\u201d years it has fallen to about 5000 K. Then the luminosity rises slightly to the final plotted point at \u201c7.02 \u00d7 107\u201d years near 4000 K. Next, a star of \u201c3 solar masses\u201d leaves the main sequence near L = 102 and 15,000 K. After \u201c2.21 \u00d7 108\u201d years its temperature has fallen to near 11,000 K. After \u201c2.46 \u00d7 108\u201d years its temperature has dropped to near 6000 K. Then, its luminosity increases by about a factor of ten where its curve ends at \u201c2.51 \u00d7 107\u201d years and 5000 K. Next, a star of \u201c1.5 solar masses\u201d leaves the main sequence near L = 30 and 9000 K. After \u201c1.55 \u00d7 109\u201d years its temperature has fallen to near 7500 K. After \u201c2.09 \u00d7 109\u201d years, its temperature has dropped to near 5000 K. Then, its luminosity increases by about a factor of one hundred where its curve ends at \u201c2.39 \u00d7 109\u201d years and 4000 K. Next, a star of \u201c1 solar mass\u201d leaves the main sequence at L = 1 and 5700 K. After \u201c7 \u00d7 109\u201d years its temperature is nearly the same, but its luminosity has increased slightly. After \u201c10.4 \u00d7 109\u201d years, its temperature has dropped to near 5000 K, and its luminosity has increased about 20 times. Then, its luminosity steadily increases to where its curve ends at \u201c11.4 \u00d7 109\u201d years, L ~ 103 and T ~ 4000 K. Finally, a \u201c0.5 solar mass\u201d star is partially plotted. Its curve begins at L ~ 10-1 near T ~ 5000. Its curve is a short arrow pointing upward as its evolutionary timescale is too great for this diagram.\" width=\"710\" height=\"742\" \/> <strong>Figure 4.<\/strong> The solid black lines show the predicted evolution from the main sequence through the red giant or supergiant stage on the H\u2013R diagram. Each track is labeled with the mass of the star it is describing. The numbers show how many years each star takes to become a giant after leaving the main sequence. The red line is the zero-age main sequence.[\/caption]<\/figure>\r\n<p id=\"fs-id1168047339662\">Note that the most massive star in this diagram has a mass similar to that of <span class=\"no-emphasis\">Betelgeuse<\/span>, and so its evolutionary track shows approximately the history of Betelgeuse. The track for a 1-solar-mass star shows that the Sun is still in the main-sequence phase of evolution, since it is only about 4.5 billion years old. It will be billions of years before the Sun begins its own \u201cclimb\u201d away from the main sequence\u2014the expansion of its outer layers that will make it a red giant.<\/p>\r\n\r\n<\/section><section id=\"fs-id1168047297091\" class=\"summary\">\r\n<h1>Key Concepts and Summary<\/h1>\r\n<p id=\"fs-id1168047722412\">When stars first begin to fuse hydrogen to helium, they lie on the zero-age main sequence. The amount of time a star spends in the main-sequence stage depends on its mass. More massive stars complete each stage of evolution more quickly than lower-mass stars. The fusion of hydrogen to form helium changes the interior composition of a star, which in turn results in changes in its temperature, luminosity, and radius. Eventually, as stars age, they evolve away from the main sequence to become red giants or supergiants. The core of a red giant is contracting, but the outer layers are expanding as a result of hydrogen fusion in a shell outside the core. The star gets larger, redder, and more luminous as it expands and cools.<\/p>\r\n\r\n<\/section>\r\n<div>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id1168047360151\" class=\"definition\">\r\n \t<dt>zero-age main sequence<\/dt>\r\n \t<dd id=\"fs-id1168047918819\">a line denoting the main sequence on the H\u2013R diagram for a system of stars that have completed their contraction from interstellar matter and are now deriving all their energy from nuclear reactions, but whose chemical composition has not yet been altered substantially by nuclear reactions<\/dd>\r\n<\/dl>\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p id=\"fs-id1168581963707\">By the end of this section, you will be able to:<\/p>\n<ul id=\"fs-id1168047596857\">\n<li>Explain the zero-age <span class=\"no-emphasis\">main sequence<\/span><\/li>\n<li>Describe what happens to main-sequence stars of various masses as they exhaust their hydrogen supply<\/li>\n<\/ul>\n<\/div>\n<p>One of the best ways to get a \u201csnapshot\u201d of a group of stars is by plotting their properties on an <span class=\"no-emphasis\">H\u2013R diagram<\/span>. We have already used the H\u2013R diagram to follow the evolution of protostars up to the time they reach the main sequence. Now we\u2019ll see what happens next.