refer to figure 35-3. what is measured along the vertical axis of the left-hand graph?

Learning Objectives

By the end of this section, yous will be able to:

• Place the concrete characteristics of stars that are used to create an H–R diagram, and describe how those characteristics vary amid groups of stars
• Discuss the concrete properties of most stars found at different locations on the H–R diagram, such as radius, and for principal sequence stars, mass

In this chapter and Analyzing Starlight, nosotros described some of the characteristics past which we might allocate stars and how those are measured. These ideas are summarized in Tabular array 1. We have besides given an example of a relationship between two of these characteristics in the mass-luminosity relation. When the characteristics of large numbers of stars were measured at the beginning of the twentieth century, astronomers were able to begin a deeper search for patterns and relationships in these information.

Table 1. Measuring the Characteristics of Stars
Feature	Technique
Surface temperature	1. Determine the color (very rough). ii. Measure the spectrum and become the spectral type.
Chemical composition	Decide which lines are nowadays in the spectrum.
Luminosity	Mensurate the apparent brightness and recoup for distance.
Radial velocity	Measure the Doppler shift in the spectrum.
Rotation	Measure the width of spectral lines.
Mass	Measure the menstruum and radial velocity curves of spectroscopic binary stars.
Bore	1. Measure the manner a star's light is blocked past the Moon. two. Measure the light curves and Doppler shifts for eclipsing binary stars.

Effigy 1. Summit versus Weight: The plot of the heights and weights of a representative group of human beings. Most points lie along a "main sequence" representing most people, merely there are a few exceptions.

To help sympathize what sorts of relationships might be found, permit's look briefly at a range of data about human beings. If you want to understand humans by comparing and contrasting their characteristics—without assuming whatever previous knowledge of these foreign creatures—yous could try to determine which characteristics lead y'all in a fruitful direction. For case, y'all might plot the heights of a large sample of humans against their weights (which is a measure out of their mass). Such a plot is shown in Figure i and it has some interesting features. In the way we have chosen to present our data, tiptop increases upward, whereas weight increases to the left. Notice that humans are not randomly distributed in the graph. Most points fall along a sequence that goes from the upper left to the lower right.

We can conclude from this graph that homo height and weight are related. Generally speaking, taller human beings weigh more, whereas shorter ones counterbalance less. This makes sense if yous are familiar with the structure of human beings. Typically, if we have bigger bones, we have more than flesh to fill out our larger frame. It's not mathematically verbal—at that place is a wide range of variation—merely it's not a bad overall dominion. And, of course, there are some dramatic exceptions. Yous occasionally see a short man who is very overweight and would thus be more to the bottom left of our diagram than the average sequence of people. Or yous might have a very alpine, skinny fashion model with great height but relatively minor weight, who would be found nigh the upper right.

A similar diagram has been found extremely useful for agreement the lives of stars. In 1913, American astronomer Henry Norris Russell plotted the luminosities of stars against their spectral classes (a way of denoting their surface temperatures). This investigation, and a similar independent study in 1911 by Danish astronomer Ejnar Hertzsprung, led to the extremely important discovery that the temperature and luminosity of stars are related (Figure ii).

Figure 2. Hertzsprung (1873–1967) and Russell (1877–1957): (a) Ejnar Hertzsprung and (b) Henry Norris Russell independently discovered the relationship between the luminosity and surface temperature of stars that is summarized in what is now called the H–R diagram.

Henry Norris Russell

When Henry Norris Russell graduated from Princeton University, his work had been so vivid that the faculty decided to create a new level of honors caste across "summa cum laude" for him. His students later remembered him as a human being whose thinking was iii times faster than just about everyone else's. His retention was and so astounding, he could correctly quote an enormous number of poems and limericks, the entire Bible, tables of mathematical functions, and most anything he had learned about astronomy. He was nervous, active, competitive, disquisitional, and very articulate; he tended to boss every coming together he attended. In outward appearance, he was an quondam-fashioned product of the nineteenth century who wore loftier-summit black shoes and high starched collars, and carried an umbrella every day of his life. His 264 papers were enormously influential in many areas of astronomy.

