What Can We Learn About A Star From A Life Track On An H-r Diagram

Learning Objectives

By the end of this department, y'all will be able to:

Understand how spectral types are used to approximate stellar luminosities
Examine how these techniques are used by astronomers today

Variable stars are non the only way that nosotros can estimate the luminosity of stars. Another way involves the H–R diagram, which shows that the intrinsic effulgence of a star can be estimated if nosotros know its spectral type.

Distances from Spectral Types

As satisfying and productive as variable stars have been for distance measurement, these stars are rare and are non found almost all the objects to which we wish to measure distances. Suppose, for instance, we need the altitude to a star that is not varying, or to a group of stars, none of which is a variable. In this example, information technology turns out the H–R diagram tin come to our rescue.

If nosotros tin can detect the spectrum of a star, we tin estimate its distance from our understanding of the H–R diagram. Equally discussed in Analyzing Starlight, a detailed test of a stellar spectrum allows astronomers to classify the star into one of the spectral types indicating surface temperature. (The types are O, B, A, F, G, K, M, 50, T, and Y; each of these can exist divided into numbered subgroups.) In general, however, the spectral type lone is not enough to allow united states of america to estimate luminosity. A G2 star could be a master-sequence star with a luminosity of i L _Sunday, or it could be a giant with a luminosity of 100 L _{Lord's day}, or even a supergiant with a still college luminosity.

We can acquire more from a star's spectrum, however, than just its temperature. Remember, for instance, that we tin can notice pressure differences in stars from the details of the spectrum. This knowledge is very useful considering giant stars are larger (and take lower pressures) than main-sequence stars, and supergiants are still larger than giants. If nosotros wait in detail at the spectrum of a star, nosotros can determine whether it is a main-sequence star, a behemothic, or a supergiant.

Suppose, to start with the simplest case, that the spectrum, color, and other backdrop of a afar G2 star match those of the Lord's day exactly. It is then reasonable to conclude that this distant star is likely to exist a primary-sequence star but like the Sun and to take the same luminosity as the Sun. Just if there are subtle differences betwixt the solar spectrum and the spectrum of the distant star, so the distant star may be a giant or even a supergiant.

The most widely used system of star nomenclature divides stars of a given spectral class into six categories called luminosity classes. These luminosity classes are denoted past Roman numbers as follows:

Ia: Brightest supergiants
Ib: Less luminous supergiants
2: Brilliant giants
Iii: Giants
IV: Subgiants (intermediate between giants and primary-sequence stars)
V: Main-sequence stars

The full spectral specification of a star includes its luminosity form. For example, a chief-sequence star with spectral class F3 is written as F3 V. The specification for an M2 giant is M2 3. Effigy 1 illustrates the approximate position of stars of various luminosity classes on the H–R diagram. The dashed portions of the lines stand for regions with very few or no stars.

Luminosity Classes. In this graph the vertical axis is labeled

Effigy 1: Luminosity Classes. Stars of the same temperature (or spectral class) can autumn into different luminosity classes on the Hertzsprung-Russell diagram. By studying details of the spectrum for each star, astronomers can determine which luminosity grade they autumn in (whether they are main-sequence stars, behemothic stars, or supergiant stars).

With both its spectral and luminosity classes known, a star's position on the H–R diagram is uniquely adamant. Since the diagram plots luminosity versus temperature, this means nosotros can at present read off the star'southward luminosity (one time its spectrum has helped us place it on the diagram). As before, if we know how luminous the star really is and see how dim it looks, the difference allows us to calculate its distance. (For historical reasons, astronomers sometimes call this method of altitude conclusion spectroscopic parallax, even though the method has zero to do with parallax.)

The H–R diagram method allows astronomers to estimate distances to nearby stars, as well equally some of the nearly afar stars in our Milky way, but it is anchored by measurements of parallax. The distances measured using parallax are the gold standard for distances: they rely on no assumptions, only geometry. Once astronomers have a spectrum of a nearby star for which we also know the parallax, nosotros know the luminosity that corresponds to that spectral type. Nearby stars thus serve equally benchmarks for more distant stars considering we can assume that 2 stars with identical spectra take the aforementioned intrinsic luminosity.