<\/p>\n<p id=\"fs-id1168047141287\">Once a star has reached the main-sequence stage of its life, it derives its energy almost entirely from the conversion of hydrogen to helium via the process of nuclear fusion in its core (see <a class=\"target-chapter\" href=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/16-0-thinking-ahead\/\">The Sun: A Nuclear Powerhouse<\/a>). Since hydrogen is the most abundant element in stars, this process can maintain the star\u2019s equilibrium for a long time. Thus, all stars remain on the main sequence for most of their lives. Some astronomers like to call the main-sequence phase the star\u2019s \u201cprolonged adolescence\u201d or \u201cadulthood\u201d (continuing our analogy to the stages in a human life).<\/p>\n<p id=\"fs-id1168047644759\">The left-hand edge of the main-sequence band in the H\u2013R diagram is called the zero-age main sequence (see <a class=\"autogenerated-content\" href=\"#OSC_Astro_18_04_HR\">chapter 18 HR<\/a>). We use the term <em>zero-age<\/em> to mark the time when a star stops contracting, settles onto the main sequence, and begins to fuse hydrogen in its core. The zero-age main sequence is a continuous line in the H\u2013R diagram that shows where stars of different masses but similar chemical composition can be found when they begin to fuse hydrogen.<\/p>\n<p id=\"fs-id1168047948993\">Since only 0.7% of the hydrogen used in fusion reactions is converted into energy, fusion does not change the <em>total<\/em> mass of the star appreciably during this long period. It does, however, change the chemical composition in its central regions where nuclear reactions occur: hydrogen is gradually depleted, and helium accumulates. This change of composition changes the luminosity, temperature, size, and interior structure of the star. When a star\u2019s luminosity and temperature begin to change, the point that represents the star on the H\u2013R diagram moves away from the zero-age main sequence.<\/p>\n<p id=\"fs-id1168047215933\">Calculations show that the temperature and density in the inner region slowly increase as helium accumulates in the centre of a star. As the temperature gets hotter, each proton acquires more energy of motion on average; this means it is more likely to interact with other protons, and as a result, the rate of fusion also increases. For the proton-proton cycle described in <a class=\"target-chapter\" href=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/16-0-thinking-ahead\/\">The Sun: A Nuclear Powerhouse<\/a>, the rate of fusion goes up roughly as the temperature to the fourth power.<\/p>\n<p id=\"fs-id1168047363968\">If the rate of fusion goes up, the rate at which energy is being generated also increases, and the luminosity of the star gradually rises. Initially, however, these changes are small, and stars remain within the main-sequence band on the H\u2013R diagram for most of their lifetimes.<\/p>\n<div id=\"fs-id1168047963854\" class=\"example\">\n<div class=\"textbox shaded\">\n<p id=\"fs-id1168047651163\"><strong>Star Temperature and Rate of Fusion<\/strong><br \/>\nIf a star\u2019s temperature were to double, by what factor would its rate of fusion increase?<\/p>\n<p id=\"fs-id1168047642421\"><strong>Solution<\/strong><br \/>\nSince the rate of fusion (like temperature) goes up to the fourth power, it would increase by a factor of 2<sup>4<\/sup>, or 16 times.<\/p>\n<p id=\"fs-id1168047663003\"><strong>Check Your Learning<\/strong><br \/>\nIf the rate of fusion of a star increased 256 times, by what factor would the temperature increase?<\/p>\n<div id=\"fs-id1168047690291\" class=\"note\">\n<div class=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-id1168047544097\">The temperature would increase by a factor of 256<sup>0.25<\/sup> (that is, the 4<sup>th<\/sup> root of 256), or 4 times.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<section id=\"fs-id1168047996934\">\n<h1>Lifetimes on the Main Sequence<\/h1>\n<p id=\"fs-id1168047387270\">How many years a star remains in the main-sequence band depends on its mass. You might think that a more massive star, having more fuel, would last longer, but it\u2019s not that simple. The lifetime of a star in a particular stage of evolution depends on how much nuclear fuel it has and on <em>how quickly<\/em> it uses up that fuel. (In the same way, how long people can keep spending money depends not only on how much money they have but also on how quickly they spend it. This is why many lottery winners who go on spending sprees quickly wind up poor again.) In the case of stars, more massive ones use up their fuel much more quickly than stars of low mass.