Built-in in 1877, the son of a Presbyterian minister, Russell showed early promise. When he was 12, his family sent him to alive with an aunt in Princeton and so he could attend a top preparatory schoolhouse. He lived in the aforementioned business firm in that town until his death in 1957 (interrupted but past a brief stay in Europe for graduate work). He was fond of recounting that both his mother and his maternal grandmother had won prizes in mathematics, and that he probably inherited his talents in that field from their side of the family unit.

Before Russell, American astronomers devoted themselves mainly to surveying the stars and making impressive catalogs of their properties, especially their spectra (as described in Analyzing Starlight. Russell began to encounter that interpreting the spectra of stars required a much more sophisticated understanding of the physics of the atom, a subject area that was existence developed past European physicists in the 1910s and 1920s. Russell embarked on a lifelong quest to ascertain the physical conditions inside stars from the clues in their spectra; his piece of work inspired, and was continued by, a generation of astronomers, many trained by Russell and his collaborators.

Russell as well made of import contributions in the study of binary stars and the measurement of star masses, the origin of the solar organisation, the atmospheres of planets, and the measurement of distances in astronomy, among other fields. He was an influential instructor and popularizer of astronomy, writing a column on astronomical topics for Scientific American magazine for more than forty years. He and ii colleagues wrote a textbook for college astronomy classes that helped train astronomers and astronomy enthusiasts over several decades. That book set the scene for the kind of textbook you are now reading, which not but lays out the facts of astronomy but too explains how they fit together. Russell gave lectures around the country, oftentimes emphasizing the importance of understanding modern physics in society to grasp what was happening in astronomy.

Harlow Shapley, managing director of the Harvard College Observatory, called Russell "the dean of American astronomers." Russell was certainly regarded every bit the leader of the field for many years and was consulted on many astronomical problems by colleagues from effectually the world. Today, i of the highest recognitions that an astronomer can receive is an accolade from the American Astronomical Society called the Russell Prize, set upward in his memory.

Features of the H–R Diagram

Figure 3. H–R Diagram for a Selected Sample of Stars: In such diagrams, luminosity is plotted forth the vertical axis. Forth the horizontal axis, nosotros can plot either temperature or spectral type (as well sometimes called spectral class). Several of the brightest stars are identified by name. Most stars autumn on the chief sequence.

Following Hertzsprung and Russell, let us plot the temperature (or spectral class) of a selected group of nearby stars against their luminosity and see what nosotros notice (Figure iii). Such a plot is frequently chosen the Hertzsprung–Russell diagram, abbreviated H–R diagram. Information technology is one of the near important and widely used diagrams in astronomy, with applications that extend far beyond the purposes for which it was originally adult more than a century ago.

Information technology is customary to plot H–R diagrams in such a fashion that temperature increases toward the left and luminosity toward the superlative. Find the similarity to our plot of elevation and weight for people (Effigy 1). Stars, like people, are not distributed over the diagram at random, as they would be if they exhibited all combinations of luminosity and temperature. Instead, we see that the stars cluster into certain parts of the H–R diagram. The dandy bulk are aligned along a narrow sequence running from the upper left (hot, highly luminous) to the lower right (cool, less luminous). This band of points is called the main sequence. Information technology represents a human relationship between temperature and luminosity that is followed by well-nigh stars. We can summarize this relationship past saying that hotter stars are more than luminous than cooler ones.

A number of stars, however, lie in a higher place the main sequence on the H–R diagram, in the upper-correct region, where stars have low temperature and high luminosity. How can a star exist at in one case cool, significant each square meter on the star does not put out all that much energy, and yet very luminous? The just way is for the star to be enormous—to take and then many square meters on its surface that the full energy output is still large. These stars must be giants or supergiants, the stars of huge bore we discussed earlier.

Figure four. Schematic H–R Diagram for Many Stars: Ninety percent of all stars on such a diagram fall along a narrow ring called the main sequence. A minority of stars are constitute in the upper correct; they are both cool (and hence red) and bright, and must be giants. Some stars fall in the lower left of the diagram; they are both hot and dim, and must be white dwarfs.

There are too some stars in the lower-left corner of the diagram, which have high temperature and low luminosity. If they accept high surface temperatures, each square meter on that star puts out a lot of energy. How so can the overall star be dim? It must exist that it has a very small total surface area; such stars are known as white dwarfs (white considering, at these high temperatures, the colors of the electromagnetic radiation that they emit blend together to make them wait blueish-white). We will say more than about these puzzling objects in a moment. Figure iv is a schematic H–R diagram for a large sample of stars, drawn to make the different types more credible.