A Few Words about the Real World

Introductory textbooks such equally ours work hard to present the material in a straightforward and simplified way. In doing so, we sometimes do our students a disservice past making scientific techniques seem too clean and painless. In the real world, the techniques we accept just described turn out to be messy and difficult, and often give astronomers headaches that final long into the day.

For instance, the relationships we have described such as the period-luminosity relation for certain variable stars aren't exactly straight lines on a graph. The points representing many stars scatter widely when plotted, and thus, the distances derived from them also have a sure congenital-in scatter or uncertainty.

The distances we measure out with the methods we take discussed are therefore only authentic to within a certain pct of error—sometimes x%, sometimes 25%, sometimes as much as l% or more. A 25% error for a star estimated to be 10,000 light-years away ways information technology could be anywhere from 7500 to 12,500 lite-years away. This would exist an unacceptable uncertainty if yous were loading fuel into a spaceship for a trip to the star, simply it is not a bad first figure to work with if y'all are an astronomer stuck on planet Earth.

Nor is the construction of H–R diagrams as easy equally you might think at first. To make a adept diagram, i needs to measure the characteristics and distances of many stars, which can exist a time-consuming task. Since our own solar neighborhood is already well mapped, the stars astronomers most want to report to advance our cognition are likely to be far abroad and faint. It may take hours of observing to obtain a single spectrum. Observers may have to spend many nights at the telescope (and many days dorsum home working with their data) before they get their distance measurement. Fortunately, this is irresolute because surveys like Gaia will study billions of stars, producing public datasets that all astronomers can use.

Despite these difficulties, the tools we accept been discussing allow us to mensurate a remarkable range of distances—parallaxes for the nearest stars, RR Lyrae variable stars; the H–R diagram for clusters of stars in our ain and nearby galaxies; and cepheids out to distances of 60 one thousand thousand light-years. Table 1 describes the altitude limits and overlap of each method.

Each technique described in this chapter builds on at least i other method, forming what many call the cosmic distance ladder. Parallaxes are the foundation of all stellar altitude estimates, spectroscopic methods use nearby stars to calibrate their H–R diagrams, and RR Lyrae and cepheid altitude estimates are grounded in H–R diagram distance estimates (and even in a parallax measurement to a nearby cepheid, Delta Cephei).

This chain of methods allows astronomers to push the limits when looking for even more distant stars. Recent piece of work, for example, has used RR Lyrae stars to place dim companion galaxies to our ain Milky Mode out at distances of 300,000 light-years. The H–R diagram method was recently used to identify the ii most distant stars in the Galaxy: ruby-red giant stars way out in the halo of the Milky Way with distances of almost 1 million calorie-free-years.

Nosotros tin can combine the distances nosotros discover for stars with measurements of their composition, luminosity, and temperature—made with the techniques described in Analyzing Starlight and The Stars: A Angelic Census. Together, these brand upwardly the arsenal of information we need to trace the evolution of stars from birth to decease, the discipline to which we plow in the capacity that follow.

Table 1: Distance Range of Angelic Measurement Methods
Method	Altitude Range
Trigonometric parallax	iv–30,000 light-years when the Gaia mission is complete
RR Lyrae stars	Out to 300,000 light-years
H–R diagram and spectroscopic distances	Out to 1,200,000 low-cal-years
Cepheid stars	Out to 60,000,000 light-years

Key concepts and summary

Stars with identical temperatures but different pressures (and diameters) have somewhat different spectra. Spectral classification can therefore be used to gauge the luminosity grade of a star likewise as its temperature. As a event, a spectrum can let united states to pinpoint where the star is located on an H–R diagram and plant its luminosity. This, with the star'southward apparent effulgence, once again yields its distance. The various distance methods tin can be used to check ane against another and thus make a kind of distance ladder which allows us to observe even larger distances.

Glossary

luminosity grade: a classification of a star according to its luminosity within a given spectral class; our Sun, a G2V star, has luminosity class V, for instance