<\/p>\n<p id=\"fs-id1168048151186\">The reason massive stars are such spendthrifts is that, as we saw above, the rate of fusion depends <em>very<\/em> strongly on the star\u2019s core temperature. And what determines how hot a star\u2019s central regions get? It is the <em>mass<\/em> of the star\u2014the weight of the overlying layers determines how high the pressure in the core must be: higher mass requires higher pressure to balance it. Higher pressure, in turn, is produced by higher temperature. The higher the temperature in the central regions, the faster the star races through its storehouse of central hydrogen. Although massive stars have more fuel, they burn it so prodigiously that their lifetimes are much shorter than those of their low-mass counterparts. You can also understand now why the most massive main-sequence stars are also the most luminous. Like new rock stars with their first platinum album, they spend their resources at an astounding rate.<\/p>\n<p id=\"fs-id1168047642455\">The main-sequence lifetimes of stars of different masses are listed in <a class=\"autogenerated-content\" href=\"#fs-id1168047645207\">Figure 1<\/a>. This table shows that the most massive stars spend only a few million years on the main sequence. A star of 1 solar mass remains there for roughly 10 billion years, while a star of about 0.4 solar mass has a main-sequence lifetime of some 200 billion years, which is longer than the current age of the universe. (Bear in mind, however, that every star spends <em>most<\/em> of its total lifetime on the <span class=\"no-emphasis\">main sequence<\/span>. Stars devote an average of 90% of their lives to peacefully fusing hydrogen into helium.)<\/p>\n<table id=\"fs-id1168047645207\" class=\"span-all aligncenter\" summary=\"This table contains four columns and eight rows. The first row is a header row, and it labels each column, \u201cSpectral Type,\u201d \u201cSurface Temperature (K),\u201d \u201cMass (Mass of Sun = 1),\u201d and \u201cLifetime on Main Sequence (years).\u201d Under the \u201cSpectral Type\u201d column are the values: \u201cO 5,\u201d \u201cB 0,\u201d \u201cA 0,\u201d \u201cF 0,\u201d \u201cG 0,\u201d \u201cK 0,\u201d and \u201cM 0.\u201d Under the \u201cSurface Temperature (K)\u201d column are the values: \u201c54,000,\u201d \u201c29,200,\u201d \u201c9600,\u201d \u201c7350,\u201d \u201c6050,\u201d \u201c5240,\u201d and \u201c3750.\u201d Under the \u201cMass (Mass of Sun = 1)\u201d column are the values: \u201c40,\u201d \u201c16,\u201d \u201c3.3,\u201d \u201c1.7,\u201d \u201c1.1,\u201d \u201c0.8,\u201d and \u201c0.4.\u201d Finally, under the \u201cLifetime on Main Sequence (years)\u201d column are the values: \u201c1 million,\u201d \u201c10 million,\u201d \u201c500 million,\u201d \u201c2.7 billion,\u201d \u201c9 billion,\u201d \u201c14 billion,\u201d and \u201c200 billion.\u201d\">\n<thead>\n<tr valign=\"top\">\n<th colspan=\"4\">Figure 1. Lifetimes of Main-Sequence Stars<\/th>\n<\/tr>\n<tr valign=\"top\">\n<th>Spectral Type<\/th>\n<th>Surface Temperature (K)<\/th>\n<th>Mass<\/p>\n<div><\/div>\n<p>(Mass of Sun = 1)<\/th>\n<th>Lifetime on Main Sequence (years)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>O5<\/td>\n<td>54,000<\/td>\n<td>40<\/td>\n<td>1 million<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>B0<\/td>\n<td>29,200<\/td>\n<td>16<\/td>\n<td>10 million<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>A0<\/td>\n<td>9600<\/td>\n<td>3.3<\/td>\n<td>500 million<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>F0<\/td>\n<td>7350<\/td>\n<td>1.7<\/td>\n<td>2.7 billion<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>G0<\/td>\n<td>6050<\/td>\n<td>1.1<\/td>\n<td>9 billion<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>K0<\/td>\n<td>5240<\/td>\n<td>0.8<\/td>\n<td>14 billion<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>M0<\/td>\n<td>3750<\/td>\n<td>0.4<\/td>\n<td>200 billion<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168047166304\">These results are not merely of academic interest. Human beings developed on a planet around a G-type star. This means that the Sun\u2019s stable main-sequence lifetime is so long that it afforded life on Earth plenty of time to evolve. When searching for intelligent life like our own on planets around other stars, it would be a pretty big waste of time to search around O- or B-type stars. These stars remain stable for such a short time that the development of creatures complicated enough to take astronomy courses is very unlikely.