Now, think dorsum to our discussion of star surveys. Information technology is hard to plot an H–R diagram that is truly representative of all stars considering most stars are so faint that we cannot see those outside our immediate neighborhood. The stars plotted in Figure 3 were selected because their distances are known. This sample omits many intrinsically faint stars that are nearby but accept non had their distances measured, so it shows fewer faint main-sequence stars than a "off-white" diagram would. To exist truly representative of the stellar population, an H–R diagram should be plotted for all stars within a sure altitude. Unfortunately, our knowledge is reasonably complete only for stars within x to 20 light-years of the Sun, amongst which at that place are no giants or supergiants. Still, from many surveys (and more can now be done with new, more powerful telescopes), we estimate that most 90% of the true stars overall (excluding chocolate-brown dwarfs) in our office of space are main-sequence stars, virtually 10% are white dwarfs, and fewer than 1% are giants or supergiants.

These estimates tin can be used direct to empathize the lives of stars. Let us another quick illustration with people. Suppose we survey people simply like astronomers survey stars, only we want to focus our attention on the location of young people, ages 6 to 18 years. Survey teams fan out and have data about where such youngsters are plant at all times during a 24-hour day. Some are constitute in the local pizza parlor, others are comatose at habitation, some are at the movies, and many are in school. Later surveying a very large number of young people, ane of the things that the teams decide is that, averaged over the course of the 24 hours, one-3rd of all youngsters are found in schoolhouse.

How tin can they interpret this result? Does it mean that ii-thirds of students are truants and the remaining one-3rd spend all their time in school? No, nosotros must bear in mind that the survey teams counted youngsters throughout the full 24-hour day. Some survey teams worked at nighttime, when most youngsters were at home comatose, and others worked in the late afternoon, when near youngsters were on their mode home from schoolhouse (and more likely to be enjoying a pizza). If the survey was truly representative, nosotros tin conclude, however, that if an average of one-third of all youngsters are plant in school, then humans ages 6 to 18 years must spend most one-third of their time in school.

We can do something similar for stars. We find that, on boilerplate, 90% of all stars are located on the main sequence of the H–R diagram. If we can place some activity or life stage with the chief sequence, then it follows that stars must spend 90% of their lives in that activeness or life stage.

Understanding the Main Sequence

In The Dominicus: A Nuclear Powerhouse, nosotros discussed the Sun every bit a representative star. We saw that what stars such as the Sun "do for a living" is to catechumen protons into helium deep in their interiors via the process of nuclear fusion, thus producing energy. The fusion of protons to helium is an excellent, long-lasting source of energy for a star considering the majority of every star consists of hydrogen atoms, whose nuclei are protons.

Our computer models of how stars evolve over time evidence u.s. that a typical star volition spend about 90% of its life fusing the abundant hydrogen in its core into helium. This then is a good caption of why 90% of all stars are plant on the master sequence in the H–R diagram. But if all the stars on the chief sequence are doing the same thing (fusing hydrogen), why are they distributed forth a sequence of points? That is, why practice they differ in luminosity and surface temperature (which is what nosotros are plotting on the H–R diagram)?

To help us understand how main-sequence stars differ, we tin utilise one of the virtually important results from our studies of model stars. Astrophysicists have been able to show that the structure of stars that are in equilibrium and derive all their energy from nuclear fusion is completely and uniquely determined by just two quantities: the total mass and the limerick of the star. This fact provides an interpretation of many features of the H–R diagram.

Imagine a cluster of stars forming from a cloud of interstellar "raw cloth" whose chemical composition is similar to the Sun's. (We'll describe this process in more detail in The Nascence of Stars and Discovery of Planets exterior the Solar System, but for at present, the details will not concern us.) In such a cloud, all the clumps of gas and dust that become stars brainstorm with the aforementioned chemical composition and differ from ane some other only in mass. Now suppose that nosotros compute a model of each of these stars for the fourth dimension at which it becomes stable and derives its energy from nuclear reactions, but earlier it has time to modify its limerick appreciably every bit a result of these reactions.