<\/p>\n<\/section>\n<div class=\"textbox shaded\">\n<p><strong style=\"text-align: initial;font-size: 0.9em\">Calculating the Lifetime of a Star &#8211; Mass and Luminosity<\/strong><\/p>\n<p id=\"fs-id1168047651163\">The lifetime of a star depends on its mass and is inversely proportional to its luminosity.\u00a0 If T = lifetime in solar lifetimes, M = masses in solar mass and L = luminosity in solar luminosities them T = M \/ L.\u00a0 \u00a0 \u00a0If you want it in year, remember that our Sun will live for about 10 billion or 1 x 10 <sup>10<\/sup> years.\u00a0 The equation then becomes.<\/p>\n<p>T = M \/ L (1 x 10 <sup>10<\/sup> years )<\/p>\n<p><strong>\u00a0<\/strong>If a star has 1\/4 the mass of the Sun and is 1\/8 as luminous, a) how long will it live in solar lifetimes and b) how many years?<\/p>\n<p id=\"fs-id1168047663003\"><strong>Solution<\/strong><\/p>\n<p>T = M \/ L = (1\/4 ) \/ (1\/8) = 2.\u00a0 It would live twice as long.<\/p>\n<p>b) In years that would equal 2 (1 x 10<sup>10<\/sup> year) = 2 x 10<sup>10<\/sup> years.<\/p>\n<div id=\"fs-id1168047690291\" class=\"note\">\n<div><\/div>\n<div class=\"title\"><strong>Check Your Learning<\/strong><\/div>\n<div>If a star has 3 times the mass of the Sun and is 21 times as luminous a) how long will it live in solar lifetimes and b) how many years<\/div>\n<div><\/div>\n<div class=\"title\"><strong>Answer: <\/strong>a) 7 times b) 7 x 10 <sup>10<\/sup> years<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<p id=\"fs-id1168047651163\"><strong>Calculating the Lifetime of a Star\u00a0 Using Only the Mass\u00a0<\/strong><br \/>\nIt makes sense that the lifetime of a star depends on its mass ( the amount of fuel) and its luminosity (how quickly it burns that fuel). Remember that the luminosity also depends directly on the mass.\u00a0 The greater the mass of the star, the greater the gravity pressure at the core and the faster the rate of fusion.\u00a0 There must be more outwards pressure due to the fusion to balance the inwards pressure of gravity.\u00a0 This means that the equation shown above can be simplified such that the lifetime of the star T = 1 \/ M <sup>2.5\u00a0\u00a0<\/sup>where T is in solar lifetimes and M is in solar masses.<\/p>\n<p>Calculate the lifetime of a star that has a mass that is 1\/2 or 0.5 that of our Sun in a) solar lifetimes and b) years.<\/p>\n<p id=\"fs-id1168047642421\"><strong>Solution<\/strong><br \/>\nT = 1 \/ (0.5) <sup>2.5<\/sup> = 6 times longer than our Sun<\/p>\n<p>Our Sun has a lifetime of about 10 billion years so that equals 6 x 10 <sup>10<\/sup> years.<\/p>\n<p id=\"fs-id1168047663003\"><strong>Check Your Learning<\/strong><br \/>\nWhat is the lifetime of a star that\u00a0 has a mass that is 16 times greater than that of our Sun?<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-id1168047690291\" class=\"note\">\n<div class=\"title\"><strong>Answer<\/strong><\/div>\n<p id=\"fs-id1168047544097\">The lifetime would be 1 \/ (16) <sup>2.5\u00a0<\/sup> = 0.00097 = 9.7 x10<sup>-4<\/sup> times.\u00a0 Our Sun has a lifetime of about 10 billion years or 1 x 10<sup>10<\/sup> years.\u00a0 \u00a0In years this massive star would live 9.7 x10<sup>6<\/sup> years.\u00a0 To one significant figures that is 10 million years which agrees nicely with the table shown above.<\/p>\n<\/div>\n<\/div>\n<p><span style=\"font-family: Helvetica, Arial, 'GFS Neohellenic', sans-serif;font-size: 1.2em;font-weight: bold\">Frpm Main-Sequence Star to Red Giant<\/span><\/p>\n<section id=\"fs-id1168047784110\">Eventually, all the hydrogen in a star\u2019s core, where it is hot enough for fusion reactions, is used up. The core then contains only helium, \u201ccontaminated\u201d by whatever small percentage of heavier elements the star had to begin with. The helium in the core can be thought of as the accumulated \u201cash\u201d from the nuclear \u201cburning\u201d of hydrogen during the main-sequence stage.<\/p>\n<p id=\"fs-id1168047367284\">Energy can no longer be generated by hydrogen fusion in the stellar core because the hydrogen is all gone and, as we will see, the fusion of helium requires much higher temperatures. Since the central temperature is not yet high enough to fuse helium, there is no nuclear energy source to supply heat to the central region of the star. The long period of stability now ends, gravity again takes over, and the core begins to contract. Once more, the star\u2019s energy is partially supplied by gravitational energy, in the way described by Kelvin and Helmholtz (see <a class=\"target-chapter\" href=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/16-1-sources-of-sunshine-thermal-and-gravitational-energy\/\">Sources of Sunshine: Thermal and Gravitational Energy<\/a>). As the star\u2019s core shrinks, the energy of the inward-falling material is converted to heat.