The models calculated for these stars permit u.s.a. to determine their luminosities, temperatures, and sizes. If we plot the results from the models—one indicate for each model star—on the H–R diagram, nosotros get something that looks just like the main sequence we saw for real stars.

And hither is what nosotros find when we do this. The model stars with the largest masses are the hottest and most luminous, and they are located at the upper left of the diagram.

The least-massive model stars are the coolest and to the lowest degree luminous, and they are placed at the lower right of the plot. The other model stars all lie forth a line running diagonally beyond the diagram. In other words, the primary sequence turns out to be a sequence of stellar masses.

This makes sense if yous think well-nigh it. The almost massive stars accept the about gravity and tin can thus compress their centers to the greatest degree. This means they are the hottest within and the all-time at generating energy from nuclear reactions deep within. As a result, they shine with the greatest luminosity and have the hottest surface temperatures. The stars with everyman mass, in turn, are the coolest inside and least effective in generating energy. Thus, they are the least luminous and current of air up being the coolest on the surface. Our Sun lies somewhere in the middle of these extremes (as you can see in Figure iii. The characteristics of representative main-sequence stars (excluding chocolate-brown dwarfs, which are not true stars) are listed in Table 2.

Tabular array 2. Characteristics of Main-Sequence Stars
Spectral Blazon	Mass (Sun = 1)	Luminosity (Sun = 1)	Temperature	Radius (Sun = 1)
O5	40	7 × ten5	40,000 K	xviii
B0	sixteen	2.7 × 105	28,000 1000	seven
A0	3.3	55	10,000 One thousand	2.5
F0	ane.7	5	7500 K	ane.4
G0	1.ane	1.4	6000 Grand	1.1
K0	0.eight	0.35	5000 K	0.8
M0	0.four	0.05	3500 Yard	0.6

Note that nosotros've seen this ninety% effigy come up up before. This is exactly what nosotros plant earlier when we examined the mass-luminosity relation. Nosotros observed that 90% of all stars seem to follow the relationship; these are the 90% of all stars that lie on the principal sequence in our H–R diagram. Our models and our observations agree.

What about the other stars on the H–R diagram—the giants and supergiants, and the white dwarfs? Equally nosotros will run across in the side by side few chapters, these are what main-sequence stars turn into as they age: They are the later stages in a star's life. Every bit a star consumes its nuclear fuel, its source of free energy changes, as do its chemic composition and interior structure. These changes cause the star to alter its luminosity and surface temperature so that it no longer lies on the chief sequence on our diagram. Because stars spend much less time in these later stages of their lives, we run into fewer stars in those regions of the H–R diagram.

Extremes of Stellar Luminosities, Diameters, and Densities

Nosotros tin can apply the H–R diagram to explore the extremes in size, luminosity, and density found among the stars. Such extreme stars are non only interesting to fans of the Guinness Book of World Records; they tin teach us a lot about how stars piece of work. For example, we saw that the most massive main-sequence stars are the most luminous ones. We know of a few extreme stars that are a million times more than luminous than the Sun, with masses that exceed 100 times the Dominicus'south mass. These superluminous stars, which are at the upper left of the H–R diagram, are exceedingly hot, very blueish stars of spectral blazon O. These are the stars that would be the most conspicuous at vast distances in space.

Figure five. The Sunday and a Supergiant: Here you see how small the Sun looks in comparison to one of the largest known stars: VY Canis Majoris, a supergiant.

The cool supergiants in the upper corner of the H–R diagram are equally much every bit ten,000 times as luminous equally the Sun. In improver, these stars have diameters very much larger than that of the Sun. Equally discussed above, some supergiants are and then large that if the solar system could be centered in 1, the star'south surface would lie beyond the orbit of Mars (see Effigy five). Nosotros will have to ask, in coming chapters, what process can make a star slap-up upwards to such an enormous size, and how long these "bloated" stars can last in their distended state.