<\/p>\n<p id=\"fs-id1168044897935\">The heat generated in this way, like all heat, flows outward to where it is a bit cooler. In the process, the heat raises the temperature of a layer of hydrogen that spent the whole long main-sequence time just outside the core. Like an understudy waiting in the wings of a hit Broadway show for a chance at fame and glory, this hydrogen was almost (but not quite) hot enough to undergo fusion and take part in the main action that sustains the star. Now, the additional heat produced by the shrinking core puts this hydrogen \u201cover the limit,\u201d and a shell of hydrogen nuclei just outside the core becomes hot enough for hydrogen fusion to begin.<\/p>\n<p id=\"fs-id1168047201373\">New energy produced by fusion of this hydrogen now pours outward from this shell and begins to heat up layers of the star farther out, causing them to expand. Meanwhile, the helium core continues to contract, producing more heat right around it. This leads to more fusion in the shell of fresh hydrogen outside the core as shown in <a class=\"autogenerated-content\" href=\"#OSC_Astro_22_01_Shell\">Figure 2<\/a>. The additional fusion produces still more energy, which also flows out into the upper layer of the star.<\/p>\n<figure id=\"OSC_Astro_22_01_Shell\">\n<div class=\"title\" style=\"text-align: center\"><strong>Star Layers during and after the Main Sequence.<\/strong><\/div>\n<figure style=\"width: 975px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-content\/uploads\/sites\/235\/2017\/08\/OSC_Astro_22_01_Shell-1.jpg\" alt=\"Stellar Structure During and After the Main Sequence. In (a), on the left, the \u201cHydrogen burning core\u201d is shown as a small disk within a larger, yellow disk depicting the non-fusion \u201cStellar envelope.\u201d In (b), on the right, the \u201cHelium core\u201d is drawn as a smaller disk within a larger disk labeled, \u201cHydrogen burning shell.\u201d These are within a larger \u201cStellar envelope,\u201d which is drawn in yellow.\" width=\"975\" height=\"262\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 2.<\/strong> (a) During the main sequence, a star has a core where fusion takes place and a much larger envelope that is too cold for fusion. (b) When the hydrogen in the core is exhausted (made of helium, not hydrogen), the core is compressed by gravity and heats up. The additional heat starts hydrogen fusion in a layer just outside the core. Note that these parts of the Sun are not drawn to scale.<\/figcaption><\/figure>\n<\/figure>\n<p id=\"fs-id1168047129383\">Most stars actually generate more energy each second when they are fusing hydrogen in the shell surrounding the helium core than they did when hydrogen fusion was confined to the central part of the star; thus, they increase in luminosity. With all the new energy pouring outward, the outer layers of the star begin to expand, and the star eventually grows and grows until it reaches enormous proportions as illustrated in <a class=\"autogenerated-content\" href=\"#OSC_Astro_22_01_Delta\">Figure 3<\/a>.<\/p>\n<figure id=\"OSC_Astro_22_01_Delta\">\n<div class=\"title\" style=\"text-align: center\"><strong>Relative Sizes of Stars.<\/strong><\/div>\n<figure style=\"width: 731px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-content\/uploads\/sites\/235\/2017\/08\/OSC_Astro_22_01_Delta-1.jpg\" alt=\"Relative Sizes of Stars Compared to the Sun. In this illustration the Sun is represented at center-left with a yellow disk labeled \u201cSun.\u201d The giant star labeled \u201cDelta Bo\u00f6tis\u201d is drawn at right with an orange disk about 10 times the size of the Sun\u2019s disk. At the top of this image, covering the entire upper portion of the figure, a small part of the supergiant labeled \u201cXi Cygni\u201d is shown in red.\" width=\"731\" height=\"360\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 3.<\/strong> This image compares the size of the Sun to that of Delta Bo\u00f6tis, a giant star, and Xi Cygni, a supergiant. Note that Xi Cygni is so large in comparison to the other two stars that only a small portion of it is visible at the top of the frame.<\/figcaption><\/figure>\n<\/figure>\n<p id=\"fs-id1168047969818\">When you take the lid off a pot of boiling water, the steam can expand and it cools down. In the same way, the expansion of a star\u2019s outer layers causes the temperature at the surface to decrease. As it cools, the star\u2019s overall colour becomes redder. (We saw in <a class=\"target-chapter\" href=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/5-0-thinking-ahead\/\">Radiation and Spectra<\/a> that a red colour corresponds to cooler temperature.)