In contrast, the very common red, cool, low-luminosity stars at the lower cease of the primary sequence are much smaller and more compact than the Sun. An example of such a red dwarf is Ross 614B, with a surface temperature of 2700 K and only 1/2000 of the Sun'due south luminosity. Nosotros telephone call such a star a dwarf because its bore is only 1/x that of the Dominicus. A star with such a low luminosity as well has a low mass (about 1/12 that of the Sunday). This combination of mass and diameter means that it is so compressed that the star has an average density about 80 times that of the Dominicus. Its density must be higher, in fact, than that of any known solid found on the surface of Globe. (Despite this, the star is fabricated of gas throughout because its center is and then hot.)

The faint, cerise, main-sequence stars are not the stars of the most extreme densities, however. The white dwarfs, at the lower-left corner of the H–R diagram, take densities many times greater still.

The White Dwarfs

Figure 6. Two Views of Sirius and Its White Dwarf Companion: (a) A visible light epitome taken by the Hubble Space Telescope. Sirius B is the faint speck in the lower left had quadrant of the image, and nearly lost in the glare of bright Sirius A. (b) X-ray image from the Chandra 10-ray telescope. Sirius B is much brighter in X-rays and is the bright object at the centre of the paradigm. In a higher place and slightly to the correct is Sirius A.

The start white dwarf star was detected in 1862. Called Sirius B, it forms a binary system with Sirius A, the brightest-appearing star in the sky. It eluded discovery and analysis for a long time because its faint light tends to be lost in the glare of nearby Sirius A (Figure 5). (Since Sirius is oftentimes called the Dog Star—being the brightest star in the constellation of Canis Major, the big dog—Sirius B is sometimes nicknamed the Pup.)

Nosotros have now found thousands of white dwarfs. A Stellar Census shows that well-nigh 7% of the true stars (spectral types O–Grand) in our local neighborhood are white dwarfs. A expert example of a typical white dwarf is the nearby star 40 Eridani B. Its surface temperature is a relatively hot 12,000 K, merely its luminosity is only 1/275 L _{Lord's day}. Calculations show that its radius is only 1.4% of the Sun'south, or virtually the same as that of Earth, and its book is 2.5 × x^–six that of the Sun. Its mass, however, is 0.43 times the Sun'southward mass, just a little less than half. To fit such a substantial mass into so tiny a volume, the star's density must be about 170,000 times the density of the Sun, or more than 200,000 m/cm³. A teaspoonful of this material would take a mass of some 50 tons! At such enormous densities, thing cannot be in its usual land; nosotros will examine the particular behavior of this type of matter in The Death of Stars. For now, we merely note that white dwarfs are dying stars, reaching the end of their productive lives and set up for their stories to be over.

The British astrophysicist (and science popularizer) Arthur Eddington (1882–1944) described the beginning known white dwarf this way:

The message of the companion of Sirius, when decoded, ran: "I am composed of cloth 3 yard times denser than anything you've ever come up across. A ton of my fabric would be a fiddling nugget yous could put in a matchbox." What reply could one make to something like that? Well, the reply near of us fabricated in 1914 was, "Shut upwardly; don't talk nonsense."

Today, however, astronomers not merely accept that stars every bit dumbo as white dwarfs exist merely (as nosotros will see) take establish even denser and stranger objects in their quest to understand the evolution of different types of stars.

Fundamental Concepts and Summary

The Hertzsprung–Russell diagram, or H–R diagram, is a plot of stellar luminosity against surface temperature. About stars prevarication on the main sequence, which extends diagonally across the H–R diagram from loftier temperature and high luminosity to low temperature and low luminosity. The position of a star along the master sequence is adamant past its mass. High-mass stars emit more than energy and are hotter than low-mass stars on the principal sequence. Main-sequence stars derive their energy from the fusion of protons to helium. About 90% of the stars lie on the main sequence. Only nearly 10% of the stars are white dwarfs, and fewer than 1% are giants or supergiants.

Glossary

H–R diagram: (Hertzsprung–Russell diagram) a plot of luminosity against surface temperature (or spectral type) for a group of stars

main sequence: a sequence of stars on the Hertzsprung–Russell diagram, containing the majority of stars, that runs diagonally from the upper left to the lower right

white dwarf: a low-mass star that has exhausted nigh or all of its nuclear fuel and has collapsed to a very minor size; such a star is near its terminal state of life

shipleywerseree.blogspot.com

Source: https://courses.lumenlearning.com/astronomy/chapter/the-h-r-diagram/

Share this post