<\/p>\n<p id=\"fs-id1168047124729\">So the star becomes simultaneously more luminous and cooler. On the H\u2013R diagram, the star therefore leaves the main-sequence band and moves upward (brighter) and to the right (cooler surface temperature). Over time, massive stars become red supergiants, and lower-mass stars like the Sun become red giants. (We first discussed such giant stars in <a class=\"target-chapter\" href=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/18-0-thinking-ahead\/\">The Stars: A Celestial Census<\/a><em>;<\/em> here we see how such \u201cswollen\u201d stars originate.) You might also say that these stars have \u201csplit personalities\u201d: their cores are contracting while their outer layers are expanding. (Note that red giant stars do not actually look deep red; their colors are more like orange or orange-red.)<\/p>\n<p id=\"fs-id1168047194984\">Just how different are these red giants and supergiants from a main-sequence star? <a class=\"autogenerated-content\" href=\"#fs-id1168048147581\">Figure 4<\/a> compares the <span class=\"no-emphasis\">Sun<\/span> with the red supergiant <span class=\"no-emphasis\">Betelgeuse<\/span>, which is visible above Orion\u2019s belt as the bright red star that marks the hunter\u2019s armpit. Relative to the Sun, this supergiant has a much larger radius, a much lower average density, a cooler surface, and a much hotter core.<\/p>\n<table id=\"fs-id1168048147581\" class=\"span-all aligncenter\" summary=\"This table contains three columns and eight rows. The first row is a header row, and it labels each column, \u201cProperty,\u201d \u201cSun,\u201d and \u201cBetelgeuse.\u201d Under the \u201cProperty\u201d column are the values: \u201cMass (2 \u00d7 1033 g),\u201d \u201cRadius (k m),\u201d \u201cSurface temperature (K),\u201d \u201cCore temperature (K),\u201d \u201cLuminosity (4 \u00d7 1026 W),\u201d \u201cAverage density (g\/c m3),\u201d and \u201cAge (million years).\u201d Under the \u201cSun\u201d column are the values: \u201c1,\u201d \u201c700,000,\u201d \u201c5,800,\u201d \u201c15,000,000,\u201d \u201c1,\u201d \u201c1.4,\u201d and \u201c4,500.\u201d Finally, under the \u201cBetelgeuse\u201d column are the values: \u201c16,\u201d \u201c500,000,000,\u201d \u201c3,600,\u201d \u201c160,000,000,\u201d \u201c46,000,\u201d \u201c1.3 \u00d7 10\u20137,\u201d and \u201c10.\u201d\">\n<thead>\n<tr valign=\"top\">\n<th colspan=\"3\">Figure 4. Comparing a Supergiant with the Sun<\/th>\n<\/tr>\n<tr valign=\"top\">\n<th>Property<\/th>\n<th>Sun<\/th>\n<th>Betelgeuse<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Mass (2 \u00d7 10<sup>33<\/sup> g)<\/td>\n<td>1<\/td>\n<td>16<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Radius (km)<\/td>\n<td>700,000<\/td>\n<td>500,000,000<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Surface temperature (K)<\/td>\n<td>5,800<\/td>\n<td>3,600<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Core temperature (K)<\/td>\n<td>15,000,000<\/td>\n<td>160,000,000<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Luminosity (4 \u00d7 10<sup>26<\/sup> W)<\/td>\n<td>1<\/td>\n<td>46,000<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Average density (g\/cm<sup>3<\/sup>)<\/td>\n<td>1.4<\/td>\n<td>1.3 \u00d7 10<sup>\u20137<\/sup><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Age (millions of years)<\/td>\n<td>4,500<\/td>\n<td>10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168047355141\">Red giants can become so large that if we were to replace the Sun with one of them, its outer atmosphere would extend to the orbit of Mars or even beyond as shown in <a class=\"autogenerated-content\" href=\"#OSC_Astro_22_01_Orion\">Figure 3<\/a>. This is the next stage in the life of a star as it moves (to continue our analogy to human lives) from its long period of \u201cyouth\u201d and \u201cadulthood\u201d to \u201cold age.\u201d (After all, many human beings today also see their outer layers expand a bit as they get older.) By considering the relative ages of the Sun and Betelgeuse, we can also see that the idea that \u201cbigger stars die faster\u201d is indeed true here. Betelgeuse is a mere 10 million years old, which is relatively young compared with our Sun\u2019s 4.5 billion years, but it is already nearing its death throes as a red supergiant.<\/p>\n<figure id=\"OSC_Astro_22_01_Orion\">\n<div class=\"title\" style=\"text-align: center\"><strong>Betelgeuse.<\/strong><\/div><figcaption><\/figcaption><figure style=\"width: 731px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-content\/uploads\/sites\/235\/2017\/08\/OSC_Astro_22_01_Orion-1.jpg\" alt=\"Direct Image of the Star Betelgeuse. In this figure the H S T image of Betelgeuse is presented in the inset in the upper left of this image where the reddish, extended atmosphere surrounds the brighter, yellow core. Below the inset is a list of relative scales based on the image. At the top the \u201cSize of Star\u201d is indicated with a bar the width of Betelgeuse in the image. At the center the \u201cSize of Earth\u2019s Orbit\u201d is shown with a much smaller bar. Finally, at the bottom, the \u201cSize of Jupiter\u2019s Orbit\u201d is also shown with a bar. Both the orbits of Earth and Jupiter fit comfortably within the size of Betelgeuse. The right hand panel shows the full constellation of Orion, with Betelgeuse indicated at the upper left of the image.\" width=\"731\" height=\"457\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 3.<\/strong> Betelgeuse is in the constellation Orion, the hunter; in the right image, it is marked with a yellow \u201cX\u201d near the top left. In the left image, we see it in ultraviolet with the Hubble Space Telescope, in the first direct image ever made of the surface of another star. As shown by the scale at the bottom, Betelgeuse has an extended atmosphere so large that, if it were at the center of our solar system, it would stretch past the orbit of Jupiter. (credit: Modification of work by Andrea Dupree (Harvard-Smithsonian CfA), Ronald Gilliland (STScI), NASA and ESA)<\/figcaption><\/figure>\n<\/figure>\n<\/section>\n<section id=\"fs-id1168047149982\">\n<h1>Models for Evolution to the Giant Stage<\/h1>\n<p>As we discussed earlier, astronomers can construct computer models of stars with different masses and compositions to see how stars change throughout their lives. <a class=\"autogenerated-content\" href=\"#OSC_Astro_22_01_Mass\">Figure 4<\/a>, which is based on theoretical calculations by University of Illinois astronomer Icko Iben, shows an H\u2013R diagram with several tracks of evolution from the main sequence to the giant stage. Tracks are shown for stars with different masses (from 0.5 to 15 times the mass of our Sun) and with chemical compositions similar to that of the Sun. The red line is the initial or zero-age main sequence. The numbers along the tracks indicate the time, in years, required for each star to reach those points in their evolution after leaving the main sequence. Once again, you can see that the more massive a star is, the more quickly it goes through each stage in its life.<\/p>\n<figure id=\"OSC_Astro_22_01_Mass\">\n<div class=\"title\" style=\"text-align: center\"><strong>Evolutionary Tracks of Stars of Different Masses.<\/strong><\/div>\n<figure style=\"width: 710px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-content\/uploads\/sites\/235\/2017\/08\/OSC_Astro_22_01_Mass-1.jpg\" alt=\"Evolutionary Tracks of Stars of Different Masses. In this plot the vertical axis is labeled \u201cLuminosity (LSun)\u201d and goes from 10-2 at the bottom to over 104 at the top. The horizontal axis is labeled \u201cSurface Temperature (K)\u201d and goes from 25,000 on the left to 4,000 on the right. The \u201cZero-age main sequence\u201d is drawn as a diagonal red line beginning above L = 104 at the upper left of the image down to T ~ 4000 at the lower right. Six evolutionary tracks are drawn. Beginning at the top, a star of \u201c15 solar masses\u201d is plotted. It leaves the main sequence above L ~ 104 and T ~ 25,000. The track moves rightward across the top of the plot. The star maintains a relatively constant luminosity, but its surface temperature decreases with time. At \u201c1.01 \u00d7 107\u201d years its temperature is about 20,000 K. At \u201c1.11 \u00d7 107\u201d years it has fallen to about 15,000 K. At \u201c1.19 \u00d7 107\u201d years T is about 9000 K, and the track ends at \u201c1.2 \u00d7 107\u201d years near 4000 K. Next, a star of \u201c5 solar masses\u201d is plotted beginning near L ~ 103, where it leaves the main sequence. The star maintains a relatively constant luminosity, but its surface temperature decreases with time. At \u201c6.55 \u00d7 107\u201d years its temperature is about 12,000 K. but its surface temperature decreases with time. At \u201c2.39 \u00d7 107\u201d years it has fallen to about 5000 K. Then the luminosity rises slightly to the final plotted point at \u201c7.02 \u00d7 107\u201d years near 4000 K. Next, a star of \u201c3 solar masses\u201d leaves the main sequence near L = 102 and 15,000 K. After \u201c2.21 \u00d7 108\u201d years its temperature has fallen to near 11,000 K. After \u201c2.46 \u00d7 108\u201d years its temperature has dropped to near 6000 K. Then, its luminosity increases by about a factor of ten where its curve ends at \u201c2.51 \u00d7 107\u201d years and 5000 K. Next, a star of \u201c1.5 solar masses\u201d leaves the main sequence near L = 30 and 9000 K. After \u201c1.55 \u00d7 109\u201d years its temperature has fallen to near 7500 K. After \u201c2.09 \u00d7 109\u201d years, its temperature has dropped to near 5000 K. Then, its luminosity increases by about a factor of one hundred where its curve ends at \u201c2.39 \u00d7 109\u201d years and 4000 K. Next, a star of \u201c1 solar mass\u201d leaves the main sequence at L = 1 and 5700 K. After \u201c7 \u00d7 109\u201d years its temperature is nearly the same, but its luminosity has increased slightly. After \u201c10.4 \u00d7 109\u201d years, its temperature has dropped to near 5000 K, and its luminosity has increased about 20 times. Then, its luminosity steadily increases to where its curve ends at \u201c11.4 \u00d7 109\u201d years, L ~ 103 and T ~ 4000 K. Finally, a \u201c0.5 solar mass\u201d star is partially plotted. Its curve begins at L ~ 10-1 near T ~ 5000. Its curve is a short arrow pointing upward as its evolutionary timescale is too great for this diagram.\" width=\"710\" height=\"742\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 4.<\/strong> The solid black lines show the predicted evolution from the main sequence through the red giant or supergiant stage on the H\u2013R diagram. Each track is labeled with the mass of the star it is describing. The numbers show how many years each star takes to become a giant after leaving the main sequence. The red line is the zero-age main sequence.<\/figcaption><\/figure>\n<\/figure>\n<p id=\"fs-id1168047339662\">Note that the most massive star in this diagram has a mass similar to that of <span class=\"no-emphasis\">Betelgeuse<\/span>, and so its evolutionary track shows approximately the history of Betelgeuse. The track for a 1-solar-mass star shows that the Sun is still in the main-sequence phase of evolution, since it is only about 4.5 billion years old. It will be billions of years before the Sun begins its own \u201cclimb\u201d away from the main sequence\u2014the expansion of its outer layers that will make it a red giant.<\/p>\n<\/section>\n<section id=\"fs-id1168047297091\" class=\"summary\">\n<h1>Key Concepts and Summary<\/h1>\n<p id=\"fs-id1168047722412\">When stars first begin to fuse hydrogen to helium, they lie on the zero-age main sequence. The amount of time a star spends in the main-sequence stage depends on its mass. More massive stars complete each stage of evolution more quickly than lower-mass stars. The fusion of hydrogen to form helium changes the interior composition of a star, which in turn results in changes in its temperature, luminosity, and radius. Eventually, as stars age, they evolve away from the main sequence to become red giants or supergiants. The core of a red giant is contracting, but the outer layers are expanding as a result of hydrogen fusion in a shell outside the core. The star gets larger, redder, and more luminous as it expands and cools.<\/p>\n<\/section>\n<div>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1168047360151\" class=\"definition\">\n<dt>zero-age main sequence<\/dt>\n<dd id=\"fs-id1168047918819\">a line denoting the main sequence on the H\u2013R diagram for a system of stars that have completed their contraction from interstellar matter and are now deriving all their energy from nuclear reactions, but whose chemical composition has not yet been altered substantially by nuclear reactions<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":9,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-657","chapter","type-chapter","status-publish","hentry"],"part":650,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/657","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/users\/9"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/657\/revisions"}],"predecessor-version":[{"id":2821,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/657\/revisions\/2821"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/parts\/650"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/657\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/media?parent=657"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapter-type?post=657"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/contributor?post=657"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/license?post=657"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}